Refractive Index and Dispersion of Fluorides and Oxides

Transcrição

Refractive Index and Dispersion of Fluorides and Oxides
Robert D. Shannona…
Geological Sciences/CIRES, University of Colorado, Boulder, Colorado 80309
Ruth C. Shannon
118 Left Fork Road, Boulder, Colorado 80302
Olaf Medenbachb…
Institut für Mineralogie, Fakultät fur Geowissenschaften, Ruhr-Universität Bochum, Universitätsstraße 150, D-44780 Bochum, Germany
Reinhard X. Fischerc…
Fachbereich Geowissenschaften, Universität Bremen, Klagenfurter Straße, D-28359 Bremen, Germany
共Received 19 September 2001; accepted 13 May 2002; published 25 October 2002兲
The refractive indices of 509 oxides and 55 fluorides were analyzed using two forms of
a one-term Sellmeier equation: 共1兲 1/(n 2 ⫺1)⫽⫺A/␭ 2 ⫹B, where A, the slope of the
plot of (n 2 ⫺1) ⫺1 versus ␭ ⫺2 in units of 10⫺16 m2 , gives a measure of dispersion and B,
the intercept of the plot at ␭⫽⬁, gives n ⬁ ⫽(1⫹1/B) 1/2 and 共2兲 n 2 ⫺1⫽E dE o /(E 2o
⫺(ប ␻ ) 2 ), where ប ␻ ⫽the photon energy, E o⫽the average single oscillator 共Sellmeier兲
energy gap, and E d⫽the average oscillator strength, which measures the strength of
interband optical transitions. Form 共1兲 was used to calculate n at ␭⫽589.3 nm (n D) and
n at ␭⫽⬁ (n ⬁ ), and the dispersion constant A. The total mean polarizabilility for each
compound was calculated using the Lorenz–Lorentz equation: ␣ e⫽3/4␲ 关 (V m) (n ⬁2
⫺1)/(n ⬁2 ⫹2)], where V m is the molar volume in Å 3 . Provided for each compound are:
n D , n ⬁ , V m , 具 ␣ e典 , 具 A 典 , 具 B 典 , 具 E d典 , 具 E o典 , the literature reference, the method of measurement of n and estimated errors in n. Results obtained by prism, infrared reflectivity,
ellipsometry, and interference methods are compared. Consistency of dispersion values
among like compounds and structural families is used to evaluate the accuracy of refractive index data. Dispersion values range from 40 to 260⫻10⫺16 m2 with the majority of
values in the range of 60– 100⫻10⫺16 m2 . High dispersion is associated with s 2 , p 6 , d 10,
and transition metal ions, H2 O, and crystalline hydrates, whereas normal dispersion values are found in borates, aluminates, gallates, silicates, germanates, phosphates, and
sulfates not containing H2 O or any of the above ions. Exceptionally high dispersion is
observed in liquid H2 O, Fe2 O3 , Y3 Fe5 O12 , FeOOH, Fe2 (SO4 ) 3 , UO2 , Cu2 O, V2 O5 ,
MgCrO4 •7H2 O, and Cs2 Mg共CrO4 ) 2 •6H2 O. © 2002 American Institute of Physics.
关DOI: 10.1063/1.1497384兴
Key words: ellipsometry; infrared reflectivity; interband optical transitions; interference method; optical
dispersion; oscillator strength; prism method; refractive index; Sellmeier equation; single oscillator energy gap
2.4. Error Limits. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. Results and Discussion. . . . . . . . . . . . . . . . . . . . . . .
3.1. Comparison of Data Using Different
Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2. Comparison of Dispersion Values. . . . . . . . . .
3.3. Analysis of Dispersion Values. . . . . . . . . . . . .
3.3.1. Transition Metal Ions. . . . . . . . . . . . . . .
3.3.2. d 10 Ions. . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3. p 6 Ions. . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4. s 2 Ions. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.5. H2 O and Hydrates. . . . . . . . . . . . . . . . .
3.3.6. Summary of Effect of Electron
Configuration and E o and E d on
Contents
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Presentation of Data. . . . . . . . . . . . . . . . . . . . . . . . .
2.1. Composition, Characterization, and Source...
2.2. Method of Measuring Dispersion or n ⬁ . . . . .
2.3. Sellmeier Analysis. . . . . . . . . . . . . . . . . . . . . . .
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a兲
Electronic mail: [email protected]
Electronic mail: [email protected]
c兲
Author to whom correspondence should be addressed; electronic mail:
[email protected]
© 2002 American Institute of Physics.
b兲
0047-2689Õ2002Õ31„4…Õ931Õ40Õ$35.00
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J. Phys. Chem. Ref. Data, Vol. 31, No. 4, 2002
Downloaded 24 Jul 2013 to 200.145.3.28. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jpcrd.aip.org/about/rights_and_permissions
SHANNON ET AL.
932
4.
5.
6.
7.
8.
Dispersion. . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . .
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References for Tables 1 and 3. . . . . . . . . . . . . . . . .
Appendix 1. List of Codens. . . . . . . . . . . . . . . . . . .
Appendix 2. Alternative Forms of the Sellmeier
Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
List of Tables
1. Refractive index and dispersion data. . . . . . . . . . . .
2. Comparison of n ⬁ values determined by prism
methods and reflectivity methods. . . . . . . . . . . . . .
3. Inconsistent dispersion values. . . . . . . . . . . . . . . . .
4. Dispersion parameters for oxides and fluorides:
Transition metal. . . . . . . . . . . . . . . . . . . . . . . . . . . .
5. Dispersion parameters for oxides and fluorides
d 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
p 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
s 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8. Dispersion parameters for H2 O and crystalline
hydrates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9. Dispersion parameters associated with ions. . . . . .
List of Figures
1. Mean dispersion values 具 A 典 vs frequency of
occurrence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Dispersion A vs average Sellmeier energy gap
Eo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. Dispersion A vs average oscillator strength. . . . . .
967
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1. Introduction
Refractive indices (n) and their dispersion are useful for
the characterization of synthetic materials and minerals and
for the prediction of linear and nonlinear refractive indices
(n 2 ). Nonlinear refractive indices are defined by: n⫽n o
⫹n 2 具 E 2 典 where n⫽observed refractive index at wavelength
␭, n o⫽the linear refractive index, and E⫽the applied optical
electric field 关Adair et al. 共1989兲兴. For example, nonlinear
refractive indices of crystalline and glassy optical crystals
have been related to linear refractive indices and their dispersion 关Boling et al. 共1978兲; Adair et al. 共1989兲; Dimitrov
and Sakka 共1996兲兴. Also, in conjunction with dispersion
studies and derived values of n ⬁ , sets of empirical electronic
ion polarizabilities ␣ e have been derived from 共1兲 the
Lorenz–Lorentz 共LL兲 equation:
␣ e⫽1/b 关共 V m兲共 n ⬁2 ⫺1 兲 / 共 n ⬁2 ⫹2 兲兴 ,
共1兲
where V m is the molar volume in Å , b⫽4 ␲ /3 关Lorentz
共1880兲; Lorenz 共1880兲; Tessman et al. 共1953兲; Kip 共1962兲;
Anderson 共1974兲兴 and n ⬁ is the value of n extrapolated to
infinite wavelength from a Sellmeier equation and 共2兲 the
additivity rule for the compound M2 M⬘ X4 . The additivity
rule states
3
␣ e共 M2 M⬘ X4 兲 ⫽2 ␣ e共 M2⫹ 兲 ⫹ ␣ e共 M⬘ 4⫹ 兲 ⫹4 ␣ e共 X⫽ 兲 ,
共2兲
where ␣ e(M2 M⬘ X4 ) is the total polarizability of the compound M2 M⬘ X4 and ␣ e(M2⫹ ), ␣ e(M⬘ 4⫹ ), and ␣ e(X⫽ ) are
the electronic polarizabilities of M2⫹ , M⬘ 4⫹ , and X⫽ , respectively. Using these relations, sets of ion polarizabilities
were derived from data on the alkali halides and alkaline
earth chalcogenides by Tessman et al. 共1953兲; Pirenne and
Kartheuser 共1964兲; Wilson and Curtis, 共1970兲; Boswarva
共1970兲; Coker 共1976兲; Raghurama and Narayan 共1983兲; and
from data on a variety of minerals by Lasaga and Cygan
共1982兲.
During the course of the determination of an improved set
of electronic polarizabilities, it was necessary to obtain a
relatively complete database of refractive indices and dispersion over the visible part of the spectrum 共400–700 nm兲.
Although dispersion data such as those given in the compilations of Hintze 共1897兲, 共1933兲, 共1938兲, 共1960兲; Doelter
共1914兲, 共1917兲; Li 共1980兲 and the Landolt-Börnstein 共1962兲,
共1969兲, 共1979兲, 共1981兲, 共1996兲, 共hereafter referred to as LB兲
series have been published, there was no central location for
these data and it was frequently necessary to go to original
publications to obtain dispersion data. Often there is no indication of the reliability of the data. In order to obtain n ⬁
and dispersion constants, it is convenient to use Sellmeier
analyses. Sellmeier constants have been provided for many
compounds in these publications, but because of the large
variety of Sellmeier equations 关Tropf et al. 共1995兲兴, analysis
using a common Sellmeier equation was not available.
To remedy this situation a literature search from the mid
1800s to the present was done to provide a relatively complete list of refractive indices and dispersion for minerals and
synthetic fluorides and oxides 共509 oxides and 55 fluorides兲.
To be of use in the LL analysis, it is necessary that composition and unit cell volumes be available. Using the dispersion data and the one-term Sellmeier equation described by
DiDomenico and Wemple 共1969兲, we calculate dispersion
parameters, the long-wavelength index n ⬁ , and n D, the index of refraction at the NaD line. Using estimated experimental errors in n, comparisons of data on like compounds and
trends in n and dispersion in structural families, we make a
critical evaluation of the data. Finally, from the values of n ⬁ ,
the unit cell volumes, and the LL equation, we calculate the
total mean polarizability 具 ␣ e典 for each compound.
2. Presentation of Data
2.1. Composition, Characterization, and Source
This publication provides the composition, the refractive
indices at ␭⫽⬁ (n ⬁ ), and 589.3 nm (n D), molar volume of
the compounds V m , volume per anion V o , total mean electronic polarizabilities 具 ␣ e典 , the mean dispersion parameters
具 A 典 , 具 B 典 , 具 E o典 , and 具 E d典 , along with documentation providing an indication of the method of measuring n, the precision
of the measurement of n, and source reference in an easily
accessible form. Molar volume V m is the unit cell volume
divided by Z, the number of molecules per unit cell. Volume
REFRACTIVE INDEX AND DISPERSION
per anion V o is defined as the molar volume divided by the
number of water molecules and anions (H2 O⫹O⫽ ⫹OH⫺
⫹F⫺ ). In the text the values of 具 A 典 , 具 B 典 , 具 E o典 , and 具 E d典 for
uniaxial and biaxial compounds, although written A, B, E o ,
and E d , are mean values. The compositions of synthetic
compounds are generally accepted as correct. In the case of
synthetic compounds, we give, when known, the crystal
grower. Almost all of the data reported here are from single
crystals. Exceptions are PLZT (Pb–La–Zr–Ti–O3 ) compositions. In this case the data from PbTiO3 ceramic with n
⫽2.523 ( ␣ e⫽9.668) was found to compare well to single
crystal data where one paper 共Singh 1971兲 reported n o
⫽2.5218 and n e⫽2.5226 ( ␣ e ⫽9.665) and another 关Nomura
et al. 共1973兲兴 n⫽2.5617 ( ␣ e⫽9.792). In those cases where
single crystal data were not available, ceramic or polycrystalline sample is specified.
In the case of minerals we give the mineral name, the
color, and where available, the source of the specimen. Mineral compositions are generally those given by the original
author. Following the composition, the symbol * refers to
well known compositions, either as-grown synthetic crystals
or analyzed compositions of minerals. Many values of n and
dispersion for oxides and minerals have been reported in the
literature but we have only included those for which the unit
cell is known and the composition is relatively certain. In
some instances such as phenacite (Be2 SiO4 ), even though no
analysis was reported in the original papers, the data were
included because of the high probability of the composition
being correct. Many compositions, especially those reported
in LB 共1962兲, 共1969兲, 共1979兲, 共1981兲, 共1996兲; Hintze 共1897兲,
共1933兲, 共1938兲, 共1960兲; and Doelter 共1914兲, 共1917兲 are uncertain or questionable. In the case of the minerals, narsarsukite, leucosphenite, and sodalite, even though the analysis
or unit cell dimensions are not well known, we have included
the data because the refractive index was well determined.
For these entries, we have used in parentheses the nominal or
ideal compositions. In some cases, data from LB was omitted
if the composition was uncertain and there were other examples available where the composition was known, e.g.,
garnets, cordierites, and beryls. In some instances such as for
KH2 PO4 , where a number of accurate determinations of n
have been made, we have included only 1 or 2 of the more
accurate measurements.
Finally, we give the source of the data. In many cases, we
give the compilation from which the data were taken, e.g.,
Palik 共1991兲; Hintze 共1897兲, 共1933兲, 共1938兲, 共1960兲; or
Landolt-Börnstein 共1962兲, 共1969兲, 共1979兲, 共1981兲, 共1996兲.
When convenient, we give the original reference using the
CASSI 共Coden listed in the Chemical Abstracts Service
Source Index兲共1999兲. Appendix 1 lists the Codens used in
this paper. The effective cutoff date for literature search is
January 2000, whereas the earliest source was around 1850.
Although Table 1 lists many of the dispersion data published
between 1850 and 2000, it is not meant to be a complete
tabulation. Overall, we present data for 509 oxides and 55
fluorides.
933
2.2. Method of Measuring Dispersion or n ⴥ
Although prism techniques have been used in the majority
of dispersion determinations, a variety of other techniques
have also been used. We include a code describing the
method used to measure the refractive indices. The prism
method using either minimum deviation or perpendicular incidence 关Tilton 共1935兲; Tilton et al. 共1949兲; Werner 共1968兲;
Tentori and Lerma 共1990兲; Medenbach and Shannon 共1997兲;
Medenbach et al. 共2001兲兴 has been used most often 共about
60% of the data given here兲 and can give the refractive indices accurate to the fourth or fifth decimal place. The immersion method 关Werner 共1968兲; Verkouteren et al. 共1992兲兴
共about 10% of the data given here兲 is less accurate but can
give values accurate to the 4th decimal place. Infrared reflectivity 共IR兲 measurements in conjunction with Kramers–
Kronig analysis or the Lorentz oscillator model and classical
dispersion theory 关Barker 共1964兲兴 give the long wavelength
dielectric constant, ␧ ⬁ ⫽n ⬁2 , from fitting the parameter ␧ ⬁ to
the reflectivity data. In general, data obtained in this manner
共about 10% of the data given here兲 are accurate to the third
decimal place. Some papers use an independent measurement of n ⬁ and it is not always possible to distinguish these
values from the fitted values. When both IR and minimum
deviation measurements have been made, they have both
been tabulated for comparison. Ellipsometer methods 关Jellison 共1997兲; Jellison and Modine 共1997兲兴 have been used
more recently and give results somewhat less accurate than
prism methods. We have compared several sets of data using
both ellipsometer and prism methods and find agreement to
⫾0.02– 0.05. Critical angle methods including the use of the
Abbe–Pulfrich refractometer 关Straat and Forrest 共1939兲; Tilton 共1942, 1943兲; Hurlbut 共1984兲兴 have been used often but
not in determining dispersion. Finally, interference methods
using a Michelson-type interferometer have also been used
for determining dispersion 关Grehn 共1959兲; Werner 共1968兲;
Moskalev and Smirnova 共1987兲; Shumate 共1966兲兴. The
method of measuring n is not always given. Values quoted to
four decimal places in LB were assumed to be obtained by
prism methods and therefore to be accurate to
⫾0.0001– 0.0005, except when indicated otherwise.
2.3. Sellmeier Analysis
There are many dispersion formulas that have been developed to fit the refractive index over a wide range of frequencies. Many of the most common formulas are described by
Tropf et al. 共1995兲. However, the single-term Sellmeier
equation used by DiDomenico and Wemple 共1969兲 and
Wemple and DiDomenico 共1971兲 has the advantages of simplicity and of providing derived parameters that have physical significance. In the form
1/共 n 2 ⫺1 兲 ⫽⫺A/␭ 2 ⫹B,
共3a兲
A, the slope of the plot of (n 2 ⫺1) ⫺1 versus ␭ ⫺2 in units of
10⫺16 m2 gives a measure of dispersion and B, the intercept
Simple Fluorides
LiF*⫹
NaF*⫹
KF*
RbF*
CsF* alpha
CsF* beta
AgF film
MgF*⫹
2
MgF*2
CaF*⫹
2
CaF*2
SrF*⫹
2
SrF*2
BaF*⫹
2
BaF*2
MnF*2
FeF*2
FeF*2
NiF*2 FL
ZnF*2
ZnF*2
CdF*2
PbF*⫹
2
PbF*⫹
2
PbF*2
EuF*2
LaF*⫹
3
LaF*⫹
3
CeF*⫹
3
PrF*⫹
3
NdF*⫹
3
TbF*⫹
3
Complex Fluorides
NaCoF*3 IR
NaNiF*3 IR
KMgF*⫹
3
KMgF*3
KMnF*3
KMnF*⫹
3 FL
KMnF*3 FL
KCoF*3
KCoF*3
KNiF*⫹
3
Chemical composition,
sample designations
1.3858
1.3196
1.355
1.389
1.469
1.566
1.73
1.3722
1.38
1.4255
1.430
1.4306
1.44
1.4655
1.47
1.462
1.498
1.508
1.493
1.486
1.45
1.49
1.7248
1.7272
1.58
1.555
1.5954
1.5934
1.6050
1.6077
1.6074
1.5768
1.470
1.442
1.3975
1.43
1.45
1.4382
1.439
1.500
1.50
1.4827
1.470
1.442
1.3975
1.43
1.45
1.4382
1.439
1.500
1.50
1.4827
ny
1.3858
1.3196
1.355
1.389
1.469
1.566
1.73
1.3722
1.38
1.4255
1.430
1.4306
1.44
1.4655
1.47
1.462
1.498
1.508
1.493
1.486
1.45
1.49
1.7248
1.7272
1.58
1.555
1.5954
1.5934
1.6050
1.6077
1.6074
1.5931
nx
1.470
1.442
1.3975
1.43
1.45
1.4382
1.439
1.500
1.50
1.4827
1.3858
1.3196
1.355
1.389
1.469
1.566
1.73
1.3838
1.38
1.4255
1.430
1.4306
1.44
1.4655
1.47
1.491
1.509
1.512
1.529
1.517
1.61
1.49
1.7248
1.7272
1.58
1.555
1.5910
1.5860
1.5985
1.6017
1.6016
1.5510
nz
1.526
1.495
1.7668
1.7680
1.6058
1.6039
1.6183
1.6207
1.6191
1.5868
1.526
1.495
1.7668
1.7680
1.6058
1.6039
1.6183
1.6207
1.6191
1.6034
1.4929
1.472
1.514
1.472
1.514
1.4929
1.4742
1.4742
1.4469
1.4377
1.4377
1.4469
1.4336
1.4336
1.4030
1.3774
1.3774
1.4030
1.3916
1.3255
1.360
1.398
1.479
1.578
nDy
1.3916
1.3255
1.360
1.398
1.479
1.578
nDx
1.4929
1.4469
1.4030
1.6004
1.5968
1.6113
1.6146
1.6132
1.5603
1.7668
1.7680
1.561
1.525
1.501
1.524
1.4742
1.4377
1.4336
1.3892
1.3916
1.3255
1.360
1.398
1.479
1.578
nDz
59.11
57.13
64.00
64.00
73.45
73.45
73.45
67.32
67.32
64.67
16.21
24.88
38.07
45.13
54.05
54.38
29.77
32.55
32.55
40.74
40.74
48.60
48.60
59.44
59.44
39.30
36.56
36.56
33.35
34.75
34.75
39.14
52.38
52.38
52.38
48.98
54.77
54.77
53.14
51.94
51.35
49.64
Vm
19.70
19.04
21.33
21.33
21.33
24.48
24.48
22.44
22.44
21.56
16.21
24.88
38.07
45.13
54.05
54.38
29.77
16.28
16.28
20.37
20.37
24.30
24.30
29.72
29.74
19.65
18.28
18.28
16.67
17.38
17.38
19.57
26.19
26.19
26.19
24.49
18.26
18.26
17.71
17.31
17.12
16.54
Vo
3.937
3.609
3.683
3.947
4.712
4.605
4.612
4.727
4.727
4.407
0.909
1.177
1.981
2.548
3.594
4.235
2.837
1.783
1.800
2.489
2.512
3.001
3.058
3.927
3.959
2.626
2.574
2.608
2.361
2.425
2.454
2.701
4.964
4.977
4.162
3.753
4.436
4.418
4.357
4.275
4.225
3.908
具 ␣ e典
0.0071
0.0075
0.0058
0.0046
0.0049
0.0058
0.0057
0.0051
0.0049
0.0114
0.0125
0.0198
0.0059
0.0063
0.0095
0.0066
0.0064
0.0074
0.0062
0.0064
0.0096
0.0074
0.0101
0.0074
0.0058
具A典
0.8344
0.9360
1.0494
0.6490
0.6532
0.6374
0.6336
0.6339
0.6782
0.5042
0.5063
0.7909
0.8076
0.8547
0.7961
0.8714
0.9555
0.9689
1.1193
1.0863
1.3489
1.1977
1.0770
0.8642
0.6884
具B典
13.69
14.17
16.96
15.03
14.59
13.23
13.36
14.08
14.94
8.41
8.05
8.00
14.83
14.76
11.57
14.52
15.51
14.47
16.97
16.47
14.97
16.04
13.03
13.69
13.78
具 Eo典
16.41
15.14
16.16
23.15
22.34
20.76
21.09
22.21
22.03
16.67
15.90
10.11
18.37
17.27
14.54
16.66
16.23
14.93
15.16
15.16
11.10
13.39
12.10
15.84
20.02
具 Ed典
73
73
75
67
67
75
72
72
67
84
51
78
76
76
76
62
72
78
64
63
62
80
62
64
62
73
73
80
73
73
64
65
86
78
65
66
66
83
83
83
83
81
Year
PSSABA
PSSABA
OPSUA3
JAPIAU
JAPIAU
OPSUA3
OPSUA3
OPSUA3
JAPIAU
SPHJAR
JRNBAG
Ref. 7
JPCRBU
JPCRBU
JPCRBU
Ref. 1
JCPSA6
Ref. 7
PRVAAH
APOPAI
PHRVAO
JPCRBU
PHRVAO
JOSAAH
PHRVAO
PSSBBD
PSSBBD
JOPQAG
PSSBBD
PSSBBD
PRVAAH
PRVAAH
Ref. 4
Ref. 7
PRVAAH
JPCSAW
APOPAI
PMABDJ
PMABDJ
PMABDJ
PMABDJ
PRBMDO
Coden
16
16
39
38
38
39
33
33
38
59
139
27
5
48
48
48
48
23
136
2
127
9
127
54
127
57
57
41
57
57
136
139
5
5
5
Rf
56
47
Vol
419
419
390
4616
4616
390
97
97
4616
1316
25
7-105
329
329
329
189
3735
7-95
1290
1103
1950
161
1950
628
1950
681
681
543
681
681
1290
1211
28
7-94
1211
621
1966
203
203
203
203
6307
Page
M
3
3
1
3
3
1
3
3
3
6
1
1
1
1
1
1
4
1
3
1
3
1
3
1
3
8
8
5
8
8
3
3
1
1
3
2
1
1
1
1
1
1
E
4
4
1
5
5
1
4
4
5
1
1
2?
3
3
3
4
5
1
5
1
4
1
5
1
5
5
5
4
5
5
5
7
1
1
7
4
1
2
2
2
2
2
TABLE 1. Refractive index and dispersion data, listing refractive indices 共n x , n y , n z兲 at ␭ ⫽ ⬁, refractive indices 共n Dx , n Dy , n Dz兲 at ␭ ⫽ 589.3 nm, molar volume, V m , volume per O atom, V o , and mean values of electronic polarizabilities
具␣e典, mean dispersion values 具 A 典 and 具 B 典 according to Eq. 共3a兲, and average of E o and E d according to Eq. 共3b兲. Source references use Codens from the American Chemical Society, Chemical Abstracts Service Source Index 1907–1999
Cumulative 共American Chemical Society, Washington, DC, 2000兲. 共Symbols * and ⫹ and numerical values for method and error can be found at the end of the table.兲
934
SHANNON ET AL.
RbMnF*⫹
3
RbMnF*3
CsNiF*⫹
3
BaLiF*3
LiYF*⫹
4
LiTbF*⫹
4
NaBF*⫹
4
*⫹
KBF4 avogadroite 共synthetic兲
BaMgF*⫹
4 FE
BaMgF*4 FE
BaZnF*⫹
4 FE
Na2 SbF*5
Na2 SiF6 malladrite
Rb2 SiF*⫹
6
Cs2 SiF*⫹
6
*
Cs2 SiF6
Na3 Li3 Al2 F12 cryolithionite
Na2 GeF*⫹
6
Rb2 GeF*⫹
6
*⫹
Cs2 GeF6
Cs2 GeF*6
LiCaAl.99Cr.01F*⫹
6
BaY2 F*⫹
8
MgSiF6•6 H2 O*⫹ FL 298 K
MnSiF6•6 H2O*⫹ FL 223 K
FeSiF6•6 H2O*⫹ FL?
NiSiF6•6 H2O*⫹ FL?
CuSiF6•6 H2O*⫹ FL?
ZnSiF6•6 H2O*⫹ FL?
PbFCl* matlockite 共Cromford, Derbyshire兲
Chlorides
LiCl*⫹
NaCl*⫹ halite
KCl*⫹ sylvite
RbCl*⫹
CuCl*
AgCl*⫹
TlCl*
SrCl*2
Simple Oxides
H2 O*⫹ ice
H2 O*⫹ ice
H2 O* water
KNiF*3
KZnF*3
sample designations
1.52
1.53
1.4745
1.59
1.4681
1.50
1.4464
1.4648
1.3035
1.3197
1.4411
1.435
1.4871
1.463
1.3090
1.3484
1.3793
1.382
1.3337
1.3311
1.3904
1.3921
1.417
1.3869
1.5266
1.3372
1.3492
1.3556
1.3799
1.3998
1.3747
2.058
1.6580
1.5260
1.4732
1.4760
1.884
1.9911
2.112
1.691
1.3011
1.3007
1.319
1.6580
1.5260
1.4732
1.4760
1.884
1.9911
2.112
1.691
1.3011
1.3007
1.319
ny
1.52
1.53
1.4745
1.59
1.4681
1.50
1.4464
1.4648
1.2973
1.3193
1.4660
1.465
1.5107
1.441
1.3090
1.3484
1.3793
1.382
1.3337
1.3311
1.3904
1.3921
1.417
1.3869
1.5149
1.3372
1.3492
1.3556
1.3799
1.3998
1.3747
2.058
nx
1.3025
1.3021
1.319
1.6580
1.5260
1.4732
1.4760
1.884
1.9911
2.112
1.691
1.52
1.53
1.4745
1.59
1.4983
1.50
1.4684
1.4934
1.2971
1.3200
1.4585
1.455
1.5037
1.422
1.3053
1.3484
1.3793
1.382
1.3337
1.3252
1.3839
1.3921
1.417
1.3854
1.5063
1.3532
1.3663
1.3780
1.3962
1.4017
1.3876
1.944
nz
1.3091
1.3090
1.333
1.3091
1.3090
1.333
1.973
2.0615
2.249
1.973
2.0615
2.249
1.4536
1.4735
1.3071
1.3248
1.4490
1.447
1.4967
1.476
1.3124
1.3534
1.3847
1.391
1.3395
1.3376
1.3961
1.3985
1.430
1.3923
1.5356
1.3440
1.3568
1.3638
1.3902
1.4092
1.3823
2.145
1.4536
1.4735
1.3009
1.3243
1.4724
1.471
1.5214
1.467
1.3124
1.3534
1.3847
1.391
1.3395
1.3376
1.3961
1.3985
1.430
1.3923
1.5235
1.3440
1.3568
1.3638
1.3902
1.4092
1.3823
2.145
1.5443
1.4898
1.4784
1.4784
1.5443
1.4898
1.4837
nDy
1.4837
nDx
1.3105
1.3105
1.333
1.973
2.0615
2.249
1.5443
1.4898
1.4763
1.5029
1.3006
1.3113
1.4657
1.465
1.5144
1.435
1.3088
1.3534
1.3847
1.391
1.3395
1.3317
1.3898
1.3985
1.430
1.3909
1.5145
1.3601
1.3738
1.3845
1.4060
1.4090
1.3954
2.006
1.5102
1.4837
nDz
32.14
32.14
33.94
44.86
62.31
71.26
39.72
42.72
56.72
84.90
64.67
66.68
76.20
76.20
87.98
63.66
75.67
73.33
72.89
83.42
86.93
86.93
89.38
123.63
114.44
150.94
177.37
177.37
222.82
121.01
147.13
183.53
183.53
104.71
154.39
255.66
265.60
257.70
240.65
235.10
245.30
61.00
Vm
32.14
32.14
33.94
44.86
62.31
71.26
39.72
42.72
56.72
42.45
21.56
22.22
25.40
25.40
29.33
21.22
18.92
18.33
18.22
20.85
21.73
21.73
22.35
24.73
19.07
25.16
29.56
29.56
18.57
20.17
24.52
30.59
30.59
17.45
19.30
21.30
22.13
21.47
20.05
19.62
20.44
30.55
Vo
1.442
1.440
2.984
3.287
4.174
4.798
4.356
5.069
7.253
7.756
4.694
4.917
5.117
6.139
5.947
4.470
4.890
4.923
3.247
3.947
5.633
5.595
6.281
7.809
5.230
7.722
9.792
9.854
10.963
5.880
8.293
10.436
11.018
5.877
11.131
12.880
13.816
13.681
13.474
13.619
13.533
7.378
具 ␣ e典
0.0146
0.0152
0.0225
0.0161
0.0103
0.0148
0.0106
0.0120
0.0059
0.0066
0.0067
0.0082
0.0057
0.0075
0.0067
0.0142
0.0061
0.0068
0.0062
0.0098
0.0087
0.0101
0.0064
0.0068
0.0117
0.0061
0.0053
0.0097
0.0101
0.0097
0.0112
0.0089
0.0089
0.0106
0.0077
0.0066
具A典
1.4408
1.4428
1.3536
0.3919
0.3373
0.2888
0.7527
0.8546
0.8988
0.8529
1.4532
1.3706
0.8953
0.9034
0.7994
0.9276
1.4078
1.2221
1.1081
1.0985
1.2841
1.3047
1.0786
1.0660
0.9918
1.0845
0.7707
1.2470
1.1974
1.1667
1.0885
1.0402
1.1093
0.3260
0.8447
0.8516
具B典
12.57
12.31
9.80
6.25
7.24
5.59
10.64
10.68
15.55
14.40
18.64
16.36
15.79
13.85
13.80
10.23
19.26
16.96
16.90
13.39
15.40
14.40
16.47
15.80
11.67
16.91
15.28
14.34
13.78
13.89
12.45
13.66
14.14
7.01
13.26
14.32
具 Eo典
8.72
8.53
7.24
15.94
21.46
19.37
14.14
12.50
17.30
16.89
12.82
11.94
17.64
15.33
17.27
11.0
13.6
13.8
15.2
12.1
12.0
11.0
15.2
14.8
11.7
15.5
19.8
11.5
11.5
11.9
11.4
13.1
12.7
21.50
15.70
16.81
具 Ed典
62
62
91
76
62
62
76
28
62
62
74
67
67
84
67
82
89
75
78
86
38
77
75
75
78
62
82
82
35
62
82
82
82
35
95
95
74
62
62
74
62
62
62
Year
Ref. 1
Ref. 1
Ref. 9
JPCRBU
Ref. 1
Ref. 1
JPCRBU
ZEKRDZ
Ref. 1
Ref. 1
PSSBBD
JAPIAU
JAPIAU
SPHJAR
JAPIAU
PRBMDO
JCOMEL
APOPAI
JAPIAU
ZEKRDZ
Ref. 10C
APHYCC
JAPIAU
JAPIAU
JSSCBI
Ref. 1
INOMAF
INOMAF
ZPCBAL
Ref. 1
INOMAF
INOMAF
INOMAF
ZPCBAL
Ref. 13
Ref. 13
ACPHAA
Ref. 1
Ref. 1
ACPHAA
Ref. 1
Ref. 1
Ref. 1
Coden
Rf
Rf
5
Rf
Rf
5
68
Rf
Rf
62
1
Rf
Rf
1
Rf
Rf
Rf
14
46
46
23
Rf
18
18
31
Rf
18
18
18
31
38
38
59
38
25
1
14
49
174
Vol
2835
2835
1059
329
3905
237
329
82
2749
12
511
4616
4616
1316
4616
6474
5613
2056
3464
313
48
403
4645
4645
187
143
570
570
292
18
570
570
570
292
599
600
5
189
589
5
2737
2737
300
Page
1
1
8
1
1
1
1
2
1
1
3
3
3
6
3
1
3
1
5
1
1
1
1
1
5
1
2
2
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
M
1
1
3
1
1
1
1
3
2
4
4
5
5
1
5
1
4
1
1
1
2
1
3?
2
5
2
2
2
3?
2
2?
2
2
3?
1
1
2
2
2
2
2
2
4
E
Cumulative 共American Chemical Society, Washington, DC, 2000兲. 共Symbols * and ⫹ and numerical values for method and error can be found at the end of the table.兲 —Continued
935
Li2 O
LiOH*
Cu2 O cuprite film
Cu2 O cuprite polyxtal
Cu2 O cuprite polyxtal
Cu2 O cuprite
Cu2 O cuprite 关polyxtal reflectance data兴
BeO*⫹
MgO*⫹
Mg共OH兲⫹
2 brucite 共Wood Mine, Lancaster, PA兲
CaO*⫹
SrO*⫹
BaO*⫹
MnO*
MnO*
MnO 关polyxtal reflectance data兴
CoO*
NiO*
NiO*
ZnO*⫹
ZnO*
ZnO*
ZnO 关polyxtal reflectance data兴
CdO film
PbO* red litharge FL 200 K
EuO*
EuO*
B2 O*3 共estimated n ⬁ values兲
B2 O*3 共n D values兲
Al2 O*⫹
3
Al2 O*⫹
3
Al2 O*3
Al0.99Fe.01OOH*⫹ diaspore 共Turkey兲
Sc2 O*⫹
3 共W. Yen兲
Cr2 O*3
Mn2 O3 关polyxtal reflectance data兴
Fe1.98Fe共2⫹ 兲.02O*3 hematite 共Elba兲
Fe2 O3 关average n, polyxtal reflectance data兴
FeOOH goethite
FeOOH lepidocrocite
Y2 O*⫹
3
Y2 O*⫹
3
Y2 O*⫹
3
Y2 O*⫹
3
sample designations
1.637
1.4491
2.54
2.55
2.57
2.27
2.68
1.7050
1.7147
1.5501
1.8053
1.8277
1.9167
2.11
2.22
2.07
2.30
2.39
2.32
1.9102
1.901
1.898
1.90
2.37
2.535
1.960
2.30
1.635
1.648
1.7520
1.7504
1.79
1.6881
1.9536
2.490
2.81
2.602
2.50
2.123
1.861
1.8915
1.8962
1.8903
1.8815
nx
1.637
1.4491
2.54
2.55
2.57
2.27
2.68
1.7050
1.7147
1.5501
1.8053
1.8277
1.9167
2.11
2.22
2.07
2.30
2.39
2.32
1.9102
1.901
1.898
1.90
2.37
2.535
1.960
2.30
1.635
1.648
1.7520
1.7504
1.79
1.7070
1.9536
2.490
2.81
2.602
2.50
2.209
2.011
1.8915
1.8962
1.8903
1.8815
ny
1.637
1.4408
2.54
2.55
2.57
2.27
2.68
1.7201
1.7147
1.5728
1.8053
1.8277
1.9167
2.11
2.22
2.07
2.30
2.39
2.32
1.9245
1.911
1.914
1.90
2.37
2.665
1.960
2.30
1.602
1.615
1.7449
1.7430
1.76
1.7325
1.9536
2.470
2.81
2.446
2.50
2.220
2.194
1.8915
1.8962
1.8903
1.8815
nz
1.4639
2.67
2.88
1.7184
1.7355
1.5665
1.8396
1.8710
1.9841
2.15
2.0222
2.008
2.004
1.99
1.7673
1.7233
1.9943
2.62
3.190
3.10
2.403
2.200
1.9311
1.9294
1.9301
1.9489
2.67
2.88
1.7184
1.7355
1.5665
1.8396
1.8710
1.9841
2.15
2.0222
2.008
2.004
1.99
1.7673
1.7028
1.9943
2.62
3.190
3.10
2.274
1.938
1.9311
1.9294
1.9301
1.9489
nDy
1.4639
nDx
2.62
2.912
3.10
2.409
2.515
1.9311
1.9294
1.9301
1.9489
1.7503
1.9943
1.7598
2.0256
2.023
2.021
1.99
2.15
2.67
2.88
1.7342
1.7355
1.5853
1.8396
1.8710
1.9841
1.4518
nDz
24.51
27.44
38.91
38.91
38.91
38.91
38.91
13.79
18.67
40.90
27.83
33.16
42.48
22.00
22.00
22.00
19.30
18.21
18.21
23.55
23.55
23.55
23.55
25.88
38.35
34.00
34.00
45.26
45.26
42.45
42.45
42.45
29.51
59.64
48.10
52.15
50.32
50.32
34.65
37.34
74.50
74.50
74.50
74.50
Vm
24.51
27.44
38.91
38.91
38.91
38.91
38.91
13.79
18.67
20.45
27.83
33.16
42.48
22.00
22.00
22.00
19.30
18.21
18.21
23.55
23.55
23.55
23.55
25.88
38.35
34.00
34.00
15.09
15.09
14.15
14.15
14.15
14.75
19.88
16.03
17.38
16.77
16.77
17.33
18.67
24.83
24.83
24.83
24.83
Vo
2.100
1.748
5.992
6.012
6.051
5.393
6.254
1.286
1.750
3.146
2.854
3.469
4.779
2.810
2.978
2.745
2.711
2.656
2.581
2.646
2.624
2.622
2.616
3.745
5.979
3.948
4.777
3.815
3.878
4.127
4.120
4.252
2.750
6.894
7.265
8.676
7.774
7.645
4.606
4.522
8.220
8.250
8.212
8.154
具 ␣ e典
0.0226
0.0255
0.0162
0.0215
0.0075
0.0062
0.0075
0.0126
0.0051
0.0066
0.0042
0.0159
0.0185
0.0182
0.0152
0.0099
0.0267
0.0086
0.0043
0.0064
0.0079
0.0080
0.0095
0.0116
0.0110
具A典
0.1453
0.1824
0.1898
0.2658
0.3323
0.3879
0.3853
0.3886
0.3937
0.5209
0.3550
0.4851
0.3690
0.3808
0.3814
0.3813
0.3050
0.2401
0.1616
0.5197
0.5154
0.7014
0.4426
0.4272
0.3740
0.9160
具B典
5.16
3.59
3.45
5.12
4.97
9.11
9.93
9.09
7.07
12.77
9.24
13.53
6.09
5.74
5.79
6.33
7.02
3.79
5.48
13.94
11.35
11.94
9.38
8.48
7.17
11.53
具 Eo典
35.4
19.68
18.17
19.28
14.96
23.50
25.78
23.38
17.95
24.51
26.03
27.89
16.51
15.08
15.19
16.61
23.02
15.80
33.90
26.82
22.02
17.03
21.19
19.85
19.17
12.59
具 Ed典
84
33
63
73
66
62
79
66
52
62
66
66
75
69
69
79
65
65
59
65
54
98
79
60
77
68
69
38
38
58
94
63
97
01
65
79
62
79
62
19
68
91
91
91
Year
SSCOA4
ZPCBAL
JCPSA6
JPCSAW
PHRVAO
Ref. 1
JJAPA5
AMMIAY
JRNBAG
Ref. 1
JAPIAU
PHRVAO
JAPIAU
SSCOA4
SSCOA4
JJAPA5
JAPIAU
JAPIAU
PHRVAO
JAPIAU
ZAPHAX
PRBMDO
JJAPA5
ZEPYAA
JCDTBI
PKOMA3
JPCSAW
AJSCAP
AJSCAP
JOSAAH
JAPIAU
PRVAAH
JOBPDE
JOAOF8
PHVAAH
JJAPA5
Ref. 1
JJAPA5
Ref. 1
AJSCAP
JJAPA5
Ref. 9
Ref. 9
Ref. 9
Coden
51
20
39
34
141
Rf
18
51
49
Rf
37
143
46
7
7
18
36
36
114
36
6
58
18
158
1977
8
30
35
35
48
76
132
14
3
138
18
Rf
18
Rf
47
7
Vol
421
65
1789
2201
803
2749
1043
141
249
697
2450
595
443
977
109
1043
2446
2446
1507
1674
257
3586
1043
511
1096
80
1403
143
143
629
8032
1474
3299
174
A530
1043
685
1043
3562
311
404
1079
1079
1079
Page
M
3
2
3
3
3
8
8
1
1
1
1
1
1
3
3
8
3
3
3
1
1
4
8
8
3
1
3
2
2
1
4
3
1
1
3
8
8
8
8
2
8
1
1
1
E
5
1
5
5
5
5
5?
1
1
2
1
1
1
5
5
5
5
5
5
1
3
3
5
5
4
4
7
5
5
1
2
5
1
1
4
5?
3
5
3
5
2
2?
2
2?
Cumulative 共American Chemical Society, Washington, DC, 2000兲. 共Symbols * and ⫹ and numerical values for method and error can be found at the end of the table.兲—Continued
936
SHANNON ET AL.
In2 O3 film
As2 O*⫹
3 arsenolite 共probably synthetic兲
As2 O*3 arsenolite
Sb2 O*⫹
3 senarmontite 共Algeria兲
Sb2 O*3 senarmonite
Bi2 O*3 alpha
Bi2 O*3 关IR data, not accurate, not cubic兴
*
Bi12SiO20
*⫹
Bi12GeO20
*⫹
Bi12TiO20
Bi12TiO20 :Ga*⫹
*
Bi12TiO20
Bi12Ga.72Bi.28O19.5
Pr2 O*3 cubic
Nd2 O*3 cubic FL 293 K
Nd2 O3 hexagonal
共n ⬁ from extrapolation of ␣ vs at. no.兲
Sm2 O3 monoclinic
共n ⬁ from extrapolation of ␣ vs. at. no.兲
Eu2 O*3
Eu2 O*3 cubic
共n ⬁ from interpolation of n ⬁ vs at. no.兲
Gd1.98Nd.02O*3 关Sci. Mat. Corp
共assume n y⫽n z兲兴
Gd2 O*3 cubic
Gd2 O*3 cubic
Tb2 O*3
Tb2 O*3
Dy2 O*⫹
3 共W. Yen兲
Dy2 O*3
Ho2 O*3
Ho2 O*3 共n ⬁ from interpolation of n ⬁ vs at. no.兲
Er2 O*3 共n ⬁ from interpolation of n ⬁ vs at. no.兲
Er2 O*3
Er2 O*3
Er2 O*3
Tm2 O*3
Tm2 O*3 共n ⬁ from interpolation of n ⬁ vs at. no.兲
Yb2 O*⫹
3
Yb2 O*⫹
3 共W. Yen兲
Y2 O*3
sample designations
1.90
1.935
1.90
1.935
1.9332
1.895
1.892
1.928
1.923
1.930
1.888
1.95
1.882
1.918
1.9088
1.9096
2.055
2.021
1.9332
1.895
1.892
1.928
1.923
1.930
1.888
1.95
1.882
1.918
1.9088
1.9096
1.901
1.940
1.901
1.940
1.90
1.935
2.052
2.052
1.90
1.935
1.884
2.00
1.7185
1.725
2.0000
2.03
2.437
2.0
2.370
2.386
2.4065
2.4005
2.419
2.403
1.88
1.86
2.067
ny
1.884
2.00
1.7185
1.725
2.0000
2.03
2.344
2.0
2.370
2.386
2.4065
2.4005
2.419
2.403
1.88
1.86
2.067
nx
1.9332
1.895
1.892
1.928
1.923
1.930
1.888
1.95
1.882
1.918
1.9088
1.9096
1.90
1.935
1.90
1.935
2.055
1.901
1.940
2.052
1.884
2.00
1.7185
1.725
2.0000
2.03
2.530
2.0
2.370
2.386
2.4065
2.4005
2.419
2.403
1.88
1.86
2.067
nz
1.9757
1.963
1.960
1.959
1.956
1.950
1.9468
1.9470
1.959
1.956
1.950
1.9468
1.9470
1.96
1.96
2.102
1.9757
1.963
1.960
1.96
1.96
2.065
1.969
2.558
2.561
2.5873
2.5945
2.588
2.611
1.94
1.92
2.558
2.561
2.5873
2.5945
2.588
2.611
1.94
1.92
1.969
1.7537
1.755
2.0817
2.09
2.660
1.912
nDy
1.7537
1.755
2.0817
2.09
2.572
1.912
nDx
1.9468
1.9470
1.950
1.959
1.956
1.9757
1.963
1.960
1.96
1.96
2.102
1.969
2.558
2.561
2.5873
2.5945
2.588
2.611
1.94
1.92
1.7537
1.755
2.0817
2.09
2.785
1.912
nDz
75.86
75.86
74.57
74.57
73.33
73.33
73.33
73.33
72.07
72.07
70.98
70.98
77.19
77.19
79.01
79.01
72.41
80.05
80.05
74.87
74.50
64.72
84.96
84.96
86.68
86.68
82.60
82.60
514.80
521.30
526.54
526.54
526.54
526.60
86.87
85.01
76.78
Vm
25.29
25.29
24.86
24.86
24.44
24.44
24.44
24.44
24.02
24.02
23.66
23.66
25.73
25.73
26.34
26.34
24.13
26.68
26.68
24.96
24.83
21.57
28.32
28.32
28.89
28.89
27.53
27.53
25.74
26.07
26.33
26.33
26.33
26.33
28.96
28.34
25.59
Vo
8.640
8.393
8.231
8.461
8.289
8.333
8.068
8.455
7.892
8.116
7.937
7.942
8.573
8.804
8.775
9.011
8.890
8.898
9.163
9.240
8.171
7.725
7.998
8.053
10.347
10.551
12.268
9.860
74.494
75.920
77.301
77.121
77.673
77.205
9.497
9.143
9.563
具 ␣ e典
0.0069
0.0068
0.0126
0.0050
0.0125
0.0073
0.0123
0.0124
0.0122
0.0122
0.0062
0.0121
0.0126
0.0115
0.0115
0.0123
0.0106
0.0130
0.0119
0.0126
0.0105
0.0087
0.0116
0.0080
0.0138
0.0053
具A典
0.3782
0.3778
0.3933
0.3668
0.3898
0.3653
0.3858
0.3875
0.3853
0.3847
0.3151
0.3825
0.2167
0.2130
0.2087
0.2100
0.2060
0.2094
0.3947
0.4085
0.5119
0.5059
0.3334
0.3209
0.2034
0.3921
具B典
9.38
9.44
7.05
10.82
7.07
8.97
7.09
7.08
7.09
7.10
9.01
7.11
5.25
5.44
5.39
5.22
5.58
5.07
7.28
7.21
8.85
9.63
6.78
8.03
4.85
10.84
具 Eo典
24.81
24.98
17.93
29.51
18.14
24.54
18.38
18.27
18.41
18.44
28.61
18.58
24.2
25.5
25.8
24.8
27.0
24.2
18.44
17.65
17.28
19.03
20.33
25.02
23.86
27.65
具 Ed典
01
73
73
01
01
56
73
87
73
01
97
01
73
01
73
01
01
73
01
01
56
86
97
62
97
62
76
70
71
83
97
96
93
96
73
73
01
Year
JOAOF8
JSTCAM
JSTCAM
JOAOF8
JOAOF8
ANCHAM
JSTCAM
SPSSA7
JSTCAM
JOAOF8
JOBPDE
JOAOF8
JSTCAM
JOAOF8
JSTCAM
JOAOF8
JOAOF8
JSTCAM
JOAOF8
JOAOF8
ANCHAM
JAPIAU
JOBPDE
Ref. 1
JOBPDE
Ref. 1
MRBUAC
PSSABA
JAPIAU
JOSAAH
JNOMFV
JOBPDE
PSSABA
JOBPDE
JSTCAM
JSTCAM
JOAOF8
Coden
3
13
13
3
3
28
13
29
13
3
14
3
13
3
13
3
3
13
3
3
28
60
14
Rf
14
Rf
11
2
42
73
6
13
140
13
13
13
3
Vol
174
871
871
174
174
2023
871
1904
871
174
3299
174
871
174
871
174
174
871
174
174
2023
R123
3299
2565
3299
204
1551
K149
493
495
235
908
273
908
871
871
174
Page
1
2
2
8
8
2
2
4
2
8
1
1
2
8
2
8
1
2
8
8
2
3
1
8
1
8
1
8
1
8
1
1
1
1
2
2
8
M
1
4?
4?
4
3
3
3?
5
3?
3
1
1
5?
3
5?
3
3
5?
3
3
3?
5
1
3?
1
5?
3
5
4
6
2
2
3
4
5?
5?
3
E
937
Yb2 O*3
Lu2 O*⫹
3 共W. Yen兲
Lu2 O*3
SiO*⫹
2
SiO*⫹
2 smoky quartz
SiO*⫹
2 amethyst 共Zambia兲
SiO*⫹
2 amethyst 共Para, Brazil兲
SiO*⫹
2 共G. Rossman, X-O兲
SiO*⫹
2 共G. Rossman, X-13兲
SiO*⫹
2 共A. Ballman兲
SiO*⫹
2 共G. Rossman, X-488-3兲
SiO*⫹
2 smoky quartz
SiO*2
GeO*⫹
2
GeO*2 tetragonal
GeO*2 tetragonal
TiO*⫹
2 rutile 共synthetic?兲
TiO*⫹
2 rutile 共synthetic?兲
TiO*2 rutile mineral
TiO*2
TiO*2 关average n, polyxtal reflectance data兴
TiO*2 brookite, brown
TiO*⫹
2 anatase, yellow 共Binnental兲
TiO*2 anatase 共Binnental兲
TiO*2 anatase 共Binnental兲
TeO*⫹
2 FL 9 KBAR
TeO*⫹
2 FL 9 KBAR
TeO*2 FL 9 KBAR
SnO⫹
2 cassiterite 共Araca, Bolivia兲
SnO*⫹
2 cassiterite 共synthetic兲
SnO*⫹
2 cassiterite 共synthetic兲
SnO*2
ZrO*2 cubic
*⫹
Zr.869Y.131O1.934
*⫹
Zr.671Y.329O1.835
*⫹
Zr.894Y.095Hf.011O1.95
*⫹
Hf.904Y.096O1.952
*⫹
Hf.85Y.15O1.925
*
CeO2
CeO*2
ThO*⫹
2 共synthetic兲
ThO*2 共synthetic, Norton Refractories兲
ThO*2
ThO*2
sample designations
1.879
1.8997
1.867
1.5324
1.5306
1.5330
1.5330
1.5327
1.5326
1.5328
1.5327
1.5331
1.535
1.9250
1.927
2.02
2.4252
2.4096
2.422
2.38
2.41
2.411
2.3852
2.3781
2.3740
2.1614
2.1690
2.27
1.9462
1.9442
1.9319
1.945
2.256
2.1082
2.0180
2.1193
2.0690
2.0486
2.36
2.31
2.0679
2.070
2.07
2.20
nx
1.879
1.8997
1.867
1.5324
1.5306
1.5330
1.5330
1.5327
1.5326
1.5328
1.5327
1.5331
1.535
1.9250
1.927
2.02
2.4252
2.4096
2.422
2.38
2.41
2.422
2.3852
2.3781
2.3740
2.1614
2.1690
2.27
1.9462
1.9442
1.9319
1.945
2.256
2.1082
2.0180
2.1193
2.0690
2.0486
2.36
2.31
2.0679
2.070
2.07
2.20
ny
1.879
1.8997
1.867
1.5411
1.5393
1.5418
1.5415
1.5412
1.5413
1.5416
1.5416
1.5417
1.544
2.0138
2.018
2.10
2.6666
2.6515
2.666
2.63
2.41
2.504
2.3386
2.3330
2.3294
2.3024
2.3070
2.43
2.0471
2.0449
2.0298
2.043
2.256
2.1082
2.0180
2.1193
2.0690
2.0486
2.36
2.31
2.0679
2.070
2.07
2.20
nz
1.942
1.9349
1.930
1.5435
1.5439
1.5444
1.5444
1.5441
1.5441
1.5442
1.5441
1.5443
1.9577
1.960
2.6190
2.6098
2.613
2.65
2.54
2.584
2.5621
2.5621
2.5608
2.2730
2.2753
2.0004
1.9982
1.9871
2.1581
2.0691
2.1698
2.1109
2.0881
2.1113
2.105
1.9577
1.960
2.6190
2.6098
2.613
2.65
2.54
2.585
2.5621
2.5621
2.5608
2.2730
2.2753
2.0004
1.9982
1.9871
2.1581
2.0691
2.1698
2.1109
2.0881
2.1113
2.105
nDy
1.942
1.9349
1.930
1.5435
1.5439
1.5444
1.5444
1.5441
1.5441
1.5442
1.5441
1.5443
nDx
2.1113
2.105
2.1581
2.0691
2.1698
2.1109
2.0881
2.0971
2.0942
2.0817
2.9031
2.8976
2.900
2.93
2.54
2.702
2.4889
2.4891
2.4879
2.4288
2.4310
2.0454
2.048
1.942
1.9349
1.930
1.5526
1.5530
1.5535
1.5533
1.5531
1.5531
1.5533
1.5533
1.5534
nDz
70.98
70.10
70.10
37.66
37.66
37.66
37.66
37.66
37.66
37.66
37.66
37.66
37.66
27.62
27.62
27.62
31.21
31.21
31.21
31.21
31.21
32.30
34.07
34.07
34.07
43.85
43.85
43.85
35.77
35.77
35.77
35.77
34.97
33.86
34.46
33.98
33.64
33.90
39.61
39.61
43.90
43.90
43.90
43.90
Vm
23.66
23.37
23.37
18.83
18.83
18.83
18.83
18.83
18.83
18.83
18.83
18.83
18.83
13.81
13.81
13.81
15.61
15.61
15.61
15.61
15.61
16.10
17.03
17.03
17.03
21.93
21.93
21.93
17.87
17.87
17.87
17.87
17.48
17.51
18.78
17.42
17.23
17.61
19.81
19.81
21.95
21.95
21.95
21.95
Vo
7.754
7.784
7.583
2.800
2.793
2.803
2.803
2.801
2.801
2.802
2.802
2.803
2.812
3.195
3.201
3.397
4.751
4.725
4.747
4.680
4.588
4.813
4.929
4.916
4.908
5.902
5.921
6.223
4.212
4.206
4.167
4.206
4.816
4.321
4.162
4.363
4.195
4.175
5.708
5.589
5.471
5.478
5.478
5.884
具 ␣ e典
0.0056
0.0044
0.0059
0.0072
0.0058
0.0053
0.0053
0.0081
0.0081
0.0086
0.0113
0.0119
0.0111
0.0152
0.0084
0.0107
0.0114
0.0119
0.0121
0.0108
0.0103
0.0054
0.0052
0.0119
0.0066
0.0123
0.0063
0.0076
0.0065
0.0065
0.0065
0.0065
0.0065
0.0065
0.0064
具A典
0.3052
0.3043
0.2903
0.3255
0.2863
0.3047
0.3128
0.3436
0.3446
0.3508
0.1911
0.1940
0.1915
0.1987
0.2070
0.2010
0.2168
0.2182
0.2191
0.2591
0.2571
0.3555
0.3540
0.3953
0.3833
0.4024
0.7369
0.7399
0.7359
0.7360
0.7364
0.7365
0.7362
0.7363
0.7358
具B典
9.37
10.49
8.89
8.50
8.91
9.56
9.74
8.22
8.24
8.08
5.21
5.11
5.24
4.57
6.27
5.49
5.52
5.42
5.37
6.20
6.32
10.30
10.40
7.27
9.67
7.24
13.62
12.47
13.45
13.46
13.45
13.41
13.45
13.44
13.52
具 Eo典
30.70
34.46
30.64
26.13
31.14
31.38
31.14
23.93
23.92
23.04
27.25
26.35
27.37
23.00
30.29
27.29
25.46
24.82
24.53
23.94
24.60
28.97
29.37
18.41
25.23
17.99
18.49
16.86
18.28
18.28
18.26
18.21
18.27
18.26
18.37
具 Ed典
73
01
73
78
97
97
97
97
97
97
97
97
61
00
82
72
65
97
28
97
79
28
28
16
08
90
71
73
62
62
76
68
86
82
90
97
90
77
87
82
97
64
66
66
Year
JSTCAM
JOAOF8
JSTCAM
Ref. 7
NJMIAK
JOBPDE
JOBPDE
JOBPDE
JOBPDE
JOBPDE
JOBPDE
JOBPDE
PHRVAO
Ref. 14
MRBUAC
JPCSAW
JAPIAU
JAPIAU
ZEKRDZ
OPLEDP
JJAPA5
ZEKRDZ
ZEKRDZ
NJGAAY
ZEKRDZ
ZPSBAX
PLRBAQ
PLRBAQ
Ref. 1
Ref. 1
JCRGAE
JAPIAU
JACTAW
APOPAI
APOPAI
JOBPDE
APOPAI
INOMAF
SPSSA7
PSSBBD
JOBPDE
OPACAT
PHRVAO
PHRVAO
Coden
17
33
36
82
67
22
18
67
67
41
44
51
4
8
Rf
Rf
32
39
69
21
29
14
29
13
29
114
14
11
151
151
11
14
14
14
14
14
14
14
121
13
3
13
Vol
1313
293
1674
994
485
1808
1043
485
485
342
313
790
3736
768
350
2810
259
3762
277
2978
2485
3299
604
1747
1904
189
3299
287
676
676
871
174
871
7-82
259
3299
3299
3299
3299
3299
3299
3299
1324
Page
2
1
2
1
1
1
1
1
1
1
1
1
3
1
1
3
1
8
1
4
8
1
1
1
1
1
1
8
1
1
1
3
8
1
1
1
1
1
4
3
1
1
1
3
M
3?
1
3?
1
1?
1
1
1
1
1
1
1
3
1
3
7
1
1
3
5?
5?
3
1
1
1
1
2
3
1
1
1
4
3
1
1
1
1
2
5
5
1
3
3?
7
E
938
SHANNON ET AL.
NaBeSi3 O7 OH⫹ eudidymite
NaBe4 SbO⫹
7 swedenborgite
Ba.98Ca.02Be2 Si2 O*⫹
7 barylite
共Langban, Sweden兲
Borates
BO共OH兲* ⫽ HBO2 I
共estimated n ⬁ values兲
BO共OH兲* ⫽ HBO2 I 共n D values兲
B3O4共OH兲•H2O*⫽HBO2 II
B3O4共OH兲•H2O*⫽HBO2 (n D values兲
B共OH兲*3 ⫽ H3 BO3 sassolite
B共OH兲*3 ⫽ H3 BO3 sassolite 共n D values兲
B共OH兲3 * ⫽ H3 BO3 sassolite
B共OH兲*3 ⫽ H3 BO3 sassolite 共nD values兲
LiB3 O*⫹
5
Li2 B4 O*⫹
7 FE 863 K
CsB3 O⫹
5
BeSO4•4 H2O*⫹
crystalline FL 31 K
UO2 film FL 31 K
UO*2 FL 31 K
UO*2 FL 31 K
V2 O*5
V2 O*5
Beryllates
BeAl2 O*⫹
4 chrysoberyl
BeAl2 O*⫹
4 chrysoberyl
La2 Be2 O*⫹
5
BeAlSiO4 OH⫹ euclase
Be1.00Al.99Si1.00O4 OH*⫹ euclase
共San Sebastao de Maranhao, Minas Gerais兲
Be1.00Al.99Si4 OH*⫹ euclase
共Diamantina, Minas Gerais兲
⫹
beryl 共no indication of H2 O
Be3 Al2 Si6 O18
content or method of preparation兲
⫹
beryl, colorless
Be3 Al2 Si6 O18
共Santa Rita, Minas Gerais兲
⫹
beryl, light-blue
Be3 Al2 Si6 O18
共Klein Spitzkopje, SW Africa兲
⫹
beryl, emerald,
Be3 Al2 Si6 O18
light-green 共Columbia兲
UO*2
sample designations
1.6422
1.5650
1.5562
1.5591
1.5617
1.6388
1.5650
1.5562
1.5591
1.5617
1.61
1.619
1.56
1.570
1.44
1.457
1.45
1.461
1.5889
1.5943
1.5376
1.61
1.619
1.42
1.434
1.33
1.340
1.32
1.337
1.5625
1.5943
1.5190
1.4585
1.5383
1.7550
1.6659
1.7270
1.7309
1.9820
1.6412
1.6425
1.7254
1.7291
1.9490
1.6380
1.6382
1.4585
1.5380
1.7550
1.6619
2.12
2.16
2.30
2.35
1.97
1.98
ny
2.12
2.16
2.30
2.35
2.07
2.20
nx
1.462
1.6026
1.5502
1.5654
1.459
1.45
1.588
1.45
1.619
1.57
1.61
1.4233
1.5424
1.7527
1.6820
1.5565
1.5545
1.5520
1.5589
1.6588
1.7325
1.7354
2.0180
1.6580
1.6589
2.12
2.16
2.30
2.35
2.12
2.29
nz
1.5752
1.6075
1.5308
1.4713
1.5457
1.7732
1.6921
1.5738
1.5715
1.5684
1.5774
1.6523
1.6023
1.6075
1.5615
1.4713
1.5461
1.7732
1.6977
1.5738
1.5715
1.5684
1.5774
1.6557
1.7417
1.7469
2.0243
1.6548
1.6558
2.10
2.89
1.7397
1.7442
1.9897
1.6509
1.6524
2.39
2.40
nDy
2.39
2.40
nDx
1.6172
1.5620
1.5892
1.4328
1.5512
1.7704
1.7029
1.5684
1.5667
1.5640
1.5708
1.6727
1.7473
1.7528
2.0629
1.6713
1.6730
2.55
2.39
2.40
nDz
68.52
80.09
115.47
121.37
68.52
68.52
35.48
68.52
29.22
35.48
29.22
170.86
158.02
113.46
134.37
338.40
338.40
338.40
338.40
78.05
56.99
56.99
102.90
78.05
78.05
40.87
40.87
40.87
40.87
89.52
89.52
Vm
22.84
16.02
16.49
24.27
22.84
22.84
17.73
22.84
14.61
17.73
14.61
21.36
19.75
16.21
19.20
18.80
18.80
18.80
18.80
15.61
14.25
14.25
20.58
15.61
15.61
20.43
20.43
20.43
20.43
17.90
17.90
Vo
4.140
6.405
9.169
9.100
4.128
4.024
2.619
4.024
2.447
2.561
2.419
10.894
11.828
11.082
11.982
26.121
26.029
25.922
26.236
6.768
5.421
5.441
12.143
6.761
6.768
5.250
5.366
5.742
5.866
11.057
11.732
具 ␣ e典
0.0064
0.0061
0.0107
0.0095
0.0046
0.0050
0.0096
0.0062
0.0064
0.0064
0.0062
0.0052
0.0043
0.0047
0.0065
0.0051
0.0053
0.0264
0.0264
0.0210
具A典
0.6624
0.6699
0.7291
0.9164
0.7298
0.4814
0.5592
0.6976
0.7012
0.7056
0.6931
0.5845
0.5033
0.5002
0.3415
0.5854
0.5846
0.2796
0.2876
0.2715
具B典
12.89
13.27
10.45
12.41
15.99
12.47
9.63
13.39
13.25
13.27
13.33
13.42
13.61
12.98
9.14
13.58
13.28
4.12
4.17
4.54
具 Eo典
19.46
19.8
14.3
13.5
21.9
25.9
17.2
19.2
18.8
18.8
19.2
22.96
27.05
25.94
26.7
23.20
22.71
14.73
14.51
16.74
具 Ed典
38
89
85
93
57
38
38
57
38
38
38
78
62
24
62
34
62
62
87
97
80
62
76
62
97
64
59
66
66
66
55
Year
AJSCAP
JOBPDE
JAPNDE
APPLAB
AMMIAY
AJSCAP
AJSCAP
AMMIAY
AJSCAP
AJSCAP
AJSCAP
APPLAB
Ref. 1
ZEKRDZ
Ref. 1
NJGAAY
Ref. 1
Ref. 1
Ref. 5
JOBPDE
IEJQA7
Ref. 1
JAPIAU
Ref. 1
JOBPDE
JOSAAH
JOSAAH
PHRVAO
PHRVAO
JPCSAW
JACTAW
Coden
35
6
24
62
42
35
35
42
35
35
35
33
Rf
60
Rf
68
Rf
Rf
14
QE-16
Rf
47
Rf
14
54
49
151
151
27
38
Vol
143
616
25
2614
56
143
143
56
143
143
143
413
2537
262
743
401
424
424
305
3299
1302
1838
1496
4106
3299
265
1107
676
676
1237
306
Page
02
1
1
1
2
02
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
8
8
8
3
8
2
M
3
1
1
1?
3
5
4
5
3
4
4
1
1
1
1
1
1
1
2
1
1
1
1
1
1
5
5
5
7
5
5
E
939
*⫹
hambergite
Be2 BO3 共OH兲.96F.04
共Antsirabe, Tanarive, Madagascar兲
Be2 BO3 OH*⫹ hambergite
Be2 BO3 OH*⫹ hambergite 共Madagascar兲
SrB4 O*⫹
7
PbB4 O*⫹
7
PbB4 O*7
BaB2 O4 -alpha*⫹
BaB2 O4 -alpha*⫹
BiB3 O*⫹
6 piezoelectric
LiGeBO*⫹
4
Mg.98Fe.02AlBO*⫹
4 sinhalite 共Ratnapura兲
KNbB2 O*6
RbNbB2 O*6
RbNbB2 O*6
Ca4 YOB3 O*9
Ca4 GdOB3 O*⫹
9
KBe2 BO3 F*2
Mg3 BO3 F3 fluoborite, light brown
Mg3 B7 O13Cl⫹ boracite FE 538K
Mg3 B7 O13Cl⫹ boracite FE 538K
LaGeBO*⫹
5 FE 805 K
*⫹
Y.99Nd.01Al3 B4 O12
*⫹
Gd.99Nd.01Al3 B4 O12
Na2B4O5共OH兲4•8 H2O*⫹ borax
Na2B4O5共OH兲4•3 H2O*⫹
tincalconite 共synthetic兲
KB5O6共OH兲4•2 H2O*⫹⫽KB5O8•4 H2O
K2B4O5共OH兲4•2 H2O*⫹
CaB3O4共OH兲3•H2O⫹
colemanite FE 266 K
Cs.44K.31Rb.16Na.03Al4 Be4 B11O25共OH兲⫹
4
rhodizite 共Manjaka, Madagascar兲
Aluminates
LiAlO*⫹
2 gamma-tetragonal
Y.99Nd.01AlO*⫹
3 FL?
Y.99Nd.01AlO*⫹
3 FL?
YAlO*⫹
3 FL?
LaAlO*3
Mg1.02Al1.98Fe.01O*⫹
4 spinel, purple
共Sri Lanka兲
CsB3 O*⫹
5
*⫹
CsLiB6 O10
Zn4 O共BO2 兲*⫹
6
sample designations
1.5480
1.4825
1.7257
1.5759
1.5760
1.5764
1.7222
1.9013
1.901
1.656
1.6504
1.7724
1.6682
1.6826
1.731
1.737
1.737
1.6926
1.6995
1.471
1.5004
1.6553
1.6608
1.7948
1.7472
1.7732
1.4573
1.4518
1.4238
1.4556
1.5792
1.6777
1.6048
1.9173
1.9166
1.9162
2.00
1.6979
1.5434
1.5433
1.7210
1.8979
1.897
1.656
1.6504
1.7473
1.6682
1.6529
1.759
1.720
1.754
1.6613
1.6747
1.471
1.5004
1.6553
1.6608
1.7948
1.7472
1.7732
1.4356
1.4518
1.4745
1.4528
1.5734
1.6777
1.6048
1.9030
1.9035
1.9025
2.00
1.6979
ny
1.5298
1.4825
1.7257
1.5435
nx
1.5884
1.9249
1.9252
1.9246
2.00
1.6979
1.6777
1.4121
1.4690
1.6002
1.6148
1.6147
1.7247
1.9032
1.902
1.544
1.5390
1.9025
1.6725
1.6904
1.731
1.756
1.719
1.7098
1.7079
1.393
1.4798
1.6553
1.6608
1.8314
1.6803
1.7005
1.4605
1.4638
1.5746
1.4323
1.7257
1.6143
nz
1.6223
1.9432
1.9432
1.9423
1.7153
1.7153
1.6932
1.4336
1.4658
1.5919
1.5885
1.5885
1.7353
1.9351
1.934
1.676
1.6699
1.8111
1.6857
1.6967
1.777
1.778
1.777
1.7137
1.7216
1.479
1.5086
1.6713
1.6753
1.8201
1.7743
1.7886
1.4693
1.4625
1.5605
1.4943
1.7464
1.5886
nDy
1.6223
1.9525
1.9523
1.9277
1.6932
1.4863
1.4632
1.5861
1.5545
1.5542
1.7340
1.9304
1.930
1.676
1.6699
1.7806
1.6857
1.6664
1.806
1.758
1.802
1.6815
1.6957
1.479
1.5086
1.6713
1.6753
1.8201
1.7743
1.7886
1.4467
1.4625
1.5416
1.4943
1.7464
1.5546
nDx
1.7153
1.6038
1.9285
1.9285
1.9515
1.6932
1.4211
1.4799
1.6139
1.6288
1.6284
1.7377
1.9368
1.936
1.558
1.5523
1.9518
1.6914
1.7047
1.777
1.804
1.757
1.7268
1.7300
1.401
1.4858
1.6713
1.6753
1.8593
1.7023
1.7122
1.4723
1.4746
1.5879
1.4421
1.7464
1.6285
nDz
42.02
50.09
50.09
50.09
54.44
66.14
391.74
279.40
260.42
140.56
66.06
66.06
100.35
102.45
102.45
96.15
96.46
111.34
69.90
60.73
132.10
137.94
137.94
223.79
226.24
106.04
104.07
220.62
220.62
97.87
180.62
181.69
370.96
250.18
121.37
246.10
209.08
66.06
Vm
21.01
16.95
16.95
16.95
18.15
16.53
13.50
23.28
23.67
17.57
16.51
16.51
14.33
14.64
14.64
24.01
24.11
18.56
17.47
15.18
22.03
22.99
22.99
22.39
22.62
21.21
17.34
15.76
15.76
19.57
15.05
15.14
21.82
20.84
24.27
24.61
16.08
16.51
Vo
3.429
5.628
5.628
5.626
6.498
6.089
35.249
17.468
17.000
11.235
5.234
5.235
9.489
11.386
11.379
8.049
8.018
11.440
6.231
5.449
12.723
13.249
13.235
20.372
20.738
6.738
7.227
19.334
19.462
10.052
17.119
17.653
23.851
16.229
9.242
16.265
19.834
5.233
具 ␣ e典
0.0056
0.0075
0.0048
0.0048
0.0047
0.0054
0.0088
0.0081
0.0061
0.0060
0.0059
0.0040
0.0062
0.0062
0.0072
0.0073
0.0093
0.0063
0.0049
0.0127
0.0117
0.0117
0.0065
0.0071
0.0068
0.0050
0.0059
0.0053
0.0062
0.0075
0.0040
0.0093
0.0085
0.0067
0.0084
0.0061
0.0061
具A典
0.5311
0.6421
0.3749
0.3749
0.3753
0.5510
0.9437
0.8859
0.6626
0.6732
0.6731
0.5083
0.3827
0.3829
0.6231
0.6303
0.4453
0.5594
0.5539
0.4930
0.4952
0.4962
0.5415
0.5351
0.9268
0.8130
0.5747
0.5687
0.4417
0.5076
0.4871
0.9050
0.8936
0.7128
0.8735
0.5055
0.6734
具B典
12.27
11.73
11.21
11.23
11.26
12.83
13.12
13.19
13.13
13.36
13.48
14.35
9.94
9.95
11.76
11.73
8.73
11.89
13.48
7.88
8.24
8.25
11.53
11.00
14.78
16.07
12.46
13.12
10.70
10.40
14.03
12.46
12.98
13.06
12.93
11.48
13.26
具 Eo典
23.10
18.27
29.89
29.96
30.02
23.2
13.9
14.8
19.8
19.84
20.03
28.2
25.9
25.9
18.88
18.61
19.6
21.25
24.34
15.9
16.6
16.6
21.2
20.5
15.9
19.7
21.6
23.0
24.21
20.4
28.8
13.7
14.5
18.3
14.8
22.7
19.69
具 Ed典
81
78
90
73
94
97
62
76
00
56
62
11
95
95
97
83
87
99
01
97
97
97
97
00
97
96
62
62
62
91
90
98
62
00
00
98
82
97
Year
JCRGAE
JAPAIU
APOPAI
APOPAI
JOBPDE
JOBPDE
Ref. 1
JOSAAH
CRTEDF
NJMMAW
Ref. 1
ZEKRDZ
OMATET
OMATET
OMATET
ZEKRDZ
JAPIAU
SSCOA4
CRTEDF
JOBPDE
OMATET
APOPAI
OMATET
CRTEDF
JOBPDE
OMATET
Ref. 1
Ref. 1
Ref. 1
PSSABA
OPCOB8
CHSCBU
Ref. 1
CRTEDF
JJAPA5
JCRGAE
ZEKRDZ
JOBPDE
Coden
54
49
29
12
11
14
Rf
66
35
1956
Rf
48
4
4
8
165
62
109
36
14
8
36
8
35
14
5
Rf
Rf
Rf
125
77
43
Rf
35
39
191
161
14
Vol
546
4223
1281
941
2252
3299
226
72
1151
265
2969
473
669
669
185
91
1968
249
119
3299
215
8587
215
1361
2238
105
688
250
250
671
221
1973
2578
1151
L1164
492
157
3299
Page
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
6
6
6
1
1
8
1
1
1
1
1
1
1
1
1
1
1
1
M
1
1
1
1
5
1
1
2
1
1
1
1
1?
1
4
3
1
1
1
1
4
3
3
1
1
3
1
2
2
1
1
1?
1
1
1
1
1
1
E
940
SHANNON ET AL.
1.6991
1.6981
1.6976
1.6974
1.6978
1.7002
1.7008
1.6989
1.7045
1.6985
1.7014
1.7010
1.7006
1.6992
1.6994
1.6997
1.7108
1.7102
1.7130
1.6994
1.6977
1.6986
1.7095
1.7107
1.7086
1.710
1.7282
1.7725
1.8113
1.8087
1.8093
1.8095
1.8084
1.8363
1.8327
1.8279
1.8184
1.6991
1.6981
1.6976
1.6974
1.6978
1.7002
1.7008
1.6989
1.7045
1.6985
1.7014
1.7010
1.7006
1.6992
1.6994
1.6997
1.7108
1.7102
1.7130
1.6994
1.6977
1.6986
1.7095
1.7107
1.7086
1.710
1.7282
1.7725
1.8113
1.8087
1.8093
1.8095
1.8084
1.8363
1.8327
1.8279
1.8184
spinel, blue-gray
共Sri Lanka兲
Mg1.00Al1.99Fe.02O*⫹
4 spinel, pink
共Tanzania兲
Mg1.00Al1.99Fe.02O*⫹
4 spinel, pink
共Tanzania兲
Mg.97Al2.01Fe.01O*⫹
4 spinel, colorless
共unknown source兲
Mg1.00Al2.00O*⫹
4 spinel, colorless
共Union Carbide兲
Mg.98Fe.01Al2.01O*⫹
4 spinel 共Siberia兲
MgAl2 O*⫹
4 spinel 共Linde兲
MgAl2 O⫹
4 spinel, red 共Ceylon兲
MgAl2 O⫹
4 spinel, dark-red 共Ceylon兲
MgAl2 O⫹
MgAl2 O⫹
MgAl2 O⫹
MgAl2 O⫹
MgAl2 O⫹
MgAl2 O⫹
4 spinel, brown 共Ceylon兲
MgAl2 O⫹
4 spinel, brown 共Ceylon兲
MgAl2 O*⫹
4 spinel 共0.001% Co兲
MgAl2 O*⫹
MgAl2 O*⫹
MgAl2 O*⫹
4 spinel 共Schott兲
MgAl2 O*⫹
4 spinel 共Kodak兲
MgAl2 O*⫹
4 spinel 共General Dynamics兲
Mg.41Al2.39O*⫹
4 spinel, colorless
共A. Mellor兲
Mg.41Al2.39O*⫹
4 spinel, dark-blue 共A兲
Mg.38Al2.41O*⫹
4 spinel, blue 共B兲
Mg.348Al2.435O*⫹
4 spinel
Mg.66Zn.34Fe.04Al1.96O*4 ⫹ spinel, blue
共Ceylon兲
Zn.92Fe.07Mg.01Al1.97Fe.03O*⫹
4 gahnite
共Jos, Nigeria兲
*⫹
Y3 Al5 O12
*⫹
Y3 Al5 O12
*⫹
Y3 Al5 O12
*⫹
Y3 Al5 O12
*⫹
Y3 Al5 O12
*⫹
Dy3 Al5 O12
*⫹
Ho3 Al5 O12
*⫹
Er3 Al5 O12
*⫹
Lu3 Al5 O12
Mg1.00Al1.98Fe.02O*⫹
4
ny
nx
sample designations
1.8113
1.8087
1.8093
1.8095
1.8084
1.8363
1.8327
1.8279
1.8184
1.7725
1.7107
1.7086
1.710
1.7282
1.7002
1.7008
1.6989
1.7045
1.6985
1.7014
1.7010
1.7006
1.6992
1.6994
1.6997
1.7108
1.7102
1.7130
1.6994
1.6977
1.6986
1.7095
1.6978
1.6974
1.6976
1.6981
1.6991
nz
1.8352
1.8326
1.8323
1.8328
1.8324
1.8613
1.8567
1.8522
1.8423
1.7944
1.7269
1.7251
1.727
1.7465
1.7173
1.7179
1.7165
1.7219
1.7154
1.7187
1.7179
1.7174
1.7160
1.7161
1.7167
1.7274
1.7271
1.7285
1.7161
1.7154
1.7153
1.7261
1.7150
1.7142
1.7146
1.7151
1.7164
nDx
1.8352
1.8326
1.8323
1.8328
1.8324
1.8613
1.8567
1.8522
1.8423
1.7944
1.7269
1.7251
1.727
1.7465
1.7173
1.7179
1.7165
1.7219
1.7154
1.7187
1.7179
1.7174
1.7160
1.7161
1.7167
1.7274
1.7271
1.7285
1.7161
1.7154
1.7153
1.7261
1.7150
1.7142
1.7146
1.7151
1.7164
nDy
1.8352
1.8326
1.8323
1.8328
1.8324
1.8613
1.8567
1.8522
1.8423
1.7944
1.7269
1.7251
1.727
1.7465
1.7173
1.7179
1.7165
1.7219
1.7154
1.7187
1.7179
1.7174
1.7160
1.7161
1.7167
1.7274
1.7271
1.7285
1.7161
1.7154
1.7153
1.7261
1.7150
1.7142
1.7146
1.7151
1.7164
nDz
216.50
216.50
216.50
216.50
216.50
218.00
216.80
215.00
211.30
66.40
63.66
63.71
63.35
66.02
66.31
66.00
66.00
66.00
66.00
66.00
65.93
66.00
66.00
66.00
66.00
66.00
66.00
66.00
66.01
66.01
66.01
63.44
65.98
66.11
66.11
66.11
66.14
Vm
18.04
18.04
18.04
18.04
18.04
18.17
18.07
17.92
17.60
16.60
15.92
15.93
15.83
16.50
16.58
16.50
16.50
16.50
16.50
16.50
16.50
16.50
16.50
16.50
16.50
16.50
16.50
16.50
16.50
16.50
16.50
15.86
16.49
16.53
16.53
16.53
16.53
Vo
22.323
22.271
22.283
22.287
22.265
22.980
22.782
22.498
21.926
6.603
5.943
5.934
5.910
6.279
6.120
6.095
6.082
6.120
6.080
6.099
6.090
6.094
6.084
6.086
6.088
6.162
6.158
6.177
6.087
6.075
6.081
5.915
6.073
6.083
6.084
6.087
6.097
具 ␣ e典
0.0056
0.0056
0.0054
0.0054
0.0057
0.0055
0.0053
0.0055
0.0055
0.0056
0.0051
0.0052
0.0055
0.0054
0.0055
0.0055
0.0057
0.0055
0.0054
0.0055
0.0054
0.0054
0.0054
0.0054
0.0055
0.0052
0.0053
0.0048
0.0054
0.0057
0.0054
0.0052
0.0056
0.0055
0.0055
0.0055
0.0056
具A典
0.4384
0.4403
0.4398
0.4395
0.4406
0.4216
0.4239
0.4271
0.4335
0.4667
0.5190
0.5210
0.5201
0.5033
0.5288
0.5283
0.5301
0.5249
0.5305
0.5277
0.5282
0.5285
0.5299
0.5297
0.5294
0.5189
0.5196
0.5170
0.5297
0.5313
0.5305
0.5202
0.5312
0.5316
0.5314
0.5309
0.5299
具B典
11.19
11.18
11.39
11.39
11.12
11.08
11.28
11.18
11.22
11.50
12.80
12.70
12.26
12.21
12.41
12.42
12.23
12.32
12.48
12.34
12.46
12.50
12.50
12.52
12.43
12.65
12.51
13.11
12.54
12.17
12.50
12.65
12.32
12.47
12.41
12.44
12.33
具 Eo典
25.5
25.4
25.9
25.9
25.2
26.2
26.6
26.1
25.8
24.64
24.66
24.38
23.58
24.26
23.47
23.51
23.07
23.47
23.53
23.38
23.59
23.66
23.59
23.65
23.47
24.37
24.09
25.36
23.68
22.91
23.57
24.33
23.19
23.46
23.36
23.43
23.26
具 Ed典
65
86
89
97
81
97
97
81
81
97
97
97
61
37
97
78
62
62
62
62
62
62
62
62
62
62
62
62
91
91
91
97
97
97
97
97
97
Year
JAPIAU
Ref. 3
SPHCA6
JOBPDE
INOMAF
JOBPDE
JOBPDE
INOMAF
INOMAF
JOBPDE
JOBPDE
JOBPDE
ACELAZ
MNLMBB
JOBPDE
Ref. 7
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 9
Ref. 9
Ref. 9
JOBPDE
JOBPDE
JOBPDE
JOBPDE
JOBPDE
JOBPDE
Coden
34
14
17
14
14
17
17
36
14
14
14
6
24
14
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
14
14
14
14
14
14
Vol
1674
120
712
3299
308
3299
3299
308
308
3299
3299
3299
120
547
3299
7-106
244
267
267
267
267
267
267
155
155
173
173
173
883
883
883
3299
3299
3299
3299
3299
3299
Page
1
1
1
1
1
1
1
1
1
1
1
1
8
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
M
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1?
1
1
1
1
1
1
1
1
1
E
941
*⫹
Y2.93Nd.07Sc2 Al3 O12
*
Gd3 Sc2 Al3 O12
CaYAlO*⫹
4
CaYAlO*⫹
4
CaNdAlO*⫹
4
SrLaAlO*⫹
4
*
SrLaAlO4
SrLaAl.75Ga.25O*4
*
La.8Nd.2MgAl11O19
Gallates
LiGaO*⫹
2
LiGaO*2
LaGaO*3 IR FL
NdGaO*3 IR FL
CoGa2 O*4 关IR, not accurate兴
*
Y3 Ga5 O12
*
Y3 Ga5 O12
*⫹
Nd3.01Ga4.99O12
*⫹
Nd3 Ga5 O12
*⫹
Sm3.02Ga4.98O12
*⫹
Eu3.02Ga4.98O12
*⫹
Gd3 Ga5 O12
*⫹
Gd3 Ga5 O12
*⫹
Gd3 Ga5 O12
*⫹
Gd3.03Ga4.97O12
*⫹
Gd3 Ga5 O12 共BTL兲
*⫹
Tb3.04Ga4.96O12
*⫹
共Allied Signal兲
Tb3.04Ga4.96O12
*
Tb3 Ga5 O12
*⫹
Dy3.05Ga4.95O12
*⫹
Ho3.06Ga4.94O12
*
Tm3 Ga5 O12
*⫹
Y3 Sc2 Ga3 O12
*⫹
Nd3 Sc2 Ga3 O12
*⫹
Sm3 Sc2 Ga3 O12
*⫹
Gd3 Sc2 Ga3 O12
*⫹
La3 Lu2 Ga3 O12
*⫹
La2.7Lu2.3Ga3 O12
*⫹
La1.3GdLu2.7Ga3 O12
*⫹
Nd3 Lu2 Ga3 O12
*⫹
Y2.545Er.455Ga1.977Cr.023Ga3 O12
*
Gd2.96Nd.04Ga4.8Al.2O12
*
Gd2.964Nd.036Ga4 AlO12
*⫹
Y1.5Er1.5Al5 O12
sample designations
1.8198
1.8515
1.87
1.8767
1.8757
1.9266
1.9316
1.92
1.92
1.771
1.7061
1.730
2.02
2.02
2.00
1.878
1.882
1.9470
1.9476
1.9452
1.9407
1.9328
1.9330
1.9326
1.9332
1.9334
1.9325
1.9335
1.932
1.9311
1.9281
1.9187
1.9068
1.9300
1.9410
1.9315
1.9187
1.9186
1.9200
1.9295
1.9097
1.929
1.909
1.7061
1.705
2.02
2.02
2.00
1.878
1.882
1.9470
1.9476
1.9452
1.9407
1.9328
1.9330
1.9326
1.9332
1.9334
1.9325
1.9335
1.932
1.9311
1.9281
1.9187
1.9068
1.9300
1.9410
1.9315
1.9187
1.9186
1.9200
1.9295
1.9097
1.929
1.909
ny
1.8198
1.8515
1.87
1.8767
1.8757
1.9266
1.9316
1.92
1.92
1.771
nx
1.7339
1.734
2.02
2.02
2.00
1.878
1.882
1.9470
1.9476
1.9452
1.9407
1.9328
1.9330
1.9326
1.9332
1.9334
1.9325
1.9335
1.932
1.9311
1.9281
1.9187
1.9068
1.9300
1.9410
1.9315
1.9187
1.9186
1.9200
1.9295
1.9097
1.929
1.909
1.8198
1.8515
1.87
1.8990
1.8978
1.9513
1.9516
1.95
1.94
1.764
nz
1.7350
1.763
1.919
1.916
1.9871
1.9872
1.9840
1.9794
1.9698
1.9698
1.9693
1.9699
1.9702
1.9707
1.9710
1.971
1.9679
1.9638
1.9582
1.9417
1.9671
1.9797
1.9687
1.9564
1.9561
1.9575
1.9695
1.9444
1.964
1.944
1.919
1.916
1.9871
1.9872
1.9840
1.9794
1.9698
1.9698
1.9693
1.9699
1.9702
1.9707
1.9710
1.971
1.9679
1.9638
1.9582
1.9417
1.9671
1.9797
1.9687
1.9564
1.9561
1.9575
1.9695
1.9444
1.964
1.944
1.8432
1.8795
1.90
1.9077
1.9068
1.9620
1.9663
1.95
1.96
1.791
nDy
1.7350
1.735
1.8432
1.8795
1.90
1.9077
1.9068
1.9620
1.9663
1.95
1.96
1.791
nDx
1.919
1.916
1.9871
1.9872
1.9840
1.9794
1.9698
1.9698
1.9693
1.9699
1.9702
1.9707
1.9710
1.971
1.9679
1.9638
1.9582
1.9417
1.9671
1.9797
1.9687
1.9564
1.9561
1.9575
1.9695
1.9444
1.964
1.944
1.7654
1.765
1.8432
1.8795
1.90
1.9290
1.9280
1.9867
1.9865
1.97
1.99
1.783
nDz
21.54
21.54
19.57
19.19
18.12
19.27
19.27
20.39
20.37
20.02
19.90
19.77
19.77
19.77
19.77
19.77
19.61
19.61
19.61
19.48
19.37
19.16
19.15
21.23
21.03
20.67
22.87
22.78
22.52
19.72
19.51
236.67
234.16
17.96
19.24
19.88
19.72
19.72
20.57
22.29
22.29
22.51
15.60
Vo
43.08
43.08
58.70
57.56
72.50
231.31
231.31
244.70
244.49
240.50
238.80
237.30
237.30
237.30
237.30
237.30
235.40
235.40
235.40
233.80
232.40
230.00
229.80
254.80
252.40
248.10
274.43
273.40
270.20
215.50
230.90
238.60
78.88
78.88
82.30
89.15
89.15
90.06
296.44
Vm
26.873
26.189
4.042
4.075
7.099
6.962
8.654
25.247
25.328
28.154
28.142
27.634
27.349
27.020
27.024
27.016
27.028
27.032
26.798
26.818
26.788
26.588
26.370
25.915
25.658
28.953
28.913
28.223
30.921
30.802
30.474
22.390
24.658
25.874
8.652
8.645
9.385
10.192
10.130
10.208
29.369
具 ␣ e典
0.0080
0.0065
0.0067
0.0066
0.0065
0.0065
0.0064
0.0063
0.0063
0.0063
0.0063
0.0066
0.0064
0.0066
0.0063
0.0062
0.0070
0.0064
0.0064
0.0065
0.0064
0.0067
0.0067
0.0066
0.0069
0.0063
0.0061
0.0063
0.0090
0.0092
0.0054
0.0059
0.0066
0.0059
0.0060
0.0061
0.0059
0.0039
0.0073
0.0052
具A典
0.3960
0.3933
0.3583
0.3580
0.3592
0.3615
0.3655
0.3654
0.3656
0.3653
0.3652
0.3657
0.3651
0.3659
0.3664
0.3680
0.3729
0.3794
0.3670
0.3613
0.3662
0.3729
0.3730
0.3722
0.3672
0.3778
0.3676
0.3779
0.5150
0.5080
0.4326
0.4119
0.3999
0.3922
0.3929
0.3646
0.3628
0.3646
0.3694
0.4696
具B典
8.90
9.83
9.28
9.33
9.43
9.40
9.59
9.60
9.62
9.62
9.62
9.45
9.54
9.40
9.61
9.73
9.24
9.75
9.57
9.41
9.56
9.44
9.47
9.49
9.22
9.78
9.79
9.81
9.57
9.39
11.33
10.55
9.81
10.27
10.24
9.80
9.90
12.25
8.97
12.04
具 Eo典
22.4
24.9
25.9
26.0
26.2
26.0
26.2
26.2
26.3
26.3
26.3
25.8
26.1
25.6
26.2
26.4
24.7
25.6
26.0
26.0
26.0
25.3
25.3
25.4
25.10
25.89
26.6
25.9
18.58
18.48
26.2
25.6
24.5
26.19
26.05
26.87
27.28
33.59
24.27
25.6
具 Ed典
70
65
94
94
78
87
74
97
84
97
97
87
78
89
97
90
97
97
94
97
97
82
97
84
97
87
89
89
89
84
89
88
88
97
97
73
97
97
97
97
96
96
83
Year
JAPIAU
APOPAI
JOBPDE
JOBPDE
SPSSA7
Ref. 5
PLRBAQ
JOBPDE
SPHCA6
JOBPDE
JOBPDE
Ref. 5
KRTEAW
SPHCA6
JOBPDE
APOPAI
JOBPDE
JOBPDE
PSSBBD
JOBPDE
JOBPDE
JCRGAE
JOBPDE
SPHCA6
JOBPDE
Ref. 5
SPHCA6
SPHCA6
SPHCA6
SPHCA6
SPHCA6
JCRGAE
JCRGAE
JOBPDE
JOBPDE
JAPIAU
JOBPDE
JOBPDE
JOBPDE
JOBPDE
PSSBBD
PSSBBD
SJQEAF
Coden
34
34
34
29
34
92
92
13
34
14
29
14
14
182
14
14
57
14
29
14
10
14
29
14
14
41
4
11
11
20
14
14
44
14
14
14
14
195
195
13
Vol
3008
1036
2252
2252
1451
314
971
3299
704
3299
3299
307
K10
712
3299
3704
3299
3299
K91
3299
3299
600
3299
704
3299
308
712
712
712
704
712
17
17
3299
3299
1395
3299
3299
3299
3299
625
625
1082
Page
1
5
03
03
03
8
1
1
1
1
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
1
1
1
1
8
8
5
M
2
3
5
5
5
3?
3
1
2
1
1
1
1
1
1
1
1
1
3
1
1
3?
1
2
1
1
1
1
1
2
1
3
3
1
1
5?
1
1
1
1
5?
5
3
E
942
SHANNON ET AL.
Ferrites
MnFe2 O*4
CoFe2 O4
ZnFe2 O*4
*⫹
共BTL兲
Y3 Fe5 O12
*
Y3 Fe5 O12
*
Y3 Fe5 O12
*
films
Y3 Fe5 O12
Silicates
Be2 SiO*⫹
4 phenacite
Be2 SiO*⫹
4 phenacite
Be2 SiO*4 phenacite
Mg2 SiO*⫹
4 forsterite 共synthetic兲
Mg2 SiO⫹
4 共Fayal兲, contains Fe?
Mg1.80Fe.225Ni.01SiO*⫹
4 peridot
共San Carlos, AZ兲
Mg2 SiO*4 forsterite 共synthetic兲
Mn1.98Si1.00O*⫹
4 tephroite 共synthetic兲
Mn2 SiO*4 tephroite 共synthetic兲
Mn1.85Mg.15SiO*4 tephroite 共Pajsberg兲
Fe2 SiO*⫹
4 fayalite 共Oberharz兲
Fe1.72Mn.09Mg.16Ca.03Si.98Ti.02O*⫹
4 fayalite
共Cuddia Mida, Isola de Pantelleria, It.兲
Fe2 SiO*⫹
4 fayalite 共synthetic-O. Kopp,
C. Finch兲
Fe2 SiO*⫹
4 fayalite 共synthetic-O. Kopp,
C. Finch兲
⫹
Fe2 SiO*⫹
4 fayalite 共8A1 8C2兲
*⫹
⫹
Fe2 SiO4 fayalite 共8C2 8B1兲
Zn2 SiO4 -alpha*⫹ willemite
共Altenberg near Aachen兲
Zn2 SiO4 willemite
*⫹
Gd2.286Er.714Ga1.976Cr.024Ga3 O12
*⫹
Nd2.7Yb2.3Ga3 O12
*⫹
LaEr3 ScGa3 O12
*⫹
La2.37Nd.07Pb.01Lu2.54Cr.01Ga3 O12
*⫹
La2.37Nd.07Pb.01Lu2.54Cr.01Ga3 O12
SrLaGa3 O*⫹
7
SrGdGa3 O*7
BaLaGa3 O*7
*⫹
La3 Ga5 SiO14
*⫹
La3 Ga5 GeO14
*⫹
La3 Ga5.5Nb.5O14
*⫹
La3 Ga5.5Ta.5O14
sample designations
1.631
1.7803
1.768
1.760
1.8289
1.8006
1.8311
1.8306
1.8306
1.8306
1.6661
1.6728
1.7933
1.7924
1.7923
1.7927
1.6661
1.6728
1.6403
1.6392
1.66
1.6353
1.6717
1.6569
1.6403
1.6392
1.66
1.6211
1.6529
1.6407
1.651
1.7545
1.739
1.737
1.7918
1.7708
2.18
2.480
2.16
2.1287
2.165
2.15
2.17
1.9319
1.9329
1.9422
1.9188
1.9239
1.7947
1.793
1.845
1.8712
1.8875
1.9122
1.9055
ny
2.18
2.480
2.16
2.1287
2.165
2.15
2.17
1.9319
1.9329
1.9422
1.9188
1.9239
1.7947
1.793
1.845
1.8712
1.8875
1.9122
1.9055
nx
1.7020
1.8411
1.8406
1.6940
1.8410
1.8414
1.668
1.7937
1.778
1.770
1.8429
1.8085
1.6559
1.6561
1.66
1.6530
1.6902
1.6758
2.18
2.480
2.16
2.1287
2.165
2.15
2.17
1.9319
1.9329
1.9422
1.9188
1.9239
1.7831
1.810
1.850
1.8829
1.9005
1.9397
1.9298
nz
1.6939
1.8253
1.8254
1.6893
1.8253
1.8258
1.6939
1.8660
1.8660
1.6893
1.8660
1.8664
1.8092
1.806
1.787
1.8662
1.8368
1.6506
1.6897
1.6744
1.6358
1.6702
1.6569
1.7809
1.774
1.761
1.8246
1.8031
1.6538
1.6536
1.6538
1.6536
2.3266
2.485
2.31
2.34
1.9043
1.9249
1.9543
1.9434
1.9043
1.9249
1.9543
1.9434
2.3266
2.485
2.31
2.34
1.9684
1.9722
1.9668
1.9561
1.9616
1.8287
1.836
nDy
1.9684
1.9722
1.9668
1.9561
1.9616
1.8287
1.836
nDx
1.7230
1.8747
1.8749
1.7179
1.8748
1.8752
1.8219
1.816
1.799
1.8782
1.8447
1.6687
1.7086
1.6934
1.6696
1.6693
2.3266
2.485
2.31
2.34
1.9157
1.9377
1.9846
1.9699
1.9684
1.9722
1.9668
1.9561
1.9616
1.8182
1.842
nDz
87.02
76.92
76.92
87.02
76.92
76.92
72.48
81.33
81.33
81.33
77.53
77.53
61.73
61.73
61.73
72.48
72.48
73.06
21.75
19.23
19.23
21.75
19.23
19.23
18.12
20.33
20.33
20.33
19.38
19.38
15.43
15.43
15.43
18.12
18.12
18.27
19.18
18.49
18.74
19.74
19.74
19.74
19.74
22.51
22.51
24.78
23.93
25.49
20.96
21.21
21.40
21.43
270.20
270.20
173.45
167.50
178.40
293.48
296.91
299.56
300.13
76.74
73.98
74.96
236.90
236.90
236.90
236.90
22.13
Vo
265.60
Vm
7.874
8.003
8.002
7.809
8.003
8.007
6.311
8.116
8.003
7.955
8.065
7.863
5.346
5.341
5.440
6.207
6.476
6.422
10.181
11.161
9.841
30.578
31.184
30.936
31.266
30.446
30.564
17.551
17.073
18.973
31.958
32.767
33.820
33.686
30.245
具 ␣ e典
0.0071
0.0077
0.0077
0.0081
0.0077
0.0076
0.0071
0.0098
0.0072
0.0079
0.0085
0.0060
0.0063
0.0063
0.0052
0.0054
0.0197
0.0271
0.0159
0.0157
0.0065
0.0071
0.0075
0.0069
0.0063
0.0068
0.0042
0.0066
0.0066
0.0084
0.0094
具A典
0.5464
0.4321
0.4318
0.5537
0.4319
0.4315
0.4644
0.4758
0.4805
0.4320
0.4516
0.5962
0.5577
0.5723
0.5857
0.5864
0.2832
0.2711
0.2767
0.2696
0.3975
0.3878
0.3716
0.3758
0.3660
0.3655
0.3607
0.3729
0.3702
0.4531
0.4475
具B典
11.08
9.46
9.50
10.48
9.48
9.51
10.21
8.82
10.35
9.34
9.24
12.61
11.92
12.08
13.43
13.22
4.80
4.00
5.27
5.24
9.88
9.38
8.88
9.31
9.64
9.31
11.71
9.49
9.47
9.30
8.71
具 Eo典
20.28
21.90
21.99
18.93
21.96
22.04
21.99
18.53
21.53
21.63
20.47
21.14
21.38
21.11
22.93
22.54
16.9
14.7
19.0
19.4
24.8
24.1
23.8
24.7
26.34
25.4
32.46
25.4
25.5
20.5
19.4
具 Ed典
62
97
97
23
97
97
73
97
32
62
62
09
62
62
73
28
28
97
89
78
89
97
65
74
73
89
84
84
97
97
96
91
84
83
87
87
87
Year
Ref. 1
JOBPDE
JOBPDE
ZEKRDZ
JOBPDE
JOBPDE
PSSBBD
JOBPDE
AMMIAY
Ref. 1
Ref. 1
ZEKRDZ
Ref. 1
Ref. 1
PSSBBD
AMMIAY
AMMIAY
JOBDE
PSSBBD
SPSSA7
PSSBBD
JOBPDE
BJAPAJ
PLRBAQ
APPLAB
SPHCA6
SPHCA6
SPHCA6
JOBPDE
JOBPDE
JOBPDE
JOBPDE
PHBCDQ
PSSABA
SPHCA6
SPHCA6
SPHCA6
Coden
Rf
14
14
58
14
14
55
14
17
Rf
Rf
46
Rf
Rf
55
13
13
14
152
20
152
14
16
10
23
34
29
29
14
14
13
8
123
80
32
32
32
Vol
2883
3299
3299
460
3299
3299
677
3299
135
1236
1390
138
2688
2903
143
559
559
3299
657
1451
657
3299
475
971
702
712
704
704
3299
3299
1941
1668
215
387
236
236
236
Page
1
1
1
1
1
1
3
1
2
1
1
1
1
1
3
1
1
1
3
3
3
1
1
6
7
1
1
1
1
1
1
1
8
1
1
1
1
M
1
1
1
1?
1
1
3
1
3?
3
1
1?
1
1
4
1
1?
1
5
5
5
2
3?
5
5
1
2
2?
1
1
2
3?
6
2
1
1
1
E
具␣e典, mean dispersion values 具 A 典 and 具 B 典 according to Eq. 共3a兲, and average of E O and E d according to Eq. 共3b兲. Source references use Codens from the American Chemical Society, Chemical Abstracts Service Source Index 1907–1999
943
CaMnSiO*4
共synthetic兲
Ca1.22Fe.40Mn.24Mg.14SiO*⫹
4
monticellite 共Gute-HoffnungshXtte兲
Ca.82Fe1.02Mg.10Zn.06SiO*⫹
4 olivine
共Clausthaler Silberhütte兲
Sr2 SiO*4 monoclinic 共synthetic兲 FL 367 K
Eu2 SiO4 -beta* monoclinic
*⫹
trimerite
CaMn1.69Fe.24Mg.07Be3 Si3 O12
共Harstigsgrube兲
ZrSiO⫹
4 zircon, colorless
共Chantaboon, Thailand兲
ZrSiO⫹
4 zircon
ZrSiO*⫹
4 zircon, blue 共Chantaboon,
Thailand兲
ZrSiO⫹
4 zircon 共unknown source兲
ZrSiO4 zircon
Zr.99Hf.01SiO*⫹
4 zircon 共Nigeria?兲
ZrSiO*4 zircon, red-brown
共North Burgess, Ontario兲
Al2 SiO*⫹
5 kyanite
Al2 SiO5 andalusite 共Brazil兲
Al2 SiO⫹
5 sillimanite, pale-blue
共Mogok, Upper Burma兲
Al2 SiO⫹
5 sillimanite 共Ceylon兲
Al2 SiO5 sillimanite
Y2 SiO5 :Nd*⫹
Al2 SiO4 F*⫹
2 topaz 共Schneckenstein兲
Al2 SiO4 F*⫹
2 topaz
Al2 SiO4 F2 topaz
*⫹
topaz
Al2 SiO4 F1.89共OH兲.11
*⫹
topaz
Al2 SiO4 F1.89共OH兲.11
*⫹
Bi4 Si3 O12
*⫹
Bi4 Si3 O12
CaBSiO4 OH*⫹ datolite 共Serra dei Zanchetti兲
CaBSiO4 OH*⫹ datolite 共Westfield, MA兲
Ca.95 Mg.05B2 Si2 O*⫹
8 danburite
共Okira, Japan兲
Ca1.00B1.99Al.01Si2.00O*⫹
8 danburite
共Charcus, Mexico兲
Cu6Si6O18•6 H2O⫹ dioptase
Cu6Si6O18•6 H2O⫹ dioptase 共Kirgensteppe兲
Pb9Mg9Si9O24共OH兲24 molybdophyllite
共Langbanshuttan, Varmland, Sweden兲
Pb3Al2CaSi10O27•3 H2O*⫹ wickenburgite 共Wickenburg, AZ兲
sample designations
1.6851
1.6826
1.7090
1.707
1.817
1.7020
1.8911
1.8819
1.8942
1.8898
1.8948
1.8939
1.908
1.7053
1.6257
1.6443
1.6425
1.6426
1.7655
1.6063
1.6217
1.6036
1.6031
1.6023
1.9674
1.9559
1.6377
1.6383
1.6200
1.6192
1.6338
1.6291
1.7836
1.6550
1.6743
1.702
1.813
1.6990
1.8911
1.8819
1.8942
1.8898
1.8948
1.8939
1.908
1.6984
1.6197
1.6426
1.6408
1.6407
1.7629
1.6035
1.6191
1.6009
1.5998
1.5992
1.9674
1.9559
1.6109
1.6121
1.6167
1.6166
1.6338
1.6291
1.7836
1.6550
ny
1.6570
1.6554
nx
1.6183
1.6800
1.6720
1.7309
1.6227
1.6610
1.6600
1.7851
1.6131
1.6303
1.6104
1.6094
1.6096
1.9674
1.9559
1.6544
1.6550
1.6226
1.7114
1.6293
1.6613
1.9463
1.9527
1.9519
1.956
1.9433
1.9519
1.9508
1.736
1.841
1.7100
1.7189
1.6974
1.6857
nz
1.6911
1.6573
1.6611
1.8145
1.6299
1.6563
1.6576
1.7865
1.6153
1.6293
1.6120
1.6112
1.6107
2.0293
2.0217
1.6246
1.6253
1.6302
1.7130
1.6327
1.6581
1.9254
1.9262
1.9256
1.936
1.9195
1.9255
1.9239
1.727
1.889
1.7155
1.6957
1.6861
1.6744
nDx
1.6911
1.6573
1.6809
1.8145
1.6327
1.6577
1.6592
1.7894
1.6179
1.6308
1.6146
1.6142
1.6136
2.0293
2.0217
1.6527
1.6530
1.6333
1.7221
1.6387
1.6593
1.9254
1.9262
1.9256
1.936
1.9195
1.9255
1.9239
1.732
1.896
1.7192
1.7339
1.7117
1.7043
nDy
1.6478
1.7091
1.6886
1.7609
1.6361
1.6766
1.6797
1.8104
1.6248
1.6379
1.6215
1.6208
1.6209
2.0293
2.0217
1.6694
1.6697
1.6361
1.7287
1.6439
1.6785
1.9796
1.9841
1.9847
1.990
1.9803
1.9843
1.9838
1.756
1.914
1.7255
1.7431
1.7217
1.7095
nDz
635.17
476.77
476.77
1043.38
136.33
82.92
82.92
106.90
85.84
85.84
85.84
85.84
85.84
273.10
273.10
88.59
88.59
136.30
73.29
85.54
82.92
65.94
65.94
65.32
65.94
65.94
65.94
65.94
97.59
97.77
214.61
87.60
89.06
Vm
21.17
19.86
19.86
21.74
17.04
16.58
16.58
21.38
14.30
14.30
14.30
14.30
14.30
22.76
22.76
17.72
17.72
17.04
14.65
17.11
16.58
16.49
16.49
16.33
16.49
16.49
16.49
16.49
24.40
24.44
17.88
21.90
22.26
Vo
54.820
41.475
41.181
103.106
11.425
7.204
7.201
10.617
7.083
7.233
7.058
7.049
7.046
31.881
31.623
7.566
7.574
11.427
6.800
7.219
7.215
7.373
7.404
7.329
7.459
7.337
7.400
7.386
9.153
10.193
19.882
8.089
8.033
具 ␣ e典
0.0127
0.0094
0.0066
0.0080
0.0056
0.0059
0.0067
0.0063
0.0051
0.0037
0.0049
0.0050
0.0050
0.0096
0.0104
0.0058
0.0056
0.0056
0.0051
0.0056
0.0060
0.0064
0.0057
0.0058
0.0054
0.0069
0.0057
0.0060
0.0072
0.0162
0.0053
0.0075
0.0090
0.0074
具A典
0.5893
0.5822
0.5711
0.4726
0.6162
0.5828
0.5832
0.4680
0.6312
0.6110
0.6346
0.6357
0.6363
0.3483
0.3539
0.5990
0.5981
0.6159
0.5244
0.6097
0.5813
0.3788
0.3759
0.3764
0.3705
0.3823
0.3762
0.3776
0.5155
0.4300
0.5258
0.5289
0.5493
0.5546
具B典
8.62
9.96
11.79
9.70
13.26
12.61
11.81
10.88
14.07
16.31
14.44
14.29
14.20
7.62
7.37
12.89
13.04
13.23
12.77
13.24
12.45
9.75
10.29
10.17
10.51
9.40
10.24
10.04
10.72
6.52
12.60
10.64
9.86
10.93
具 Eo典
14.6
17.1
20.6
20
21.5
21.64
20.26
23.2
22.28
26.69
22.75
22.48
22.32
21.8
20.8
21.51
21.80
21.4
24.35
21.72
21.41
25.74
27.37
27.02
28.37
24.59
27.22
26.60
20.80
15.17
23.9
20.11
17.94
19.71
具 Ed典
68
62
62
38
97
62
62
90
62
62
62
97
97
72
95
62
97
62
62
08
62
03
10
97
62
62
62
62
22
71
60
62
32
62
Year
AMMIAY
Ref. 1
Ref. 1
Ref. 10C
JOBPDE
Ref. 1
Ref. 1
IEJQA7
Ref. 1
Ref. 1
Ref. 1
JOBPDE
JOBPDE
JAPIAU
OPSUA3
Ref. 1
JOBPDE
Ref. 1
Ref. 1
ZEKRDZ
Ref. 1
ZEKRDZ
ZEKRDZ
JOBPDE
Ref. 1
Ref. 1
Ref. 1
Ref. 1
AJSCAP
PKOMA3
Ref. 10D
Ref. 1
AMMIAY
Ref. 1
Coden
53
Rf
Rf
14
Rf
Rf
26
Rf
Rf
Rf
14
14
43
79
Rf
14
Rf
Rf
44
Rf
37
47
14
Rf
Rf
Rf
Rf
4
14
Rf
17
Rf
Vol
1433
621
2889
368
3299
4038
4085
1405
4046
4071
1833
3299
3299
5110
868
2950
3299
1044
4085
313
1520
235
1
3299
647
514
595
514
331
37
871
1082
135
843
Page
2
1
1
1
1
1
1
5
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
2
6
1
1
2
1
M
2
1
1?
1?
1
1
1?
1
1
1?
1
1
1
1
2
1
1
1
1
2
1
1?
1
1
3
1?
1
1
3
3
1
1
3?
1
E
944
SHANNON ET AL.
*⫹
Be3.0Al1.96Cr.07Si5.96O18
*⫹
Be3.0Al1.96Cr.07Si5.96O18
beryl 共synthetic-Chatham兲
beryl 共synthetic-Chatham兲
Na.02Be3.04Al1.95Fe.02Mg.01Si5.99O18• 共.32H2 O兲*⫹ aquamarine
共Nuristan, Pakistan兲
Na.04Cs.02Be3.06Al1.96Fe.02Zn.01Si5.97O18• 共.41H2 O兲*⫹ aquamarine
共Nuristan, Pakistan兲
Na.04Be3.06Al1.93Fe.03 Mg.02Zn.01Si5.97O18•(.49H2O兲*⫹ beryl, green
共Padre Paraiso, Minas Gerais兲
Na.04Be3.06Al1.93Fe.03 Mg.02Zn.01Si5.97O18•(.49H2O兲*⫹ beryl, green
共Padre Paraiso, Minas Gerais兲
Na.03Cs.04Be3.05Al1.97 Fe.01Si5.97O18•共.46H2O兲*⫹ goshenite
共Hunza, Pakistan兲
Na.20Cs.14Be3.15Al1.90 Si5.90V.01O18•共.88H2O兲*⫹ morganite 共Brazil兲
Li.37Na.24Cs.11Mg.04 Be2.58B.06Al2.02Si5.94O18.共67H2O兲*⫹ beryl, Maxize
共Minas Gerais兲
*⫹
* Si5 O18•共H2O兲.49共CO2 兲.07
cordierite, blue
Na.04Mg1.72Fe.27Al3.97 Fe.03
共Madagascar兲
*⫹
Na.03Mg1.97Fe.03Al3.97 Fe*
.03 Si5 O18•共H2O兲.41共CO2 兲.07 cordierite, colorless
共unknown source兲
*⫹
pyrope 共Northeast AZ兲
Mg2.04Fe.53Ca.43Mn.02 Al1.96Cr.03Fe.01Si3 O12
*⫹
pyrope 共Madagascar兲
Mg1.95Fe.99Ca.09Mn.01Al1.98Si3 O12
*⫹
pyrope 共Sri Lanka兲
Mg1.64Fe1.17Ca.19Mn.03Al2 Si3 O12
*⫹
almandine 共North Creek, NY兲
Fe1.45Mg1.18Ca.20Mn.04Al2 Si3 O12
*⫹
pyrope 共Tanzania兲
Mg1.23Fe.90Mn.56Ca.33Al1.98V.02Cr.01Zn.01Si3 O12
*
pyrope
Mg3 Al2 Si3 O12
*⫹
spessartine 共Ramona, CA兲
Mn2.80Fe.17Ca.01Al2.03Si3 O12
(2⫹) (3⫹)
*⫹
Fe.123 Al2.01Si2.98O12
spessartine 共Kenya兲
Mn2.16Ca.14Fe.512
*⫹
grossular 共Asbestos, Quebec兲
Ca2.92Mn.04Fe.135Al2 Si3 O12
Ca2.95Al1.97Mg.04Mn.01Ti.02Fe.01Si2.99O*⫹
12 grossular
共Umba River, Tanzania兲
*⫹
grossular 共Jeffrey Quarry, Quebec兲
Ca2.98Mn.01Fe.01Al1.97Fe.02Si2.94O12
*⫹
grossular 共Passo del Termine兲
Ca2.66Mg.20Fe.14Al1.84Fe.16Si3 O12
*⫹
demantoid 共Val Malenco兲
Ca3.00Fe1.99Mg.02Al.01Si2.98O12
*⫹
demantoid 共Ala Valley兲
Ca2.99Fe2.00Mg.02Al.01Si2.98O12
*⫹
demantoid 共Val Malenco兲
Ca3.00Fe1.99Mg.02Al.01Si2.98O12
Ca3 Fe2 Si3 O12 andradite
(3⫹)
*⫹
Al0.04Fe0.01共SiO4 兲2.07共O4 H4 兲0.93
Ca3 Mn1.95
henritermierite, n data from O. Medenbach
Li1.00Al.97Si2.02O*⫹
6 spodumene 共Nuristan, Afghanistan兲
Li.95Na.05AlSi2 O*⫹
6 spodumene, rose 共Maharitra, Madagascar兲
LiAlSi2 O*⫹
6 spodumene, colorless
sample designations
1.5526
1.5511
1.5633
1.5650
1.5661
1.5665
1.5653
1.5794
1.5792
1.5285
1.5231
1.7219
1.7342
1.7489
1.7536
1.7511
1.730
1.7816
1.7794
1.7208
1.7232
1.7169
1.7444
1.8344
1.8347
1.8319
1.841
1.7594
1.6504
1.6509
1.6510
1.5650
1.5661
1.5665
1.5653
1.5794
1.5792
1.5227
1.5193
1.7219
1.7342
1.7489
1.7536
1.7511
1.730
1.7816
1.7794
1.7208
1.7232
1.7169
1.7444
1.8344
1.8347
1.8319
1.841
1.7594
1.6462
1.6454
1.6454
ny
1.5526
1.5511
1.5633
nx
1.6606
1.6600
1.6597
1.7169
1.7444
1.8344
1.8347
1.8319
1.841
1.8198
1.7219
1.7342
1.7489
1.7536
1.7511
1.730
1.7816
1.7794
1.7208
1.7232
1.5263
1.5312
1.5722
1.5720
1.5600
1.5609
1.5607
1.5597
1.5487
1.5477
1.5581
nz
1.6601
1.6602
1.6602
1.7339
1.7565
1.8863
1.8867
1.8855
1.889
1.7967
1.7395
1.7525
1.7678
1.7735
1.7706
1.749
1.8028
1.8018
1.7383
1.7414
1.5318
1.5358
1.5923
1.5920
1.5777
1.5788
1.5784
1.5775
1.5650
1.5633
1.5757
nDx
1.6648
1.6651
1.6649
1.7339
1.7565
1.8863
1.8867
1.8855
1.889
1.7967
1.7395
1.7525
1.7678
1.7735
1.7706
1.749
1.8028
1.8018
1.7383
1.7414
1.5357
1.5413
1.5923
1.5920
1.5777
1.5788
1.5784
1.5775
1.5650
1.5633
1.5757
nDy
1.6755
1.6759
1.6756
1.7339
1.7565
1.8863
1.8867
1.8855
1.889
1.8726
1.7395
1.7525
1.7678
1.7735
1.7706
1.749
1.8028
1.8018
1.7383
1.7414
1.5389
1.5442
1.5848
1.5844
1.5722
1.5732
1.5730
1.5721
1.5610
1.5598
1.5703
nDz
97.31
97.31
97.31
208.04
206.97
219.40
219.40
219.40
219.40
232.19
191.88
189.74
190.85
192.04
193.28
187.89
195.79
195.77
207.89
208.04
387.67
388.39
339.38
339.00
337.88
338.09
338.09
337.90
338.41
338.41
337.87
Vm
16.22
16.22
16.22
17.34
17.25
18.28
18.28
18.28
18.28
19.34
15.99
15.81
15.90
16.00
16.11
15.66
16.32
16.31
17.32
17.34
21.53
21.57
18.85
18.80
18.77
18.28
18.28
18.77
18.80
18.80
18.77
Vo
8.498
8.495
8.494
19.552
20.017
23.089
23.095
23.039
23.221
23.246
18.129
18.159
18.542
18.746
18.819
17.904
19.640
19.597
19.619
19.683
28.267
28.527
26.850
26.812
26.218
26.276
26.263
26.208
25.787
25.736
26.142
具 ␣ e典
0.0054
0.0056
0.0056
0.0052
0.0035
0.0110
0.0111
0.0115
0.0101
0.0105
0.0053
0.0053
0.0053
0.0055
0.0054
0.0055
0.0054
0.0057
0.0053
0.0055
0.0075
0.0075
0.0062
0.0062
0.0063
0.0062
0.0062
0.0063
0.0066
0.0065
0.0063
具A典
0.5780
0.5783
0.5784
0.5135
0.4895
0.4226
0.4226
0.4245
0.4183
0.4623
0.5089
0.4982
0.4857
0.4819
0.4839
0.5013
0.4599
0.4616
0.5099
0.5077
0.7580
0.7501
0.6725
0.6729
0.6922
0.6905
0.6911
0.6927
0.7110
0.7130
0.6952
具B典
13.08
12.85
12.88
12.54
15.03
7.83
7.81
7.68
8.13
8.40
12.38
12.22
12.15
11.86
11.96
12.06
11.70
11.37
12.40
12.18
12.75
12.62
13.19
13.22
13.27
13.32
13.30
13.21
13.14
13.26
13.27
具 Eo典
22.63
22.22
22.27
24.4
30.7
18.5
18.4
18.1
19.4
18.1
24.3
24.5
25.0
24.6
24.7
24.0
25.4
24.6
24.3
23.9
16.8
16.8
19.6
19.6
19.1
19.2
19.2
19.0
18.4
18.6
19.0
具 Ed典
97
13
13
97
62
97
97
97
62
00
97
97
97
97
97
62
97
78
97
97
97
97
97
35
97
97
97
97
97
97
97
Year
JOBPDE
ZEKRDZ
ZEKRDZ
JOBPDE
Ref. 1
JOBPDE
JOBPDE
JOBPDE
Ref. 1
Ref. 14
JOBPDE
JOBPDE
JOBPDE
JOBPDE
JOBPDE
Ref. 1
JOBPDE
AFSLAO
JOBPDE
JOBPDE
JOBPDE
JOBPDE
JOBPDE
ZMGPAS
JOBPDE
JOBPDE
JOBPDE
JOBPDE
JOBPDE
JOBPDE
JOBPDE
Coden
14
13
13
14
Rf
14
14
14
Rf
14
14
14
14
14
Rf
14
29
14
14
14
14
14
1935
14
14
14
14
14
14
14
Vol
3299
294
294
3299
235
3299
3299
3299
244
3299
3299
3299
3299
3299
138
3299
275
3299
3299
3299
3299
3299
37
3299
3299
3299
3299
3299
3299
3299
Page
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
M
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1?
1
1
1
6
1
E
945
spodumene, green 共Maharitra, Madagascar兲
LiAlSi2 O⫹
6 spodumene, colorless
LiAlSi2 O*⫹
6 amorphous spodumene
共Corning ESI glass兲
*
petalite 共Karabib, SW Africa兲
Li0.90Na.10Al1.0Si4 O10
CaSiO*3 pseudowollastonite 共synthetic兲
BaSiO*3 共synthetic兲
BaSi2 O*5 sanbornite 共synthetic兲
Ca.46Mg.35Fe.15Mn.01Al.09Si.93O*⫹
3 pigeonite
Ca1.47Mn1.44Mg.09Si3 O*⫹
9 bustamite 共Langban兲
Mn.8Ca.2SiO*⫹
3 rhodonite 共Broken Hill兲
Mn.65Fe.13Ca.19Mg.03SiO*⫹
3 rhodonite 共Morocco兲
Mn.80Ca.14Mg.05Fe.01SiO*⫹
3 rhodonite 共Harstigen兲
(2⫹)
Si2 O*⫹
CaMg.94Fe.06
6 diopside, colorless
共Nordmarken兲
(2⫹)
Al.01Si1.99O*⫹
Ca.99Mn.01Mg.92Fe.08
6
diopside, yellow-green 共Nordmarken兲
CaMgSi2 O⫹
6 diopside, colorless 共Zillertal兲
Ca.97Na.02Mg.93Fe.03Cr.02Al.01Si2 O*⫹
6
diopside 共Russia兲
(2⫹)
(2⫹) (3⫹)
Ca.96Mn.01Fe.03 Mg.42Fe.56 Fe.02 Si2 O*⫹
6
diopside, black 共Nordmarken兲
(2⫹)
*⫹
CaMg.92Fe.08 Si2 O6 diopside 共Ala Valley兲
CaMgSi2 O*6 amorphous 共Corning兲
Ca2 MgSi2 O*⫹
7 akermanite
Ca2 MgSi2 O⫹
7 akermanite
Ca2 ZnSi2 O⫹
7 hardystonite
Ca2 ZnSi2 O*⫹
7 hardystonite 共synthetic-Liebertz兲
Ca2 Al2 SiO*7 gehlenite 共synthetic兲
Ca2 Ga2 SiO*⫹
7
Ca2 CoSi2 O*⫹
7
Sr2 CoSi2 O*⫹
7
(3⫹)
Al.05Ti.03
Na.87K.02Ca.02Mn.02Fe.92
* aegirine 共Quincy, MA兲
Fe.03Si2 O5.95共OH兲.05
(3⫹) (2⫹)
Fe.09
Na.70Ca.18Mg.12Fe.78
*
Al.04Ti.02Si2 O5.95共OH兲.05
aegirine 共Laven, Norway兲
(3⫹) ⫹
Fe(2) .16
Ca.90Mn.01Na.06K.01Mg.63Fe.11
*
Ti.12Al.29Si1.71O6 titanaugite 共Stoffel, Westerwald兲
(3⫹) (3⫹)
Fe.10 Ti.10
Ca.87Mn.01Na.05K.03Mg.69Fe.16
*
Al.24Si1.78O6 titanaugite 共Stoffel, Westerwald兲
(3⫹)
*⫹
Mg.8Al17.2Fe(3⫹)
Ti.1Si7.7O44共OH兲 3.2
Fe3.0
.3
staurolite 共St. Gotthard兲
⫹
’’ narsarsukite 关comp. not certain兴
‘‘Na2 TiSi4 O11
(3⫹)
Si2 O*6
Li.95Na.05Al0.95Fe.05
sample designations
1.6510
1.5052
1.502
1.594
1.654
1.602
1.6843
1.6658
1.7125
1.7021
1.7030
1.6618
1.6647
1.6621
1.6621
1.6898
1.6620
1.5968
1.6152
1.6214
1.6530
1.6542
1.646
1.6998
1.5731
1.6174
1.758
1.729
1.703
1.682
1.7267
1.5351
1.497
1.594
1.654
1.587
1.6780
1.6528
1.7081
1.6980
1.6991
1.6549
1.6573
1.6527
1.6552
1.6829
1.6552
1.5968
1.6152
1.6214
1.6530
1.6542
1.646
1.6998
1.5731
1.6174
1.731
1.706
1.689
1.680
1.7218
1.5351
1.6580
ny
1.6454
1.5052
1.6541
nx
1.5702
1.7316
1.700
1.712
1.740
1.6828
1.5968
1.6237
1.6261
1.6431
1.6440
1.639
1.6909
1.6490
1.6510
1.769
1.7101
1.6839
1.6831
1.6877
1.508
1.631
1.656
1.601
1.7017
1.6671
1.7200
1.7101
1.7107
1.6821
1.6597
1.5052
1.6666
nz
1.5534
1.7392
1.700
1.719
1.743
1.6705
1.6125
1.6326
1.6391
1.6723
1.6735
1.665
1.7251
1.6197
1.6487
1.768
1.6991
1.6726
1.6715
1.6734
1.507
1.610
1.673
1.597
1.6981
1.6730
1.7296
1.7188
1.7219
1.6712
1.6602
1.5176
1.6684
nDx
1.5534
1.7449
1.707
1.723
1.768
1.6775
1.6125
1.6326
1.6391
1.6723
1.6735
1.665
1.7251
1.6197
1.6487
1.806
1.7063
1.6795
1.6785
1.6804
1.512
1.610
1.674
1.612
1.7043
1.6860
1.7344
1.7231
1.7262
1.6781
1.6649
1.5176
1.6713
nDy
1.5835
1.7508
1.728
1.742
1.782
1.6995
1.6125
1.6407
1.6431
1.6610
1.6618
1.657
1.7135
1.6764
1.6766
1.823
1.7281
1.7024
1.7001
1.7026
1.518
1.653
1.678
1.621
1.7228
1.6879
1.7424
1.7315
1.7338
1.7003
1.6756
1.5176
1.6809
nDz
228.64
369.95
111.28
111.28
107.75
109.90
125.95
153.63
153.63
153.55
153.55
149.09
155.83
154.60
166.50
107.28
110.94
109.90
109.94
109.90
211.21
66.41
79.87
120.52
54.13
184.04
58.38
58.38
58.38
109.83
97.31
129.37
97.31
Vm
20.78
15.41
18.55
18.55
17.96
18.32
20.99
21.95
21.95
21.94
21.94
21.30
22.26
22.08
23.78
17.99
18.49
18.32
18.32
18.32
21.12
22.14
26.62
24.10
18.04
20.45
19.46
19.46
19.46
18.30
16.22
21.56
16.22
Vo
17.305
35.131
10.124
10.283
10.214
9.762
10.242
12.850
12.933
13.366
13.384
12.882
14.328
12.599
14.117
10.462
10.172
9.758
9.768
9.800
14.889
5.470
6.994
9.799
4.928
16.256
5.467
5.407
5.412
9.752
8.494
9.164
8.572
具 ␣ e典
0.0090
0.0054
0.0080
0.0086
0.0114
0.0057
0.0071
0.0072
0.0072
0.0071
0.0070
0.0069
0.0078
0.0178
0.0117
0.0122
0.0055
0.0066
0.0059
0.0055
0.0067
0.0078
0.0074
0.0060
0.0068
0.0073
0.0067
0.0067
0.0073
0.0060
0.0056
0.0079
0.0051
具A典
0.7189
0.5047
0.5415
0.5281
0.5064
0.5628
0.6453
0.6181
0.6120
0.5809
0.5797
0.5872
0.5321
0.6460
0.6057
0.4826
0.5348
0.5632
0.5626
0.5594
0.7961
0.6334
0.5754
0.6454
0.5408
0.5676
0.5165
0.5259
0.5251
0.5631
0.5784
0.7901
0.5701
具B典
11.28
12.19
10.43
9.94
8.44
12.59
12.07
11.71
11.70
11.45
11.49
11.64
10.41
7.62
9.10
7.97
12.42
11.65
12.34
12.74
13.83
11.38
11.16
13.11
11.31
11.12
11.06
11.23
10.75
12.20
12.88
12.66
13.35
具 Eo典
15.6
24.1
19.2
18.8
16.6
22.3
18.7
18.9
19.1
19.7
19.8
19.8
19.5
11.8
15.0
16.5
23.2
20.6
21.9
22.7
17.3
17.96
19.39
20.3
20.90
19.5
21.42
21.35
20.47
21.6
22.27
16.0
23.42
具 Ed典
62
23
34
34
27
62
97
97
62
62
97
93
96
97
97
27
97
62
97
97
46
22
22
22
62
31
56
56
31
97
62
97
13
Year
1
ZEKRDZ
ZEKRDZ
ZEKRDZ
AMMIAY
Ref.
JOBPDE
JOBPDE
Ref.
Ref.
JOBPDE
JOAOD6
JOBPDE
JOBPDE
JOBPDE
AMMIAY
Ref. 1
1
1
1
1
Ref.10A
Ref.
JOBPDE
Ref.10A
AMMIAY
AJSCAP
AJSCAP
AJSCAP
Ref. 1
AMMIAY
HAMBA6
HAMBA6
AMMIAY
Ref.10A
Ref.
JOBPDE
ZEKRDZ
Coden
Rf
57
87
87
12
Rf
14
14
Rf
Rf
14
10
13
14
14
12
Rf
14
31
4
4
4
Rf
16
1
1
16
Rf
14
13
Vol
365
310
1
1
233
1767
3299
3299
414
414
3299
2246
1941
3299
3299
233
1027
1697
3299
1027
51
331
331
331
2173
488
137
137
488
1027
2966
3299
294
Page
M
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
5
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
E
1
2
3
3
3
2
1
1
1
1
1
3
2
1?
1
3
1
1
1
1
3
3
3
3
1
1
1
1
2
1
2
1
2?
TABLE 1. Refractive index and dispersion data, listing refractive indices 共n x , n y , n z兲 at ␭ ⫽ ⬁, refractive indices 共n Dx , n Dy , n Dz兲 at ␭ ⫽ 589.3 nm, molar volume, V m , volume per O- atom, V o , and mean values of electronic polarizabilities
946
SHANNON ET AL.
1.5136
1.5115
1.5082
1.5130
1.5063
1.5091
1.527
1.527
1.5092
1.5076
1.524
1.524
1.5097
1.5147
1.526
1.526
1.5060
1.5103
1.7099
1.7099
1.5117
1.5203
1.5208
1.4741
1.4710
1.4705
1.4703
1.7020
1.4741
1.4710
1.4705
1.4703
1.7020
1.5117
1.5167
1.5168
1.8619
1.8457
1.4970
1.8356
1.8752
1.8801
1.8232
1.8595
1.8698
1.4970
1.8508
1.8404
1.528
1.8693
1.8327
1.8785
1.8513
1.8124
1.8731
1.528
1.6461
1.6277
leucosphenite
共Narsarsuk, Greenland?兲
CaTiSiO5 :Fe⫹ titanite1 共Pfitschtal兲
CaTiSiO5 :Al,Fe⫹ titanite2 共Muttenhoernern兲
Ca1.0Ti1.0SiO*⫹
5 titanite, light green
共Eisbruckalp, Pfunders, Tirol兲
Ca1.0Ti1.0SiO*⫹
5 titanite, light brown
共Glimmerschiefer, St.Gotthard兲
Ca1.0Ti.98Mn.02SiO*⫹
5 titanite 共Val Maggia, Tessin兲
Ca1.0Ti0.96Fe.04SiO*⫹
5 titanite 共unknown source兲
Ca0.85Ti1.02Si1.04O⫹
5 titanite 共Schwarzenstein,
Zillertal兲
Ca0.75Ti1.05Si1.07O⫹
5 titanite
共Wildkreuzjoch, Pfitsch, Tirol兲
Na4 Al3 Si3 O12Cl*⫹ sodalite 共Tiahuanaco兲
Na4 Al3 Si3 O12Cl*⫹ sodalite 共Tiahuanaco兲
‘‘Na4 Al3 Si3 O12Cl’’⫹ sodalite 共Vesuvius兲
‘‘Na4 Al3 Si3 O12Cl’’⫹ sodalite 共Vesuvius兲
*⫹
Ca19Mg.1AlFeMg1.7Fe.6Si18O69共OH兲10
vesuvianite 共Ala Valley兲
*⫹
Ca18.1Mg.1Al4 FeAl5.2Mg1.6Fe • 0.5Ti0.8Si18O69共OH兲10
vesuvianite 共Val D’Aosta兲
Na.69K.16Ca.06Al.98Si1.02O*4 nepheline
共Monte Somma, Mt. Vesuvius, xtal #2兲
Na.69K.16Ca.06Al.98Si1.02O*4
nepheline 共Monte Somma, Mt. Vesuvius, xtal #1兲
共Larvik, #VII兲 Norway
共Monte Somma, #VII兲 Mt. Vesuvius
KAlSi2 O⫹
6 leucite,
cubic but with tetragonal cell 共Rome兲
CsAlSi2 O6 . x H2 O⫹ pollucite
Na.97K.02AlSi3 O*⫹
8 albite 共Amelia兲 FL 1250 K
Na.97K.02Ca.01Al.97Fe.01Mg.02Si3 O*⫹
8
albite 共Rischuna兲 FL 1250 K
K.90Na.10AlSi3 O*⫹
8 adularia 共St. Gotthard兲
K.73Na.24Ca.03Al1.03Si2.97O*⫹
8 orthoclase,
moonstone 共Ceylon兲
KAlSi3 O⫹
8 orthoclase 共Madagascar兲
K.92Na.08Al.97Fe.03Si3 O*⫹
8 orthoclase
共Madagascar兲
KAlSi3 O8 ⫹ microcline, green amazonite
K.85Na.15AlSi3 O*⫹
8 sanidine 共Eifel兲
⫹
’’
‘‘BaNa4 Ti2 B2 Si10O30
ny
nx
sample designations
1.5102
1.5133
1.5136
1.5122
1.5120
1.5168
1.5117
1.5265
1.5267
1.4970
1.525
1.524
1.521
1.522
1.7051
1.4741
1.4710
1.4705
1.4703
1.6992
1.8739
1.9233
2.0199
2.0028
1.9570
2.0049
1.9240
1.9345
1.6671
nz
1.5184
1.5208
1.5214
1.5193
1.5163
1.5224
1.5246
1.5285
1.5291
1.5087
1.541
1.540
1.537
1.538
1.7314
1.4831
1.4826
1.4839
1.4825
1.7224
1.9032
1.8876
1.9097
1.9159
1.8879
1.9004
1.8713
1.9057
1.6441
nDx
1.5221
1.5253
1.5258
1.5237
1.5199
1.5269
1.5246
1.5324
1.5330
1.5087
1.541
1.540
1.537
1.538
1.7314
1.4831
1.4826
1.4839
1.4825
1.7224
1.9057
1.8942
1.9178
1.9216
1.8941
1.9117
1.8761
1.9090
1.6607
nDy
1.5247
1.5254
1.5261
1.5242
1.5216
1.5289
1.5246
1.5386
1.5388
1.5087
1.537
1.536
1.534
1.535
1.7275
1.4831
1.4826
1.4839
1.4825
1.7209
1.9174
1.9796
2.1145
2.0529
2.0087
2.0959
1.9941
1.9913
1.6877
nDz
179.68
180.82
180.10
180.10
179.60
180.10
159.80
166.00
166.15
146.59
91.00
90.90
90.79
90.79
1432.70
349.92
349.92
349.92
349.92
1431.09
92.22
92.22
92.60
92.22
92.22
92.22
92.22
92.22
593.15
Vm
22.46
22.60
22.51
22.51
22.46
22.51
26.63
20.75
20.77
24.43
22.75
22.72
22.70
22.70
18.13
26.91
26.91
26.91
26.91
18.11
18.44
18.44
18.52
18.44
18.44
18.44
18.44
18.44
19.77
Vo
12.792
12.949
12.905
12.868
12.807
12.943
11.442
12.070
12.087
10.241
6.679
6.661
6.621
6.639
133.403
23.481
23.350
23.328
23.320
132.203
9.922
9.924
10.430
10.382
10.104
10.310
9.888
10.206
51.458
具 ␣ e典
0.0085
0.0075
0.0076
0.0074
0.0063
0.0075
0.0079
0.0072
0.0073
0.0077
0.0072
0.0072
0.0075
0.0075
0.0068
0.0065
0.0085
0.0098
0.0089
0.0067
0.0097
0.0120
0.0104
0.0081
0.0091
0.0104
0.0115
0.0073
0.0065
具A典
0.7844
0.7779
0.7773
0.7804
0.7826
0.7740
0.7780
0.7611
0.7607
0.8058
0.7505
0.7524
0.7576
0.7552
0.5213
0.8524
0.8592
0.8603
0.8606
0.5281
0.4064
0.4076
0.3765
0.3757
0.3949
0.3813
0.4106
0.3863
0.5844
具B典
12.17
12.92
12.79
12.96
14.07
12.88
12.52
13.04
12.93
12.95
12.88
12.91
12.69
12.66
11.06
14.46
12.69
11.82
12.41
11.25
8.17
7.37
7.60
8.59
8.32
7.66
7.56
9.18
11.99
具 Eo典
15.5
16.6
16.4
16.6
17.9
16.6
16.0
17.1
17.0
16.0
17.17
17.16
16.76
16.76
21
16.9
14.7
13.7
14.4
21
20.10
18.08
20.18
22.87
21.08
20.10
18.42
23.76
20.5
具 Ed典
62
16
16
97
21
16
62
24
24
62
31
31
31
31
97
62
62
97
97
97
97
97
97
97
97
56
56
97
38
Year
Ref. 1
MNLMBB
MNLMBB
JOBPDE
TTMMDZ
MNLMBB
Ref. 1
ZEKRDZ
ZEKRDZ
Ref. 1
MNLMBB
MNLMBB
MNLMBB
MNLMBB
JOBPDE
Ref. 1
Ref. 1
Ref. 10A
Ref. 10A
JOBPDE
Ref. 10A
Ref. 10A
JOBPDE
Ref. 10A
Ref. 10A
HAMBA6
HAMBA6
Ref. 10A
Ref. 10C
Coden
Rf
17
17
14
35
17
Rf
61
61
Rf
22
22
22
22
14
14
Rf
Rf
14
1
1
Vol
2966
237
253
3299
231
253
2748
226
226
2791
569
569
569
569
3299
2597
2597
885
885
3299
1609
1609
3299
1609
1609
285
285
1609
293
Page
M
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
E
1?
1
1
1
1?
1
1
1
1
2
3
3
1
2?
2
2?
2
1
3
2
1
3?
2?
1
1
4?
2
947
CaAl2 Si2 O8 anorthite 共Vesuvius兲 FL?
CaAl2 Si2 O⫹
8 anorthite 共hi-temp form兲 FL?
CaAl2 Si2 O8 anorthite 共Mijakejima兲 FL?
Ca0.96Na.05Al1.93Fe.02Si2.04O*⫹
8 anorthite
共Great Sitka Island兲 FL?
CaAl2 Si2 O*⫹
8 amorphous 共Corning兲
Na.56Ca.36K.08Al1.40 Si2.60O*⫹
8
andesine 共Maeyama, Shinano, Japan兲
Na.75Ca.24K.01Al1.25Si2.75O*⫹
8 oligoclase
共Hawke Mine, Bakersville, NC兲
Ca.61Na.32K.05Al1.62 Fe.01Si2.37O*⫹
8
labradorite 共County Down, Ireland兲
Ba.98K.02Al1.98Si2.02O8 celsian 共1920兲
关anomalous dispersion兴
Ba.93K.04Na.02Mg.01 Al1.98Fe.02Si2 O*⫹
8
paracelsian
共Benallt mine, Rhiw, Carnarvonshire兲
Ca3 Si2 O6 共OH兲2 共OH2 兲*⫹
2 afwillite
共Dutoitspan-Mine, Kimberley兲 used 3 n’s
Ca3 Si2 O6 共OH兲2 共OH2 兲*⫹
2 afwillite
共Dutoitspan-Mine, Kimberly兲 used only 2 n’s
Ca2 Al3 Si3 O12OH⫹ clinozoisite
共Schwarzensteinalpe, Zillertal兲
Ca1.99Sr.01Al2.99Mg.01V.01Si3 O12OH*⫹ zoisite1
共Merelani Hill, Arusha, Tanzania兲
Ca2.00Al3.00V.02Si2.98O12OH*⫹ zoisite2
共Merelani Hills, Arusha, Tanzania兲
Ca1.90Mg.04Fe.06Al2.4Fe.6Si3 O12OH*⫹
epidote 共Pfarreb, Zoptau兲
Ca2 Al2 FeSi3 O12OH*⫹ epidote 共pistazite,
Rauhbeerstein, Zoptau兲
Ca1.94Fe.06Al2.1Fe.9Si3 O12OH*⫹ epidote
共Knappenwand, Sulzbachtal兲
Ca2.00Al2.46Fe.52Si3 O12OH*⫹ epidote 共Pakistan兲
Na2.67K.28Ca1.06Sr.01Al3.79Si8.19Fe.02Cl.76
*⫹
共CO3 兲.19共SO4 兲.08 O24
scapolite
⫹
scapolite
具共Na,K兲3 Ca典关Al4 Si8 兴共Cl,CO3 兲O24
scapolite⫹
scapolite⫹
scapolite⫹
scapolite⫹ 共Lago Tremorgio兲
Ca共UO2 兲共UOOH兲共SiO4 兲共SiO3 OH兲•4 H2O*
beta-uranophane 共Mitchell County, NC兲
sample designations
1.5666
1.5680
1.5679
1.5689
1.5609
1.5357
1.5317
1.5523
1.6168
1.5666
1.6067
1.6093
1.6990
1.6772
1.6775
1.7184
1.7438
1.7293
1.6969
1.5431
1.5694
1.5713
1.5754
1.5556
1.5714
1.676
1.5609
1.5315
1.5275
1.5477
1.6133
1.5472
1.6043
1.6076
1.6958
1.6752
1.6754
1.7022
1.7053
1.6957
1.6950
1.5431
1.5694
1.5713
1.5754
1.5556
1.5714
1.654
ny
1.5613
1.5591
1.5589
1.5600
nx
1.5391
1.5419
1.5457
1.5354
1.5412
1.676
1.6993
1.5318
1.7479
1.7617
1.7230
1.6846
1.6839
1.6997
1.6230
1.6206
1.5743
1.6227
1.5568
1.5354
1.5609
1.5393
1.5740
1.5714
1.5737
1.5729
nz
1.5833
1.5858
1.5904
1.5696
1.5850
1.663
1.7147
1.5569
1.7266
1.7287
1.7215
1.6914
1.6913
1.7139
1.6169
1.6175
1.5691
1.5885
1.5620
1.5403
1.5751
1.5449
1.5743
1.5737
1.5738
1.5743
nDx
1.5833
1.5858
1.5904
1.5696
1.5850
1.687
1.7191
1.5569
1.7573
1.7632
1.7423
1.6937
1.6933
1.7175
1.6204
1.6209
1.5829
1.5927
1.5661
1.5447
1.5751
1.5489
1.5824
1.5820
1.5818
1.5829
nDy
1.5516
1.5549
1.5590
1.5485
1.5531
1.697
1.7236
1.5449
1.7742
1.7794
1.7501
1.7010
1.7006
1.7191
1.6336
1.6340
1.5872
1.5984
1.5711
1.5480
1.5751
1.5528
1.5877
1.5871
1.5871
1.5876
nDz
353.37
227.84
552.19
227.80
227.80
227.80
225.40
225.80
225.80
214.83
214.83
186.52
183.95
167.00
166.40
172.05
166.90
167.51
167.51
167.51
167.51
Vm
22.08
17.52
22.09
17.52
17.52
17.52
17.34
17.37
17.37
21.48
21.48
23.31
22.99
20.87
20.80
21.50
20.86
20.94
22.51
22.51
20.94
Vo
31.464
20.955
41.318
21.578
21.863
21.354
20.316
20.342
20.793
17.859
17.794
14.455
15.378
12.744
12.301
13.299
12.414
13.069
13.048
13.061
13.069
具 ␣ e典
0.0069
0.0072
0.0072
0.0073
0.0067
0.0050
0.0071
0.0076
0.0084
0.0059
0.0071
0.0056
0.0056
0.0060
0.0044
0.0059
0.6991
0.6958
0.6898
0.7151
0.6960
0.5608
0.5319
0.7303
0.5074
0.4965
0.5157
0.5496
0.5500
0.5309
0.6240
0.6275
0.6938
0.6186
⫺0.0109
0.0087
0.7095
0.7433
0.6962
0.7365
0.6866
0.6884
0.6874
0.6867
具B典
0.0075
0.0074
0.0073
0.0075
0.0071
0.0074
0.0070
0.0072
具A典
12.72
12.47
12.34
12.51
12.93
13.44
10.94
12.42
9.81
11.62
10.74
12.58
12.53
11.86
15.01
13.08
11.32
9.51
12.32
12.71
12.35
12.50
12.45
12.19
12.49
12.38
具 Eo典
18.20
17.92
17.89
17.49
18.58
23.9
20.5
17.0
19.3
23.4
20.8
22.8
22.7
22.3
24.0
20.8
16.3
15.
17.3
17.1
17.7
16.9
18.1
17.7
18.1
18.0
具 Ed典
62
62
62
62
62
39
97
97
62
62
62
97
97
17
25
25
42
65
23
23
97
23
62
62
78
97
Year
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
AMMIAY
JOBPDE
JOBPDE
Ref. 1
Ref. 1
Ref. 1
JOBPDE
JOBPDE
TTMMDZ
MNLMBB
MNLMBB
MNLMBB
MNLMBB
MNLMBB
MNLMBB
JOBPDE
MNLMBB
Ref. 1
Ref. 1
AMMIAY
JOBPDE
Coden
Rf
Rf
Rf
Rf
Rf
24
14
14
Rf
Rf
Rf
14
14
34
20
20
26
35
20
20
14
20
Rf
Rf
63
14
Vol
2852
2852
320
496
417
324
3299
3299
2983
2983
2983
3299
3299
23
277
277
231
508
93
93
3299
93
1751
4151
394
3299
Page
1
1
1
1
1
2
1
1
1
1
1
1
1
1
5
5
1
2
1
1
1
1
1
1
2
1
M
1
1
1
1
2
3?
1
1
1
1?
1
1
1
1
2?
2
2?
1
1
1
1
1
1
1
1
E
948
SHANNON ET AL.
*
Ca共UO2 兲共UOOH兲共SiO4 兲共SiO3 OH兲•4 H2O
beta-uranophane 共Jachymov, Joachimstal兲
Germanates
*
Na4 Ge9 O20
*⫹
K2 Ge4 O9 共synthetic-H. Weber兲
*⫹
共synthetic-H. Weber兲 FL?
K2 Ge8 O17
*⫹
Bi4 Ge3 O12
*⫹
Bi4 Ge3 O12
*
Bi4 Ge3 O12
*⫹
Bi4 Ge3 O12
*⫹
Ca3 Ga2 Ge3 O12
*⫹
CaY2 Mg2 Ge3 O12
*⫹
Ca.90Y1.88Mg2.27Ge3 O12
*⫹
CaY1.92Nd.08Zn2 Ge3 O12
*⫹
Nd2.95Mg1.48In.68Ga1.54Ge1.32O12
*⫹
Ca3 Ga2 Ge4 O14
*⫹
Sr3 Ga2 Ge4 O14
Ba1.92Nd.04Ce.04MgGe2 O*⫹
7
Ba1.99Nd.01ZnGe2 O*7
*⫹
Pb5 Ge3 O11 FE 450 K
*⫹
FE 450 K
Pb5 Ge3 O11
Tellurites
Bi2 TeO*⫹
5
Titanates
Li2 Ti3 O*⫹
7
CaTiO3
CaTiO⫹
3
SrTiO*⫹
3 FE FL 100 K
SrTiO*⫹
3 FE FL 100 K
SrTiO*⫹
3 FE FL 100 K
SrTiO*⫹
3 FE FL 100 K
*⫹
FE FL
SrTiO2.929
*
SrTiO3 FE FL 100 K
BaTiO*⫹
3 FE 403 K FL 393 K
BaTiO*⫹
3 FE 403 K FL 393 K
Ba.77Ca.23TiO*⫹
3 FE FL
PbTiO*⫹
3 FE 763 K
PbTiO*⫹
3 FE 763 K
PbTiO*3 ceramic
Pb.88La.08Zr.80Ti.20O*3 ceramic
Pb.76La.16Ti.60Zr.40O*3 ceramic
sample designations
1.658
1.665
1.7026
1.6679
2.0267
2.0218
2.022
2.0338
1.8186
1.8137
1.8065
1.8646
1.9039
1.7701
1.7690
1.6833
1.732
2.0332
2.0275
2.2520
2.2204
1.5554
2.261
2.2675
2.2629
2.2647
2.2485
2.2950
2.268
2.2943
2.2957
2.2726
2.5617
2.5218
2.523
2.363
2.374
2.395
2.421
2.478
1.665
1.7026
1.6666
2.0267
2.0218
2.022
2.0338
1.8186
1.8137
1.8065
1.8646
1.9039
1.7701
1.7690
1.6833
1.732
2.0332
2.0275
2.2075
2.0496
1.5554
2.261
2.2675
2.2629
2.2647
2.2485
2.2950
2.268
2.2943
2.2957
2.2726
2.5617
2.5218
2.523
2.363
2.374
2.395
2.421
2.478
ny
1.653
nx
2.2883
1.3304
2.261
2.2675
2.2629
2.2647
2.2485
2.2950
2.268
2.2605
2.2613
2.2449
2.5617
2.5226
2.523
2.363
2.374
2.395
2.421
2.478
2.2760
1.675
1.7326
1.6757
2.0267
2.0218
2.022
2.0338
1.8186
1.8137
1.8065
1.8646
1.9039
1.7954
1.7876
1.7211
1.735
2.0661
2.0579
1.665
nz
2.1600
1.5849
2.407
2.4088
2.4145
2.4152
2.4053
2.4035
2.410
2.4408
2.4401
2.4197
2.7899
2.6955
2.693
2.498
2.509
2.543
2.575
2.656
2.3402
1.688
1.7273
1.6913
2.1077
2.1001
2.097
2.1083
1.8480
1.8410
1.8341
1.8975
1.9425
1.7996
1.7984
1.7089
1.752
2.1304
2.1262
1.661
nDx
2.3513
1.5849
2.407
2.4088
2.4145
2.4152
2.4053
2.4035
2.410
2.4408
2.4401
2.4197
2.7899
2.6955
2.693
2.498
2.509
2.543
2.575
2.656
2.3904
1.688
1.7273
1.6928
2.1077
2.1001
2.097
2.1083
1.8480
1.8410
1.8341
1.8975
1.9425
1.7996
1.7984
1.7089
1.752
2.1304
2.1262
1.681
nDy
2.4297
1.3358
2.407
2.4088
2.4145
2.4152
2.4053
2.4035
2.410
2.3833
2.3829
2.3708
2.7899
2.6848
2.693
2.498
2.509
2.543
2.575
2.656
2.4264
1.699
1.7591
1.7012
2.1077
2.1001
2.097
2.1083
1.8480
1.8410
1.8341
1.8975
1.9425
1.8239
1.8166
1.7477
1.764
2.1662
2.1606
1.689
nDz
141.19
56.03
56.03
59.20
59.20
59.20
59.20
59.33
59.20
64.60
64.60
63.30
63.14
63.14
63.14
69.73
68.22
68.67
65.89
63.09
131.85
417.82
198.19
395.50
291.60
291.60
291.60
291.60
229.89
233.00
233.01
237.50
253.10
280.00
299.28
194.43
193.48
325.12
325.12
353.37
Vm
20.17
18.68
18.68
19.70
19.70
19.70
19.70
20.25
19.70
21.50
21.50
21.10
21.05
21.05
21.05
23.24
22.74
22.89
21.96
21.03
26.37
20.88
22.02
23.26
24.30
24.30
24.30
24.30
19.16
19.42
19.42
19.79
21.09
20.00
21.38
27.77
27.64
29.47
29.47
22.08
Vo
18.790
3.803
7.734
8.196
8.179
8.185
8.124
8.317
8.198
9.007
9.012
8.747
9.792
9.665
9.668
10.062
9.888
10.036
9.727
9.511
18.065
37.188
18.540
35.273
35.420
35.308
35.313
35.581
23.860
24.077
23.921
25.641
28.197
28.006
29.839
17.859
18.494
39.930
39.767
31.093
具 ␣ e典
0.0122
0.0127
0.0120
0.0115
0.0124
0.0123
0.0131
0.0087
0.0116
0.0110
0.0109
0.0115
0.0112
0.0092
0.0092
0.0096
0.0093
0.0098
0.0098
0.0102
0.0119
0.0082
0.0078
0.0087
0.0109
0.0106
0.0103
0.0099
0.0067
0.0063
0.0065
0.0067
0.0071
0.0074
0.0075
0.0084
0.0066
0.0125
0.0129
0.0066
具A典
0.2676
0.9026
0.2430
0.2415
0.2427
0.2422
0.2466
0.2343
0.2414
0.2375
0.2371
0.2426
0.1798
0.1865
0.1864
0.2186
0.2156
0.2111
0.2058
0.1945
0.2477
0.5605
0.5176
0.5589
0.3218
0.3239
0.3237
0.3189
0.4334
0.4368
0.4418
0.4037
0.3810
0.4624
0.4649
0.5335
0.4990
0.3147
0.3173
0.5711
具B典
5.92
10.65
5.70
5.78
5.60
5.62
5.50
6.58
5.77
5.87
5.90
5.81
5.06
5.70
5.71
6.04
6.09
5.87
5.80
5.53
5.77
10.44
10.33
10.13
6.88
6.98
7.10
7.17
10.15
10.50
10.41
9.84
9.27
9.99
9.96
10.10
10.96
6.34
6.27
11.79
具 Eo典
22.1
11.80
23.44
23.96
23.07
23.21
22.29
28.09
23.92
24.71
24.90
23.93
28.14
30.55
30.61
27.61
28.24
27.79
28.18
28.41
23.2
18.6
19.9
18.1
21.3
21.5
21.9
22.4
23.4
24.0
23.5
24.3
24.3
21.6
21.4
18.9
21.9
20.1
19.7
20.6
具 Ed典
84
78
58
86
78
79
95
95
65
71
86
97
73
71
77
77
77
77
77
77
94
82
00
95
72
95
71
96
97
79
97
97
97
87
87
97
90
72
97
39
Year
WLHPAR
Ref. 7
JCPSA6
Ref. 4
Ref. 7
Ref. 2B
SPHCA6
SPHCA6
JAPIAU
Ref. 6
Ref. 4
PSSABA
JJAPA5
Ref. 6
APOPAI
APOPAI
APOPAI
APOPAI
APOPAI
APOPAI
PAOAE1
MRBUAC
Ref. 14
Ref. 12
JAPIAU
OPSUA3
Ref. 6
APOPAI
JOBPDE
PRBMDO
JOBPDE
JOBPDE
JOBPDE
SPHCA6
SPHCA6
JOBPDE
JOBPDE
JAPIAU
PSSABA
AMMIAY
Coden
16
16
16
16
16
16
159
12
Rf
40
40
36
28
33
3
1301
7-80
824
29
7-106
72b1
640
640
1674
509
24
559
531
513
3210
3210
3210
3210
3210
3210
839
5110
868
510
3562
3299
4343
3299
3299
3299
236
236
3299
1190
4907
559
43
79
35
14
20
14
14
14
32
32
14
7
43
159
1313
324
Page
17
24
Vol
M
1
1
7
1
1
1
1
1
1
1
1
1
8
1
1
1
1
1
1
1
1
1
1
1
1
6
8
1
1
1
1
1
1
1
1
1
1
1
1
2
E
1
7
5
1
1
1
1
1?
3
1
1
2
1
2?
3?
3
3
3
3
3
1
3
1
2
1
2
3
1
1
1
1
1
1
1
1
1
3?
2
2
3?
949
K
Phosphates
AlPO*⫹
4 berlinite 共synthetic兲
AlPO*⫹
4 berlinite, 20 ppm H2 O 共synthetic兲
AlPO*⫹
AlPO*⫹
AlPO*⫹
AlP3 O*⫹
9
GaPO*⫹
4
ScPO*4
YPO*4
TbPO*4
DyPO*4
HoPO*4
ErPO*4
TmPO*4
YbPO*4
LuPO*4
LuPO*4
Pb3 P2 O⫹
8 共Pb5 P3 O12F?兲 composition uncertain, FL 453 K
Pb3 P2 O8 :2%CePO⫹
4 共Pb5 P3 O12F?兲 composition uncertain, FL
Pb5 P3 O12Cl*⫹ pyromorphite, green 共Ems, Naussau兲
Pb5 P3 O12Cl*⫹ pyromorphite, brown 共Holzappel, Nassau兲
*⫹
FL 419 K
NdP5 O14
*
FL 175 K
GdP5 O14
*⫹
FL?
ErP5 O14
NaBePO*⫹
4 beryllonite 共Stoneham, ME兲
NaBePO*⫹
4 beryllonite 共Stoneham, ME兲
KGeOPO*⫹
4
KTiOPO*⫹
4 probable FE 1207 K
*
KTiOPO4 probable FE 1207 K
K.85Rb.15TiOPO*⫹
4
RbTiOPO*⫹
Li.95Ca.03Mg.02Fe.59Mn.41PO*4 triphylite 共Grafton, NH兲
*⫹
fluorapatite
Ca4.91Na.08Y.04共PO4 兲2.95共SiO4 兲.03共SO4 兲.02F1.90Cl.12
*⫹
Ca4.95Mn.03Fe.02共PO4 兲2.96F1.02 fluorapatite 共unknown source兲
Ca5 共PO4 兲3 共OH.6F.4兲⫹ fluorapatite 共Zillertal, Tirol兲
*⫹
fluorapatite 共Rotenkopf兲
Ca4.98Fe.02共PO4 兲3 F.99Cl.01
Ca4.98Fe.02共PO4 兲3 F*⫹ fluorapatite 共Knappenwand兲
*⫹
montebrasite
Li.97Na.03AlPO4 共OH兲.88F.12
Li1.93Na.04K.01Mg.02Al2 P2 O8 共F.9OH1.1兲*⫹ montebrasite
共Karibib, SW Africa兲
*⫹
montebrasite 共Minas Gerais兲
Li1.0Al1.0P1.0O4 共OH兲.98F.02
*⫹
KH2 PO4 FE 123 K FL 220 K
Ba2 TiSi2 O*⫹
8 fresnoite FE ⬎670
sample designations
1.5140
1.5136
1.5136
1.5137
1.5136
1.5488
1.5862
1.696
1.636
1.657
1.663
1.660
1.660
1.660
1.661
1.659
1.68
1.9144
1.9157
1.9929
1.9944
1.5972
1.5883
1.6022
1.5459
1.5477
1.6472
1.7313
1.729
1.7337
1.7567
1.670
1.6218
1.6198
1.6313
1.6318
1.6253
1.6096
1.598
1.6160
1.4972
1.6083
1.4972
2.500
1.7379
ny
1.5140
1.5136
1.5136
1.5137
1.5136
1.5488
1.5862
1.696
1.636
1.657
1.663
1.660
1.660
1.660
1.661
1.659
1.68
1.9144
1.9157
1.9929
1.9944
1.5922
1.6135
1.6080
1.5404
1.5410
1.6420
1.7252
1.732
1.7304
1.7508
1.670
1.6218
1.6198
1.6313
1.6318
1.6253
1.6000
1.584
2.500
1.7379
nx
1.6347
1.4587
1.5226
1.5223
1.5224
1.5224
1.5223
1.5488
1.6036
1.894
1.810
1.842
1.844
1.843
1.837
1.832
1.837
1.834
1.74
1.8873
1.8832
1.9835
1.9841
1.6132
1.5778
1.5880
1.5531
1.5509
1.6553
1.8091
1.809
1.8117
1.8300
1.678
1.6186
1.6175
1.6275
1.6283
1.6227
1.6259
1.606
2.500
1.7390
nz
1.6290
1.4682
1.9701
1.9696
2.0585
2.0587
1.6067
1.6159
1.6076
1.5578
1.5590
1.6636
1.7780
1.777
1.7794
1.8057
1.688
1.6363
1.6348
1.6461
1.6462
1.6391
1.6219
1.608
1.9701
1.9696
2.0585
2.0587
1.6116
1.6298
1.6128
1.5519
1.5523
1.6585
1.7683
1.771
1.7722
1.7943
1.687
1.6363
1.6348
1.6461
1.6462
1.6391
1.6121
1.594
1.6211
1.4682
1.5244
1.5247
1.5244
1.5247
1.5246
1.5606
1.6008
1.718
1.652
1.677
1.682
1.678
1.676
1.678
1.676
1.675
2.669
1.7641
nDy
1.5244
1.5247
1.5244
1.5247
1.5246
1.5606
1.6008
1.718
1.652
1.677
1.682
1.678
1.676
1.678
1.676
1.675
2.669
1.7641
nDx
1.6480
1.5092
1.9363
1.9323
2.0477
2.0476
1.6285
1.6097
1.5954
1.5620
1.5624
1.6732
1.8724
1.874
1.8765
1.8947
1.694
1.6328
1.6323
1.6417
1.6417
1.6360
1.6387
1.616
1.5335
1.5339
1.5336
1.5338
1.5337
1.5606
1.6189
1.922
1.831
1.866
1.861
1.861
1.852
1.849
1.853
1.855
2.669
1.7617
nDz
80.54
96.85
77.34
77.34
77.34
77.34
77.34
161.73
76.65
62.57
71.25
73.07
72.10
71.35
70.65
70.00
69.30
68.67
68.67
301.10
301.10
316.58
316.58
256.90
250.81
248.54
75.10
75.11
99.45
108.89
108.89
108.99
111.26
73.24
262.65
261.57
262.00
262.00
262.00
80.54
80.54
63.59
189.00
Vm
16.11
24.21
19.34
19.34
19.34
19.34
19.34
17.97
19.16
15.64
17.81
18.27
18.02
17.84
17.66
17.50
17.32
17.17
17.17
23.16
23.16
24.35
24.35
18.35
17.91
17.75
18.77
18.78
19.89
21.78
21.78
21.80
22.25
18.31
20.53
20.32
20.15
20.15
20.15
16.11
16.11
21.20
23.62
Vo
6.751
6.619
5.585
5.581
5.582
5.582
5.581
12.278
6.192
6.159
6.531
6.880
6.822
6.735
6.655
6.582
6.532
6.457
6.336
33.582
33.569
37.530
37.561
21.006
20.296
20.282
5.681
5.682
8.640
10.646
10.662
10.692
11.135
6.552
22.046
21.908
22.255
22.272
22.097
6.682
6.542
9.661
18.164
具 ␣ e典
0.0054
0.0076
0.0096
0.0094
0.0096
0.0094
0.0065
0.0114
0.0027
0.0059
0.0062
0.0064
0.0133
0.0130
0.0131
0.0128
0.0059
0.0060
0.0062
0.0059
0.0057
0.0056
0.0053
0.0047
0.0064
0.0068
0.0067
0.0068
0.0068
0.0063
0.0068
0.0063
0.0059
0.0064
0.0057
0.0056
0.0048
0.0055
0.0048
0.0054
0.0094
0.0071
具A典
0.6162
0.8596
0.3803
0.3806
0.3379
0.3374
0.6400
0.6506
0.6420
0.7187
0.7185
0.5826
0.4822
0.4806
0.4794
0.4631
0.5560
0.6147
0.6169
0.6035
0.6028
0.6102
0.6260
0.6469
0.7687
0.7694
0.7694
0.7693
0.7694
0.7149
0.6518
0.4839
0.5441
0.5208
0.5163
0.5185
0.5197
0.5211
0.5194
0.5214
0.1905
0.4947
具B典
13.47
13.46
7.96
8.04
7.51
7.57
12.53
9.53
19.62
13.99
13.66
12.07
7.62
7.69
7.66
7.62
12.27
12.81
12.57
12.81
13.06
13.22
13.73
14.83
13.83
13.41
13.56
13.44
13.49
13.42
12.41
11.04
12.12
11.39
12.02
12.20
13.19
12.26
13.12
12.39
5.69
10.53
具 Eo典
21.85
15.65
20.9
21.1
22.2
22.4
19.5
14.6
30.5
19.46
19.01
20.72
15.8
16.0
15.9
16.4
22.07
20.8
20.3
21.2
21.6
21.6
21.93
22.92
18.00
17.42
17.62
17.48
17.53
18.7
19.04
22.82
22.27
21.87
23.29
23.53
25.37
23.54
25.26
23.76
29.86
21.2
具 Ed典
97
69
65
97
97
97
97
97
97
00
00
00
00
00
00
00
00
00
76
23
23
31
31
97
87
87
62
97
94
91
94
94
93
33
97
97
62
08
08
54
46
77
77
Year
JOBPDE
Ref. 2A
JAPIAU
JOBPDE
JOBPDE
JOBPDE
JOBPDE
JOBPDE
JOBPDE
OMATET
OMATET
OMATET
OMATET
OMATET
OMATET
OMATET
OMATET
OMATET
JPCSAW
ZEKRDZ
ZEKRDZ
ZEKRDZ
ZEKRDZ
JOBPDE
WLHPAR
WLHPAR
Ref. 1
JOBPDE
CRTEDF
Ref. 8
CRTEDF
CRTEDF
PSISDG
Ref. 10B
JOBPDE
JOBPDE
Ref. 1
ZEKRDZ
ZEKRDZ
NJGMA2
AMMIAY
APOPAI
JCRGAE
Coden
14
Rf
14
14
Rf
45
45
1954
31
29
29
1863
36
14
14
14
14
14
14
15
15
15
15
15
15
15
15
15
37
58
58
77
77
14
36
36
Rf
14
29
16
40
Vol
3299
93
1674
3299
3299
3299
3299
3299
3299
103
103
103
103
103
103
103
103
103
321
226
226
437
437
3299
823
823
2556
3299
583
103
583
583
43
227
3299
3299
2850
555
555
257
51
3210
200
Page
1
1
1
1
1
1
1
1
1
4
4
4
4
4
4
4
4
4
7
1
1
1
1
1
8
8
1
1
1
8
1
1
5
8
1
1
1
1
1
1
2
1
1
M
3
1
1
1
1
1
1
1
1
1
1
4
4
4
4?
4?
4?
4?
4?
4?
4
2
2
1
1
1
1?
1?
1
1
1
1
3
2
1
4
1
1
1
1
1
1
3?
E
950
SHANNON ET AL.
Cu共UO2PO4兲2•8 H2O metatorbernite
Vanadates
YVO*⫹
4
YVO*⫹
4
Y.976Nd.024VO*⫹
4
Y.95Tm.05VO*4
YVO*4
Gd.987Nd.013VO*⫹
4
Gd.96Tm.04VO*⫹
4
*⫹
Gd.7Er.3VO4
LuVO*4
Ca3 V2 O*⫹
*⫹
NaCa2 Mg2 V3 O12
*⫹
NaCa2 Mg2 V3 O12
*⫹
Sr5 V3 O12F
Pb5 V2.63As.30P.07O12Cl*⫹ vanadinite, yellow 共Hillsboro, NM兲
Pb5 V2.96As.02P.02O12Cl*⫹ vanadinite, red 共Gila County, AZ兲
Arsenates
YAsO*4
SmAsO*4
LuAsO*4
KTiOAsO*⫹
4
KTiAsO*⫹
4
KTiOAsO*⫹
4
RbTiOAsO*⫹
4
RbTiOAsO*⫹
4
CsTiOAsO*⫹
4
*⫹
KH2 AsO4 FE 97 K
KH2 AsO*⫹
4 FE 97 K
RbH2 AsO*⫹
4 FE 110 K
CsH2 AsO*⫹
4 FE 143 K
Pb5 As3 O9 Cl⫹ finnemanite
Pb4.95Ca.05As3 O12Cl*⫹ mimetite 共Wheal-Alfred, Cornwall兲
Pb4.92Ca.08As2.93P.07O12Cl*⫹ mimetite 共Tsumeb, SW Africa兲
NaD2AsO4•D2O*⫹
KH2 PO*⫹
4 FE 123 K FL 220 K
RbH2 PO*⫹
4 FE 147 K FL 144 K
RbH2 PO*⫹
4 FE 147 K FL 144 K
RbH2 PO*⫹
4 FE 147 K FL 144 K
PbHPO*4 FE 310 K
NaH2PO4•H2O*⫹
NaH2PO4•2 H2O*⫹
Na2HPO4•7 H2O*⫹
Na2HPO4•12 H2O*⫹
Na4P2O7•10 H2O*⫹
sample designations
1.70
1.72
1.83
1.7701
1.7708
1.7654
1.7934
1.7940
1.8441
1.5485
1.5446
1.5411
1.5511
2.1786
2.0619
2.0584
1.5362
1.9387
1.9330
1.9407
1.901
1.99
1.9468
1.9421
1.9521
1.97
1.8376
1.8741
1.8720
1.8067
2.2477
2.2596
1.9387
1.9330
1.9407
1.901
1.99
1.9468
1.9421
1.9521
1.97
1.8376
1.8741
1.8720
1.8067
2.2477
2.2596
1.70
1.72
1.83
1.7664
1.7679
1.7692
1.7883
1.7892
1.8341
1.5485
1.5446
1.5411
1.5511
2.1786
2.0619
2.0584
1.5212
1.4975
1.4936
1.4937
1.4874
1.782
1.4720
1.4507
1.4304
1.4231
1.4403
1.594
ny
1.4975
1.4936
1.4937
1.4874
1.782
1.4433
1.4296
1.4290
1.4193
1.4376
1.594
nx
1.76
1.73
1.85
1.8458
1.8470
1.8488
1.8591
1.8596
1.8953
1.5016
1.5016
1.5064
1.5310
2.1814
2.0459
2.0433
1.5423
2.1391
2.1322
2.1431
2.249
2.01
2.1547
2.1550
2.1576
2.00
1.8177
1.8741
1.8720
1.7911
2.2132
2.2190
1.4587
1.4662
1.4660
1.4661
1.846
1.4738
1.4679
1.4404
1.4239
1.4484
1.603
nz
1.8919
1.9342
1.9339
1.8576
2.4051
2.4112
1.8919
1.9342
1.9339
1.8576
2.4051
2.4112
1.8206
1.8210
1.8193
1.8450
1.8455
1.9023
1.5671
1.5630
1.5583
1.5688
2.2977
2.1469
2.1434
1.5535
2.0164
2.0145
2.0223
2.0164
2.0145
2.0223
1.8139
1.8150
1.8141
1.8358
1.8365
1.8866
1.5671
1.5630
1.5583
1.5688
2.2977
2.1469
2.1434
1.5381
2.0022
2.0011
1.9996
2.003
1.5093
1.5054
1.5054
1.5052
1.822
1.4852
1.4628
1.4423
1.4361
1.4524
1.624
nDy
2.0022
2.0011
1.9996
2.003
1.5093
1.5054
1.5054
1.5052
1.822
1.4556
1.4400
1.4411
1.4320
1.4499
1.624
nDx
1.9137
1.9144
1.9194
1.9279
1.9276
1.9698
1.5178
1.5164
1.5211
1.5472
2.2866
2.1282
2.1261
1.5606
1.8682
1.9342
1.9339
1.8416
2.3427
2.3469
2.2563
2.2566
2.2594
2.2285
2.2246
2.2269
2.419
1.4682
1.4764
1.4764
1.4767
1.885
1.4873
1.4814
1.4525
1.4373
1.4603
1.626
nDz
78.50
82.94
75.17
116.42
116.42
116.42
119.31
119.31
123.62
104.12
104.12
113.65
125.75
317.21
338.63
338.63
117.25
79.70
79.70
79.70
79.72
79.80
82.61
82.39
81.49
76.90
183.28
241.51
241.51
322.12
338.96
338.96
96.85
105.60
105.60
105.60
89.30
111.02
136.80
264.60
386.25
407.50
421.07
Vm
19.62
20.73
18.79
23.28
23.28
23.28
23.86
23.86
24.72
26.03
26.03
28.41
31.43
24.40
26.05
26.05
23.45
19.93
19.93
19.93
19.93
19.95
20.65
20.60
20.37
19.27
22.90
20.12
20.12
24.78
26.07
26.07
24.21
26.40
26.40
26.40
22.32
22.20
22.79
24.05
24.14
23.97
21.05
Vo
7.402
7.848
7.926
11.816
11.829
11.820
12.328
12.335
13.272
7.713
7.681
8.375
9.483
42.073
41.910
41.828
8.691
9.548
9.510
9.565
9.623
9.504
9.966
9.920
9.860
9.056
19.231
26.277
26.232
32.919
46.243
46.461
6.622
7.218
7.218
7.165
9.141
7.300
8.766
16.426
23.437
25.745
34.250
具 ␣ e典
0.0129
0.0128
0.0131
0.0124
0.0123
0.0122
0.0100
0.0098
0.0094
0.0093
0.0111
0.0106
0.0107
0.0099
0.0114
0.0115
0.0119
0.0118
0.0126
0.0121
0.0109
0.0113
0.0109
0.0102
0.0109
0.0095
0.0164
0.0076
0.0078
0.0078
0.0107
0.0093
0.0099
0.0096
0.0105
0.0119
0.0101
0.0121
具A典
0.4520
0.4511
0.4518
0.4378
0.4373
0.4084
0.7425
0.7467
0.7475
0.7222
0.2666
0.3097
0.3109
0.7406
0.4252
0.3981
0.3993
0.4454
0.2500
0.2473
0.3304
0.3320
0.3284
0.3349
0.3376
0.3338
0.3370
0.8322
0.8315
0.8316
0.8398
0.4447
0.8778
0.9097
0.9487
0.9782
0.9263
0.6447
具B典
7.48
7.51
7.42
7.51
7.53
7.31
10.87
11.05
11.29
11.14
6.19
6.84
6.82
10.95
7.72
7.42
7.32
7.77
5.62
5.71
6.95
6.85
6.94
7.26
7.05
7.51
5.74
13.19
13.07
13.03
11.21
8.73
11.93
12.28
12.03
11.45
12.09
9.24
具 Eo典
16.5
16.6
16.4
17.1
17.2
17.9
14.6
14.8
15.1
15.4
23.2
22.0
21.9
14.7
8.1
18.6
18.3
17.4
22.4
23.1
21.03
20.65
21.14
21.67
20.87
22.51
17.03
15.85
15.7
15.6
13.3
19.63
13.5
13.5
12.6
11.7
13.0
14.3
具 Ed典
76
87
76
93
95
94
93
96
93
64
87
87
87
62
31
31
62
90
97
78
93
76
95
95
95
76
78
97
97
95
31
31
64
67
67
67
88
62
62
62
62
62
62
Year
JPCSAW
JPCSAW
JPCSAW
PSISDG
JOBPDE
CRTEDF
PSISDG
JOBPDE
PSISDG
Ref. 11B
FEROA8
FEROA8
FEROA8
Ref. 1
ZEKRDZ
ZEKRDZ
Ref. 1
REKEDA
JOBPDE
JAPIAU
JAPNDE
JPCSAW
SJQEAF
SJQEAF
SJQEAF
JPCSAW
OPCOB8
JOBPDE
JOBPDE
Ref. 13
ZEKRDZ
ZEKRDZ
JOSAAH
SPHCA6
SPHCA6
SPHCA6
JPSOAW
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Coden
72
72
72
Rf
77
77
Rf
37
48
37
1863
12
29
1863
13
1863
77
77
18
14
49
32
37
25
25
25
37
27
14
14
54
11
11
12
21
Rf
Rf
Rf
Rf
Rf
Rf
Vol
321
509
321
43
794
583
43
1935
43
187
95
95
95
288
437
437
2577
616
3299
5517
1651
321
1162
1162
1162
321
393
3299
3299
604
437
437
1215
711
711
383
1661
2577
2577
2577
2577
2577
317
Page
3
3
7
5
1
1
5
1
5
8
1
1
1
1
1
1
1
1
1
8
8
3
1
1
1
3
5
1
1
5
1
1
1
1
1
8
1
1
1
1
1
1
2
M
5
5
4
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3?
4
1
1
1
5
1
1
1
2
2
1
1
1
1
2?
4
1
1
1
1
1
4
E
951
Na2HAsO4•7H2O*
Mn6.5Ca.25Mg.25As2 O8 共OH兲*⫹
8 allactite 共Langbanshuttan兲
Antimonates
Ca1.0Na.8Mn.2Sb2 O*⫹
7 atopite 共Miguel Burnier, Minas Gerais兲
Niobates
LiNbO*⫹
3 FE 1483 K FL 1470 K
LiNbO*⫹
3 Li:Nb ⫽ 0.946:1 共poled crystal兲 FE 1493 K FL 1470 K
LiNbO*⫹
3 共vapor-grown crystal兲 FE 1493 K
LiNbO*⫹
3 共congruent melt兲 FE 1493 K
Li.97Mg.03NbO*⫹
3 FE FL
Li.95Mg.05NbO*⫹
3 FE FL
KNbO*⫹
3 FE 691 K
KNbO*⫹
3 FE 691 K
KNbO*⫹
3 FE 691 K
Sr2 Nb2 O*7 FE 1615 K
Sr2 Nb2 O*7 FE 1615 K
LaNbO*4 FL 792 K
*
Cs8 Nb22O59
Ba.25Sr.75Nb2 O*⫹
6 FE 333 K
Ba.25Sr.75Nb2 O*6 FE 333 K
Ba.39Sr.61Nb2 O*6 FE 348 K
Ba.39Sr.61Nb2 O*6 FE 348 K
Ba.5Sr.5Nb2 O*⫹
6 FE 403 K
Ba.54Sr.46Nb2 O*6 FE
Ba.67Sr.33Nb2 O*6 FE
Ba.75Sr.25Nb2 O*6 FE 473 K
*⫹
FE 703 K
K3 Li2 Nb5 O15
*⫹
FE 418 K
Sr4.25Na1.25Li.25Nb10O30
*
Ba3 LaNb3 O12
*⫹
FE 833 K FL
Ba2 NaNb5 O15
*
FE 518 K
Ba6 Ti2 Nb8 O30
*⫹
FE 813 K
PbNb4 O11
PbMg.333Nb.666O*3 FE 265 K
PbMg.333Nb.666O3 FE 400 K
PbZn.333Nb.667O*3 FE 400 K
*⫹
FE 723 K
Pb2 KNb5 O15
Tantalates
LiTaO*⫹
3 FE 938 K FL 895 K
LiTaO*⫹
3 FE 938 K FL 895 K
LiTaO*⫹
3 共melt-grown兲 FE 938 K
LiTa.92Nb.08O*⫹
3 共melt-grown兲 FE
LiTa.81Nb.19O*⫹
3 共melt-grown兲 FE
KTaO*⫹
3 FE
KTa.66Nb.34O*3 FE
sample designations
1.4512
1.7494
1.8016
2.2093
2.2040
2.2075
2.2044
2.2011
2.1994
2.2196
2.1877
2.1877
2.00
2.00
2.053
2.13
2.226
2.217
2.220
2.218
2.223
2.220
2.220
2.219
2.1697
2.2148
2.187
2.2238
2.219
2.2671
2.422
2.49
2.421
2.2712
2.1156
2.1167
2.1159
2.1263
2.1320
2.1413
2.191
1.8016
2.2093
2.2040
2.2075
2.2044
2.2011
2.1994
2.1879
2.0923
2.0923
2.09
2.09
2.136
2.13
2.226
2.217
2.220
2.218
2.223
2.220
2.220
2.219
2.1697
2.2237
2.187
2.2251
2.219
2.2637
2.422
2.49
2.421
2.3134
2.1156
2.1167
2.1159
2.1263
2.1320
2.1413
2.191
ny
1.4475
1.7300
nx
2.1193
2.1204
2.1203
2.1223
2.1266
2.1413
2.191
2.1311
2.1314
2.1218
2.1316
2.1235
2.1219
2.0931
2.2180
2.2180
2.09
2.09
2.036
2.08
2.167
2.205
2.191
2.195
2.193
2.186
2.182
2.228
2.0857
2.1911
2.049
2.1454
2.190
2.2908
2.422
2.49
2.421
2.3230
1.8016
1.4632
1.7490
nz
2.1859
2.1862
2.1863
2.1986
2.2057
2.2425
2.302
2.563
2.3883
2.563
2.4486
2.1859
2.1862
2.1863
2.1986
2.2057
2.2425
2.302
2.3036
2.3002
2.3010
2.2998
2.2949
2.2946
2.3504
2.2957
2.3478
2.06
2.06
2.105
2.25
2.326
2.328
2.327
2.330
2.327
2.328
2.329
2.330
2.2954
2.3228
2.270
2.3376
2.333
2.3844
2.581
1.8384
1.4657
1.7786
nDy
2.3036
2.3002
2.3010
2.2998
2.2949
2.2946
2.2968
2.1810
2.2952
2.17
2.17
2.200
2.25
2.326
2.328
2.327
2.330
2.327
2.328
2.329
2.330
2.2954
2.3347
2.270
2.3389
2.333
2.3819
2.581
1.8384
1.4622
1.7744
nDx
2.1902
2.1904
2.1912
2.1950
2.1987
2.2425
2.302
2.563
2.4623
2.2113
2.2144
2.2000
2.2138
2.2035
2.2027
2.1824
2.3487
2.1810
2.16
2.16
2.087
2.18
2.322
2.316
2.297
2.299
2.287
2.286
2.280
2.265
2.1755
2.2994
2.104
2.2295
2.294
2.4103
2.581
1.8384
1.4781
1.7787
nDz
52.85
52.85
52.85
52.97
52.97
63.40
63.41
53.03
53.08
53.08
53.08
53.03
53.03
64.72
64.72
64.72
149.35
150.95
83.29
1408.40
121.45
121.45
122.38
122.38
123.00
123.25
124.08
122.14
317.10
587.30
268.97
309.63
629.56
242.96
66.38
66.38
66.97
313.02
135.80
274.40
336.14
Vm
17.62
17.62
17.62
17.65
17.65
21.13
21.14
17.68
17.69
17.69
17.69
17.68
17.68
21.58
21.58
21.58
21.53
21.56
20.82
23.47
20.24
20.24
20.40
20.40
20.50
20.54
20.67
20.36
21.14
19.58
22.41
20.64
20.98
22.09
22.13
22.13
22.32
20.87
19.40
24.94
21.01
Vo
6.777
6.781
6.779
6.823
6.843
8.240
8.460
7.047
7.041
7.038
7.042
7.018
7.012
8.528
8.524
8.524
18.523
18.721
10.424
180.236
16.329
16.383
16.487
16.487
16.592
16.590
16.691
16.549
41.223
79.102
34.953
41.459
84.771
33.735
9.803
10.049
9.887
44.025
13.879
17.739
32.456
具 ␣ e典
0.0080
0.0079
0.0080
0.0081
0.0081
0.0107
0.0107
0.0091
0.0101
0.0088
0.0091
0.0088
0.0090
0.0089
0.0091
0.0109
0.0106
0.0108
0.0088
0.0088
0.0069
0.0124
0.0110
0.0102
0.0099
0.0101
0.0093
0.0098
0.0097
0.0079
0.0118
0.0101
0.0079
0.0098
0.0102
0.0097
0.0101
0.0087
0.0116
0.0081
具A典
0.2873
0.2869
0.2871
0.2845
0.2827
0.2789
0.2632
0.2057
0.2326
0.2659
0.2669
0.2673
0.2668
0.2684
0.2689
0.2715
0.2712
0.2718
0.3088
0.3088
0.3032
0.2893
0.2587
0.2565
0.2574
0.2575
0.2566
0.2579
0.2582
0.2540
0.2793
0.2576
0.2804
0.2614
0.2577
0.2398
0.2056
0.4452
0.8978
0.4865
具B典
7.58
7.63
7.57
7.50
7.48
6.47
6.29
6.02
6.06
6.94
6.86
6.98
6.89
6.94
6.89
6.32
6.39
6.35
7.49
7.49
8.37
6.12
6.14
6.34
6.45
6.38
6.64
6.50
6.52
7.16
6.17
6.39
7.55
6.53
6.35
6.28
5.71
9.05
11.14
9.82
具 Eo典
26.38
26.58
26.38
26.38
26.48
23.18
23.88
29.26
26.0
26.11
25.69
26.10
25.81
25.86
25.63
23.29
23.58
23.36
24.2
24.2
27.61
21
23.7
24.7
25.0
24.7
25.8
25.2
25.2
28.2
22.0
24.8
26.9
25.0
24.6
26.1
27.78
20.3
12.4
20.1
具 Ed典
65
96
77
77
77
76
66
67
74
90
76
91
92
92
74
74
97
89
70
78
68
84
84
96
68
84
84
68
71
81
86
70
73
71
74
76
81
75
33
62
33
Year
JAPIAU
JAPIAU
JCRGAE
JCRGAE
JCRGAE
JUPSUA
JAPIAU
JAPIAU
JAPIAU
IEJQA7
OPCOB8
SJQEAF
CPLEEU
JOBPDE
JJAPA5
JJAPA5
FEROA8
JUPSUA
OPSUA3
JCRGAE
JAPIAU
SPHCA6
SPHCA6
PSSABA
JAPIAU
SPHCA6
SPHCA6
JAPIAU
Ref. 6
WHLPAR
INOMAF
PLRBAQ
JPCSAW
Ref. 6
SPSSA7
SPSSA7
Ref. 2C
JAPIAU
Ref. 10B
Ref. 1
Ref. 10B
Coden
36
80
42
42
42
41
37
15
18
Rf
46
30
22
2
34
38
45
26
17
21
9
9
13
13
203
58
28
43
39
29
29
154
39
29
29
39
Rf
Vol
1674
6561
579
579
579
888
388
1941
3688
135
332
225
427
380
1362
1362
75
398
38
115
343
641
641
K5
343
641
641
343
517
1259
401
2709
1639
513
2006
1851
78K13
2361
392
2577
1181
Page
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
8
1
1
1
1
8
1
3
8
1
1
1
1
M
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
5
5
3
5?
3
3
3
3
3
3
3
4?
2
1
3
1
3
2
3
5
4
2
E
TABLE 1. Refractive index and dispersion data, listing refractive indices 共n x , n y , n z兲 at ␭ ⫽ ⬁, refractive indices 共n Dx , n Dy , n Dz兲 at ␭ ⫽ 589.3 nm, molar volume,V m , volume per O- atom, V O , and mean values of electronic polarizabilities
952
SHANNON ET AL.
thoreaulite
La.294Sr.706Al.647Ta.353O*⫹
3 共synthetic-Mateika兲
La.272Sr.728Al.648Ta.352O*⫹
3 共synthetic-Hu兲
Nd.390Sr.610Al.695Ta.305O*⫹
3 共synthetic-Mateika兲
*
pyrochlore
Pb2 Sc0.5Ta1.5O6.5
*
Ba3 LaTa3 O12
SbNb.43Ta.57O*⫹
4 stibiotantalite, probably FE 673 K
SbNb.69Ta.31O*⫹
4 stibiotantalite, probably FE 673 K
Sulfates
Na2 SO*⫹
4 thenardite 共synthetic?兲
K2 SO*⫹
4 arcanite 共synthetic?兲 FL?
Rb2 SO*⫹
4
Cs2 SO*⫹
4
*⫹
Tl2 SO4
CaSO*⫹
4 anhydrite
SrSO*⫹
4 celestite
BaSO*⫹
4 barite
PbSO*⫹
4 anglesite
PbSO*⫹
4 anglesite 共Monte Poni兲
Fe2 共SO4 兲*3
Fe2 共SO4 兲*3 orthorhombic in LB but probably monoclinic
KLiSO*4 FL 190, 900, 940 K
RbLiSO*⫹
4 Phase IV, RT FE 439 K
K2 Mg2 共SO4 兲*⫹
3 langbeinite
K2 Co2 共SO4 兲*⫹
3 FL
K2 Cd2 共SO4 兲*3 FL 430 K
Rb2 Cd2 共SO4 兲*⫹
3 FE 129 K FL 129 K
Tl2 Cd2 共SO4 兲*⫹
3 FE 129 K FL 128 K
FeSO4 OH*
Li2 SO4•H2 O*⫹
MgSO4 •7 H2 O*⫹ epsomite
CaSO4 •2 H2 O*⫹ gypsum
FeSO4 OH•2 H2 O* butlerite 共synthetic兲
Fe2 共SO4 兲3 •7 H2 O* cornellite 共synthetic兲
NiSO4 •6 H2 O*⫹ retgersite 共synthetic兲
CuSO4 •5 H2 O*⫹ chalcanthite 共synthetic兲
Pr2 共SO4 兲3 •8 H2 O*⫹
Nd2 共SO4 兲3 •8 H2 O*⫹
Sm2 共SO4 兲3 •8 H2 O*
K2 UO2 共SO4 兲2 •2 H2 O*
K2 Mg共SO4 兲2 •6 H2 O*⫹
K2 Fe共SO4 兲2 •6 H2 O*⫹
K2 Co共SO4 兲2 •6 H2 O*⫹
K2 Ni共SO4 兲2 • H2 O*⫹
K2 Cu共SO4 兲2 •6 H2 O*⫹
SnTa2 O*6
sample designations
2.309
1.9846
1.9838
1.9922
2.292
2.100
2.2835
2.2907
1.4635
1.4855
1.5031
1.5517
1.8188
1.5640
1.6109
1.6240
1.8465
1.8451
1.701
1.738
1.4634
1.4718
1.5243
1.5886
1.577
1.5795
1.7029
1.734
1.4672
1.4440
1.5113
1.633
1.553
1.4973
1.5225
1.5348
1.5360
1.5369
1.510
1.4523
1.4709
1.4754
1.4803
1.4738
1.4573
1.4843
1.5031
1.5474
1.8124
1.5586
1.6092
1.6229
1.8414
1.8403
1.701
1.727
1.4634
1.4700
1.5243
1.5886
1.575
1.5795
1.7029
1.727
1.4522
1.4225
1.5094
1.557
1.545
1.4973
1.5008
1.5258
1.5274
1.5288
1.499
1.4500
1.4649
1.4695
1.4724
1.4713
ny
2.268
1.9846
1.9838
1.9922
2.292
2.100
2.2624
2.2797
nx
1.4768
1.4879
1.5042
1.5534
1.8349
1.6011
1.6174
1.6340
1.8566
1.8560
1.692
1.742
1.4623
1.4700
1.5243
1.5886
1.577
1.5795
1.7029
1.825
1.4761
1.4486
1.5190
1.681
1.593
1.4746
1.5288
1.5450
1.5467
1.5477
1.545
1.4641
1.4851
1.4884
1.4923
1.4891
2.372
1.9846
1.9838
1.9937
2.292
1.972
2.3344
2.3319
nz
1.4669
1.4934
1.5131
1.5598
1.8604
1.5698
1.6214
1.6362
1.8780
1.8775
1.770
1.802
1.4722
1.4796
1.5341
1.6074
1.590
1.5936
1.7296
1.783
1.4615
1.4326
1.5207
1.587
1.572
1.5107
1.5140
1.5399
1.5412
1.5427
1.514
1.4606
1.4757
1.4806
1.4835
1.4835
2.388
2.0256
2.0243
1.8212
2.477
2.161
2.3744
2.3976
nDx
1.4730
1.4947
1.5133
1.5644
1.8676
1.5755
1.6231
1.6374
1.8834
1.8827
1.770
1.814
1.4722
1.4818
1.5341
1.6074
1.592
1.5936
1.7296
1.805
1.4765
1.4555
1.5227
1.678
1.586
1.5107
1.5367
1.5493
1.5503
1.5521
1.527
1.4628
1.4821
1.4864
1.4916
1.4863
2.418
2.0256
2.0243
1.8212
2.477
2.161
2.4045
2.4193
nDy
1.4809
1.4973
1.5144
1.5662
1.8857
1.6137
1.6303
1.6480
1.8945
1.8943
1.760
1.818
1.4717
1.4804
1.5341
1.6074
1.593
1.5936
1.7296
1.917
1.4863
1.4607
1.5304
1.749
1.640
1.4870
1.5436
1.5608
1.5619
1.5629
1.571
1.4754
1.4969
1.5001
1.5050
1.5019
2.499
2.0256
2.0243
1.8224
2.477
2.021
2.4575
2.4592
nDz
88.57
108.76
122.13
141.28
123.56
76.40
76.79
86.66
79.59
79.59
217.17
205.80
98.94
105.10
243.97
244.25
266.89
279.60
279.96
84.02
103.63
243.47
123.65
132.75
387.47
210.72
181.27
419.68
417.50
417.03
291.37
330.20
332.69
328.88
323.40
327.50
115.64
57.89
57.77
56.76
150.56
269.13
80.28
78.03
Vm
22.14
27.19
30.53
35.32
30.89
19.10
19.20
21.66
19.90
19.90
18.09
17.15
24.74
26.27
20.33
20.35
22.23
23.31
23.26
16.80
20.73
22.13
20.61
18.96
20.39
21.07
20.14
20.98
20.87
20.85
24.28
23.59
23.76
23.49
23.10
23.39
16.52
19.19
19.26
18.91
23.16
22.43
20.07
19.51
Vo
5.855
7.453
8.626
10.758
12.863
6.023
6.377
7.333
8.475
8.468
19.994
19.726
6.506
7.008
17.829
19.640
21.095
22.199
25.915
8.270
6.841
15.269
8.876
11.185
30.072
14.537
13.100
31.202
31.113
31.131
21.078
21.407
22.306
22.215
21.998
22.134
16.362
6.839
6.821
6.742
21.077
33.324
11.246
10.966
具 ␣ e典
0.0074
0.0064
0.0065
0.0067
0.0109
0.0057
0.0053
0.0055
0.0078
0.0079
0.0206
0.0203
0.0069
0.0074
0.0058
0.0087
0.0075
0.0067
0.0084
0.0181
0.0072
0.0096
0.0070
0.0180
0.0172
0.0088
0.0085
0.0082
0.0081
0.0082
0.0114
0.0085
0.0082
0.0081
0.0080
0.0089
0.0091
0.0062
0.0062
0.0074
0.0139
0.0073
0.0095
0.0098
具A典
0.8750
0.8279
0.7933
0.7117
0.4311
0.6769
0.6250
0.6072
0.4140
0.4146
0.5307
0.4967
0.8768
0.8602
0.7555
0.6563
0.6737
0.6689
0.5264
0.4773
0.8725
0.9364
0.7754
0.6167
0.6935
0.8206
0.7683
0.7368
0.7347
0.7328
0.7681
0.8943
0.8539
0.8451
0.8362
0.8443
0.2294
0.3402
0.3407
0.4528
0.2348
0.3108
0.2350
0.2330
具B典
13.78
14.37
13.96
13.02
7.97
13.74
13.69
13.27
9.21
9.14
6.41
6.26
14.26
13.63
14.42
11.01
11.99
12.60
10.00
6.49
13.87
12.51
13.28
7.40
8.03
12.19
12.04
12.01
12.07
11.94
10.36
12.97
12.89
12.92
12.93
12.32
6.34
9.33
9.37
9.88
5.19
8.27
6.30
6.18
具 Eo典
15.75
17.3
17.5
18.3
18.4
20.30
21.91
21.85
22.25
22.05
12.0
12.6
16.26
15.8
19.0
16.7
17.7
18.8
18.9
13.60
15.9
13.3
17.1
11.9
11.5
14.8
15.6
16.2
16.4
16.3
13.4
14.5
15.1
15.2
15.4
14.5
27.6
27.43
27.51
21.81
22.1
26.6
26.83
26.52
具 Ed典
34
62
62
62
08
11
11
62
11
23
22
22
29
94
87
87
84
87
87
22
67
62
62
22
22
62
42
62
62
62
19
62
13
62
62
62
60
97
01
97
98
86
06
06
Year
ZEKRDZ
Ref. 1
Ref. 1
Ref. 1
ZEKRDZ
ZEKRDZ
ZEKRDZ
Ref. 1
ZEKRDZ
ZEKRDZ
JACSAT
JACSAT
ZEKRDZ
OPSUA3
SPHCA6
SPHCA6
SPSSA7
SPHCA6
SPHCA6
JACSAT
JAPIAU
Ref. 1
Ref. 1
JACSAT
JACSAT
Ref. 1
SMPTA8
Ref. 1
Ref. 1
Ref. 1
CIWPAV
Ref. 1
ZEKRDZ
Ref. 1
Ref. 1
Ref. 1
Ref. 10D
JOBPDE
CPLEEU
JOBPDE
CRTEDF
INOMAF
AJSCAP
AJSCAP
Coden
87
Rf
Rf
Rf
44
49
49
Rf
49
58
44
44
71
75
32
32
26
32
32
44
38
Rf
Rf
44
44
Rf
22
Rf
Rf
Rf
298
Rf
52
Rf
Rf
Rf
14
18
14
33
22
22
22
Vol
43
2742
1567
2742
138
14
14
4046
14
460
1965
1965
141
473
76
76
2222
76
76
1965
4365
2533
2652
1965
1965
2737
1
1769
1769
1769
207
2743
433
2743
4088
2743
390
3299
278
3299
119
1208
61
61
Page
M
1
1
1
1
1
1
1
1
1
1
2
2
1
8
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
8
1
1
1
1
1
1
1
1
1
1
1
1
1
E
1
1
1
1
1
1
1
1
1
1
3
3
1
2
1
1
3
1
1
3
1
1
1
3
3
2
1
2
2
2
5
1
1
1
1
1
3
1
1
1
4
3
2
2
953
*⫹
K2 Zn共SO4 兲2 •6 H2 O
Rb2 Mg共SO4 兲2 •6 H2 O*⫹
Rb2 Fe共SO4 兲2 •6 H2 O*⫹
Rb2 Co共SO4 兲2 •6 H2 O*⫹
Rb2 Ni共SO4 兲2 •6 H2 O*⫹
Rb2 Cu共SO4 兲2 •6 H2 O*⫹
Rb2 Zn共SO4 兲2 •6 H2 O*⫹
Cs2 Mg共SO4 兲2 •6 H2 O*⫹
Cs2 Mn共SO4 兲2 •6 H2 O*⫹
Cs2 Fe共SO4 兲2 •6 H2 O*⫹
Cs2 Co共SO4 兲2 •6 H2 O*⫹
Cs2 Cu共SO4 兲2 •6 H2 O*⫹
Cs2 Zn共SO4 兲2 •6 H2 O*⫹
Tl2 Fe共SO4 兲2 •6 H2 O*⫹
Tl2 Co共SO4 兲2 •6 H2 O*⫹
Tl2 Ni共SO4 兲2 •6 H2 O*⫹
Tl2 Cu共SO4 兲2 •6 H2 O*⫹
Tl2Zn共SO4兲2•6 H2O*⫹
NaAl共SO4 兲2 •12 H2O*⫹
KAl共SO4 兲2 •12 H2O*⫹
KAl共SO4 兲2 •12 H2O*⫹
KCr共SO4 兲2 •12 H2O
KFe共SO4 兲2 •12 H2O
KGa共SO4 兲2 •12 H2O
RbAl共SO4 兲2 •12 H2O
RbCr共SO4 兲2 •12 H2O
RbFe共SO4 兲2 •12 H2O
RbGa共SO4 兲2 •12 H2O
RbIn共SO4 兲2 •12 H2O
CsAl共SO4 兲2 •12 H2O
CsCr共SO4 兲2 •12 H2O
CsFe共SO4 兲2 •12 H2O
CsGa共SO4 兲2 •12 H2O
CsIn共SO4 兲2 •12 H2O
TlAl共SO4 兲2 •12 H2O
TlCr共SO4 兲2 •12 H2 O
TlFe共SO4 兲2 •12 H2O
TlGa共SO4 兲2 •12 H2O
Selenites and Selenates
LiHSeO*3
K2 SeO*⫹
4 FE 93 K
Rb2 SeO*⫹
4
SeO*⫹
4
*⫹
Tl2 SeO4
sample designations
1.4720
1.4583
1.4760
1.4806
1.4845
1.4785
1.4771
1.4743
1.4847
1.4917
1.4967
1.4934
1.4930
1.5866
1.5942
1.6001
1.5866
1.5866
1.4274
1.4447
1.4453
1.4685
1.4657
1.4538
1.4453
1.4682
1.4662
1.4541
1.4517
1.4473
1.4682
1.4679
1.4534
1.4531
1.4827
1.5060
1.5043
1.4916
1.632
1.5247
1.5391
1.5830
1.8922
1.561
1.5212
1.5369
1.5827
1.8834
ny
1.4667
1.4567
1.4701
1.4750
1.4780
1.4767
1.4723
1.4739
1.4830
1.4887
1.4938
1.4920
1.4904
1.5711
1.5789
1.5847
1.5767
1.5723
1.4274
1.4447
1.4453
1.4685
1.4657
1.4538
1.4453
1.4682
1.4662
1.4541
1.4517
1.4473
1.4682
1.4679
1.4534
1.4531
1.4827
1.5060
1.5043
1.4916
nx
1.643
1.5301
1.5434
1.5834
1.8976
1.4844
1.4671
1.4859
1.4897
1.4932
1.4910
1.4857
1.4802
1.4903
1.4974
1.5010
1.5024
1.4971
1.5918
1.5996
1.6047
1.5958
1.5934
1.4274
1.4447
1.4453
1.4685
1.4657
1.4538
1.4453
1.4682
1.4662
1.4541
1.4517
1.4473
1.4682
1.4679
1.4534
1.4531
1.4827
1.5060
1.5043
1.4916
nz
1.580
1.5352
1.5515
1.5991
1.9490
1.4774
1.4672
1.4815
1.4858
1.4895
1.4886
1.4833
1.4855
1.4946
1.5003
1.5055
1.5047
1.5021
1.5930
1.6010
1.6025
1.5997
1.5930
1.4387
1.4562
1.4560
1.4813
1.4815
1.4653
1.4565
1.4814
1.4822
1.4657
1.4637
1.4585
1.4809
1.4836
1.4648
1.4652
1.4974
1.5226
1.5234
1.5066
nDx
1.655
1.5390
1.5538
1.5998
1.9588
1.4832
1.4689
1.4873
1.4915
1.4960
1.4906
1.4883
1.4857
1.4964
1.5035
1.5084
1.5061
1.5047
1.6093
1.6176
1.6186
1.6097
1.6092
1.4387
1.4562
1.4560
1.4813
1.4815
1.4653
1.4565
1.4814
1.4822
1.4657
1.4637
1.4585
1.4809
1.4836
1.4648
1.4652
1.4974
1.5226
1.5234
1.5066
nDy
1.669
1.5446
1.5583
1.6002
1.9636
1.4967
1.4780
1.4977
1.5012
1.5051
1.5036
1.4975
1.4915
1.5024
1.5093
1.5130
1.5152
1.5092
1.6166
1.6238
1.6225
1.6191
1.6166
1.4387
1.4562
1.4560
1.4813
1.4815
1.4653
1.4565
1.4814
1.4822
1.4657
1.4637
1.4585
1.4809
1.4836
1.4648
1.4652
1.4974
1.5226
1.5234
1.5066
nDz
73.80
120.10
133.26
152.48
132.19
327.13
344.94
346.80
341.76
339.74
343.00
343.24
364.50
373.04
368.06
363.40
363.70
363.89
346.79
343.19
338.78
344.00
342.82
455.43
449.28
449.28
453.51
458.89
452.40
458.78
462.84
467.60
462.05
479.66
471.94
477.23
480.59
476.72
492.39
457.32
461.03
466.00
463.85
Vm
24.60
30.02
33.31
38.12
33.05
23.37
24.64
24.77
24.41
24.27
24.50
24.52
26.04
26.64
26.29
25.96
25.98
25.99
24.77
24.51
24.20
24.57
24.49
22.78
22.46
22.46
22.67
22.94
22.62
22.94
23.14
23.38
23.10
23.98
23.60
23.86
24.03
23.84
24.62
22.87
23.05
23.30
23.19
Vo
6.125
8.791
9.978
12.166
14.580
21.963
22.584
23.408
23.251
23.255
23.347
23.210
24.549
25.569
25.519
25.394
25.361
25.269
27.675
27.683
27.538
27.575
27.394
27.938
28.530
28.563
30.124
30.325
29.236
29.167
30.727
30.929
29.877
30.874
30.121
31.682
31.888
30.785
31.778
31.164
32.700
32.958
32.104
具 ␣ e典
0.0096
0.0084
0.0081
0.0078
0.0121
0.0082
0.0082
0.0082
0.0078
0.0081
0.0085
0.0081
0.0082
0.0081
0.0079
0.0078
0.0084
0.0079
0.0108
0.0105
0.0081
0.0106
0.0103
0.0101
0.0096
0.0088
0.0095
0.0118
0.0091
0.0092
0.0098
0.0119
0.0092
0.0096
0.0091
0.0095
0.0117
0.0091
0.0096
0.0102
0.0105
0.0120
0.0100
具A典
0.6288
0.7539
0.7294
0.6640
0.3882
0.8522
0.8822
0.8458
0.8365
0.8294
0.8359
0.8436
0.8482
0.8277
0.8145
0.8055
0.8079
0.8127
0.6640
0.6534
0.6458
0.6595
0.6627
0.9638
0.9199
0.9183
0.8646
0.8708
0.8981
0.9183
0.8653
0.8697
0.8974
0.9030
0.9135
0.8654
0.8661
0.8990
0.8997
0.8345
0.7887
0.7918
0.8165
具B典
10.25
12.00
11.98
11.65
7.16
12.86
13.10
12.83
13.10
12.83
12.51
12.95
12.85
12.78
12.84
12.87
12.40
12.80
9.94
9.96
11.32
9.95
10.16
12.34
12.40
12.88
12.10
10.88
12.54
12.62
11.90
10.83
12.50
12.24
12.64
12.07
10.90
12.59
12.24
11.42
10.97
10.26
11.41
具 Eo典
16.30
15.9
16.4
17.5
18.4
15.0
14.8
15.1
15.6
15.4
14.9
15.3
15.1
15.4
15.7
15.9
15.3
15.7
14.9
15.2
17.5
15.0
15.3
12.8
13.4
14.0
13.9
12.4
13.9
13.7
13.7
12.4
13.9
13.5
13.8
13.9
12.5
14.0
13.6
13.6
13.9
12.9
13.9
具 Ed典
84
62
62
62
08
62
62
13
62
62
62
62
62
62
13
62
62
62
62
62
62
62
10
62
62
33
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
Year
ZEKRDZ
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ZEKRDZ
Ref. 1
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ZEKRDZ
Ref. 1
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Ref. 1
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Ref. 1
ZEKRDZ
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
PPSAAM
Ref. 1
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ZEKRDZ
Ref. 1
Ref. 1
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Ref. 1
Ref. 1
Ref. 1
Ref. 1
Ref. 1
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Ref. 1
Coden
169
Rf
Rf
Rf
44
Rf
Rf
52
Rf
Rf
Rf
Rf
Rf
Rf
52
Rf
Rf
Rf
Rf
Rf
Rf
Rf
83
Rf
Rf
85
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Rf
Vol
249
2744
2744
2744
138
2743
2743
433
2743
2743
2743
2743
2743
2743
433
2743
2743
2743
1572
1571
1571
1572
211
3797
3798
169
189
189
189
189
189
189
189
189
189
189
189
189
189
189
189
189
189
Page
M
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
E
3
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1?
1
1
1
1?
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
954
SHANNON ET AL.
Cs2
NiSeO4 •6 H2 O*⫹
ZnSeO4 •6 H2 O*⫹
K2 Mg共SeO4 兲2 •6 H2O*⫹
K2 Cu共SeO4 兲2 •6 H2O*⫹
Rb2 Mg共SeO4 兲2 •6 H2O*⫹
Cs2 Mg共SeO4 兲2 •6 H2O*⫹
KAl共SeO4 兲2 •12 H2O
KAl共SeO4 兲2 •12 H2O
Molybdates
CaMoO*⫹
4
CaMoO*⫹
4
CaMoO*⫹
4
*⫹
SrMoO4
SrMoO*⫹
4
CdMoO*⫹
4
PbMoO*⫹
4 wulfenite
*⫹
PbMoO4 wulfenite
PbMoO*⫹
4 wulfenite
PbMoO*⫹
4 wulfenite
Pb2 MoO*⫹
5
*
Bi6 Mo2 O15
*
Bi2 Mo3 O12
*
Bi2 Mo3 O12
⫹
Ce2 Mo3 O12
⫹
FL 1233 K
Nd2 Mo3 O12
*⫹
FE 432 K FL 432 K
Gd2 Mo3 O12
*⫹
FE 432 K FL 432 K
Gd2 Mo3 O12
*⫹
FE 435 K
Tb2 Mo3 O12
Li.286Gd.571MoO*⫹
4
Tungstates
*⫹
CaWO4
CaWO*⫹
4
CaWO*⫹
4
SrWO*⫹
4
BaWO*⫹
4
ZnWO*⫹
4
ZnWO*⫹
4
ZnWO*⫹
4
*⫹
PbWO4 stolzite
PbWO*4
NaY共WO4 兲2
NaLa共WO4 兲2
Chlorates and Perchlorates
NaClO*⫹
3
sample designations
1.5226
1.5132
1.4855
1.5034
1.4894
1.5039
1.4666
1.4663
1.9287
1.9432
1.9367
1.8649
1.8628
2.1292
2.2508
2.2525
2.2491
2.2371
2.0936
2.222
2.187
2.047
1.9657
1.9622
1.8018
1.7990
1.8095
1.9922
1.8816
1.8812
1.8828
1.8289
1.8102
2.1201
2.1198
2.1164
2.1622
2.155
1.94
1.93
1.5022
1.9287
1.9432
1.9367
1.8649
1.8628
2.1292
2.2508
2.2525
2.2491
2.2371
2.0848
2.233
2.165
2.065
1.9657
1.9622
1.8014
1.7990
1.8090
1.9922
1.8816
1.8812
1.8828
1.8289
1.8102
2.1058
2.1018
2.1026
2.1622
2.155
1.94
1.93
1.5022
ny
1.5226
1.5132
1.4832
1.4954
1.4876
1.5036
1.4666
1.4663
nx
1.5022
1.8951
1.8948
1.8958
1.8368
1.8077
2.2475
2.2467
2.2435
2.1009
2.112
1.94
1.92
1.9345
1.9479
1.9441
1.8670
1.8654
2.1062
2.1705
2.1853
2.1756
2.1684
2.1944
2.197
2.265
2.245
1.9567
1.9618
1.8492
1.8461
1.8556
1.9838
1.4969
1.4890
1.4995
1.5161
1.4991
1.5093
1.4666
1.4663
nz
1.5152
1.9196
1.9184
1.9203
1.8618
1.8426
2.1767
2.1740
2.1756
2.2704
2.246
1.94
1.94
1.9789
1.9916
1.9909
1.9083
1.9078
2.2190
2.4152
2.4061
2.4103
2.4090
2.1885
2.370
2.284
2.210
2.0347
2.0186
1.8445
1.8427
1.8538
2.0567
1.5391
1.5288
1.4967
1.5098
1.5011
1.5177
1.4806
1.4800
nDx
1.5152
1.9196
1.9184
1.9203
1.8618
1.8426
2.1934
2.1925
2.1935
2.2704
2.246
1.94
1.94
1.9789
1.9916
1.9909
1.9083
1.9078
2.2190
2.4152
2.4061
2.4103
2.4090
2.1965
2.361
2.329
2.182
2.0347
2.0186
1.8449
1.8427
1.8542
2.0567
1.5391
1.5288
1.4991
1.5182
1.5030
1.5178
1.4806
1.4800
nDy
1.5152
1.9359
1.9347
1.9359
1.8719
1.8405
2.3412
2.3386
2.3403
2.1817
2.170
1.95
1.96
1.9891
2.0012
2.0005
1.9132
1.9125
2.1916
2.2788
2.2830
2.2795
2.2767
2.3260
2.323
2.478
2.424
2.0221
2.0168
1.8983
1.8964
1.9063
2.0489
1.5122
1.5036
1.5138
1.5318
1.5134
1.5235
1.4806
1.4800
nDz
23.69
20.79
166.35
71.08
19.53
19.53
19.53
21.73
25.22
16.58
16.58
16.58
22.23
22.23
20.53
24.12
24.12
23.84
19.04
246.36
289.50
289.50
286.17
77.44
78.10
78.10
78.10
86.91
100.90
66.33
66.33
66.33
88.92
88.92
19.51
19.51
19.51
21.65
21.65
18.59
22.36
22.36
22.36
22.36
27.59
24.44
20.05
20.05
22.08
22.29
24.89
24.66
25.96
27.52
23.75
23.75
Vo
78.03
78.03
78.03
86.62
86.62
74.37
89.42
89.42
89.42
89.42
137.97
366.59
240.62
240.62
220.82
222.92
348.42
345.30
363.55
385.24
475.04
475.04
Vm
5.009
18.856
8.580
8.577
8.587
9.124
10.386
8.698
8.690
8.681
11.560
11.553
28.652
30.016
29.942
29.862
9.178
8.871
8.963
8.927
9.359
9.344
9.561
12.128
12.164
12.131
12.070
17.765
49.557
32.341
30.891
15.872
15.788
24.023
24.449
25.181
27.306
31.444
31.427
具 ␣ e典
0.0084
0.0074
0.0073
0.0073
0.0074
0.0076
0.0082
0.0082
0.0086
0.0104
0.0086
0.0009
0.0038
0.0088
0.0083
0.0091
0.0088
0.0091
0.0098
0.0126
0.0117
0.0123
0.0132
0.0121
0.0120
0.0139
0.0160
0.0105
0.0088
0.0101
0.0104
0.0103
0.0095
0.0098
0.0097
0.0093
0.0095
0.0092
0.0089
0.0104
0.0103
具A典
0.7959
0.3911
0.3913
0.3905
0.4247
0.4398
0.2747
0.2753
0.2759
0.2790
0.2794
0.3620
0.3692
0.3667
0.3594
0.3623
0.4032
0.4043
0.2857
0.2538
0.2519
0.2535
0.2565
0.2855
0.2554
0.2591
0.2890
0.3506
0.3509
0.4346
0.4365
0.4297
0.3381
0.7744
0.7908
0.8210
0.7909
0.8156
0.7894
0.8689
0.8696
具B典
12.32
9.17
9.25
9.23
9.58
9.64
7.31
7.32
7.17
6.55
7.23
25.76
12.39
8.17
8.35
7.96
8.54
8.41
6.84
5.67
5.88
5.74
5.57
6.15
5.84
5.47
5.37
7.29
7.97
8.29
8.21
8.17
7.53
11.22
11.43
11.85
11.53
11.90
11.89
11.54
11.63
具 Eo典
15.48
23.44
23.65
23.63
22.55
21.9
26.60
26.58
26.00
23.49
25.87
71.17
33.5
22.28
23.22
21.98
21.17
20.80
23.94
22.35
23.33
22.62
21.72
21.5
22.8
21.1
18.5
20.80
22.7
19.0
18.8
19.0
22.27
14.4
14.4
14.4
14.5
14.5
15.0
13.2
13.3
具 Ed典
10
65
63
77
77
77
65
64
89
77
97
72
72
78
65
77
65
77
77
78
62
62
77
70
74
74
99
23
23
71
79
86
77
62
62
62
23
62
62
33
62
Year
NJGAAY
JAPIAU
JOSAAH
SJOTBH
SJOTBH
SJOTBH
JAPIAU
APOPAI
WLHPAR
SJOTBH
NIMAER
INOMAF
INOMAF
Ref. 7
JAPIAU
SJOTBH
JAPIAU
SJOTBH
SJOTBH
Ref. 7
Ref. 1
Ref. 1
SJOTBH
JOSAAH
MRBUAC
MRBUAC
Ref. 15
ZEKRDZ
ZEKRDZ
Ref. 6
Ref. 2B
Ref. 3
SPHCA6
Ref. 1
Ref. 1
Ref. 1
ZEKRDZ
Ref. 1
Ref. 1
ZEKRDZ
Ref. 1
Coden
29
36
53
44
44
44
36
3
38
44
385
8
8
22
Rf
58
58
Rf
Rf
44
60
9
9
36
44
36
44
44
Rf
Rf
Rf
58
Rf
Rf
85
Rf
Vol
53
1674
1286
542
542
542
1674
1084
670
542
209
1957
1957
7-79
1674
542
1674
542
542
7-94
353
2810
542
1375
41
41
525
226
226
511
69N5
155
371
2737
2737
2112
40
2112
2112
169
189
Page
1
1
1
1
1
1
1
1
1
1
8
8
8
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
8
1
8
1
1
1
1
1
1
1
5
8
M
1
1
1
1
1
1
1
1
1
1
4?
5?
5
1
1?
1
1
1
1
1
1
1
1
2
4
4
2
1
1?
1
1
1
1
2
2
1
1
1
1
1
1
E
955
1.4647
1.4616
1.4696
1.6202
1.5894
1.4711
1.5954
1.789
1.8414
1.8439
1.7831
1.7812
1.5917
1.9078
1.549
1.509
1.5910
1.5782
1.5954
1.789
1.8414
1.8439
1.6629
1.6627
1.5917
1.7986
1.589
1.545
1.5867
1.5715
ny
1.4640
1.4606
1.4661
1.6186
1.5560
1.4711
nx
1.482
1.5997
1.5876
1.7041
1.7065
1.7855
1.7834
1.6129
1.9248
1.587
1.5954
1.835
1.4678
1.4645
1.4711
1.6288
1.6089
1.4281
nz
8
Interference method.
Brewster method.
Unknown or other.
E
Error.
M
Method.
7
6
*Composition well-known – synthetic crystals or analyzed minerals.
⫹
Refractive index accurate to ⫾ 0.0001–0.0010.
1
Prism method.
2
Immersion method.
3
Reflectivity data, classical oscillator model, Kramers-Kronig analysis.
4
Ellipsometry method.
5
Critical angle method.
LiClO4 •3 H2 O*⫹
Bromates
NaBrO*⫹
3
AgBrO3
Iodates and Periodates
LiIO3 -alpha*⫹
LiIO3 -alpha*⫹
KIO3 -alpha*⫹
KIO3 -alpha*⫹
KIO*⫹
4
HIO*⫹
3 ⫽ alpha iodic acid ⫽ IO2 OH
KIO2 F*2
Chromates
MgCrO4•7 H2O
Cs2Mg共CrO4兲2•6 H2O*⫹
Rb2Mg共CrO4兲2•6 H2O*⫹
KClO*⫹
4
RbClO*⫹
4
CsClO*⫹
4
TlClO*⫹
4
Sr共ClO3 兲⫹
2
sample designations
1.568
1.6376
1.6224
1.8868
1.8870
1.6976
1.6968
1.6205
1.8436
1.615
1.6168
1.847
1.4730
1.4691
1.4752
1.6427
1.5667
1.4832
nDx
1.550
1.6432
1.6338
1.8868
1.8870
1.8342
1.8334
1.6205
1.9687
1.565
1.6168
1.847
1.4736
1.4701
1.4788
1.6446
1.6045
1.4832
nDy
245.97
381.95
359.98
67.18
67.18
88.90
88.90
103.46
62.99
105.18
75.14
74.54
90.96
100.91
115.97
102.10
134.31
140.73
Vm
22.36
27.28
25.70
22.59
22.59
29.63
29.63
25.86
21.00
26.29
25.14
24.84
22.74
25.22
28.99
25.52
22.38
20.10
Vo
17.620
30.876
28.564
6.828
6.844
8.593
8.581
8.436
6.870
8.298
6.099
7.637
6.009
6.626
7.709
8.590
10.742
9.146
具 ␣ e典
0.0209
0.0227
0.0244
0.0100
0.0095
0.0124
0.0126
0.0133
0.0111
0.0104
0.0096
0.0149
0.0068
0.0066
0.0068
0.0100
0.0066
0.0090
具A典
0.7800
0.6511
0.6697
0.4539
0.4521
0.4941
0.4952
0.6428
0.3986
0.6761
0.6471
0.4436
0.8713
0.8786
0.8637
0.6126
0.6628
0.8933
具B典
7.73
6.77
6.63
8.51
8.75
7.97
7.94
8.78
7.57
10.22
10.39
6.90
14.35
14.64
14.21
9.90
12.69
12.61
具 Eo典
9.9
10.4
9.9
18.75
19.34
16.13
16.04
13.6
18.99
15.1
16.05
15.55
16.47
16.6
16.4
16.1
19.1
14.1
Ed典
1
Error limits.
0.0001–0.0005.
2
0.0006 –0.0010.
3
0.0011–0.0050.
4
0.0051–0.0100.
5
⬎ 0.0100.
6
Not given.
7
Doubtful.
?
Dispersion, A, not consistent with like compounds or structural family trends.
??
Probably contains Fe.
1.521
1.6555
1.6444
1.7390
1.7394
1.8379
1.8363
1.6476
1.9956
1.611
1.6168
1.920
1.4768
1.4732
1.4804
1.6542
1.6256
1.4384
nDz
31
12
12
77
76
96
92
62
68
74
10
31
26
26
26
34
62
96
Year
Ref. 11A
MNLMBB
MNLMBB
OPCOB8
PLRBAQ
Ref. 2D
CPLEEU
Ref. 1
APPLAB
JCPSA6
NJGAAY
Ref. 11A
PPSAAM
PPSAAM
PPSAAM
ZEKRDZ
Ref. 1
JAPIAU
Coden
16
16
23
14
Rf
9
Rf
12
60
29
111
111
111
87
Rf
80
Vol
228
175
175
279
1693
87Y4
77
466
186
2470
53
205
462
462
462
43
4065
6097
Page
2
1
1
1
1
1
1
8
1
1
1
2
1
1
1
1
1
5
M
5
1
1
1
1
1
1
1
1
3
1
3
1
1
1
1
1
2
E
TABLE 1. Refractive index and dispersion data, listing refractive indices 共n x , n y , n z兲 at ␭ ⫽ ⬁, refractive indices 共n Dx , n Dy , n Dz兲 at ␭ ⫽ 589.3 nm, molar volume,V m , volume per O- atom, V O , and mean values of electronic polarizabilities
956
SHANNON ET AL.
957
TABLE 2. Comparison of n ⬁ values determined by prism methods and reflectivity methods
Compound
MgF2
CaF2
SrF2
BaF2
ZnF2
PbF2
P42 /mnm
Fm3m
Fm3m
Fm3m
P42 /mnm
Fm3m
KMgF3
KNiF3
KMnF3
Pm3n
Pm3n
Pm3n
RbMnF3
Cu2 O
Pm3n
Pn3m
ZnO
EuO
Al2 O3
Er2 O3
Fm3̄m
R3̄c
Ia3̄
SiO2
GeO2
P31 21
P42/mnm
TiO2
P42/mnm
ThO2
Fm3̄m
CeO2
UO2
Fm3̄m
Fm3̄m
Tb3 Ga5 O12
Y3 Fe5 O12
Be2 SiO4
Mg2 SiO4
Bi4 Si3 O12
Bi4 Ge3 O12
YVO4
PbMg.33Nb.67O3
a
Deltaa
Delta
Delta
IR-prism ellips-prism Interf-prism
Space group Prism method Reflectivity Error Ellipsometer Error Interference method
具 n ⬁典
具 n ⬁典
具 n ⬁典
Ia3̄d
R3̄
Pmnb
I41 /amd
Pm3m
1.3761
1.4255
1.4306
1.4655
1.4963
1.7248
1.7272
1.3975
1.4382
2.27
1.9150
1.904
1.960
1.7496
1.923
1.930
1.5353
1.9546
1.957
2.506
2.490
2.0679
2.07
2.12
2.16
1.9335
2.1287
2.165
1.6448
1.6455
1.6365
1.9674
2.0267
2.0338
2.0055
1.9994
2.422
1.38
1.430
1.44
1.47
1.503
1.58
1.58
1.43
1.52
1.44
1.45
1.59
2.54
2.55
2.57
⬎.01
0.01
⬎.01
⬎.01
0.01
⬎.01
⬎.01
0.05
0.05
0.01
0.05
0.05
0.02
0.05
0.05
1.4827
1.4745
1.903
1.903
2.30
1.78
0.08
1.538
2.05
0.005
⫺0.012
⫺0.001
0.003
0.003
0.34
0.03
1.7480
1.95
1.95
⫺0.05
⫺0.03
0.02
0.02
0.01
0.01
0.13
0.13
2.36
0.05
0.23
1.932
2.15
2.15
1.66
1.66
1.650
0.02
0.02
0.01
0.01
0.005
0.01
0.01
⫺0.001
0.002
0.02
0.01
0.014
1.9559
2.0218
2.00
2.00
2.49
⫺0.002
0.03
0.02
0.003
0.09
0.09
2.46
2.46
2.20
2.20
2.31
2.35
0.00
0.00
0.01
0.00
0.01
À0.14
À0.14
0.03
0.04
0.00
0.01
0.12
0.27
0.28
0.30
0.001
⫺0.01
0.00
0.07
⫺0.011
⫺0.005
⫺0.012
Boldfaced values refer to discrepancies greater than experimental values.
of the plot at ␭⫽⬁, gives n ⬁ ⫽(1⫹1/B) 1/2. In Appendix 2,
we give alternative forms of this equation. The n ⬁ values
derived from Eq. 共3a兲 are necessary for the correct application of the Lorenz–Lorentz relation to obtain ion polarizabilities. The values of n ⬁ derived in this paper from one-term
Sellmeier analyses of data from the visible region results in
n ⬁ that comes only from electronic transitions. This n ⬁ is
distinctly different from the dielectric n ⬁ derived from the
dielectric constant ␧ o⫽n ⬁2 , obtained in the kHz–MHz region
where both lattice vibrations and electronic transitions contribute to the dielectric constant. This is shown graphically
by Tropf et al. 共1995兲 in their Fig. 1, p. 33.13 and is illustrated numerically by the value of refractive indices of quartz
where from optical data, 具 n ⬁ 典 ⫽1.547, and from dielectric
constant data at 1 kHz, 具 n ⬁ 典 ⫽2.135 共Shannon, 1993兲.
An alternative form 关Wemple and DiDomenico 共1971兲;
Wemple 共1973, 1977兲兴 is
n 2 ⫺1⫽E dE o /„E 2o ⫺ 共 ប ␻ …2 兲 ,
共3b兲
where in a single oscillator model ប ␻ ⫽the photon energy,
E o⫽the average single oscillator 共Sellmeier兲 energy gap in
eV, and E d ⫽ the average oscillator strength in eV, which
measures the average strength of interband optical transitions
and E d is related to physical parameters by the expression
E d⫽ ␤ N cZ aN e , where N c is the cation coordination number,
Z a is the formal valence of the anion, N e is the effective
SHANNON ET AL.
958
TABLE 3. Inconsistent dispersion values
具A典
Compound
NaF
Cs2 SiF6
Na2 GeF6
Cs2 GeF6
BaMgF4
Cu2 O
Y2 O3
Y2 O3
Y2 O3
As2 O3
Sb2 O3
SrB4 O7
Gd.99Nd.01Al3 B4 O12
MgAl2 O4 共1.15% Co兲
SrLaAlO4
Gd3 Sc2 Al3 O12
Y3 Ga5 O12
Tm3 Ga5 O12
LaEr3 ScGa3 O12
SrGdGa3 O7
Y3 Fe5 O12
SiO2
ZrSiO4
Al2 SiO4 F2
Mn2 SiO4
CaMnSiO4
Fe1.7Mn.1Mg.2SiO4
Zn2 SiO4
ZrSiO4
Al2 SiO5
Ca2.7Mg.2Fe.1Al1.8Fe.2Si3 O12
Ca2 CoSi2 O7
Li.95Na.05Al.95Fe.05Si2 O6
CaTiSiO5
CaTiSiO5
Na4 Al3 Si3 O12Cl
Na4 Al3 Si3 O12Cl
K.9Na.1AlSi3 O8
KAlSi3 O8
Ba.93K.04Na.02Al2 Si2 O8
Ca3 Si2 O6 共OH兲2 共OH2 兲2
Ca2 Al2 FeSi3 O12OH
Cu6 Si6 O18•6 H2O
Pb9 Mg9 Si9 O24共OH兲24
Ca共UO2 兲共UOOH兲共SiO4 兲共SiO3 OH兲•4 H2O
Ca共UO2 兲共UOOH兲共SiO4 兲共SiO3 OH)•4 H2O
Ba1.99Nd.01ZnGe2 O7
TiO2
TiO2
SrTiO2.929
PbTiO3
PbTiO3
ThO2
Mineral
cuprite
arsenolite
senarmontite
spinel
smoky quartz
zircon
topaz
tephroite
fayalite
willemite
zircon
sillimanite
grossular
spodumene
titanite
titanite
sodalite
sodalite
adularia
microcline
paracelsian
afwillite
epidote
dioptase
molybdophyllite
beta-uranophane
beta-uranophane
rutile
rutile
ceramic
ceramic
RbH2 PO4
DyPO4
HoPO4
ErPO4
TmPO4
YbPO4
Reference
⫺16
10
2
m
Eo
Ed
共eV兲
共eV兲
Accuracy indexa
具A典
78 Ref. 7 7-105
35 ZPCBAL 31 292
82 INOMAF 18 570
35 ZPCBAL 31 292
75 JAPIAU 46 4645
79 JJAPA5 18 1043
91 Ref. 9 1079
91 Ref. 9 1079
56 ANCHAM 28 2023
62 Ref. 1 Rf 2565
62 Ref. 1 Rf 204
95 OMATET 4 669
96
98
101
117
75
86
126
62
53
87
80
40
15.0
13.4
14.4
11.7
13.8
5.5
7.1
9.9
10.8
9.6
8.0
14.3
11.1
12.2
11.0
11.8
15.3
33.9
18.0
25.8
27.6
19.0
25.0
28.2
2
3
2
3
3
5
2
2
3
3
5
1
high
high
high
high
high
low
high
low
low
low
low
low
98
62
96
73
87
82
84
91
65
40
48
39
66
80
70
42
94
271
14.0
13.1
12.2
9.8
8.9
9.2
11.7
8.7
4.0
28.8
25.4
33.6
24.5
22.5
24.8
32.5
19.5
14.8
1
1
5
5
3
3
2
3
3
low
low
low
high
high
high
low
high
high
97 NJMIAK 11 259
62 Ref. 1 Rf 514
62 Ref. 1 Rf 4071
32 AMMIAY 17 135
76
69
37
98
12.5
9.4
16.3
8.8
16.9
24.6
26.7
18.5
1
1
1
3
high
high
low
high
32 AMMIAY 17 135
09 ZEKRDZ 46 138
23 ZEKRDZ 58 460
03 ZEKRDZ 37 235
62 Ref. 1 Rf 4085
62 Ref. 1 Rf 235
97 JOBPDE 14 3299
13 ZEKRDZ 13 294
97 Ref. 10A 1609
97 Ref. 10A 1609
62 Ref. 1 Rf 2597
97 Ref. 10A 885
21 TTMMDZ 35 231
62 Ref. 1 Rf 2966
42 MNLMBB 26 231
25 MNLMBB 20 277
62 Ref. 1 Rf 2983
62 Ref. 1 Rf 2889
38 Ref. 10C 368
39 AMMIAY 24 324
39 AMMIAY 24 324
90 JOBPDE 7 1190
97 OPLEDP 22 1808
79 JJAPA5 18 1043
95 SPHCA6 40 640
71 Ref. 6 513
77 APOPAI 16 3210
64 OPACAT 11 287
90
85
81
64
67
35
178
51
73
91
65
98
63
85
87
44
59
66
80
50
66
66
152
84
87
92
92
44
9.9
9.2
10.5
9.7
11.8
15.0
7.6
13.3
9.2
8.3
14.5
11.8
14.1
12.2
11.3
15.0
11.6
11.8
9.7
13.4
11.8
11.0
4.6
6.3
6.6
5.7
5.7
10.5
17.9
20.5
18.9
25.7
20.3
30.7
11.8
23.4
23.8
21.1
17.0
13.7
18.0
15.5
16.3
24.1
23.4
20.6
20.5
24.0
20.6
22.0
23.0
30.3
28.1
30.5
30.6
34.5
3
1
1
1
1
1
1
2
4
2
2
2
1
1
2
2
1
1
1
3
3
3?
5
5
1
2
3
3
high
high
high
high
high
low
high
low
low
low
low
high
low
high
high
low
low
low
low
?
?
low
high
low
low
low
low
low
67
00
00
00
00
00
107
57
56
48
55
48
11.2
12.0
12.2
13.2
12.3
13.1
13.3
23.3
23.5
25.4
23.5
25.3
2
4
4
4
4
4
high
low
low
low
low
low
CHSCBU 43 1973
Ref. 1 Rf 173
PSSBBD 195 625
JAPIAU 44 1395
Ref. 5 314
JCRGAE 57 600
SPHCA6 29 704
JOBPDE 8 1668
BJAPJA 16 475
SPHCA6 12 383
OMATET 15 103
OMATET 15 103
OMATET 15 103
OMATET 15 103
OMATET 15 103
959
TABLE 3. Inconsistent dispersion values—Continued
具A典
Compound
LuPO4
GdP5 O14
ErP5 O14
Li1.93Na.04Mg.02Al2 P2 O8 共F.9OH1.1兲
Y.95Tm.05VO4
Cs8 Nb22O59
Ba.75Sr.25Nb2 O6
KAl共SO4 ) 2 •12 H2O
Tl2 Ni共SO4 ) 2 •6 H2O
CaMoO4
Nd2 Mo3 O12
PbWO4
NaY共WO4 兲2
a
Mineral
montebrasite
stolzite
Reference
10
⫺16
m
2
Eo
Ed
共eV兲
共eV兲
Accuracy indexa
具A典
00 OMATET 15 103
87 WLHPAR 36 823
87 WLHPAR 36 823
46 AMMIAY 31 51
93 JAPNDE 32 1651
78 JCRGAE 43 115
68 JAPIAU 39 343
54
114
27
47
164
124
79
12.4
9.5
19.6
14.8
5.7
6.1
7.2
23.8
14.6
30.6
22.9
17.0
21.1
28.2
4
1
1
3
3
5
4
low
high
low
low
high
high
low
62
62
65
23
97
72
96
81
83
88
86
9
12.4
11.3
8.4
8.0
7.2
25.8
13.5
17.5
23.2
22.7
25.9
71.2
1
1
1
1
4
5
high
low
low
low
low
low
Ref. 1 Rf 3798
Ref. 1 Rf 1571
JAPIAU 36 1674
ZDKRDZ 58 226
NIMAER 385 209
INOMAF 8 1957
Accuracy index defined in Table 1.
number of valence electrons/anion, ␤ ⫽0.26 for ionic compounds, and ␤ ⫽0.37 for covalent compounds. These parameters were analyzed for more than 100 compounds byWemple and DiDomenico 共1971兲. The scheme was found to
work well for simple single-bond halides and oxides as well
as a number of more complex multibond oxides containing
two cations of differing coordination. However, it was necessary to assume covalent character ( ␤ ⫽0.37) for scheelitetype molybdates and tungstates and several iodates and carbonates. In this paper we consider both single-bond and
multibond oxides and fluorides.
In general, dispersion parameters are not identical for light
polarized along the different axes of uniaxial and biaxial
crystals. This results in dispersion parameters that vary with
the crystal orientation. However, for simplicity in the tables,
we list only mean values of 具 A 典 , 具 B 典 , 具 E o典 , and 具 E d典 . In the
text following, although we omit the brackets, all values of
A, B, E o , and E d are understood to be mean values.
When numerical values were given, we have used those
data to determine the one-term Sellmeier parameters 关Eq.
FIG. 1. Mean dispersion value 具 A 典 vs frequency of occurrence.
共3a兲兴. When data were presented in the form of different
Sellmeier equations, we used the equations to calculate numerical dispersion data for use in Eq. 共3a兲 and when data
were provided only in graphical form, the dispersion data
were taken from these plots.
2.4. Error Limits
Where possible, we have given error limits as reported;
when no error limits were reported, we have either stated that
or estimated the errors. Following the composition, the
symbol ⫹ refers to compounds with the most reliable refractive indices, generally with ␦ n⫽⫾0.0001– 0.0005. When refractive indices are quoted to four decimal places in LandoltBörnstein, as for example for the many sulfates studied by
Tutton over the years 1890–1930, we have assumed error
limits of ⫾0.0001– 0.0005. Estimated error limits are only
valid for the refractive index and do not take errors in composition into consideration. Crystals studied before the early
FIG. 2. Dispersion A vs average Sellmeier energy gap E o .
SHANNON ET AL.
960
1900s and for which four significant figures are quoted in the
original papers are assumed to be measured by prism methods.
3. Results and Discussion
Table 1 provides 73 measurements on 55 fluorides, 9 measurements on chlorides, and 750 measurements on 509 oxides. In the table we give the specimen composition and
source, the refractive indices at ␭⫽⬁ and 589.3 nm, molar
volume V m , volume per anion V o , electronic polarizabilities
␣ e , the mean dispersion parameters, A, B, E o, and E d ,
along with indices that provide an indication of the method
of measuring n, the estimated error in n, the reliability of the
composition and refractive index data, and source reference
in an easily accessible form.
FIG. 3. Dispersion A vs average oscillator strength.
3.1. Comparison of Data Using Different Methods
Teller 共LST兲 relation. Similarly, the high value for
n ⬁ (RbMnF3 ) was noted by Perry and Young 共1967兲. The
three IR values of n ⬁ (Cu2 O)⫽2.54, 2.55, and 2.57, obtained
from the IR measurements, agree reasonably well and are
probably more accurate than the value of n ⬁ (Cu2 O)⫽2.27
obtained from prism data in LB. This value derived from
data determined in 1871 appears systematically low compared with the IR values and the 643.8 nm value of 2.89
determined by Medenbach and Shannon 共1997兲.
In Table 2 we compare the results of determinations of n ⬁
by prism, IR, ellipsometer, and interference methods. In general, results obtained for prism or interference and IR methods are identical within experimental error. Exceptions are
PbF2 , RbMnF3 , Cu2 O, EuO, GeO2 , ThO2 , UO2 , and
PbMg.33Nb.67O3 , as noted by boldfaced values in Table 2.
The discrepancy in n ⬁ (PbF2 ) was noted by Axe et al. 共1965兲
and attributed to an inadequacy of the Lyddane–Sachs–
TABLE 4. Dispersion parameters for oxides and fluorides: Transition metal
Compound
3⫹
Fe
3d
5
Chemical composition
Mineral
hematite
lepidocrocite
goethite
具A典b
具Eo 典c
具Ed 典c
Atom 共%兲a
10⫺16 m2
共eV兲
共eV兲
226
215
162
206
181
180
172
197–160
120–117
115–101
122
114
3.6
5.0
5.1
6.4
6.5
7.4
8.0
4.8–5.3
10.3–10.9
7.7–8.1
8.0
8.4
19.7
15.0
19.3
12.1
13.6
12.0
11.6
17.0–19.0
12.6
18.1–19.4
16.5
16.7
Fe2 O3
FeOOH
FeOOH
Fe2 共SO4 兲3
FeSO4 OH
FeSO4 OH•2 H2O
Fe2 共SO4 兲3 •7 H2O
Y3 Fe5 O12
MFe共SO4 兲2 •12 H2O
Ca3 Fe2 Si3 O12
Na.87Fe.92Al.05Ti.03Si2 O6
Na.7Ca.2Mg.1Fe.9Si2 O6
butlerite
cornellite
garnet
M⫽K,Rb,Cs,Tl
andradite
aegirine
aegirine
40
33
33
12
14
33
27
25
54
10
9
9
Cr3⫹ 3d 3
MCr共SO4兲2 •12 H2O
M⫽K,Rb,Cs,Tl
54
105–95
11.0–12.1
13.8–14.0
Mn3⫹ 3d 4
Ca3 Mn1.95共SiO4 兲2.1共O4 H4 兲.9
henritermierite
12
105
8.4
18.2
Co2⫹ 3d 7
Ca2 CoSi2 O7
Sr2 CoSi2 O7
8
8
178
117
7.6
9.1
11.8
15.0
Ni2⫹ 3d 8
NiF2
MNiF3
33
20
198
77–71
8.0
13.3–13.7
10.1
15.7–16.4
M⫽K,Cs
Eu2⫹ 4f 7
Eu2 SiO4 - beta
28
162
6.5
15.2
U4⫹ 5f 2
UO2
33
264,210
4.2,4.5
14.5,16.7
Why low 具 A 典 ?
F
Atom % ⫽共total ‘‘soft ions’’⫹H2 O兲/共total cations⫹anions兲.
b
Boldfaced values of 具 A 典 are relatively high.
c
Boldfaced values of 具 E o典 and 具 E d典 are relatively low.
a
961
TABLE 5. Dispersion parameters for oxides and fluorides d 10
Atom
Compound
⫹
Cu 3d
10
Cu2 O
CuCl
Zn 3d 10
ZnO
ZnWO4
Zn2 SiO4
Ca2 ZnSi2 O7
BaZnF4
CaY1.92Nd.08Zn2 Ge3 O12
Zn4 O共BO2 兲6
ZnF2
As5⫹ 3d 10
I7⫹ 4d 10
KH2 AsO4
RbH2 AsO4
CsH2 AsO4
Mn6.5Ca.25Mg.25As2 O8 共OH兲8
Mineral
cuprite
willemite
hardystonite
allactite
KIO4
共%兲
a
具A典b
⫺16
10
2
m
b
具Eo 典c
具Ed 典c
Why low
共eV兲
共eV兲
具A典?
67
50
267
161
3.8
6.3
15.8
15.9
50
33
28
8
53
10
17
33
185–159
86– 82
71
71
67
67
61
59
5.74–6.09
7.2–7.3
11.1
11.5
13.8
9.8
11.5
14.8
15.1–16.5
26.0–26.6
20.3
19.7–19.8
17.3
24.4
22.7
18.4
16
16
16
8
98–100
94
93
81
10.9–11.0
11.3
11.1
9.8
14.6–14.8
15.1
15.4
20.2
17
133
8.8
13.7
Si
Ca, Si
Ba, F
Ca
F
Ca, Mg
c
a
b
There is a large discrepancy between the EuO prism value
of n⫽1.96 quoted by Wachter 共1968兲 and the IR value of
2.30 from Axe 共1969兲. An alternative method of deciding
which of these is more correct is to use the data from
␤ -Eu2 SiO4 along with the additivity rule 关Eq. 共2兲兴 where the
total polarizability ␣ e ( ␤ -Eu2 SiO4 ) is 10.19 A3 共see Table 1兲.
Subtracting ␣ e(SiO2 )⫽2.803 A3 , we arrive at ␣ e (EuO)
⫽3.69 A3 , which corresponds to n ⬁ ⫽1.87, much closer to
the prism value n ⬁ ⫽1.96 than the IR value.
The large discrepancy between prism and IR data from
GeO2 is probably caused by poor data or IR analysis. This is
evident from the n ⬁ (GeO2 ) IR values of n o⫽2.02 and n e
⫽2.10, which are improbably larger than n ⬁ (SnO2 ) prism
values of n o⫽1.9442 and n e⫽2.0449. The IR values of
n ⬁ (ThO2 )⫽2.20 and n ⬁ (UO2 )⫽2.33 by Axe and Pettit
共1966兲 are significantly larger than the value of 2.070 obtained by Ellis and Lindstrom 共1964兲 for ThO2 and the UO2
value of 2.16 by Ellis 共1964兲 using prism methods. Axe and
Pettit noted this fact and attributed the discrepancy to an
inadequacy of the LST relation. The final example of the
deviation of IR results from prism methods concerning
PbMg.33Nb.67O3 where IR data give 2.49 共Karamyan, 1976兲
and prism method results in a value of n ⬁ ⫽2.422 共Kamzina,
1974兲. Here the results may be within experimental error
since the errors were not given.
3.2. Comparison of Dispersion Values
An independent method of checking accuracy is to compare dispersion constants A with values from like compounds and from trends in structural families. The value of A
is perhaps as sensitive a test for accuracy as estimated errors
in n. Table 3 shows a number of examples of inconsistencies
in A. Some examples of like-compound discrepancies are
Cs2 SiF6 , Cs2 GeF6 , Y2 O3, SiO2 , TiO2 , ThO2 , BaMgF4 ,
Zn2 SiO4 , Mn2 SiO4 , Y3 Ga5 O12 , Ca3 Al2 Si3 O12 , CaTiSiO5 ,
YVO4 , CaMoO4 , PbWO4 , and KAl共SO4 ) 2 •12 H2 O. Examples of deviations from structural family trends are
Na2 GeF6 in the M2 GeF6 family (M⫽Na,Rb,Cs兲, Y3 Ga5 O12
in the M3 Ga5 O12 garnet family 共M⫽Y,Nd,Dy,Ho,Tm兲,
Ba.75Sr.25Nb2 O6
in
the
Ba1⫺x Srx Nb2 O6
family,
Tl2 Ni共SO4 ) 2 •6 H2 O in the Tl2 M共SO4 ) 2 •6 H2 O family
共M⫽Fe,Co,Cu,Ni兲, and KAl共SO4 ) 2 •12 H2 O in the alum
family MAl共SO4 ) 2 •12 H2 O 共M⫽K, Rb兲. The samples which
show values differing substantially from the values in like
compounds and values shown in family trends have been
marked in Table 1 with a question mark following the accuracy index, as defined in Table 1.
In the example of Y2 O3 , the value of A⫽75⫻10⫺16 m2 is
consistent with accurate RE2 O3 values from Sc2 O3 (66
⫻10⫺16 m2 ), Lu2 O3 (66⫻10⫺16 m2 ), Yb2 O3 (68– 69
⫻10⫺16 m2 ), and Dy2 O3 (73⫻10⫺16 m2 ). The measurements for the outliers Y2 O3 of 125, 62, and 53⫻10⫺16 m2
probably resulted from systematic errors that influence A
more than n ⬁ . The dispersion parameter A for Y.95Tm.05VO4
of 164⫻10⫺16 m2 关Ohta et al. 共1993兲兴 seems high in light of
the values of 109 and 102⫻10⫺16 m2 for YVO4 关Kuwano
and Saito 共1990兲; Medenbach and Shannon 共1997兲兴 and 98
⫻10⫺16 m2 for Y.98Nd.02VO4 关Lonheim and DeShazer
共1978兲兴. Similarly, the dispersion value for Ba.75Sr.25Nb2 O6
of 79⫻10⫺16 m2 seems inconsistently lower than the values
of 102– 93⫻10⫺16 m2 observed for other members of the
family Ba1⫺x Srx Nb2 O6 . The value 79 was derived from only
two values of n at 633 and 1050 nm 关Venturini et al. 共1968兲兴;
the value at 1050 nm is perhaps out of range of validity for
the Sellmeier equation. Dispersion from eight samples of tiJ. Phys. Chem. Ref. Data, Vol. 31, No. 4, 2002
SHANNON ET AL.
962
TABLE 6. Dispersion parameters for oxides and fluorides p 6
Compound
4⫹
Ti
3p
6
TiO2
TiO2
TiO2
Li2 Ti3 O7
CaTiO3
SrTiO3
BaTiO3
Ba.77Ca.23TiO3
PbTiO3
MTiOPO4
MTiOAsO4
CaTiSiO5
Pb1 – x Lax Zr1 – y Tiy O3
Ba2 TiSi2 O8
V5⫹ 3p 6
V2 O5
YVO4
NaCa2 Mg2 V3 O12
Sr5 V3 O12F
Ca3 V2 O8
GdVO4
Cr6⫹ 3p 6
M2 Mg共CrO4 兲2 •6 H2O
MgCrO4 •7 H2O
Nb5⫹ 4p 6
Cs8 Nb22O59
KNbO3
MNbB2 O6
KTa.66Nb.33O3
K3 Li2 Nb5 O15
Ba6 Ti2 Nb8 O30
Pb2 KNb5 O15
Ba2 NaNb5 O15
Sr4.25Na1.25Li.25Nb10O30
Ba1-x Srx Nb2 O6
LiNbO3
Sr2 Nb2 O7
Ba3 LaNb3 O12
LaNbO4
Mo6⫹ 4p 6
Ta5⫹ 5p 6
W6⫹ 5p 6
Ba2⫹ 5p 6
PbMoO4
Bi2 Mo3 O12
Ce2 Mo3 O12
Gd2 Mo3 O12
Tb2 Mo3 O12
CdMoO4
Li2.86Gd.57MoO4
SrMoO4
CaMoO4
Mineral
rutile
anatase
brookite
M⫽K,Rb
M⫽K,Rb,Cs
fresnoite
M⫽Rb,Cs
M⫽K,Rb
wulfenite
KTaO3
LiTa1-x Nbx O3
Ba3 LaTa3 O12
PbWO4
CaWO4
SrWO4
BaWO4
ZnWO4
BaO
BaBe2 Si2 O7
BaAl2 Si2 O8
Ba2 MgGe2 O7
stolzite
barylite
paracelsian
Atom
具A典b
具Eo 典c
共%兲a
10⫺16 m2
共eV兲
具Ed 典c
c
共eV兲
Why low 具 A 典 ?
Ba
33
33
33
25
20
20
20
20
40
12
12
12
20–16
8
119–111
119–114
107
122
120
131–115
110–109
115
112
133–128
131–122
120–104
102–93
71
5.1–5.2
5.4–5.5
5.5
5.9
5.7
5.5–5.8
5.9
5.8
5.1
7.6
7.3–7.5
7.4–7.7
5.5–6.1
10.5
26.3–27.4
24.8 –25.5
27.3
22.1
23.4
22.3–24.0
24.7–24.9
23.9
28.1
15.8–16.5
16.4–17.9
18.1–20.1
27.6 –29.9
21.3
28
17
15
14
15
16
264
109–95
119–115
118
114
113–109
4.1
5.7–7.5
7.3–7.4
7.8
7.7
6.8–7.0
14.7
20.9–22.5
18.3–18.7
17.4
18.2
20.7–21.1
42
61
227–244
209
6.6–6.8
7.7
9.9–10.4
9.9
24
20
10
20
25
21
30
43
21
22
20
18
31
17
124
109–106
127–117
107
118
102
101
98
101
110–93
91–88
88
79
69
6.1
6.3–6.4
7.9–8.2
6.3
6.2
6.3
6.1
6.5
6.4
6.1–6.6
6.9–7.0
7.5
7.6
8.4
21.1
23.3–23.4
16.0–16.7
23.9
22.1
24.7
26.1
25.0
24.8
23.7–25.9
25.7–26.1
24.3
26.9
27.6
Li
Sr
Ba
La
17
42
42
42
42
33
12
16
16
132–117
160–139
105
104–101
103
98
95
91–88
91–88
5.6–5.9
5.4–5.5
7.3
8.2–8.3
8.2
6.8
7.5
8.4–8.5
8.0–8.2
21.7–22.3
21.1
20.8
18.8 –19.1
19.0
23.9
22.3
20.8 –21.2
22.0–22.3
Sr
Ca
20
20
16
107
81–79
73
6.5
7.5–7.6
8.3
23.2
26.4 –26.6
26.6
Li
Ba
33
17
17
33
33
104
73–74
74
76
82
6.6
9.2
9.6
9.6
7.3
23.5
23.4 –23.6
22.6
21.9
26.6
50
8
8
17
116
96
87
84
7.2
9.6
11.3
10.1
19.2
17.2
16.3
18.9
Sr
Ba
Ba
Ba
963
TABLE 6. Dispersion parameters for oxides and fluorides p 6 —Continued
Compound
Mineral
BaO
SrO
CaO
MgO
U6⫹ 6p 6
Cu共UO2 PO4兲2 . 8 H2O
K2 UO2 共SO4 兲2 •2 H2O
Ca共UO2 兲共UOOH兲SiO4 共SiO3 OH兲•4 H2O
metatorbernite
beta-uranophane
Atom
共%兲a
具A典b
10 ⫺16 m2
具 E o典 c
具 E d典 c
50
50
50
50
116
95
80
64
7.2
8.5
9.4
11.3
19.2
19.9
21.2
22.0
40
18
33
121
114
66
9.2
10.4
11.8
14.3
13.5
20.6
共eV兲
共eV兲
Why low 具 A 典 ?
c
a
b
tanite with a nominal composition CaTiSiO5 showed an unusually large variation with values ranging from 73 to 120
⫻10⫺16 m2 . This is perhaps not surprising in light of the
presence of twinning in most samples and a variation in
composition with analyzed compositions ranging from
Ca.75Ti1.05Si1.07O5 to Ca1.0Ti0.98Mn0.05Si0.99O5 关Hintze
共1897兲兴. However, we have judged the values of 73 and 91 in
CaTiSiO5 from Eisbruckalp in Pfunders, Tirol and Glimmerschiefer in St. Gotthard to be lower than expected for titanites.
Although many of the outliers, such as Cs2 SiF6 ,
Cs2 GeF6 , RbH2 PO4 , Mn2 SiO4 , PbWO4 , Gd3 Sc2 Al3 O12 ,
and CaTiSiO5 have lower reported accuracies, others were
reported
to
have
good
accuracy,
i.e.,
␦n
⫽⫾0.0001– 0.0005. Although the dispersion value for
CaTiO3 (127⫻10⫺16 m2 ) quoted from Driscoll and Vaughn7
共Table 1兲 is consistent with the values of A from SrTiO3 and
BaTiO3 , the values of n ⬁ of 1.5554 and 1.3304 are far too
low. The value of n ⬁ of 2.261 obtained using the Chaulnes
method by Linz and Herrington 共1958兲 is more reasonable,
suggesting either a calculation error or that the value obtained by Driscoll and Vaughn7 was from a compound other
than CaTiO3 .
3.3. Analysis of Dispersion Values
Dispersion values A range from ⬃40 to 260⫻10⫺16 m2 .
Their distribution is shown in Fig. 1. The largest number of
values is centered around 60⫻10⫺16 m2 with a second distribution centered around 90– 100⫻10⫺16 m2 and much
smaller numbers distributed over the range 140– 250
⫻10⫺16 m2 . For convenience we arbitrarily call the range
from 50 to 80 ‘‘normal dispersion,’’ and 80 to 250 ‘‘high
dispersion.’’ In this section we make an effort to rationalize
the high dispersion values A. As a framework for the analysis of dispersion parameters, we use the analysis of Wemple
and DiDomenico 共1971兲 and Wemple 共1977兲. In this scheme
A is proportional to 1/E oE d , where E o⫽the average single
oscillator energy and E d⫽the oscillator strength which measures the average strength of interband optical transitions.
According to DiDomenico and Wemple 共1971兲, E d is related
to physical parameters by the expression
E d⫽ ␤ N cZ aN e ,
共4兲
where N c is the cation coordination number, Z a is the formal
valence of the anion, N e is the effective number of valence
electrons/anion, ␤ ⫽0.26 for ionic compounds, and ␤ ⫽0.37
for covalent compounds. Using this scheme high dispersion
values should result for compounds with:
共1兲
共2兲
共3兲
共4兲
共5兲
low energy gaps,
ionic character,
cations having low N c ,
fluoride rather than oxide anions; and
cations with low N e .
DiDomenico and Wemple 共1969兲 and Wemple 共1977兲 concentrated primarily on optical dielectric constants 共refractive
indices兲 and their relationships to the above variables but
they were not concerned specifically with dispersion, although DiDomenico and Wemple 共1969兲 noted that the refractive index dispersion is approximately inversely related
to the average single oscillator Sellmeier gap E o . In this
section we focus primarily on the dispersion A and the relationship to chemical composition and electron configuration
of the atoms involved and find that many of the trends in A
can be explained by the above five factors. Wemple and DiDomenico 共1971兲 and Wemple 共1977兲 showed that low values of E o are associated with the d 10 cations Cu⫹ and Ag⫹ ,
and the s 2 cations As3⫹ , Te4⫹ , I5⫹ , Tl⫹ , Pb2⫹ , and Bi3⫹ .
Figures 2 and 3 show plots of A vs E o and A vs
E d ,respectively. The plot of A vs E o shows a better fit to
1/E o than 1/E d which we interpret to mean that variations in
E o are more important in explaining dispersion than variations in E d . We shall analyze this assumption in Secs. 3.3.1–
3.3.5. A survey of the dispersion parameters of the compounds in Table 1 shows high dispersion values A associated
with certain ions which we call ‘‘soft’’ ions, i.e., s 2 , p 6 , d 10
and transition metal ions, H2 O, and crystalline hydrates. In
Tables 4 – 8 we have listed the dispersion parameters A, E o ,
and E d of compounds containing s 2 , p 6 , d 10, and transition
metal ions. Normal values of dispersion (A⫽50– 80
⫻10⫺16 m2兲 were found in borates, aluminates, gallates, silicates, germanates, phosphates, and sulfates not containing
SHANNON ET AL.
964
TABLE 7. Dispersion parameters for oxides and fluorides s 2
Atom
具A典b
⫺16
具 E o典 c
具 E d典 c
Why low
共eV兲
共eV兲
具A典?
Mineral
共%兲
As2 O3
arsenolite
40
105
8.9
17.3
Sb3⫹ 5s 2
Sb2 O3
Na2 SbF5
senarmontite
40
12
116
142
6.8
10.2
20.3
11
Te4⫹ 5s 2
TeO2
33
108-103
6.2–6.3
23.0–24.6
I5⫹ 5s 2
HIO3
MIO3
KIO2 F2
25
20
17
111
126–95
104
7.6
7.9–8.8
10.2
19.0
16.0–19.3
15.1
50
43
28
33
20
148
121
109
100
84
5.6
7.2
8.0
9.9
10.0
19.4
18.5
18.5
16.2
19.0
33
26
33
13
38
37
40
44
38
33
33
33
40
31
30
33
23
24
17
12
17
8
132–117
132–125
139
127
126–121
121
112–92
111
107–106
114–125
106
104
102–94
97
101
101–91
96–94
96
93
80
79
62
5.6–5.9
6.3
5.2
8.6
5.6–5.7
6.2
5.1
6.2
6.8
8.0–8.4
7.0
6.5–7.2
5.5–6.0
6.3
6.1
5.7–6.0
8.0
7.6–7.5
8.7
9.7
9.1–9.2
10.0
21.7–22.3
19.8 –20.2
22.1
14.6
22.5–23.1
21.5
28.1
23.2
21.9–22.1
15.9–16.7
21.5
23.5–25.9
27.6 –29.9
26.2
26.1
27.8 –29.3
20.9–21.1
22.2–22.4
19.6
20.5
22.0–22.2
26.0
40
29
35
36
21
10
138
139,160
120
126–115
109–96
93
4.8
5.5, 5.4
5.8
5.2–5.4
6.9–7.6
8.7
23.9
21.1, 18.6
22.9
24.2–25.8
20.8 –22.5
19.6
Compound
3⫹
As
4s
2
Tl⫹ 6s 2
TlCl
Tl2 SeO4
Tl2 SO4
TlClO4
Tl2 Cd2 共SO4 兲3
Pb2⫹ 6s 2
PbMoO4
Pb5 Ge3 O11
Pb2 Sc.5Ta1.5O6.5
Pb3 Al2 CaSi10O27•3 H2O
Pb5 V2.5As.3O12Cl
Pb2 MoO5
PbTiO3
Pb5 As3 O9 Cl
Pb5 As3 O12Cl
PbF2
PbFCl
PbWO4
Pb1-x Lax Ti1-y Zry O3
PbNb4 O11
Pb2 KNb5 O15
PbM.33Nb.67O3
Pb3 P2 O8
Pb5 P3 O12Cl
PbHPO4
Pb9 Mg9 Si9 O24共OH兲24
PbSO4
PbB4 O7
Bi3⫹ 6s 2
Bi2 O3
Bi2 Mo3 O12
Bi6 Mo2 O15
Bi12MO20
Bi4 M3 O12
BiB3 O6
M⫽Li,K
wulfenite
wickenburgite
vanadinite
finnemanite
mimetite
matlockite
stolzite
M⫽Mg,Zn
pyromorphite
molybdophyllite
M⫽Si,Ge,Ti
M⫽Si,Ge
a
10
m
2
Mg, Si
SO4
c
a
b
any of the above ‘‘soft’’ ions. It appears that A depends on
the total concentration of ‘‘soft’’ ions where these ions must
be in concentrations ⬎10% – 15%. This number seems to
depend on the ion, being lower for Fe3⫹ , Co2⫹ , Ti4⫹ , and
Bi3⫹ , and higher for Zn2⫹ , Nb5⫹ , Ta5⫹ , Tl⫹ , and Pb2⫹ . In
Tables 4 –9 values of 具 A 典 in boldface type are relatively
high, whereas boldface values of 具 E o典 and 具 E d典 are relatively
low.
3.3.1. Transition Metal Ions
Table 4 shows that many of the compounds containing the
transition metal ions Fe3⫹ , Co2⫹ , Ni2⫹ , Eu2⫹ , and U4⫹
with A⫽150– 265 have some of the highest dispersion values of all oxides. Fe2 O3 共hematite兲, FeOOH 共lepidocrocite兲,
and Fe2 (SO4 ) 3 all have dispersion values greater than 200
⫻10⫺16 m2 . The high dispersion values in transition metal
965
TABLE 8. Dispersion parameters for H2 O and crystalline hydrates
Atom
Compound
Mineral
共%兲
a
具A典b
⫺16
10
2
m
具 E o典 c
具 E d典 c
Why low
共eV兲
共eV兲
具A典?
H2 O 共liquid兲
H2 O 共ice兲
H2 O 共ice兲
100
100
100
225
152
146
9.8
12.3
12.6
7.2
8.5
8.7
Na2 HPO4 •12 H2O
Na2 HPO4 . 7 H2O
Na4 P2 O7 •10 H2O
NaH2 PO4 •H2O
NaH2 PO4 •2 H2O
63
50
43
14
25
119
105
101
99
96
11.4
12.0
12.1
11.9
12.3
11.7
12.7
13.1
13.6
13.5
MAl共SO4 兲2 •12 H2O
MGa共SO4 兲2 •12 H2O
MIn共SO4 兲2 •12 H2O
M⫽Na,K,Rb,Cs
M⫽K,Rb,Cs
M⫽Rb,Cs
60
60
60
101–91
91–92
96
12.3–12.6
12.5–12.6
12.2
12.8–13.8
13.9–14.0
13.6
MSiF6 •6 H2O
MSiF6 •6 H2O
M⫽Mg,Mn,Fe
M⫽Cu,Zn
43
43
97–101
89
13.8 –14.3
13.7–14.1
11.5–11.9
12.8–13.1
Cu6 Si6 O18•6 H2O
dioptase
17
94
10.0
17.1
MgSO4 •7 H2O
BeSO4 •4 H2O
CuSO4 •5 H2O
LiSO4 •H2O
CaSO4 •2 H2O
epsomite
54
33
45
14
25
96
95
85
72
70
12.5
12.4
12
13.9
13.3
13.4
13.6
15.7
15.9
17.1
43
90
12.6
14.1
M⫽K,Rb,Cs
M⫽K,Rb,Cs
M⫽K,Rb,Cs
M⫽K,Rb,Cs
31
31
31
31
31
84–89
82–85
79–82
79–82
81
12.3–12.5
12.9–13.1
12.8 –13.0
12.8 –12.9
12.8
14.6–15.3
14.5–15.1
15.1–15.7
15.1–15.8
15.4
borax
93
88
61
12.5
13.1
13.1
13.8
13.9
19.8
M ⫽ Sm,Pr,Nd
35
11
8
32
32
81–82
11.9–12.1
16.3–16.4
pollucite
afwillite
13
79
59
12.5
13.1
16.1
20.8
chalcanthite
gypsum
LiClO4 •3 H2O
M2 Cu共SO4 兲2 •6 H2O
M2 Mg共SO4 兲2 •6 H2O
M2 Zn共SO4 兲2 •6 H2O
M2 Fe共SO4 兲2 •6 H2O
Cs2 Mn共SO4 兲2 •6 H2O
Na2 B4 O5 共OH兲4 •8 H2O
KB5 O6 共OH兲4 •2 H2O
CaB3 O4 共OH兲3 •H2O
M2 共SO4 兲3 •8 H2O
CsAlSi2 O6 •2 H2O
Ca3 Si2 O6 共OH兲2 •2 H2O
colemanite
Li
Ca
Ca
low H2 O
Ca
c
a
b
oxides correlate well with values of the parameter
E o(4 – 8 eV) and, in general, low values of the parameter
E d . Even with relatively low concentrations 共10%兲 of Fe3⫹
rather high dispersion values result. Note that although there
is only 4 at % of Fe in MFe共SO4 ) 2 •12 H2 O and 8% in cornellite, Fe2 (SO4 ) 3 •7 H2 O, the total concentrations of ‘‘soft’’
ions (Fe3⫹ ) and H2 O are 54% and 37%, respectively. Similarly, in MCr共SO4 ) 2 •12 H2 O, both Cr3⫹ and H2 O contribute
to the dispersion. It is apparently not necessary for the ions
to be linked, e.g., compounds with isolated Fe3⫹ such as
Ca3 Fe2 Si3 O12 , Na.87Fe.92Al.05Ti.03Si2 O6 共aegirine兲, and
M2 CoSi2 O7 共M⫽Ca, Sr兲 have high dispersion 共A
⫽100– 175兲. Hydrates such as FeSO4 OH•2 H2 O and
MFe共SO4 ) 2 •2 H2 O 共M⫽K, Rb, Cs and Tl兲 have higher val-
ues of E o 共8 –10 eV兲 but because of low E d 共12–13 eV兲 as
for other hydrates 共see below兲 still show high dispersion.
3.3.2. d 10 Ions
Table 5 shows the dispersion parameters for compounds
containing Cu⫹ , Zn2⫹ , As5⫹ , and I7⫹ . Among the oxides
Cu2 O has one of the highest dispersions (A⫽267), apparently because of the exceptionally low energy gap of 3.8 eV.
Among the Zn-containing compounds only ZnO (A
⫽159– 185) and ZnWO4 (A⫽82– 86) have high dispersion.
ZnO has both low E o and E d (CN⫽IV), whereas ZnWO4
has low E o but a higher E d caused by CN⫽6 for both Zn and
W. Note that the high dispersion of ZnWO4 results from the
SHANNON ET AL.
966
TABLE 9. Dispersion parameters associated with ions. N c is the cation coordination number, N e the effective number of valence electrons per anion, and Z a the
formal valence of the anion
No. of
具A典a
具A典a
具 E o典
具 E o典 b
具 E d典
具 E d典 b
Ed
Ion
compounds
10⫺16 m2
10⫺16 m2
共eV兲
共eV兲
共eV兲
共eV兲
共eV兲
Beta
Nc
Ne
Za
d 10
Cu⫹
Zn2⫹
As5⫹
I7⫹
2
8
4
1
161–267
59–185
81–100
133
mean
214
91
93
133
range
4–6
6 –15
10–11
9
mean
5.0
9.7
10.8
8.8
range
16
15–26
15–20
mean
15.9
21.0
16.0
13.7
predicted
17
17
17
17
.26
.26
.26
.26
2
4
4
4
16
8
8
8
2
2
2
2
s2
As3⫹
Sb3⫹
Te4⫹
I5⫹
Tl⫹
Pb2⫹
Bi3⫹
1
2
2
4
5
26
9
105–111
95–142
103–119
95–126
84 –148
62–139
93–160
105
129
110
110
112
104
116
9
7–10
6
8 –10
6 –10
6 –10
5–9
8.8
8.5
6.2
8.5
8.1
6.9
6.2
11–20
23–25
15–19
15–16
16 –30
20–24
17.3
15.7
24.0
17.4
18.3
23.1
23.1
14
14
19
18
.26
.26
.26
.26
.26
.26
.26
3?
3?
4?
3?
⬃8
⬃8
⬃8
9?
9?
9?
8?
10?
10?
10?
2
2
2
2
2
2
2
Ti4⫹
V5⫹
Cr6⫹
Mo6⫹
W6⫹
Nb5⫹
Ta5⫹
U6⫹
Cs⫹
Ba2⫹
20
6
3 hydrates
8
5
15
3
3 hydrates
11
16
71–119
109–264
209–244
88 –160
73–104
69–124
73–107
5–10
4–8
7– 8
6–8
7–10
6–8
6–8
6.2
7.5
7.0
7.3
8.3
6.8
7.3
9.8
14.9
10.9
16 –30
15–22
10
19–24
22–27
21–26
23–26
13–14
14 –20
17–22
22.5
19.6
10.1
21.4
24.2
24.6
25.7
13.9
17.8
17.1
25
17
.26
.26
6
4
8
8
2
2
17,25
17,25
25
25
.26
.26
.26
.26
.26
4,6
4,6
6
6
8
8
8
8
2
2
2
2
58 –107
53–116
115
124
227
107
80
99
86
117
82
78
Fe3⫹
Cr3⫹
Co2⫹
Ni2⫹
U4⫹
Eu2⫹
12
4 hydrates
2
3 fluorides
1
1
114–225
95–105
117
71–198
264
162
159
98
117
115
264
162
4 –11
11–12
8
8 –14
5
6
6.4
11.8
7.6
11.7
4.2
6.5
17–20
14
12
10–16
17.0
13.9
11.8
14.1
14.5
15.1
19
.26
6
6
2
19
13
.26
.26
.26
.26
6
6
8
6
6
6
6
2
1
2
2
1
2
73
225
146–152
59–119
225
149
90.6
10–14
9.8
12.4
12.3
p6
d5
d3
d7
d8
f2
f7
H2 O
ice
hydrates
a
11–20
19
7.2
8.6
14.4
b
combined presence of Zn2⫹ and W6⫹ . All the other Zncontaining compounds have relatively high oscillator energies and therefore lower dispersion. Arsenates which might
be expected to have low dispersion because of their high E o
have relatively high dispersion resulting from tetrahedral
As5⫹ and low E d . KIO4 , the only example of an iodate, has
high dispersion (A⫽133) because of both low E o and
E d (CN⫽IV for I7⫹ 兲.
3.3.3. p 6 Ions
In Table 6 we list the dispersion parameters for titanates,
vanadates, chromates, niobates, tantalates, molybdates, and
tungstates. All titanium-bearing compounds with ⬎10% Ti
content have high dispersion, and are associated with E o values in the range of 5– 8 eV. Between 12% and 33% Ti there
is no obvious concentration dependence. Fresnoite,
Ba2 TiSi2 O8 , the one Ti compound with Ti⬍10% has normal
dispersion.
Similarly all vanadates have high dispersion values with
V2 O5 having one of the highest values (A⫽264) and one of
lowest values of E o⫽4.1 eV. Values of the vanadate parameter E o are similar to those of the titanates, being in the range
4 – 8 eV. Although chromate dispersions are augmented by
the presence of H2 O 共see below兲, we believe because of the
exceptionally high values of A, the primary contributor to
the high dispersion is the presence of the Cr6⫹ ion. Most
niobates and tantalates have high dispersion but the values
depend on the concentration with significantly lower dispersion for Ba3 LaNb3 O12 and LaNbO4 , where E o has increased
to 8.4 eV. Tantalates, because of slightly higher E o values,
have slightly lower dispersion than niobates, e.g., compare
LiNbO3 with A⫽91– 88 and LiTaO3 with A⫽81– 79. All
reported molybdates have high dispersion. Following the
same behavior as niobates and tantalates where the
compounds lower in the periodic table have lower
dispersion, the tungstates have slightly lower dispersion
than the molybdates. Among the uranyl compounds, meta-
torbernite 关 Cu共UO2 PO4 ) 2 •8 H2 O] and K2 UO2 (SO4 ) 2
•2 H2 O have high dispersion but this high dispersion may
arise partially from the presence of water of hydration.
␤-uranophane, Ca(UO2 )(UOOH)SiO4 )(SiO3 OH)•4 H2 O,
containing 4 H2 O has, however, normal dispersion.
Cs⫹ and Ba2⫹ compounds seem to be conditionally ‘‘soft’’
ions. A few Cs compounds such as CsB3 O5 , CsLiB6 O10 ,
CsAlSi2 O6 •x H2 O and Cs2 SeO4 , and Ba compounds such
as BaO, BaBe2 Si2 O7 , BaAlSi2 O8 , and Ba2 MgGe2 O7 have
moderately high dispersion.
3.3.4. s 2 Ions
Wemple 共1977兲 noted the reduced average energy gaps E o
for the s 2 ions Tl⫹ , Pb2⫹ , and Bi3⫹ . We note in Table 7 that
all the lone-pair cations lead to high dispersion. In general E o
values are low, varying from 5 to 9 eV. The highest dispersion is observed in TlCl, Na2 SbF5 , PbMoO4 , Pb5 Ge3 O11 ,
Pb2 Sc0.5Ta1.5O6.5 , Bi2 O3 , and Bi2 Mo3 O12 . As for other
compounds, the critical concentration of metal ion or combination of ‘‘soft’’ ions appears to be ⬃10%. Both
Tl2 Cd2 (SO4 ) 3 (A⫽84) and PbB4 O7 (A⫽62) with ⬃10%
metal ions have reduced dispersion.
3.3.5. H2 O and Hydrates
DiDomenico and Wemple 共1969兲 and Wemple 共1977兲
noted the low values of the parameter E d for both liquid H2 O
and ice 共9.5 and 8.6 eV, respectively兲. We find a slightly
lower value for liquid H2 O of 7.3 eV. Table 8 shows that
almost all hydrates have relatively low values of E d , generally in the range 12–16 eV. Exceptions are dioptase (Cu6 Si6 O18•6 H2 O), K 2 UO2 (SO4 ) 2 •2 H2 O, gypsum
(CaSO4 •2 H2 O), and afwillite 关 Ca3 Si2 O6 (OH) 2 •2 H2 O兴 .
The combination of moderate E o and low E d results in most
hydrates having relatively high dispersion.
3.3.6. Summary of Effect of Electron Configuration and E o and
E d on Dispersion
Table 9 summarizes the mean and maximum dispersion
parameters A, E o , and E d along with their range for H2 O,
hydrates and compounds containing the d 10 ions Cu⫹ , Zn2⫹ ,
As5⫹ , and I7⫹ , the s 2 ions As3⫹ , Sb3⫹ , Te4⫹ , I5⫹ , Tl⫹ ,
Pb2⫹ , and Bi3⫹ , the p 6 ions Ti4⫹ , V5⫹ , Cr6⫹ , Mo6⫹ ,
Nb5⫹ , and Ta5⫹ , and the transition metal ions, Fe3⫹ , Cr3⫹ ,
Co2⫹ , Ni2⫹ , U4⫹ , and Eu2⫹ . High dispersion (A
⫽⬃140– 250) is especially noticeable for H2 O and the ions
Cu⫹ , Zn2⫹ , I7⫹ , Sb3⫹ , V5⫹ , Cr6⫹ , Fe3⫹ , U4⫹ , and
Eu2⫹ and for the compounds having a high concentration of
H2 O and these ions: liquid H2 O, ice, CuCl, Cu2 O, ZnO,
KIO4 , Na2 SbF5 , V2 O5 , Fe2 O3 , FeOOH, Fe2 (SO4 ) 3 ,
FeSO4 OH, Y3 Fe5 O12 , UO2 , and ␤ -Eu2 SiO4 . In addition
compounds containing combinations of these ions and others
967
associated with slightly lower A values have high dispersion:
PbMoO4 , Pb2 MoO5 , Pb2 Sc0.5Ta1.5O6.5 , Pb5 V2.5As.3O12Cl,
Bi2 Mo3 O12 , and Bi6 Mo2 O15 .
As noted in Sec. 3.3, dispersion is controlled by the combined effects of E o and E d. It is apparent from Fig. 2 that the
low E o values associated with these ions go a long way toward explaining the high dispersion values of compounds
containing these ions. Note for example the low energy gaps
associated with compounds containing Cu⫹ , Te4⫹ , Bi3⫹ ,
Ti4⫹ , Fe3⫹ , U4⫹ , and Eu2⫹ .
However, it is clear that not only is low E o necessary for
high dispersion but also E d must be reasonably low. Although the plot of A versus E d shows a poorer fit to 1/E o
than 1/E d , the effects of E d can be clearly seen in many
cases. The effects of formal valence Z a can be seen in low E d
and the relatively high dispersion of CuCl, Na2 SbF5 , TlCl,
and NiF2 caused by lowered E d and the effects of cation
coordination can be observed in Cu2 O, ZnO, arsenates,
vanadates, iodates, molybdates, and the ions As3⫹ , Sb3⫹ ,
Te4⫹ , and I5⫹ . As we have shown above, all hydrates have a
relatively low E d . The effects of water of hydration are apparent in the high dispersion of FeSO4 OH•2 H2 O,
Fe2 (SO4 ) 3 •7 H2 O,
Cs2 Mg(CrO4 ) 2 •6 H2 O,
MgCrO4
•7 H2 O, Pb3 Al2 CaSi10O27•3 H2 O, and Cu(UO2 PO4 ) 2
•8 H2 O.
It is tempting to try to complement this rationalization of
high dispersion values by correlating observed and calculated values of E d with dispersion. Using the Wemple and
DiDomenico 共1971兲 scheme for calculating E d for single ion
compounds, it is not possible to calculate E d for most compounds in Table 1 because of uncertainty over what to use
for: 共1兲 covalency; 共2兲 N e for s 2 and certain d 10 compounds;
and 共3兲 cation coordination when there are two or more cations with differing N c , i.e., YVO4 , CaTiO3 , CaMoO4 ,
Y3 Fe5 O12 , and more complex compounds such as crystalline
hydrates. Indeed, Wemple and DiDomenico noted that the
scheelite compounds MMoO4 with M⫽Ca, Sr, and Pb did
not fit the scheme with ␤ ⫽0.27. On the other hand Wemple
found that ‘‘anion radical’’ groups such as phosphates, sulfates, selenates, and chlorates resulted in good agreement
between observed and calculated E d but that a good fit was
obtained for the iodates HIO3 and LiIO3 only by using ␤
⫽0.42– 0.44. We have compared E d values calculated using
5⫺
the properties of the anion groups such as BO3⫺
3 , BO4 ,
3⫺
3⫺
2⫺
2⫺
2⫺
2⫺
PO4 , VO4 , SO4 , SeO4 , MoO4 , and WO4 and
find that the counter ion almost always has an effect on E d .
These uncertainties added to those about N e and N c make it
difficult to rely on calculated E d values in the majority of
multiion compounds. Thus, we make only the very general
observation that the presence of H2 O, halide ions, and cations with low CNs such as Cu⫹ , Zn2⫹ , As3⫹ , As5⫹ , Sb3⫹ ,
Te4⫹ , I5⫹ , V5⫹ , and Mo6⫹ sometimes contribute to lower
E d and therefore higher dispersion.
SHANNON ET AL.
968
4. Acknowledgments
We gratefully acknowledge the use of the libraries at Universities in Bochum, Bremen, Mainz, and Boulder, Colorado
for the literature search. We are especially indebted to Th.
Armbruster, G. E. Jellison, and G. R. Rossman for critical
reviews of the manuscript, to H. Fluck of the Gmelin Institute in Frankfort for the use of their library, E. Tillmanns for
obtaining some of the earlier mineralogical references from
the University of Vienna and Dr. U. Kalepky for use of the
library of the Schott Glaswerke in Mainz. We are also grateful to H. Spetzler and J. Smyth for encouragement and support at CIRES/CU. We thank E. Eggers for the final formatting of the manuscript. Finally, one of us 共R.D.S.兲 is indebted
to the Humboldt Foundation for financial support.
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Ref. 2B:
Ref. 2C:
Ref. 2D:
Ref. 3:
Ref. 4:
Ref. 5:
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
6:
7:
8:
9:
10A:
10B:
10C:
10D:
Ref. 11A:
Ref. 11B:
Ref.
Ref.
Ref.
Ref.
969
12:
13:
14:
15:
7. Appendix 1. List of Codens
CHEMICAL ABSTRACTS SERVICE SOURCE INDEX
1907–1999 共CASSI6 1907–1999兲
A
ACELAZ Acta. Electronica
ACPHAA Ann. Chim. Phys.
AFSLAO Aufschluss
AJSCAP
Am. J. Science
AMMIAY Am. Mineral.
ANCHAM Anal. Chem.
APHYCC Appl. Phys. v1共1973兲–v25共1981兲
APOPAI
Appl. Opt.
APPLAB
Appl. Phys. Lett.
B
BJAPAJ
Br. J. Appl. Phys. 共1950–1969兲 see J. Phys. D.
C
CHSCBU Chin. Sci. Bull.
CIWPAV
Carnegie Institution of Washington Publication
CPLEEU
Chinese Phys. Lett.
CRTEDF
Cryst. Res. Technol. 共formerly Krist.
Tech. - KRTEAW 1966 –1980兲
F
FEROA8
Ferroelectrics
H
HAMBA6 Hamberger Beitr. Z. Angew. Mineralogie u.
Kristallphys.
I
IEJQA7
INOMAF
J
JACSAT
IEEE J. Quantum Electron.
Inorg. Mater. 共Eng. transl.兲
J. Am. Chem. Soc.
JACTAW
JAPIAU
JAPNDE
JCDTBI
J. Am. Ceram. Soc.
J. Appl. Phys. 共formerly Physics 1937–兲
Jpn. J. Appl. Phys., Part 1 共1982–兲
J. Chem. Soc., Dalton Trans.
JCOMEL
JCPSA6
JCRGAE
JJAPA5
JNOMFV
JOAOD6
JOBPDE
JOAOF8
JOPQAG
JOSAAH
JPCRBU
JPCSAW
JPSOAW
JRNBAG
JSSCBI
JSTCAM
J. Phys. Condens. Matter
J. Chem. Phys.
J. Cryst. Growth
Jpn. J. Appl. Phys. 共1962–1981兲
J. Nonlinear Opt. Phys. Mater.
J. Opt. Soc. Am. A 共1984 –兲
J. Opt. Soc. Am. B 共1989–兲
J. Optics A: Pure Appl. Opt.
J. Phys.
J. Opt. Soc. Am. 共1917–1983兲
J. Phys. Chem. Ref. Data
J. Phys. Chem. Solids
J. Phys. C
J. Res. Natl. Bur. Stds. 共1934 –兲
J. Solid State Chem.
J. Struct. Chem. 共Eng. transl. of Zh. Strukt.
Khim兲
J. Phys. Soc. Jpn.
JUPSUA
K
KRTEAW
M
MNLMBB
MRBUAC
N
NIMAER
NJGAAY
Krist. Tech. 共1966 –1980兲 now Cryst. Res.
Technol.
Min. Mag.
Mater. Res. Bull.
Nucl. Instrum. Methods A
Neues Jb. Mineral. Geol. Paläont. Beilageband
Abt. A.
970
NJGAAY
SHANNON ET AL.
Neues Jb. Geol. Paläont., Abh. Abt. A.
共1925–1950兲
NJGMA2 Neues Jb. Geol. Paläont., Monatsh. 共1950–兲
NJMIAK
Neues Jb. Mineral., Abh. 共1950–兲
NJMMAW Neues Jb. Mineral., Monatsh. 1950–
O
OMATET Opt. Mater. 共Amsterdam兲
OPACAT
Optica Acta.
OPCOB8
Opt. Commun.
OPLEDP
Opt. Lett.
OPSUA3
Opt. Spectrosc.
P
PAOAE1
Pure Appl. Optics
PHBCDQ Physica B and C
PHRVAO Phys. Rev. v1共1893兲–v132共1963兲
PKOMA3 Phys. Kondens. Mater. v1共1963兲–v16共1973兲
PLRBAQ Phys. Rev. B: Solid State 共1970–1978兲
PMABDJ Philos. Mag. B.
PPSAAM Proc. Phys. Soc. London, Sect. A.
PPSBAP
Proc. Phys. Soc. London, Sect. B.
PRBMDO Phys. Rev. B: Condens. Matter 共1978 –兲
PRVAAH Phys. Rev., Sect. A. v133共1964兲–v140共1965兲
PSISDG
SPIE Opt. Thin Films Applicat. 共1990兲
共Proc. SPIE兲
PSSABA
Phys. Status Solidi A 共1970–兲
PSSBBD
Phys. Status Solidi B 共1971–兲
R
REKEDA Rev. Laser Engineer. Jpn. 共Reza Kenkyu兲
S
SJOTBH
Sov. J. Opt. Tech. 共Eng. transl. of
Opt.-Mekh. Promysh.兲
SJQEAF
Sov. J. Quantum Electron.
SMPTA8
Schweiz. Mineral. Petrogr. Mitt.
SPHCA6
Sov. Phys. - Crystallogr. 共Eng. transl. of
Kristallogr.兲
SPHJAR
Sov. Phys. - JETP.
SPSSA7
Sov. Phys. - Solid State 共Eng. transl. - Fiz.
Tverd. Tela Leningrad兲
SSCOA4
Solid State Commun.
T
TTMMDZ Tschermaks Min. Petr. Mitt.
W
WLHPAR
Z
ZAPHAX
ZEKRDZ
ZEPYAA
ZMGPAS
ZPCBAL
ZPSBAX
Wuli Xuebao⫽Acta Physica Sinica 共Chinese兲
Z. Angewandte Physik
Z. Kristallogr.
Z. Phys. 共1920–1974兲
Zbl. Mineral. Geol. Paleont., Abt. A
Z. Phys. Chem., Abt. B
J. Appl. Spectrosc.⫽Zh. Prikladnoi Spektroskopy
8. Appendix 2. Alternative Forms of the
Sellmeier Equation
The general form of the Sellmeier equation is usually
given as
n 2 ⫽1⫹
兺j
A j␭2
␭ 2 ⫺␭ 2j
with the wavelength ␭ of the incident light, and the wavelengths ␭ j with the corresponding constants A j representing
the wavelengths of maximum absorption at several absorption bands. The refractive indices used in the current work
are sufficiently approximated using a one-term Sellmeier
equation with wavelengths ␭ far distant from the immediate
region of the absorption band at ␭ o , thus yielding
n 2 ⫽1⫹
A o␭ 2
␭ 2 ⫺␭ 2o
.
Rearranging this equation gives
␭ 2o
1
1
⫽⫺
2
2⫹
n ⫺1
A o␭
Ao
and finally
1
A
⫽⫺ 2 ⫹B
n ⫺1
␭
2
关Eq. 共3a兲兴 with A⫽ ␭ 2o /A o and B⫽ 1/A o or ␭ 2o ⫽A/B. The
constant A o is related to Eq. 共3b兲 by the expression E d
⫽A o•E o .

Refractive Index and Dispersion of Fluorides and Oxides

Transcrição

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