EXAFS studies of glassy and liquid ZnCl2: A comparison with vitreous GeO2

Journal of Non-Crystalline Solids 37 (1980) 273-284 © North-Holland Publishing Company

EXAFS STUDIES OF GLASSY AND LIQUID ZnCI2: A C O M P A R I S O N WITH V I T R E O U S GeO2 Joe W O N G General Electric Corporate Research and Development, Schenectady, N Y 12301, USA and F.W. L Y T L E The Boeing Company, Seattle, WA 98124, USA Received 16 March 1979 Revised manuscript received 27 August 1979

The Zn-EXAFS (extended X-ray absorption fine structure) above its K-absorption edge has been measured for glassy ZnCI2 at low temperature, through Tg (375 K), and into the supercooled and normal liquid state (mp = 593 K) at 673 K. By Fourier filtering and fitting the normalized glass spectra using c~-ZnCl2 as a model compound, the Zn2÷-CI - distance was determined to be (2.34 _+0.01) A and the average coordination number about the Zn 2+ was found to be 5.1 *- 0.8. The latter value agrees with the value of 4.7 nearest neighbors obtained by the molecular dynamics computer simulation study of Woodcock et al., for liquid ZnCI2 just above its melting point. The agreement is supportive of the notion that short-range order in the glass is reflective of that of the corresponding liquid from which it was quenched. Spectral measurement as a function of temperature indicates that there is considerable dynamic decoupling of the Zn 2÷ from its nearest C1- neighbor even below Tg. This is contrasted with similar data in glassy GeO 2 which show that the motion of Ge is strongly coupled with its four oxygen neighbors all the way to Tg. This difference in dynamic disorder substantiates the notion that glassy ZnC12, as well as vitreous BeF2, provides a further weakened structural analog for glassy GeO 2 and SiO2. 1. I n t r o d u c t i o n By analogy with b o t h silica and germania, BeF 2 has a c a t i o n / a n i o n radius ratio o f a b o u t 0.3, a value which G o l d s c h m i d t [1] postulated in 1926 will enable glass f o r m a t i o n in AB2-type c o m p o u n d s . With its ionic charges reduced by a factor o f two f r o m those o f SiO2, BeF2 may be considered as a " w e a k e n e d " structural analog o f SiO2. This view is strongly supported by crystallographic studies [2] ; the polym o r p h i s m o f the k n o w n crystalline forms o f BeF2 is closely related to that o f SiO2. All k n o w n p o l y m o r p h s o f b o t h c o m p o u n d s contain BeF4 (SiO4) tetrahedra [3] * * Except in stishovite, a dense form of crystalline silica prepared at 1200-1400°C and 100180 K bar, which has a rutile-like structure. 273

274

J. Wong, b: W. Lytle / EXAbS studies

joined at the corners so that each anion bridges two tetrahedra. The structural analogy may even be carried into the liquid state in which BeF~, like SiO2, exhibits high viscosities above its melting point [4] and can easily be supercooled in bulk quantities into the glassy state. Likewise, fluoroberyllates behave as weakened models of silicates, provided that the modifying cations have similar ionic radius and polarizability, and that the charge in the modifying cations in the fluoroberyllate is half of those in the silicate, e.g., NaF-BeF2 system as weakened model of the CaO-SiO2 system. Although much less discussed in the literature, ZnCI2 provides a more weakened structural analog for SiO2 [5,6]. This can be seen from the melting point (mp) and glass transition temperatures (Tg) for SiO2 [7], GeO2 [7], BeF2 [4] and ZnC12 [8] shown in table 1, since each transition temperature is a good measure of the cohesive energy of the crystal lattice and glassy solid respectively. The ability of liquid ZnC12 to supercool and vitrify to the glassy state is well known [9]. Crystallographic studies by Brehler [10] clearly established a tetrahedral coordination of C1- ions about the Zn 2+ in the crystalline state. Spectral measurements in the infrared and visible regions [5] as well as radial distribution study by X-ray diffraction [11] suggest that the four-fold coordination is predominant in glassy ZnC12. Furthermore, because of its low Tg and mp, ZnC12 provides a useful model experimental system for studying and understanding the physicochemical properties of AB2-type glass-former as a function of temperature from below Tg, into the supercooled and normal liquid states. From the EXAFS (extended X-ray absorption fine structure) point of view, the fine structure above the K-absorption edge of both Zn and Ge can readily be measured at Stanford Synchrotron Radiation Laboratory (SSRL) whereas Si and Be are too light and their Kedge EXAFS are masked by the Be windows [ 12]. Because of the high intensity of synchrotron radiation, the scan time for a normal EXAFS spectrum to 1000 eV above an absorption edge only ~ l h instead of a couple of weeks with a conventional X-ray tube or a day with a rotating anode source, the X-ray intensities of which are lowered by 3 to 4 orders of magnitude. This in turn

Table 1 Melting points and glass transition temperatures, Tg of "weakened" structural analogsof SiO2 a)

mp (K) Tg (K)

SiO2

GeO2

BeF2

ZnCI2

1993 1430 b)

1389 823 b)

828 589 b)

593 375 c)

a) For further discussion, see Wong and Angell, Glass: Structure by Spectroscopy (Marcel Dekker, New York, 1976) p. 66. b) Extrapolated from viscositydata [4,61. c) Determineddilatometrically [8].

J. I¢ong, F. W. Lytle / EXAFS studies A I--

I

[

I'

t

q

I

I

t

J

I

I

275

3.0 -

I--

z.8

Q~

~ a.e z

2.4 -

<

--->___ 2.0

-400 -200

200 400 600 800 I000 1200 ENERGY, eV

Fig. l. K-edge EXAFS of polycrystalline Zn at room temperature. The spectrum is plotted versus energy above the Zn K-absorption edge at 9658 eV. enables EXAFS measurements to be made as a function of temperature conveniently in a matter of a few hours. In an EXAFS event, the observation of interest is the modulation of the absorption coefficient, x(k), on the high side of the X-ray absorption edge of a constituent atom in the sample. An experimental spectrum for the case of Zn metal at room temperature is shown in fig. 1 in which absorption is plotted versus the energy above the Zn K-absorption edge at 9658.6 eV. The EXAFS is seen in the region 3 0 - 1 0 0 0 eV superimposed on the smoother photoelectric decay. Theoretically, x(k) may be expressed in the single scattering approximation [ 13-16] by x(k) =-

1 ~N/2ri exp(-2rj/X) tj(2k) e x p ( - 2 o ~ k 2) sin[2krj + 8/(k)]

(1)

where 1

k

h

[2m(E - Eo) t/2

is the final state wave vector of the ejected photoelectron, IV~ is the number of atoms in the ]th coordination shell, rj is the average radius of the jth shell, t/(2k) is the backscattering matrix element which depends only on the kind of backscattering atom and ~ is the mean free path of the electron before it is inelastically scattered into an incoherent state. The second exponential containing o~ is the relative mean squared deviation of the atoms at r/from the absorbing atom, and 6j(k) is a k-dependent phase shift containing contributions from both the absorbing and scattering atoms. The fluctuations may be static (structural disorder) or dynamic (thermal) in origin. In this form each coordination sphere contributes a sine-like term of period 2kr i. The resultant EXAFS is a summation over all the coordination shells within range of the effect.

J. Wong,F.W. Lytle / EXAFSstudies

276

Physically, EXAFS may be regarded as a mode of electron diffraction where the source of electrons is generated from within the particular atomic species participating in the absorption event. The wave function of the ejected photo-electron experiences an interference between its outgoing part of the backscattered part (by neighboring atoms) near the origin. The interference is constructive or destructive depending on the wave vector k of the photoelectron. This varies the dipole matrix element and, hence, the transition probability, producing the EXAFS. Qualitative structural information about the absorbing atom may be obtained by Fourier transforming ×(k) given in eq. (1) to yield a radial structure function ~b(r) [17,18] according to: 1

¢(r) = (2n)1/2 f x ( k ) exp(+2ikr) dk

_

1

(27r)1/2

~ ~ _ exp(-2rj/X) Tj(Zk) exp i ri°j

ri)~ 203

(2)

From eq. (2) it is seen that ~(r) consists of a series of gaussians centered at rj. The magnitude of each gaussian contains structural parameters rj and Nj, disorder parameter oj, and inelastic loss term exp(-2ri/~ ) and Tj(2k), the Fourier transform of the backscattering matrix element plus any other k-dependent residues. Because of this convolution of terms quantitative determination of structurally significant parameters from the Fourier transform alone is not straightforward. Since, experimentally, the EXAFS is measured within a finite k-range, the transform that is actually taken is 1

~ r ) - (2~,/2

kmax

f

W(k) knx(k) exp(Zikr) dk.

(3)

kmin

W(k) is a Harming window function [19] given by [t k - kmi n \7 _1 1 - cos 27r/ . . . . I/ 2 [_ \ k m a x - kmin]-] and is applied to the first and last 10% of the k-space data to smooth the finite transform, k n is a k-weighting term where n = 1 in the present analysis, and krnin and kmax are the lower and upper k-values of the EXAFS data. In this investigation, we evaluate the structural terms by comparison with similar data from the same elements in some known reference materials, i.e., crystalline t~-ZnClz and hexagonal GeO2 by Fourier filtering and least squares fitting that portion of the EXAFS function due to the first coordination sphere. Of interest are recent molecular dynamics results on liquid ZnC12 by Woodcock et al. [6]. The partial structure functions for Zn2+-CI -, C1--CI- and Zn2÷-Zn 2÷ at just above the melting point at 632 K (350°C) exhibit patterns similar to those calculated for liquid BeFz, but the width of the radial peaks are broader and the

J. Wong, F.W. Lytle / EXAFS studies

277

area under the nearest neighbor peak in the Zn2*-CI - partial function yields a coordination number of 4.7 rather than 4.0 found for BeF2 and SiO2. In fact, the coordination about Z n 2÷ ions shows a distribution ranging from 3 to 6 with predominant values of 4 and 5 at equal probability. The molecular dynamics result differs somewhat from the X-ray diffraction work of Imaoka et al. [11] who deduced a nearest neighbor coordination number of 4 for Zn in glassy ZnC12. Conceptually the local atomic environment in a glassy solid is expected to bear a close resemblance to that of the liquid from which it was quenched. In this study we shall examine this discrepancy with the EXAFS technique using a-ZnC12 as a model compound for which the coordination number of Zn 2÷ is known from crystallographic studies [ 10,20].

2. Experimental 2.1. Materials

Anhydrous ZnC12 was prepared by passing dry HC1 gas through molten Baker A.R. grade ZnC12 (99.5% purity) at 500°C for an hour. The melt temperature was then raised to 600°C and dry nitrogen was bubbled through the melt for about 15 min to drive off the dissolved HC1. The purification apparatus was totally contained in an atmosphere purged with dry N2. To prepare spectral samples of glassy films, a drop of the purified water-clear liquid was quickly transferred (by means of a dropper) and squeezed between two preheated BN windows (one of which was 1-1'' X ~ 3- in area in the middle). The whole assembly machined with a one-rail inset, -2 was quenched immediately in liquid N 2. Formation of glassy ZnC12 was indicated by sticking together of the BN windows (crystallized fdms do not hold the BN windows together). After sealing the edges of the BN windows with a high temperature tape, the spectral specimens were stored in a double dessicator for transport to Stanford Synchrotron Radiation Laboratory (SSRL). Effectiveness of the preparation and storage procedure was shown and monitored visually by the integrity of an identical vitreous ZnC12 film prepared between two microscope slides, sealed and stored in the same dessicator. a-ZnCl2 crystals were prepared by first quenching a tube or purified ZnCl2 melt in liquid N2 to the glassy state. The open end of the tube was flame-sealed immediately. The glass was then crystallized at 150°C in an oven overnight. This procedure always produced the a-form as identified by X-ray diffraction analysis. The tube was then opened in a dry box (<5 ppm H20) and pulverized. Spectral samples of a-ZnC12 were prepared by mulling the crystalline powder with silicone gases, heatsealed between a pair of 5 mil mylar windows and stored in a double dessicator. GeO2 glass was prepared by quenching the liquid obtained by fusing hex-GeO2. Both materials were checked for phase purity by X-ray diffraction. EXAFS samples were prepared by mulling the powder with SiO2 powder.

278

J. Wong, F.W. Lytle / EXAFS studies

EXAFS measurements were performed with a cryostat-furnace inserted into the EXAFS-I spectrometer at SSRL. The cryostat-furnace consisted of an evacuable, water-cooled metal shell with Kapton windows along the X-ray path. Inside the shell a BN insulated resistance furnace provided temperature control to 600°C. The BN cells containing the sample were attached to a stainless steel, liquid-nitrogencooled back. Details of the EXAFS spectrometer are described elsewhere [12]. The Zn EXAFS above 965 eV in glassy ZnCI2 prepared in the BN cell were measured systematically as a function of temperature from 120 K through its glass transition temperature at 375 K, to the supercooled and finally to above the melting point of crystalline ZnC12 measured in the range 100-473 K in order to study the effect of structural disorder on the observed EXAFS. Similar measurements above the Ge K-absorption edge at 11 103 eV were performed in glassy GeO2 from 128 K to just above its Tg (823 K) at 848 K. Hexagonal GeO2 which has a quartz structure, was also measured at 120 K.

3. Results and discussion

In fig. 2, the normalized xk versus k for ZnC12 glass at 120 K is plotted in the range k from 3.5-13 A -1. The data were Fourier transformed according to eq. (3) to yield a radial structure function ~b(r) shown in fig. 3 which is a plot of magnitude versus radial distance from the central Zn 2+ ion in A and is characterized by a predominant peak at the first coordination distance. The features below 1 A are spurious ripples due to background removal and termination errors in our finite k-range transform. Next we perform an inverse Fourier transform of ~ r ) [eq. (3)] over a range of r encompassing the peak corresponding to the first coordination shell. This

0.4 0.3

~. 0.2 ~ 0.1

~

_l I

I

I

I

I

I

I

5.0

I

ZnCl z GLASS, 120K

4.0

~ 3.0

~z.o/ ~ Z.S ~ 1.5 ~ 1.0 0.5

-0.1

-0.2

-03

I, 4

I l l l l / I

4.5

V

I

I

i

i

5

6

7

8

9

i I0

i II

I

12 13

K (l-q Fig. 2. Normalized ×k versus k plot for Zn in glassy ZnC12 at 120 K.

00

I Z 3 4

5

6

7

8

9

I0

r,(ll Fig. 3. Fourier transtbrm of normalized ×k data shown in fig. 2.

J. Wong, F.W. Lytle / EXAFS studies

279

procedure isolates the contribution to the EXAFS function arising from that shell and is a much more simple function than the original data. Considering a range of r from rl - Ar to rl + Ar encompassing the first shell the inverse transform yields rl+Ar

knxil (k) = (27r) 1/2 f

~b(r) e x p ( - 2 i k r ) d r ,

(4)

r 1 --At

where superscript i denotes inverse values. Also from eq. (1) kn ~l (k) = k n A l (k) sin [2krl + 61 (k) ].

(5)

The phase shift may be expressed parametrically in the form [2 1]. 81 (k) = b + ak + a'k 2 + 2a"/k a .

(6)

The amplitude function is N1 A I (k) = kr--21 Q(2k) exp(-2o~ k 2) exp(-2rl/~,) .

(7)

The parameters in eq. (7) were determined by fitting the theoretical EXAFS expression on the right hand side of eq. (5) to the function k n x t ( k ) derived in eq. (4) from the first shell inverse of the measured EXAFS data. The fitting was accomplished with an iterative least squares program in which eq. (5)was first expanded in a Taylor's series (first order terms only) about a set of assumed values of the parameters. The least squares condition was then applied to derive a corrected set of parameters to be used in a new trial function and so on until the parameter adjustments approached the desired small value (1% was used here). Using a-ZnCl2 at 100 K as a reference material of known N1 = 4 and rl = 2.34 A [10] the experi-

1000 F-- T 800 ! 600 L

400~ A

-'°°t

I_

- 8.00 -I000

~

300

L

1

500

~

ZOO

k(~l-h

I

|

9.00

i

I1.00

Fig. 4. Inverse transform o f the first coordination shell o f ZnCI 2 glass at 120 K, k a x ( k ) with the values calculated from the fitted parameters shown by the plotted points. The k a factor was used so that the full range o f the data would receive the same weight in the fitting program.

J. Wong, F.W. Lytle / EXAFS studies

280

Table 2 Summary of fitted structure parameters for ZnC12 and GeO2 glass File

T (K)

N1 a)

r l (A)a)

Ao21 (A2)

1 3 4 5 6 7 8 9

120 303 373 388 473 573 603 673 Av.

5.22 5.48 5.41 5.48 5.22 4.78 5.07 4.52 5.1 ± 0.8

2.344 2.332 2.347 2.347 2.344 2.365 2.346 2.340 2.346 ± 0.010

0.00172 0.00589 0.00493 0.00592 0.00685 0.00970 0.01025 0.00835

21 20 22 23

100 298 373 473 Av.

(4.00) 5.20 3.21 3.76 4.0 ± 0.8

(2.340) 2.353 2.345 2.336 2.344 ± 0.010

(0.000) 0.00476 0.00318 0.00495

Glassy GeO2

2 2 4 5 6

128 298 543 773 848 Av.

3.84 4.06 3.94 4.19 4.00 4.0 ± 0.8

1.740 1.740 1.739 1.728 1.742 1.737 -+0.010

-0.000616 0.000187 0.000222 0.000981 0.002896

Hex-GeO2 (Crystal)

1

120

Glassy ZnC12

c~-ZnCl2 (Crystal)

(4.00)

(1.749)

(0.000)

a) Nl and r 1 values in parentheses are crystallographic values. mental data was fitted empirically to evaluate the phase shift parameters (b, a, a', a") in the form given in eq. (6). These parameters and the envelope of EXAFS function were then used to fit each set of ZnCI2 glass data while simultaneously varying NI, e l , and rl. An example for the data of ZnC12 glass at 120 K is shown in fig. 4. This provides an absolute determination of NI and rl for each data set and a relative measure of Ol (compared with a-ZnC12 at 100 K). The results are summarized in table 2. First note the data for a-ZnC12 as a function of temperature. Here it is known that N~ = 4 and r~ = 2.34 A (we do not expect r~ to vary significantly in this range of temperature). These input values are enclosed in parenthesis for the reference data set in table 2. The measured deviation from these known values provided an estimate of error for N~ Of 0.8 and r~ of +-0.010 A and although the measured precision of the ZnC12 glass data set was less, we report the error as evaluated from the known structure ofa-ZnC12. Since o~ for a-ZnCl2 at 100 K was not known, the results are reported as relative values, Aa~ and do show an increase with temperature, as expected. The data for glassy ZnC12 as a function of temperature uniformly showed a high value in contrast with a value of 4 for N~ = 5.1 + 0.8 in agreement

J. Wong, F: W. Lytle I EXAFS studies

28 l

with the calculation of Woodcock et al. [6] who found N1 ---4.7 just above the melting point. These higher average coordination numbers are simply reflecttive of the liquidlike configurations which were frozen into the glassy state during the quenching process. Indeed there is a trend in the data to lower coordination as the temperature is increased from below Tg, at which rearrangement could begin to occur and finally, at the melting point where the lowest measured coordination Nl = 4.5 is found. The determined Zn-C1 distance was ri = 2.346-+ 0.010, within experimental error of a-ZnC12 and with no obvious trend with temperature. We also evaluate Nl in ZnC12 glass with an alternative method by plotting the In of the × ratio of the inverse amplitude function of the glass and crystal versus k 2 [18]. Since rl remains essentially the same for glass and crystal (table 3), from eq. (1) we have

×i(g) __xioU,(g) exp [-2o](g) k s]

,

(8)

xil(c) = XioNl (c) exp [ - 2 o ] ( c ) k s ] ,

(9)

where 1

)~o = kr--~lf(k, 7r) exp(-2ri/X) sin[2rlk + 6 ,(k)] , and g and c denote glass and crystal values respectively. Combining eqs. (8) and (9), we obtain 1 /xil(g)

n~xi~3)=

lnfNl(g)]

~S

- 2[o](g)

_

ks "

o](c)]

(10)

The inverse data for glassy and crystalline ZnC12 at 120 K are plotted versus k 2 in fig. 5. Least squares regression analysis of the data gives a linear best fit with intercept---0.185, slope = - 0 . 0 0 4 , and a standard derivation of-+0.053. From eq. (10), using Nl(c) = 4, we calculated Nl(g) = 4.8 -+ 0.5 and Ao 2 = (o~ - oc2) = 0.002 A 2.

~

O-

"~-0. 2 -0.4

o I

I

I

20

40

6o

I

o I

80 ioo k2 ( i - i )

I

i2o

14o

leO

Fig. 5. In (Xi glass/xi cryst) versus k 2 for ZnCI2 at 120 K. x i denotes inverse-transformed values consisting of contributions from only the nearest neighbor coordination shell. The straight line is a least squares fit of the data points.

J. Wong, EW. Lytle / EXAbS studies

282 0.012

O.OlO

0.008

.

.

.

.

.

I

oZnCI2 GLASS a ZnCI2 CRYSTAL Ge02 GLASS

'o o / / / f / ,

/

o

T.,

o ~

ooo4 0002

0 -O.OOe

,

To(GeO=

° ZnCi2)

~___.~._____.~_ , " , -,, ,, , " 200 300 400 500 600 700 TEMPERATURE(K)

"I.

, 800 900 i

Fig. 6. Relative disorder in glassy ZnCI 2 and GeO 2 as a function o f temperature. The Aal2 value for each material is calculated relative to that of the corresponding crystal model c o m p o u n d at low temperature. (See table 2.)

Both values are in good agreement with the fitted values given in table 2 for ZnC12 glass at 120 K. The relative disorder Ao~ is positive everywhere with respect to a-ZnCl2 and increases fairly uniformly with temperature. This is shown in fig. 6 along with the comparable data for GeO2 glass derived similarly from hexagonal GeO2 as a reference material. The most obvious characteristic of the relative change in disorder AOl2 with temperature, i.e., the dynamic response of the metal atom and its first coordination sphere, is the difference between ZnC12 glass and GeO2 glass. While both increase with temperature, the effect is much larger for ZnC12 glass. Note that Ao~ measures the relative mean squared displacement of the first shell neighbors from the absorbing atom. Therefore, the GeO4 tetrahedron is a rigidly bonded unit with little relative motion. Above Tg there is an indication of higher disorder perhaps due to rearrangement. A similar jump in Ao~ for As2Se3 was observed by Crozier et al. [22] near the melting point. If similar discontinuities are present for ZnC12 glass, they are masked by scatter of data points. Note that Ao 2 for a-ZnC12 is generally below that of ZnC12 glass while for GeO2 glass at 120 K AOl2 is less than that of GeO2 hexagonal. The data for GeO2 was of better quality than for ZnCl2 and is apparent on the narrower point scatter for N1 and Ao~. In GeO2 glass, in agreement with Sayers et al. [23], we find that N] = 4.0 + 0.8 and rl = (1.737 +

o.olo) h. 4. Concluding remarks For GeO2 it is clear from the dynamic data shown in fig. 6 that there is little change in the disorder below Tg, indicating that the G e - O bond is so strong and

J. Wong, F.W. Lytle / EXAFS studies

283

directional that a few hundred degrees change in temperature cannot cause excess vibrations. However, above Tg, the one-data point is significantly higher showing a change in the dynamical constraints of the system at the glass transition. The behavior of ZnC12 glass is somewhat different. There is a reduction of cation and anion valence to II and I respectively which leads to a lowering of cohesive energy in ZnC12 compared with GeO2. This in turn imparts a rather ionic character to the Zn-C1 bond and is evidenced by the fact that molten ZnC12 is a typical ionic liquid [24,25] like fused NaC1. Furthermore molecular dynamic calculations showed that there exists a distribution of Zn-CI distances in the nearest neighbor sheel with predominate coordinations of 4 and 5 at equal probability about the Zn 2÷. Such configurations in the liquid when frozen into the glassy state in the process of quenching will lead to the observed thermal disorder with increasing temperature even below Tg. Of interest is the value of 5.1 -+ 0.8 for the average coordination number for Zn 2÷ in the glass found in the present EXAFS study. This is significantly higher than the value of 4 determined by X-ray diffraction study [11]. We intend to further examine the coordination problem in ZnC12 glass independently with neutron diffraction. In conclusion, ZnC12 and GeO2 are useful model experimental systems wiht which to probe the local structure and nearest neighbor dynamics in both the glassy and liquid states.

Acknowledgements We are grateful for the experimental opportunity at Stanford Synchrotron Radiation Laboratory which is supported by NSF Grant No. DMR 73-0 7692, in cooperation with the Stanford Linear Accelerator Center and the Department of Energy. Critical comments on the manuscript by E.A. Stern are appreciated. FWL would like to acknowledge support from NSF Grants DMR 74-24261 and 77-12919.

References [1] V.M. Goldschmidt, Skrifter Norske Videnskaps-Akad, Oslo I Mat-Naturvid 8, (1926) 134. [2] R.W.G.Wychoff,Crystal Structures (Interscience, New York, 1960) p. 312. [3] S.M. Stishov and S.V. Popova, Geokhimiya 10 (1961) 837. [41 C.T. Moynihan and S. Cantor, J. Chem. Phys. 48 (1968) 115. [5] C.A. Angell and J. Wong, J. Chem. Phys. 53 (1970) 2053. [6] L.V. Woodcock,C.A. Angelland P. Cheeseman, J. Chem. Phys. 65 (1976) 1565. [71 E.H. Fontana and W.H. Plummer, Phys. Chem. Glasses 7 (1966) 139. [8] M. Goldstein and M. Nakoneczny, Phys. Chem. Glasses 6 (1965) 126. [9] C.A. Angell and D.M. Gruen, J. Phys. Chem. 70 (1966) 1601. [10] B. Brehler, Naturwiss 46 (1959) 554; Forschr. Min. 38 (1960) 187; Z. Krist 115 (1961) 373.

284 11] 12] 13] 14] 15] 16] 17] 18] 19] [20] [21] [22] [23] [24] [25]

J. Wong, F.W. Lytle / EXAFS studies M. Imaoka, Y. Konagaya and H. Hasegawa, J. Ceram. Soc. Jap. 79 (1971) 97. B.M. Kincaid, Ph D Thesis, Stanford University (1975). E.A. Stern, Phys. Rev. B10 (1975) 3027. D.A. Ashley and S. Doniach, Phys. Rev. B11 (1975) 1279. P.A. Lee and J.P. Pendry, Phys. Rev. B11 (1975) 2795. B.K. Teo and P.A. Lee, J. Am. Chem. Soc. 101 (1979) 2815. D.E. Sayers, E.A. Stern and F.W. Lytle, Phys. Rev. Lett. 27 (1971) 1204. E.A. Stern, D.E. Sayers and F.W. Lytle, Phys. Rev. B11 (1975) 4836. C. Bingham, M.D. Godfrey and J.W. Tukey, IEEE Trans. on Audio and Electroacoustics, Au-15(2) (1967) 58. J. Brynestad and H.L. Yakel, lnorg. Chem. 17 (1978) 1376. P.A. Lee, B.K. Teo and A.L. Simons, J. Am. Chem. Soc. 99 (1977) 3859. E.D. Crozier, F.W. Lytle, D.E. Sayers and E.A. Stern, Can. J. Chem. 55 (1977) 1968. D.E. Sayers and E.A. Stern and F.W. Lytle, Phys. Rev. Lett. 35 (1975) 584. F.R. Duke and R.A. Fleming, J. Electrochem. Soc. 104 (1957) 251. H. Bloom and I.A. Weeks, J. Chem. Soc. (1969) 2028.