Robert D. Shannon 1, James E. Dickinson z, and George R. Rossman 3. 1 Central Research, Experimental Station 356/329, E.I. Du Pont de Nemours, ...
Phys Chem Minerals (1992) 19:148-156
PIIYSlCS CHEMISIRY ([Mlli[Pa.,LS 9 Springer-Verlag1992
Dielectric Constants of Crystalline and Amorphous Spodumene, Anorthite and Diopside and the Oxide Additivity Rule Robert D. Shannon 1, James E. Dickinson z, and George R. Rossman 3 1 Central Research, Experimental Station 356/329, E.I. Du Pont de Nemours, Wilmington, DE 19880-0356, USA z Research, Development and Engineering Division, Coming Incorporated, Coming, NY 14831, USA 3 Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA Received October 2, 1991 / Accepted March 9, 1992
Abstract. The dielectric constants and dissipation factors of LiA1Si206, CaAI2SizO8 and CaMgSi206 in both the crystalline (e-spodumene, anorthite, and diopside) and amorphous forms were determined at I MHz using a two-terminal method and empirically determined edge corrections. The results are: spodumene tc'11 = 7.30 tan 6=0.0007 KTt22 = 8.463 tan 6 = 0.0002 ~:'33 = 11.12 tan 6=0.0007 anorthite ~c'a. = 5.47 tan 6 = 0.0009 ~:'b* = 8.76 tan 6=0.0010 ~'o. = 7.19 tan 6=0.0013 diopside ~:'11 = 9.69 tan 6=0.0016 •'22 = 7.31 tan 6=0.0007 X'as = 7.29 tan 6=0.00019
and Mg ions having normal bond valence sums, exhibits no abnormal deviation from additivity. Larger positive deviations in amorphous SiO2, LiA1Si206, CaAlzSizOs and CaMgSi:O6 are postulated to arise from a combination of loosely bonded cations and disordered O = ions where the oxygen dielectric polarizability increased from its normal value of 2.0 ~ 3 in well-behaved oxides to 2.2-3.0 A s in the amorphous phases.
Introduction
LiA1SizO6 amorphous
to'
= 8.07
tan ~-- 0.047
An approach used to systematize dielectric constant data for many decades involves the use of polarizabilities. The dielectric polarizability, So, is related to the measured dielectric constant by the Clausius-Mosotti Eq. :
CaA12SizO8 amorphous
~c'
= 7.50
tan 6=0.0024
eD = l/b[(Vm)0(- 1 ) / 0 ( + 2)]
CaMgSi206 amorphous
to'
= 8.89
tan 6=0.0021
The dielectric properties of a spodumene glass, progressively crystallized at different conditions, were also determined. As the crystallization temperature was increased from 720 to 920 ~ C, ~' increased from 6.22 to 6.44. The dissipation factor, tan 6, remained constant at 0.020. Similarly, as the crystallization time at 750 ~ C increased from 0.5 hr to 6.0 hr, ~:' increased from 6.28 to 6.35. The deviations of the measured dielectric polarizabilities as determined from the Clausius-Mosotti equation from those calculated from the sum of oxide polarizabilities according to eD(mineral, glass)= S eD(Oxides) are +7.4% for ~-spodumene, +1.2% for diopside, and +28.0, + 19.6 and + 15.9% for amorphous spodumene, anorthitie and diopside compositions, respectively. Positive deviations in e-spodumene and anorthite are consistent with lower than normal apparent cation bond valence sums and are believed to be evidence for loosely bonded ~ rattling" Li and Ca ions. Diopside, with Ca
(1)
where Vm is the molar volume in ~3, b is defined to be 4~/3, and ~', the real part of the complex dielectric constant, is measured in the range 1 K H z to 10 MHz (Roberts 1950, 1951). The dielectric polarizability includes both ionic, ~i, and electronic, ae, components. The electronic polarizability, ee, is related to the refractive index, n, by the Lorenz-Lorentz equation (Lorentz 1880; Lorenz 1880): c~e= 1/b[(Vm)(n 2 - 1)/(n z + 2)]
(2)
Although the Clausius-Mosotti (C-M) equation is strictly valid only for compounds where the molecule or ion has cubic symmetry (Szigeti 1949; Bosman and Havinga 1963; Dunmur 1972; Megaw 1975, and Roberts 1949, 1950, 1951), it has been shown to be approximately valid for a number of noncubic crystals by Roberts (1949, 1951) and Lasaga and Cygan (1982). The concept of additivitiy of molecular polarizabilities whereby the molecular polarizability of a complex compound A2BX4 can be broken up into the molecular polarizabilities of the simpler compounds AX and BX2
149
according to : aD(AzBX4) = 2 aD(AX) + ~o(BX2)
(3)
is useful in systematizing dielectric constant data and has been discussed by Roberts (1949, 1950, 1951), and Lasaga and Cygan (1982). It has recently been demonstrated that the oxide additivity rule is followed to _+0.51.5% in "well-behaved" crystalline oxides which includes a group of beryllates, borates, aluminates, silicates, germanates, phosphates and vanadates (Shannon 1991; Shannon and Subramanian 1989; Shannon et al. 1989, 1990, 1991 a, b, 1992a, b; Subramanian and Shannon 1989) but has not been evaluated for amorphous materials. Molecular polarizabilities of complex substances can also be broken up into ion polarizabilities according to : a(Az BX,0 = 2 a(a 2 +) + a(B 4 +) + 4 a(X =)
(4)
Ion polarizabilities are potentially more useful and easier to use for predictive purposes than simple oxide polarizabilities. Many sets of empirical electronic ion polarizabilities, ae, have been derived from the C-M equation and the additivity rule using the alkali halides and alkaline earth chalcogenides (see Coker 1976 and references therein) and using a variety of minerals (Lasaga and Cygan 1982). These polarizabilities were found to be useful in predicting refractive indices. A set of 18 dielectric ion polarizabilities, eD, derived from cubic compounds by Roberts (1949), assuming eD(O =) =2.387 ~3 was found to give agreement between observed and calculated polarizabilities of ,,~ 5%. A second set of 11 dielectric ion polarizabilities was derived for application to minerals by Lasaga and Cygan (1982), assuming aD(O =) = 2.37/~3. Using these ion polarizabilities agreement between observed and calculated total polarizabilities of 24 common minerals was ,-~ 10% with some individual deviations as large as 20%. Recently, a preliminary set of 16 dielectric ion polarizabilities was published using dielectric constants of 63 oxides and 4 fluorides (Shannon 1991). Along with these systematics there has been some indication that the electronic polarizability of oxygen depends on its molar volume (Tessman et al. 1953; Mahan 1980; Bussman et al. 1980; Fowler and Madden 1985; Kitsch et al. 1974, and Pearson et al. 1984). Because the molar volume per oxygen ion is greater in glasses than corresponding crytalline materials, it was of some interest to see how this larger oxygen molar volume would affect the total dielectric polarizability of glasses. The purpose of this paper is to accurately determine the 1 MHz dielectric constant of several silicate glasses and crystalline compounds of the same composition and to evaluate the validity of the oxide additivity rule in these glasses from simple oxide polarizabilities and by comparing them with crystalline compounds.
Experimental The sources of the crystals were: spodumene - clear, colorless crystal from Nuristan, Afghanistan; anorthite - dear, pale straw-col-
ored crystal from Great Sitka Island, the Aleutian Islands, Alaska (USNM 137041); chromian diopside - clear, green crystal from Russia. All glasses were prepared by ball milling 2000 g of the appropriate weights of purified quartz sand, oxides and carbonates, followed by melting for 12 h at 1650 ~ C in covered Pt crucibles. The spodumene, diopside and anorthite glasses were of stoichiometric compositions LiA1Si206, CaMgSi206 and CaA12SizOs, respectively. The ESC glass had the molar composition 74.2% SiO2, 12.4% A1203, 6.07% Li20, 2.89% MgO, 0.8% ZnO, 0.32% BaO, 2.11% TiO2, 0.95% ZrO2 and 0.25% As203. Melts were poured onto a steel plate, allowed to cool until "stiff" and then transferred to an annealer set at 650 ~ C. The annealer was shut off after 1 h and samples were allowed to cool to room temperature at "furnace rate". Heat treated samples were prepared by cutting ~ 2 x 2 x 2 cm blocks from the annealed glass and placing them directly into a box furnace set at the desired temperature. Samples were quenched after the appropriate elapsed time by removing them from the furnace and allowing them to cool in air. The degree of crystallinity of the partially crystallized ESC glass was estimated fi'om TEM photographs where crystalline areas were evidenced by raised "rosettes". Crystalline samples were oriented for cutting by polarized light and by back reflection Laue photographs. X-Ray diffraction patterns were obtained on a Guinier-type focussing camera using C u K e l radiation and a Si SRM 640 internal standard. Cell dimensions were obtained by least-squares refinement. Electron microprobe analyses were made using a JEOL 733 electron microprobe. Data reduction methods are described by Armstrong (1988). Although no systematic effort was made to obtain information on possible chemical zonation, significant color variations were not observed in any of the crystals. Microprobe analyses of points on individual crystals did not reveal any significant chemical heterogeneities. The compositions of anorthite and diopside were determined by microprobe analysis to be Ca.9 6Na.osAll.93Fe.o2Si2.o40 8 and Ca.97Na.ozMg.93Fe.03C r.o2Al.olSi206, respectively. Spodumene analyzed to Lix.ooA1.97Si2.o2Or, assuming the theoretical value for Li. Rectangular- or triangular-shaped samples were cut from the bulk crystals using a low-speed diamond wheel saw. Slabs of anorthite were cut perpendicular to a*, b* and c* ; slabs of diopside were cut perpendicular to a*, b*, c* and [ - 2 . 0 , - 1 ] ; slabs of spodumene were cut perpendicular to a*, b* [-2,0,2] and parallel to [010] but 42 ~ from a of spodumene. These cuts allowed us to obtain x'a~, lc'22, and x'33 for diopside and spodurnene. The anorthite crystal was not large enought to cut appropriate slabs to obtain values of X'l~, rc'22 and x'33. Glass sample thickness and area varied from 0.1 to 0.2 cm and 0.1 to 0.5 cm 2, respectively; crystal sample thickness and area varied from 0.05 to 0.10 cm and 0.1 to 0.7 cm 2, respectively. Sputtered gold electrodes were applied over the entire parallel surfaces of the sample using a Denton Vacuum Desk II sputtering unit. Sample preparation is described in detail in Subramanian et al. (1989). Dielectric constant measurements were performed over the frequency range 30 KHz-3 MHz with a parallel plate capacitance technique using a Hewlett-Packard 4275A LCR bridge and fixture 16034B (Test Tweezers) according to the procedure described by Subramanian et al. (1989). Edge corrections were made using the expression: C~ = (0.019 l n / P / t - 0.043)P
(3)
where t = sample thickness and P = perimeter in cm. The derivation and use of this expression are described in Subramanian et al. (1989). The overall accuracy of the dielectric constant measurements using the above techniques is estimated to be 1.0-1.5%. Dissipation factor (tan c5) errors are estimated to be 5-20% at levels of tan 6 = 0.002 and 50-100% at levels of 0.0004-0.0005. The dielectric constants determined for the 4 slabs of spodumene were: a* (8.142_.004); b* (8.463+.0002); [ - 2 0 1 ] 7.958__. .0005); 42 ~ to a (10.615+.02). Similarly, the dielectric constants determined for the 4 slabs of diopside were: a* (8.471 +.02); b*
150 (7.31_+.1); c* (7.664_+.06); [-20-1] (7.373_+.02). These values were used to obtain ~'11, ~c'a2, and ~'33 using the procedure described by Takubo (1941).
Results
Table I summarizes unit cell dimensions and molar volumes of the crystals and densities and molar volumes of the glasses studied here. Table 2A lists the dielectric constants and dissipation factors at 1 MHz of the crystals and glasses studied here. Arithmetic, rather than geometric, mean values of the dielectric constants are used. Geometric mean values are smaller by 0.0-0.2% for crystals with little anisotropy such as spodumene. The dielectric constants showed deviations of less than 0.2% over the range of frequencies 30 KHz to 3 MHz. In Table 2A, we also compare our data with previously reported dielectric data for spodumene, anorthite and diopside. The dielectric constants values of 8.30 and 7.8 determined by Olhoeft (1981) on spodumene crystals of unspecified orientation correlate reasonably well with x'a= 8.05, and ~c'b= 7.82 reported by Westphat and Sils (1972) and are in the same range as our values of ~c'a, (8.14) and ~c'b* (8.46). The value of 8.45 determined by Takubo et al. (1953) on powders corresponds well with the average value of 8.39 of Westphal and Sils (1972) but is lower than our mean value of 8.96. However, Takubo's values for quartz and diaspore are also low (Shannon et al. 1992b). The 300 MHz value of 7.25 reported by Church et al. (1988) for a sample of spodumene powder appears anomalously low, but may result from dispersion arising from Li mobility. The approximate mean dielectric constant of anorthite of 7.14 compares well with the results of Takubo (1953) (~7.2), Olhoeft (1981) (6.9), Bahat (1969) (7.37) and Hayashi and Fukui (1980) (7.5) but is higher than the value reported by Gdula (1971) (6.2).
The crystallized glasses have tc's similar to those reported for fi-spodumene glass-ceramics by Larssen (1963) and Kumar et al. (1983), but higher than the fispodumene glass-ceramics of unspecified composition reported by McMillan and Partridge (1972) and Okazaki (1988). There is very little change in x' as the crystallization time and temperature and, therefore, the relative amount of fl-spodumene in the glass-ceramic is increased. However, the maximum degree of crystallization of the ESC glass was only ~ 37%. The dielectric constant of amorphous LiA1Si206 (amLiA1Si206) is less than the mean value of ~c' for the crystalline samples whereas the dielectric constant of mnCaMgSi206 is significantly greater than that of its crystalline analogue. The dissipation factors of am-LiA18i206, am-CaA12Si208 and am-CaMgSi206 (tan 6 = 0.047, 0.0024 and 0.0021, respectively) are significantly higher than those of the crystalline materials (tan 6 = 0.0002-0.0007, 0.0009-0.0013, and 0.0007-0,0019, respectively). Table 4 compares the total molecular dielectric polarizabilities determined from the measured dielectric constants using the Clausius-Mosotti relationship (Eq. 2) and fi'om the oxide additivity rule using what we believe are the most accurate dielectric polarizabilities of Li20, MgO, CaO, A1203, Cr203 and Si02 listed in Table 3. In Table 4, we have also tabulated the indices of refraction which allow us to compare the optical dielectric constants and electronic polarizabilities of some of the crystalline phases with those of the amorphous phases. Differences in specific refractivities of the crystalline and amorphous phases were also noted by Young and Finn (1940) and Roberts (1949) for SiO~ and by Larsen (1909) for anorthite and diopside. The electronic polarizabilities of the amorphous phases are greater than those of the crystalline phases by 0.6-8.5%.
Table 1. Cell dimensions, densities and molar volumes
a, ,~, ~~ SiO2 e-quartz SiO2 amorphous LiA1Si206 c~-spondumene LiA1Si206 ]~-spodumene LiA1Si206 amorphous CaA12Si2Os anorthite CaAlzSizOs amorphous CaMgSi206 diopside CaMgSizO6 amorphous
4.9031
9.4653(7) 7.541(1)
8.1807(3) 93.199(4) 9.7499(6)
b, ~,/~o 4.9031
8.3920(7) 110.164(5) 7.541(1)
12.8767(3) 115.866(3) 8.9258(6) 105.858(6)
c, ~, y~
d, g/cc
Vm, ~3
5.3937
2.648
37.66
Young and Post 1962
2.20
45.33
Coming 7940
5.2202(3)
3.176
97.31
This work
9.156(2)
2.365
130.16
Li and Peacor (1968)
2.3877
129.37
This work
2.757
167.51
This work
2.6841
172.05
This work
3.277
109.94
This work
2.854
125.95
Larsen (1909)
14.1780(5) 9t. 202(3) 5.2543(4)
References
151 Table 2A. Summary of single-crystal and glass dielectric constants tC'a, tan 6 SiO2 ~-quartz SiO2 amorphous
K'r tan 6
Vrn, ~3
~D, ~3
Reference Osaka and Shindo (1984) Fontanella et al. (1974) Subramanian et al. (1989) Fontanella et al. (1974) Fang and Brower (1963) Fontanella et al. (1974)
Li20
8.06
24.51
4.11
MgO
9.830
18.69
3.331
CaO
11.95
27.83
5.22
A1203
10.126
42.45
7.627
Cr203
12.60
48.10
9.12
37.66
4.878
SiOz
4.559
in s p o d u m e n e m i g h t b e caused b y the " r a t t l i n g c a t i o n " effect (Orgel 1958). Tables 5 a n d 6 s h o w t h a t Li in spod u m e n e ( C a m e r o n et al. 1973) is c h a r a c t e r i z e d b y a b o n d valence sum, c a l c u l a t e d f r o m the B r o w n a n d A l t e r m a t t (1985) p a r a m e t e r s , t h a t is s o m e w h a t low, 0.82 valence
units (v.u.), c o m p a r e d to the t h e o r e t i c a l v a l u e o f 1.0 v.u. Thus, Li a p p e a r s to be l o o s e l y b o n d e d in its o c t a h e d r a l M 2 p y r o x e n e site ( P a p i k e 1987). T h e low. b o n d valence s u m m a y be c o r r e l a t e d w i t h the large m e a n t h e r m a l e x p a n s i o n coefficient o f the L i - O b o n d f o u n d in s p o d u m e n e b y C a m e r o n et al. (1973). T h e b o n d valence s u m a r o u n d A1 is n o r m a l (2.97 v.u.). Similary, Table 6 s h o w s the b o n d valence o f C a in a n o r t h i t e , Vca, is also low, 1.72 v.u. ( m e a n value f r o m 4 i n d e p e n d e n t C a a t o m s ) , relative to the t h e o r e t i c a l value o f 2.0 v.u. D e s p i t e the fact t h a t the m e a n v a l u e o f the a n o r t h i t e dielectric cons t a n t is o n l y a p p r o x i m a t e , it a p p e a r s t h a t there is a sign i f i c a n t d e v i a t i o n f r o m a d d i t i v i t y t h a t m a y be a c c o u n t e d for b y a l o o s e l y b o n d e d " r a t t l i n g " C a ion. By c o n t r a s t , the s m a l l e r d e v i a t i o n o f eo(calc) f r o m C~v(obs) in d i o p s i d e is c o n s i s t e n t w i t h n o r m a l b o n d valence sums, Vca a n d VMg, in d i o p s i d e o f 2.06 a n d 2.03 v.u., respectively. The polarizabilities of fl-spodumene ceramics cannot be strictly c o m p a r e d w i t h the p o l a r i z a b i l i t y o f fl-LiA1S i 2 0 6 because o f the presence o f a m o r p h o u s c o m p o nents a n d o t h e r crystalline p h a s e s such as b i n a r y L i sili-
Table 4. Comparison of observed and predicted single crystal dielectric polarizabilities Compound
SiO2 quartz
