ESR and optical absorption of Cu2+ in Na2OSiO2 glasses

ESR and optical absorption of Cu2+ in Na2OSiO2 glasses

Journal of Non-Crystalline Solids 33 (1979) 103-115 © North-Holland Publishing Company ESR AND OPTICAL ABSORPTION OF Cu 2÷ IN N a 2 0 - S i O 2 GLASS...

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Journal of Non-Crystalline Solids 33 (1979) 103-115 © North-Holland Publishing Company

ESR AND OPTICAL ABSORPTION OF Cu 2÷ IN N a 2 0 - S i O 2 GLASSES H. HOSONO, H. KAWAZOE and T. KANAZAWA

Department of Industrial Chemistry, Faculty of Technology, Tokyo Metropolitan University, Fukazawa, Setagaya-Ku, Tokyo 158 Japan Received 25 August 1978 Revised manuscript received 23 December 1978

ESR and optical absorption spectra of Cu2+ in xNa20-(100-x)SiO2 glasses were measured, where x ranges from 12 to70 mol% Na20. This glass system was divided into three composition regions, 12 ~~55). The distribution of the ESR parameters due to the fluctuation of ligand fields was neglig~le for HFS-2 compared with that for other glasses. The Cu~" ion responsible for HFS-2 was considered to distribute in the microphase of orthosilicate, lmagawa's basicity, the covalency of the bondings between Cu2÷ and ligands, was calculated by using Maki and McGarvey's analysis. The basicity of o-type symmetry remained constant, irrespective of the glass composition, and the value was identical with those for other oxyanionic glasses. The n-type basicity was also constant for the glasses ofx < 55. Two different basicities, each corresponding to HFS-1 or 2, were obtained for the glasses ofx >~55. The value derived from HFS-I was identical with those for x < 55 glasses, whereas that derived from HFS-2 suggested the formation of much more basic ligands.

1. Introduction Since Imagawa [1] suggested that Cu 2÷ is an excellent probe for the measurement of basicity of oxyanionic glasses, ESR and optical absorption of Cu 2÷ have been reported for many glass systems [2,3]. Recently, Sakka et al. [4] found that in sodium silicate glasses, the addition of Na20 up to 40 mol% makes no substantial change in the ligand field absorption energy of the Cu 2÷ ion, whereas further addition of Na20 results in an abrupt increase in the absorption energy. However, sufficient data have not yet been published concerning the ESR parameters of Cu 2÷ in the glasses, especially in ultra-high-alkali silicate glasses. This work has been undertaken to give a comprehensive view of ESR parameters and ligand field absorption energy of the Cu 2÷ ion. The correlation between the composition dependence of these parameters and the phase diagram of the system has also been examined. 103

104

H. Hosono et al. / ESR o f Cu 2+ in N a 2 0 - S i 0 2 glasses

2. Experimental Compositions of the glasses used in the present study were xNa20-(100-x)SiO: in tool%, where x ranged from 12 to 70. The starting materials were reagent-grade Na2CO3 and CuO and silica sand which was well washed with HC1 solution; 0.2 wt% of CuO was added to each batch. Most of the glass batches were fused in a P t 10%Rh crucible in an electric furnace under ordinary atmosphere. Platinum and alumina crucibles were used in the case of ultra-high soda composition (x ~> 60), because rhodium ion dissolved in the melt and its absorption interfered with that of Cu 2+ [5]. The melts were stirred in order to produce a homogeneous glass. The temperature and time of melting varied between 1200 and 1600°C and between 20 min and 18 h respectively, depending on the Na20 content. The glass-forming region of this system estimated by air-cooling of the melt ranged from 0 to 58 tool% Na20 [6]. The melts locating outside this region were poured onto a stainless steel plate and pressed quickly with another plate into a thin glass sheet (ca. 0.5 mm). The quenched glass was immediately immersed and stored in liquid paraffin to avoid moisture attack. The optical absorption spectra of Cu 2+ in glasses were recorded on a Shimadzu UV-200 spectrophotometer at room temperature. The glasses were crushed into pieces for ESR measurements. ESR spectra were recorded at 25°C on a JEOL JES-PE-3X spectrometer for X-band measurements and an ME-3X instrument for K-band. A magnetic field modulation of 100 kHz was applied. DPPH and Mn 2÷ in MgO were used as standards for the determination of the spin hamiltonian parameters.

3. Results 3.1. E S R

Figure 1 shows derivative x-band ESR spectra of Cu 2+. Two features are recognizable in the fgure. First, two-site structure is seen in the spectrum for the glasses of x >~ 55. Second, the g- and A-tensors of the Cu2+-complex in these glasses are in approximately axial symmetry. However, the line-shape of the hyperfine (hf) structure with perpendicular orientation seems to suggest the distortion of the Cu 2+complex from axial symmetry. To confirm this, the overlap between hf structures ofgll and g± had to be removed. The K-band spectra were measured and shown in fig. 2. As seen in the line profile of the hyperfine structure (hfs) of g±, an axial symmetry of the Cu2+-complex still held for ultra-high-alkali glasses. It is therefore natural to employ an axial spin hamiltonian in the analysis of the spectra, i.e. ~c =(3[zjlI, S~ ÷ zAH~Sx + HySy)] +AfroS, + A A & S x + ]ySy) .

(I)

H. Hosono et al. / ESR o f Cu 2+ in N a 2 0 - S i O 2 glasses

1F

/ONA20 30~i0' 1

60NA20 -

105

A

55N~:- A

4ssL~ L J

A. ~ -

/ 3400 MAGNETIC

FIELD(GAUSS)

Fig. 1. X-band ESR spectra of Cu 2+ in N a 2 0 - S i O 2 glasses. The intensity of the parallel hf shoulders is about 10 times larger than that of perpendicular peaks.

HFS- 1

F-~

70NA20-

I

8400

HFS-2

L

I

I

L

I

I

8500 8600 8700 MAGNETIC FIELD(GAUSS)

Fig. 2. K-band ESR spectrum for ultra-high-soda glasses (x = 70). Perpendicular hf peaks are shown.

1t. Hosono et al. / ESR o f Cu 2+ in N a 2 0 - S i O 2 glasses

106

Here, z has been taken as the symmetry axis of the individual Cu2+-complex. The symbols in eq. (1) have their usual meanings. The sets, each consisting of four peaks, are respectively designated as parallel and perpendicular hf peaks. The peak positions are related to the principal values of the g- and A-tensors by the solution of the hamiltonian (1). Namely, for the parallel and perpendicular hf peaks [7], hv = gllflH + mArl + ( ~ -

A~

(2a)

mS) 2grl3H '

hv = g±3H + reAl + ( ~ - m 2) A IT+ A~ 4gj_~H

(2b)

Here, H is the magnitude of the static magnetic field where the Cu2+-complex with the assigned orientation ([] or 1) resonates in an applied alternating field of frequency ~,, and m is the magnetic quantum number of the copper nucleus whose spin I is ~ for both 63Cu (natural abundance is 69%) and 6SCu(31%). The small difference (7%) between nuclear magnetic momenta of the two isotopes prevents a further split of the hf peaks. The gll and AIr were determined by eq. (2a) from the positions of the sharper peaks (those of m = -~ and -½). The results are shown in fig. 3. Two sets of data are given in the figure separately for the glasses of x -> 60, each corresponding to HFS-1 and HFS-2 (fig. 1). It may be noted that the dependence of [All] and gll on the glass composition gives three distinct composition regions, I, II

I

1

I

l

I

I

x

~( /

"' iS

2.35

//

180

x ,

t

160 "~

2.30

°

cr~

,-4

,,~ /'

/

•.~--x--x''Cx

140

2.25

I

10

20

I

I

I

30

40

50

I

60

70

NA20(MOL %) Fig. 3. Variation of gll (solid line) and IZlll (dashed line) with soda content. Two-site structure was recognized for the composition o f x > 60. These are designated HFS-1 and HFS-2.

H. Hosono et al. / ESR o f Cu 2+ in Na20-Si02 glasses

107

Table 1 Characteristics of ESR parameters of Cu2÷ in sodium silicate glasses. Region

Mol%ofNa20

gll

IAIII/10-4 cm-1

zX//(m)a)

I II II1

x < 37 37 ~
ca. 2.35 2.35-2.29 2.29 (HFS-1) 2.23 (HFS-2)

ca. 142 142-160 160 (HFS-1) 180 (HFS-2)

Increase in order of m Increase in order of m Increase in order of m Independent of rn

a) Linewidth of the parallel hfs peaks.

and III. The characteristics of ESR parameters in these regions are given in table 1. In region I, gll and IAnh are approximately constant irrespective of the Na20 content, whereas in region II they depend markedly on the glass composition. In region Ill, the ESR spectrum can be viewed as the supposition of the two absorptions with fairly different spin hamiltonian parameters. This is seen in the parallel hf peaks of the X-band (fig. 1) and the perpendicular hf peaks of the K-band spectrum (fig. 2). One type o f the spectra originates from the Cu2+-complex with higher gll and lower IA I1[. The linewidth o f the parallel hf peaks of this absorption increases in the order of m (HFS-1). Another is the absorption characterized by lower gll and higher IA II1. The width of the parallel hf peaks of this absorption was almost independent of m (HFS-2). The relative intensity of HFS-2 to HFS-1 increased with increasing Na20 content, but the values of the ESR parameters themselves for both absorptions remained constant in this region. 3.2. Optical absorption

The peak energy of ligand field absorption bands is shown in fig. 4. The results are similar to those obtained by Sakka et al. [4] for the glasses of x <~ 58. The dependence of the peak energy on the Na20 content was found to be similar to 800

I

I

I

L

l

I I

1.30

u Q

1.40

700

-~

1.50

>

1.60

6OO

I

L

i0 20 30

I

I

1

I

40 50 60

70

N a 2 0 (mol %)

Fig. 4. Variation of peak wavelength of optical absorption.

108

H. Hosono et aL / ESR of Cui+ in Na20- SiO 2 glasses

Table 2 Characteristics o f the optical absorption of Cu2÷ in sodium silicate glasses. Region

Na20 content

Energy of hma x (cm -1 )

I 1I Ili

x ~< 37 37 ~
12 800 12 800-15 200 15 200

that of gll and [Ale[ obtained from ESR spectra. Accordingly, three distinct composition regions similar to those based on the ESR spectra are found. The characteristics of the absorptions of Cu 2+ are summarized in table 2. The upper and lower limits of each region I, II, or III for the optical absorption agreed with those for ESR parameters. In region I, excitation energy was substantially constant (12 800 cm-1). In region II, the peak energy shifted conspicuously to shorter wavelengths, as the content of Na20 increased. In region III, ~,max was constant (ca. 15 200 cm-l).

4. Discussion 4.1. Microenvironmental fluctuation o f Cu 2+ ions in the glasses The linewidth of the parallel hf shoulders of the X-band spectra, except HFS-2, increased in the order of m. Imagawa [1] attributed this broadening to the microenvironmental fluctuation around a Cu 2÷ ion, which is intrinsic to the glassy state. The assumption was made in his analysis, i.e. in respect of the coefficient of the molecular orbitals the fluctuation of/32 is great, but that of a 2 is negligible small, where ~31 is the coefficient of dxy atomic orbital of Cu 2÷ in p-dn back-bonding and a is that of dxy in a-type back-bonding. This postulation was derived from the experimental facts that/31 depended strikingly on glass composition but a 2 did not [1,3]. The assumption leads to the relation:

(3)

gll - A IJP = C = constant,

where P(= 2a/3/3~r-3)) is also constant (0.036 cm-1). The structural distribution in glass causes fluctuation of the ligand field, and it in turn is reflected in the distribution of spin hamiltonian parameters. The fluctuation of gll and All (dgll and dall ) gives rise to that of the resonating field (dH) according to (4) which is derived from (2a): dtt =

~

[h ~

+ mAll \-Ai

gll

"

H. Hosono et al. / ESR o f Cu 2+ in Na20-SiO 2 glasses

109

Then the peak width AH(m) is related to the variation of g,; 6g,: AH(m) = ~g,

hv + m(gllP - au)

g~l~

m ~gtl(1200 + m

400)(gauss).

X

(5)

Here, v is about 9 GHz. The validity of the previous assumption was tested by examining the average value (~) and the standard deviation (ec) of C. = 2.742,

o c = 0.0156.

The variation of gll, ~gll, was determined from the slope of the curve in fig. 5 in which AH(m) is plotted against m. The 5gll thus obtained is about 0.02. The distribution of g-value is schematically represented in fig. 6a for metasilicate composition. On the other hand, application of eq. (5) to HFS-2 resulted in null distribution of gll- In other words, the Cu2+-complex responsible for HFS-2 is lacking the fluctuation of the ligand field, i.e. the structure of all the Cu2+-complexes of this type contained in the glasses of x >~ 55 are identical within the precision of this experiment. Fig. 6b shows schematically the distributions of g-values for both HFS-1 and HFS-2 observed in 70Na20-30SiO2 glass. The difference between the behaviors of HFS-1 and HFS-2 is clearly recognized. 4.2. Composition dependence o f ESR and optical absorption parameters in relation to the phase diagram

It may be noted that the boundary compositions between the two adjacent composition regions agreed well with the eutectic points in the phase diagram (fig. 7). However, the eutectic between SiO2 and sodium disilicate missed the corresponding

v 70 50 311 10 I

_~ 2

I

_i

I

--

+i 2

2

Fig. 5. Variation of llnewidth AH(m) of parallel hf shoulders as a function of magnetic quantum number (m) of Cu nuclei.

110

H. Hosono et al. / ESR o f Cu 2+ in N a 2 0 - S i O 2 glasses

(&)

2,0

]

I

2,1

2,2 VALUE

~j.

O~

2,3

dO/z

2,4

(b)

H S- 2 "% 2,0

2,1

3

2,2

2,3

] 2,4

VALUE

Fig. 6. Schematic representation of the distribution of g-value. (a) x = 50, (b) x = 70.

break-point in the responses of the Cu 2÷ ion. This may be due to the microphase separation to SiO2 and Na20 • 2 SiO2 in the x <~ 26 glasses. The separation results because of their high miscible temperature [8], even if the melts are quenched (the scale or extent of these phases is small). Copper ions are expected to substitute for Na ÷ in the Na20 • 2 SiO2 microphase, as Cu 2÷ is regarded as a network modifier. Thus the environment of the probe cation is considered to be identical for glasses of up to 37 tool% Na20. The selective distribution of the Cu 2÷ ion into the phase containing modifier cations was similarly observed in the K 2 0 - C a O - B 2 0 3 system [10]. Robinson found the correlations between the composition dependence of various properties and the singular points in the phase diagram in the composition region 0 - 5 0 rnol% Na20 by using multiple regression analysis [ 11 ]. These properties can be classified into three types according to their composition dependences as shown in table 3. The ESR parameters and ligand field transition energy of the Cu 2÷ ion seem to belong to the P1 type, judging from figs. 3 and 4. It is significant that some of the macroscopic properties and the microscopic responses showed the same type of composition dependence. The correlations mentioned above seem to suggest that HFS-1 and HFS-2 reflect Cu 2÷ ions with ligands.of metasilicate anion and orthosilicate anion respectively.

11. Hosono et al. / ESR o f Cu 2+ in N a 2 0 - S i O 2 glasses

111

1700 1600

L

C + L

1500 1400 o v

1300 \ -U

1200

N + L \~ 2NS+L

(D ¢L

ii00 T+L 1000 900 Q+L 800

Z

I tnI N2Si ~ - - ~ ' Zl .... i._l ',

700

(56) 70

60

(37) (26) 50

Mol%

40

30

20

i0

0

of N a 2 0

Fig. 7. Phase diagram of N a 2 0 - S i O 2 system (after Kracek [9]). C: cristobalite; T: tridymite; Q: quartz ; N2S: Na2 O • 2SiO 2 ; NS: Na20 • SiO2 ; 2NS: 2Na20 " SiO2 ; N: Na20; L: liquid.

Table 3 Types o f composition dependences of the properties of sodium silicate glasses. Type

Break points

Properties [ 11 ]

number

composition

Po Pa

0 1

x = 37

P2

2

x = 26 x = 37

Molar refractivity Alkali volatilization (at 1400 ° C) Log electrical resistivity Chemical durability Thermal expansion Standard Heat o f formation Partial molar volume

112

H. Hosono .et al. / ESR of Cu2+in Na20-SiO 2 glasses

90

I

I

I

I

i

I

I

O: ~

80

O:~

C-, 70

IlD--

60 50

(HFS-2)

8 t~0

30 8 20 10 0

{HFS-I)

a

,

J

I

I

I

_

I

10 20 30 40 50 60 70 80 HA20 (bl0/ Z)

Fig. 8. Bonding parameters of Cu2+-O as a function of Na20 content. Po: covalency of o-bonding; F~r: covaleney of in-plane rr bonding.

The difference between the distribution of g-values (Sgll) of HFS-1 and HFS-2 is interpreted in terms of this model. Large 6gll of HFS-1 results from the characteristics of polymer ligands, i.e. the enormous degree of conformational freedom in the coordination of the Cu2+-metasilicate complex causes the fluctuation of the ligand fields. On the other hand, the coordination of Cu 2÷ with monomeric ligands is expected to have negligible fluctuation because of their smaller allowance for structtrral deformation. This assignment is supported by the discussion on the strength of Cu2÷-O bond (see section 4.4). 4.4. Analysis by L C A O - M O

The observed gll and g± values (gll = 2 . 2 - 2 . 4 and g, ~- 2.05) are characteristic of the Cu 2÷ ion coordinated by six ligands which form an octahedron elongated along the z-axis * due to the Jahn-Teller effect. This configuration satisfies the condition for applying the analysis developed by Maki and McGarvey [14] and slightly modified by Kivelson and Neiman [15] (see Appendix). For the calculation of the covalency of Cu2+-O back-bondings, the excitation energies from Blg to B2g (AExy) and from B,g to Eg (AExz, yz) are required. Here, AExy was assumed to be the peak energy of the broad absorption locating in the 12 8 0 0 - 1 5 200 cm -1 region. We failed to recognize any absorption assignable to the excitation from Big to Eg, * According to crystal field approximation, the following relations hold: the A, gll > g.l. for an elongated octahedral complex; B, g± > gll for a compressed octahedral complex. Most of the Cu~-complexes belong to A, but the Cu2+-Crown Ether complex in the solution [12], and Cu ~" in Mg3(PO4)2 " 8H20 crystal [13] to B.

113

H. Hosono et al. / ESR o f Cu 2+ in Na20-Si02 glasses

i Unit

0,I -0 0-t,-0-

i I

Unit

II

Unit

Ill

Unit

IV

Fig. 9. Schematic representation of electron donation in a Cu2+-silicate complex. The arrows express the donation of electrons from the oxygen to the solicon or copper atom. The dotted lines denote rr bondings. AExz, y z. Therefore, according to Kivelson and Neinman [15] additional approximations were employed in order to facilitate calculations as the covalency of Eg (outof-plane p-dnback-bonding) orbital is very small, the electron occupying this level 4 + ×o = 1 (a2×o is localized perfectly in the dxz or dyz orbital of the Cu 2÷ ion, and V the Fermi-contact interaction). The results of the calculations are shown in fig. 8 and can be summarized as follows. (1) The covalency of o-type bonding (Po) was substantially constant within the experimental error throughout the composition region measured. Its value was nearly identical with those for borate, phosphate and sulfate glasses [1,3]. (2) The covalency of in-plane n-bonding (PTr) was nearly constant for the x <~ 55 glasses. The covalency obtained from HFS-1 for x ~> 55 glasses, was identical with those for x <~ 55 glasses, whereas the value from HFS-2 was considerably higher. The degree of covalency for oxyanionic glasses increases in the order sulfate < phosphate < silicate <~ borate. The covalency of in-plane 7r-bonding (U~r) reflects the Lewis basicity of oxygen atoms in glass [1,3]. We attribute the variation of the basicity to the changes in structure of silicate anions, assuming that the structural units shown in fig. 9 are present in the glasses. Result (2) suggests that a large difference exists between F,/s for units III and IV. Namely, as the number of non-bridging oxygens per SiO4 tetrahedron increases from two to four (or three), the electron-accepting ability of the silicon atom is saturated. The covalency derived from HFS-2 was much higher than that from HFS-1. HFS-1 and 2 may be assigned to units III and IV, respectively. Therefore, the Cu2+-O bond in unit IV is expected to be stronger than that in unit III. This result supports the view that microenvironmental fluctuation for HFS-2 was negligible compared with that for HFS-1 (section 4.1). On the cooling process from a melt to a glass, the network and the complex are in competition to take their stable conformations. If the bonds forming the complex (Cu2÷-O) are strong, its stable structure will be attained and the network will be distorted.

5. Summary ESR and optical absorption spectra of Cu 2÷ in xNa20-(lO0-x)SiO2 glasses were measured, where x ranged from 12 to 70 mol%. The following results were obtained.

H. Hosono et al. / ESR o f Cu 2+ m• Na20-Si02 glasses

114

(1) The glass system can be divided into three composition regions from the composition dependences of ESR parameters and ligand field absorption energy. The boundary compositions between the adjacent regions coincided with the eutectics in the phase diagram. (2) A new absorption was observed in ESR spectra for the glasses o f x ~> 55. The fluctuations of gll for this absorption was negligible compared with those for many other glasses. This absorption was assigned to Cu 2+ with orthosilicate ligands. (3) The bonding parameters of Cu2+-O back-bondings were calculated. The covalency of o-type bonding was substantially constant and almost identical with those for other oxyanionic glasses. The covalency of in-plane ~r-type bonding was also nearly constant, but an extra Cu 2+ ion with fairly large covalency was observed in ultra-high-soda glasses.

Acknowledgement We wish to express our thanks to Professor Sumio Sakka of Mie University for reading the manuscript.

Appendix Analysis by L C A O - M O

Antibonding hole orbitals [A1-A4] are constructed from 3d orbitals of a cupric ion and 2s and 2p orbitals of the four ligand oxygen ions which are at the corners of ff square plane and nearer to the cupric ion than the two on the perdicular axis. They are constructed and labelled according to the symmetry species of D4h , assuming that the components of the lower symmetry are small. The four ligands are placed on the +-.x-and +y-axes. They are labelled by superscripts starting with one on the +x axis and proceeding counter-clockwise. Big = t~ dx 2 _ y2 _ ot'(_O(x1) + 0(2) + o(3) _ 0(4))/2,

(gl)

B2g = ~31 dx 2 - y2 _/3'1 (p(y1) + p(x2) _ 1)(3)_ P(x4))/2,

(g2)

Alg = al daz 2 _'r2 _ a,l(O(xl)+O(y2) _ Ux-(3)- 0(4))/2,

(g3)

(/3 dxz -/3'(P (1) - P(3))/21/2, Eg= / /3dyz /3'(P(2) Pz(4))/2'/2 .

(A4)

Here, o(~) are sp hybridized o-orbitals of the ligands. The hole occupies the Big orbital in the ground state. Normalization of the Big orbital yields a2 + ~,2 _ 2aa'S = 1 ,

(A5)

H. Hosono et al. / ESR o f Cu 2÷ in N a 2 0 - S i 0 2 glasses

115

where S is the overlap integral. The overlap of other orbitals is small and therefore neglected. The coefficients a 2 and tx'2 take the values b e t w e e n two e x t r e m e s , that is, a 2 = 1, and a '2 = 0 for the purely ionic b o n d and a 2 = a '2 = (1 + S)/2 for the purely covalent b o n d . T h e r e f o r e , the normalized covalency o f Cu2+-O b o n d i n g o f o or n s y m m e t r y is expressed as follows: c o = 200(1 - S)(1 - ~2) ( % ) , 1 2s

r ~ = 200(1 - ~1~) (%)

References [1] H. Imagawa, Phys. Stat. Sol. 30 (1968) 469. [2] L.D. Bogomolova, V.A. Zhachkin, V.N. Lazukin, N.F. Shapovalova and V.N. Shmukler, Sov. Phys. Solid State, 12 (1971) 2740; Fiz. Tverd. Tela, 12 (1970) 3370. [3] H. Kawazoe, H. Hosono and T. Kanazawa, J. Non-Crystalline Solids 29 (1978) 173. [4] S. Sakka, K. Kamiya and H. Yoshikawa, J. Non-Crystalline Solids 27 (1978) 289. [5] A. Paul and J.M. Parker, Phys. Chem. Glasses 16 (1975) 103. [6] M. Imaoka and T. Yamazaki, J. Ceram. Ass. Japan 71 (1963) 215. [7] P.C. Taylor, J.F. Baugher and H.M. Kriz, Chem. Rev. 75 (1975) 203. [8] M. Tomozawa, R.K. MacCrone and H. Herman, Phys. Chem. Glasses, 11 (1970) 136. [9] F.C. Kracek, J. Phys. Chem. 34 (1930) 1588. [ 10] H. Kawazoe, H. Hosono and T. Kanazawa, J. Non-Crystalline Solids 29 (1978) 249. [ 11 ] H.A. Robinson, J. Am. Ceram. Soc. 52 (1969) 392. [ 121 K. lshizu, T. Haruta, K. Nakai, K. Miyoshi and Y. Sugiura, Chem. Letters, 6 (1978) 579. [13] H. Hosono, M. Shimizu, H. Kawazoe and T. Kanazawa Bull. Chem. Soc. Japan, to be submitted. [ 14 ] A.H. Maki and B.R. McGarvey, J. Chem. Phys. 29 (1958) 31. [15] D. Kivelson and R. Neiman, J. Chem. Phys. 35 (1961) 149.