Physical evaluation and electrical properties in glassy semiconductors a-GeTe4Mx

Materials Chemistry and Physics 71 (2001) 226–234

Physical evaluation and electrical properties in glassy semiconductors a-GeTe4 Mx S.A. Fayek, S.M. El-Sayed∗ National Center for Radiation Research and Technology, P.O. Box 29, Nasr City, Cairo, Egypt Received 22 September 2000; received in revised form 27 November 2000; accepted 3 January 2001

Abstract Amorphous films of the ternary GeTe4 Mx , where M = In and Cu and x represented by 0.05 and 0.10 with thickness about 200 nm, have been prepared by thermal evaporation. Dark conductivity measurement on thin films are reported in the temperature range 100–350 K. The results indicate that at the first slope which is represented by the range from 250 to 350 K, the conduction occurs in the band tails of localized states and at the second slope which is represented by the range from 100 to 250 K, the conduction is due to variable range hopping, which is in reasonable agreement with Mott’s condition of variable range hopping conduction. Some parameters such as coordination number r, the number of constraints per atom Ncon were calculated. It was found that there is a number of correlations between the chalcogenide glass forming ability and the number of lone-pair electrons for chalcogenide system. An attempt has been made to evaluate this correlation according to simple criterion for computing the ability of a chalcogenide system to retain its vitreous states proposed by Liang. The effect of heat treatment and substrate on the structure transformation is investigated by scanning electron microscope. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Scanning electron microscope; Chalcogenide glasses; Conductivity; Thin films

1. Introduction Amorphous semiconductors are metastable materials produced by quenching techniques. Several feasibility of applying these materials to magnetic, optical, and structure media have been investigated. Among them, one remarkable application is to an optical disk memory of the reversible type. In this report GeTe4 -(In or Cu)x pseudo-binary thin films were studied as a candidate for an optical disk overwriteable at a high data rate. There are two reasons for the selection. Firstly, chalcogenide materials such as GeTe are generally known to show an appreciable optical change between their amorphous and crystalline states. Secondly, laser induced phase transitions in Ge-based chalcogenide thin films are particularly of interest for reversible optical data storage due to their structure-dependent optical properties. 2. Experimental procedure Bulk amorphous GeTe4 Mx , where M = In and Cu and x represented by 0.05 and 0.10 were prepared from fussing mixture of the appropriate quantities of the elements in ∗ Corresponding author. E-mail address: [email protected] (S.M. El-Sayed).

evacuated fused silica ampoules up to 850◦ C for 8 h and shaken several times to ensure complete homogeneity. The molten materials were quenched in saturated aqua solution of NaCl at around −15◦ C and the alloy was solidified to the glass semiconductor. Films were prepared by thermal evaporation technique using standard unit Edward 306 E coating unit with conventional rotary and oil diffusion pump maintaining residual pressure in the order of 1.3 × 10−4 Pa. High purity GeTe4 Mx , where M = In and Cu and x represented by 0.05 and 0.10, were used for evaporation. Ultrasonic cleaner cleaned the silicate glasses by distilled water and alcohol, respectively. The distance between the ion source and the substrate was about 10 cm. During the evaporation, the vapor incidence angle was continuously and periodically changed from 0◦ to 80◦ . The deposition rate was 1 nm/s. The thickness of films determined by the thickness monitor was about 200 nm. The thin films were checked by X-ray diffraction using the machine Shimadzu model XD-D1 series. The obtained data reveal that there are no sharp peaks. Thin films employed for DC conductivity measurements were deposited onto glass substrates previously equipped with coplanar silver electrodes separated by a gap of width about 0.2 cm. Keithly 616 digital electrometer was used for resistance measurements and Philips PM 2441 digital voltammeter for measuring millivolts across

0254-0584/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 1 ) 0 0 2 9 0 - 5

S.A. Fayek, S.M. El-Sayed / Materials Chemistry and Physics 71 (2001) 226–234

227

Fig. 1. The X-ray diffraction patterns for films of GeTe4 Mx , where M = In and Cu and x = 0.05 and 0.10.

the thermocouple. The electrical conductivity was measured in the temperature range 100–350 K. The surface structure and growth morphology as a function of metal additive, concentration and heat treatment at starting Tc were investigated by scanning electron microscope (SEM; Joel-JSM) at an accelerating voltage of 20 kV.

3. Results and discussion

where σ 0 is the pre-exponential factor, E the activation energy, k the Boltzmann constant, and T the temperature. The activation energies for these alloys have been calculated using the slope of the curve of Fig. 2 and Eq. (1). From the calculated values of activation energy and pre-exponential factor (Table 1), it is clear that the activation energy decreases with increasing In or Cu. It is obvious from that the DC conductivity increases with the decrease of concentration of metallic impurities in a-GeTe4 .

3.1. X-ray diffraction examination Fig. 1 shows the X-ray diffraction patterns of GeTe4 Mx , where M = In and Cu and with x = 0.05 and 0.10. The patterns reveal that there are no sharp diffraction lines, thus confirming the non-crystalline structure of the studied films deposited on silicate glass. 3.2. Effect of composition on the activation energy and conductivity To study the temperature dependence of the electrical conductivity of as-prepared specimens, measurements were carried on liquid nitrogen at about 313 K under vacuum. Figs. 2 and 3 show the temperature dependence of DC conductivity for GeTe4 Mx , where M = In and Cu and with x = 0.05 and 0.10. It is clear from the figures that σ DC vs. 1000/T curves are linear in the measurement temperature range 100–350 K. This indicates that the conduction is through activated process having a single activated energy in this entire temperature range. The DC conductivity can be explained by a conventional relation
 E σDC = σ0 exp − (1) kT

Fig. 2. Plot of ln σ DC (−1 cm−1 ) vs. 1000/T (K−1 ) for GeTe4 Inx , where x = 0.05 and 0.10.

228

S.A. Fayek, S.M. El-Sayed / Materials Chemistry and Physics 71 (2001) 226–234

Fig. 3. Plot of ln σ DC (−1 cm−1 ) vs. 1000/T (K−1 ) for GeTe4 Cux , where x = 0.05 and 0.10.

An increase in the DC conductivity with a corresponding decrease in activation energy is found to be associated with the shift of the Fermi level in impurity doped chalcogenide glass [1,2]. In some cases, an increase in the DC conductivity by excess impurity doping has been explained in terms of increased hopping conduction in impurity induced systems [3,4]. Therefore, in the present case, the observed increase in the DC conductivity for all concentrations of the metallic impurities could be interpreted in terms of either of the two processes described above. According to Mott and Davis [5] the value of σ 0 in the range 103 –104 −1 cm−1 in chalcogenide glasses indicates that the conduction takes place mostly in extended states. A smaller value of σ 0 indicates a wide range of localized states and the conduction taking place by hopping processes. The calculated values of activation energy and preexponential factor (Table 1) suggest that the conduction is due to thermally assisted tunneling of charge carriers in localized states present in the band. It should however be mentioned that the activation energy E alone does not provide any indication as to whether

conduction occurs in extended states above the mobility edge or by hopping in localized states. This is because both these conduction mechanisms can occur simultaneously, with the conduction via localized states dominating at low temperature. The activation energy in the former mechanism represents the energy difference between the mobility edge and Fermi level, i.e. Ec −Ef or Ef −Ev , whereas in the latter it represents the sum of energy separation between the occupied localized states and the Fermi level EA −Ef , and the mobility activation energy for the hopping process between the localized states. To obtain a definite distinction between these two conduction mechanisms, Mott [6] has suggested that the pre-exponential factor σ 0 in Eq. (1) for conduction in the localized states should be two or three orders lower than conduction in the extended states. Also, it should become still lower for conduction in localized states near the Fermi level. For conduction in the extended states the values of σ 0 reported for a-Te and other Te alloyed films [7] are of the order of 104 −1 cm−1 , whereas in the present work the values of σ 0 is in the order of 101 −1 cm−1 . Therefore, the possibility of extended state conduction is completely ruled out and localized state conduction in the band tail is most probable. According to various workers [8], the value of the pre-exponential factor σ 0 depends also on the product of mobility and the density of states. In low-temperature region, as in Figs. 4 and 5, the conduction occurs via variable range hopping of the charge carriers in the localized states near the Fermi level, and is characterized by Mott’s variable-range hoping relation [9].
  σ0 σDC (T ) = exp(−AT)−1/4 (2) T 1/2 The pre-exponential factor σ0 depends primarily on phonon frequencies and is different from that in Eq. (1), and A4 = T0 =

λα 3 kN(Ef )

(3)

where T0 represents the degree of disorder, α the coefficient of the exponential decay of the localized state wave function, λ the dimensionless constant (≈18), and N(Ef ) the density of localised states at Ef . Hence α is calculated as [10] α = 22.52σ0 A2 cm−1

(4)

and N (Ef ) = 2.12 × 109 σ0 A2 cm3 eV−1

(5)

Table 1 Effect of compositions on the dark conductivity σ 300 , the pre-exponential factors σ 0 and activation energies E in GeTe4 (Cu, In)x , where x = 0.05 and 0.1 for glassy system in the temperature range 250–350 K

E (eV) σ 0 (−1 cm−1 ) σ 300 (−1 cm−1 )

GeTe4 In0.05

GeTe4 In0.10

GeTe4 Cu0.05

GeTe4 Cu0.10

0.116 1.131 0.996 × 10−2

0.108 2.142 0.604 × 10−2

0.096 0.732 4.564 × 10−2

0.082 2.789 1.474 × 10−2

S.A. Fayek, S.M. El-Sayed / Materials Chemistry and Physics 71 (2001) 226–234

Fig. 4. Plot of ln σ DC T1/2 (−1 cm−1 K1/2 ) vs. T−1/4 (K−1/4 ) for GeTe4 Inx , where x = 0.05 and 0.10.

Various Mott parameters A, α, σ0 and N(Ef ) have been calculated using the above equations and are given in Table 2. It is found that the value of T0 and α increases with increasing metal additive and T0 decreases with increasing Cu or In composition, and also the amorphicity of the samples decreases with increasing Cu or In. 3.3. Relation of morphological to metal additive and type of substrate Fig. 6(a1) for GeTe4 In0.05 shows a homogenous droplet micrometer sized structure, a well-developed phase separated structure can be seen. After heat treatment (Fig. 6(a2)), further separation of the surrounding media gives rise to large droplets in size, by another way large crystalline particles are observed at the surface of the glass after heating at 200◦ C. By increasing the time of annealing to about 8 h at 200◦ C (Fig. 6(a3)), the composition changed to cellular structures followed by crystals formed. The increased number of crystals is due to an increase in the number of nuclei formed during the nucleation heat treatment. On the other

229

Fig. 5. Plot of ln σ DC T1/2 (−1 cm−1 K1/2 ) vs. T−1/4 (K−1/4 ) for GeTe4 Cux , where x = 0.05 and 0.10.

hand, by increasing In up to 0.1, the films possess an irregular surface made up of plate-like crystal grains as illustrated in Fig. 6(b1) by annealing at 200◦ C for 4 h. The aggregation of the particles proceeds to form more and more island regions. Finer dispersed particles, 20–30 nm in diameter, are observed in such an island region as seen in Fig. 6(b2). Also, increasing the time of annealing (Fig. 6(b3)) characterized by the matrix consists of randomly mixed grains of all involved elements. Inside the nanocrystalline matrix, separated amorphous regions are formed. These regions are up to a few micrometers in diameter and have a sharp boundary with the surrounding matrix. By adding Cu0.05 to GeTe4 as in Fig. 7(a1), the droplets are substantially spherical and have a convex surface. Fig. 7(a2) shows the annealing of the portion solidified as a crystal, which showed that annealed-pit density was very high. The observed image clearly indicates the island structures of deposited films on the glass substrate, and thereby confirms the growth of GeTe4 Cu0.05 on a silicate substrate. After annealing for 8 h, the microstructure obtained for these film crystallites are well oriented. They

Table 2 Mott parameters in the temperature range 100–250 K

(K1/4 )

A T0 (K) σ0 (−1 cm−1 ) α (cm−1 ) N(Ef ) (eV−1 cm−3 )

GeTe4 In0.05

GeTe4 In0.10

GeTe4 Cu0.05

GeTe4 Cu0.10

36.690 18.124×105 8.524×104 2.874×109 17.676×1026

31.818 10.249×105 20.455×104 4.664×109 18.368×1027

42.878 3.381×106 4.806×104 1.989×109 4.327×1026

35.195 1.534×106 7.288×104 2.033×109 10.165×1026

230

S.A. Fayek, S.M. El-Sayed / Materials Chemistry and Physics 71 (2001) 226–234

Fig. 6. SEM morphology for GeTe4 In0.05 as: (a1) deposited films, (a2) after heating for 4 h, (a3) after heating for 8 h at 200◦ C. SEM morphology for GeTe4 In0.1 as: (b1) deposited films, (b2) after heating for 4 h, (b3) after heating for 8 h at 200◦ C.

possess plate-like morphology. The crystallographic c-axis is the short axis oriented perpendicular to the crystallization direction as in Fig. 7(a3). Fig. 7(b1) shows the SEM micrographs of GeTe4 Cu0.1 film deposited at room temperature. The film consisted of individual grains, which were irregular in size and shape and separated by well-defined inter-grain boundaries. A similar

image contrast has also been observed in other thin films of amorphous elemental and compound semiconductor. The three-dimensional morphology with its probable thermal cracks and voids appears independent of crystallization process after annealing composition for 4 h, as in Fig. 7(b2). In Fig. 7(b3) the large rods are the crystallite phase, spinal forms of the small blocky crystal and the fine needle.

S.A. Fayek, S.M. El-Sayed / Materials Chemistry and Physics 71 (2001) 226–234

231

Fig. 7. SEM morphology for GeTe4 Cu0.05 as: (a1) deposited films, (a2) after heating for 4 h, (a3) after heating for 8 h at 200◦ C. SEM morphology for GeTe4 Cu0.1 as: (b1) deposited films, (b2) after heating for 4 h, (b3) after heating for 8 h at 200◦ C.

For films of composition GeTe4 In0.1 on silicon substrate, there are small size droplets as in Fig. 8(a1), by heating at 200◦ C the size of droplets increases and the number is reduced. It is evident that small particles state of the material is thermodynamically metastable because of high free energy increase associated with the high ratio of surface atom

as in Fig. 8(a2). The observed image clearly in Fig. 8(a3) indicates island structures of deposited GeTe4 In0.1 film on the Si substrate and thereby confirms the growth mode of composition on a Si substrate. Also, Fig. 8(b1) shows that for GeTe4 Cu0.1 film on Si substrate, the matrix consists of randomly mixed grains of all

232

S.A. Fayek, S.M. El-Sayed / Materials Chemistry and Physics 71 (2001) 226–234

Fig. 8. SEM morphology for GeTe4 In0.1 on Si wafer as: (a1) deposited films, (a2) after heating for 4 h, (a3) after heating for 8 h at 200◦ C. SEM morphology for GeTe4 Cu0.1 on Si wafer as: (b1) deposited films, (b2) after heating for 4 h, (b3) after heating for 8 h at 200◦ C.

involved elements. Inside the nanocrystalline matrix, separated amorphous region is formed. These regions are up to a few micrometers in diameter and have a sharp boundary with the surrounding matrix. For Fig. 8(b2) and (b3), SEM micrographs of the same sample after annealing at 200◦ C for 4–8 h, respectively, show that large rods are the anorthic phases, spinal forms the small blocky crystal.

3.4. Determination of the average number of constraints per atom Ncon and average coordination number per atom r In describing our results, it is interesting to mention the glassy networks are influenced by mechanical constraints (Ncon ) associated with the atomic bonding, and an average coordination number r which is also related to Ncon will

S.A. Fayek, S.M. El-Sayed / Materials Chemistry and Physics 71 (2001) 226–234

233

be explained below. In a covalently bonded glass network, two types of constraints, bond bending Nβ and bond stretching Nα need to be counted [11]. For an atomic species with coordination number r, the number of constraints per atom arising from bond bending is N β = 2r − 3 and from bond stretching is N α = 21 r. Knowing the average number of constraints Ncon = N α +N β , and the average coordination number r for different compositions of GeTe4 (Cu, In)x , where x = 0.05 and 0.1 glassy system, the average coordination number r can be calculated using the formula (Table 3):

strongly bond to Ge, the Ge atom also fill the available valence of the Cu or In. After all these bonds are formed, there are still unsatisfied Te valences (excess bonds) which must be satisfied by the formation Te–Te bonds. The stabilization energy per atom is obtained for an infinitely large cluster of the material and all the parameters exhibit the same trend with increasing Te content. If we analyze the chalcogenide glass forming ability, we may find the (Ge, Te) based chalcogenide compound (Cu, In) as shown in Table 4. The variation of these abilities can be explained, according to the Pauli Force Model [13] from which they obtained the orbitally dependent ionic radii. In discussing the ionic radii of the elements used, we are talking of rs and rp which are the orbitally dependent ionic radii of s-orbital and p-orbital, respectively, the previous correlation is given also in terms of the chemical bond approach. The difference of chemical bonds formed by Te and Ge elements with Cu or In atoms is given in Table 4. The Rσ AB and Rι AB scales correspond to the ionicity and the metallicity of A–B, and are defined as [14]:

r = 25 (Ncon + 3)

Rσ = (rs A + rp A ) − (rs B + rp B )

(8)

Rι = (rs A − rp A ) + (rs B − rp B )

(9)

Table 3 The value of Nα , Nβ and Ncon along with r for GeTe4 (Cu, In)x , where x = 0.05 and 0.1 for glassy system Compositions

Nα

Nβ

Ncon

r

GeTe4 In0.05 GeTe4 In0.1 GeTe4 Cu0.05 GeTe4 Cu0.1

1.215 1.240 1.210 1.214

1.860 1.960 1.840 1.854

3.075 3.200 3.050 3.068

2.430 2.480 2.420 2.427

(6)

3.5. Chemical bond determination, a relation between glass forming ability and lone-pair electrons of structure According to Zarcharia Sen [12], atoms combine more favorably with atoms of different kinds than with the same kind, which is generally found to be valid for glass structure. This condition is equivalent to assuming the maximum amount of chemical ordering possible. It favors the formation of a glass structure by increasing the glass transition temperature Tg . In using this assumption, bonds between like atoms are formed in the sequence of decreasing bond energies until all available valences for the atoms are saturated. The bond energies D(A–B) for heteronuclear bonds have been calculated by using the relation D(A–B) = [D(A–A) × D(B–B)]1/2 + 30(χA − χB )2

(7)

proposed by Pauling, where D(A–A) and D(B–B) are the energies of the homonuclear bonds, the D(A–A) values are used in units of kcal mol−1 (48.279 for Cu, 23.9 for In, 65.488 for Ge and 33 for Te). Also χ A and χ B are electronegativity values for atoms involved, the χ values used are 1.9 for Cu, 1.7 for In, 2.10 for Te and 1.8 for Ge. The energies of bonds expected to occur in GeTe4 (Cu, In)x , where x = 0.05 and 0.1, systems are given in Table 4. The Te atoms Table 4 Energies of bonds expected to occur in GeTe4 (Cu, In)x , where x = 0.05 and 0.1 for glassy system and glass forming abilities A–B

D(A–B)

Rσ AB

Rι AB

Ge–Te Cu–Te In–Te

109.0 66.6 52.0

0.02 0.46 0.35

0.48 1.38 0.61

The change of R␴ from Ge–Te bond to Cu–Te or In–Te bond is very important to understand the chalcogenide glass forming ability. As shown in Table 4, the metallicity of Ge–Te bond is less than Cu–Te or In–Te, while the ionicity of Ge–Te bond is much lower than Cu–Te or In–Te. As we know, the p-orbitals have a very marked directivity, which leads to well-defined structure that are malleable and possible within certain limits. These properties of ␴ bonds are in favor of the glass formation. The lower ionicity of Ge–Te bond means that ␴ bond has a preponderance over that of Cu–Te or In–Te bond. This means that the small ionicity of Ge–Te bond of the typical ␴ bond. Thus the chalcogenide glass forming abilities of Ge is very good. As we know, most of the substances that can solidify in the vitreous state are found to possess that structure (bridges) which give rise to tri-dimensional or bi-dimensional or linear heteropolymeric formation VI and VII. The Te atoms in glass structures have two pairs of lone-pair electrons, which can eliminate the strain force caused by the formation of amorphous materials. In terms of the viewpoint proposed by Pauling [14], the chemical bonds with lone-pair electrons have a character of flexibility. Increasing the number of lone-pair electrons decreases the strain energy in the system, and hence structures with large numbers of lone-pair electrons are favored for glass formation. The number of lone-pair electrons can be calculated from L=V −r

(10)

where L, V, and r are the number of lone-pair electrons, valence electrons and coordination number, respectively. The

234

S.A. Fayek, S.M. El-Sayed / Materials Chemistry and Physics 71 (2001) 226–234

Table 5

V r L

GeTe4 In0.05

GeTe4 In0.10

GeTe4 Cu0.05

GeTe4 Cu0.10

5.574 2.420 3.154

5.549 2.427 3.122

5.564 2.430 3.134

5.529 2.480 3.049

number of lone-pair electrons of Ge–Te–Cu or Ge–Te–In glass system can be obtained using Eq. (10); the results are listed in Table 5. It is seen from Table 5 that the number of lone-pair electrons decreases continuously with the increase of the content of Cu or In in the Ge–Te. This result is caused by the interaction between Cu or In ion and the lone-pair electrons of a bridging Te atom. The interaction decreases the role of lone-pair electrons in the glass formation. Liang [15] introduced a simple criterion for computing the ability of chalcogenide system to retain its vitreous state. The criterion contains the number of lone-pair electrons, which is necessary for obtaining the system in its vitreous state. For a binary system, the number of lone-pair electrons must be larger than 2.6, and for ternary system, it must be larger than 1. The obtained data given in Table 5 agrees with the former suggestion given by Liang [15].

4. Conclusions 1. The electrical results show two types of conduction that contributes two conduction mechanisms. At higher temperature up to 350 K, conduction occurs in the band tails of the localized states. Also for lower temperature to 100 K, the conduction due to variable range hopping with a kink at a temperature of ∼270 K is in fair agreement with the Mott condition of variable range hopping conduction. 2. It has been shown that the activation energy is closely correlated with the character of the chemical order so, we can say the conductivity is inversely proportional to the metal additive. The reduction of lone-pair electrons (L) is followed by a decrease in the ability of amorphization. The average coordination number r and the number of constraints Ncon  are useful in relating the activation energy to chemical composition. The magnitude of lone- pair electrons L can further help us to understand the effect

of adding Cu or In in (GeTe4 ) compositions and experiment correlation more deeply. 3. For increasing coordination number and decreasing ability of amorphization, the photographs declare that the excess of In on glass substrate affects the size of the spherulites embedded in amorphous zones due to heterogeneous nucleation. On the other hand, for Cu additive the spherulite turned convex as a result of increasing the ionicity and metallicity of Cu–Te bond more than In–Te bond. 4. In the case of Si substrate the In deposited contain droplets increased in size and reduced in number by heating but for Cu deposited a covalent bond forms with Si or Ge. 5. For application these compounds are characterized by the coordination number r = 2.5, which was used for memory switch, and affected by pulse or optical wave as a result of which these compounds were used for erasable programs read only memory (EPROM) which work by optical waves for erasing and programming. Some disks store memory by optical method. References [1] B.T. Kolemiets, E.A. Lebedev, N.A. Rogachev, Fiz. Tekh. Poluprovodn. 8 (1974) 545. [2] S. Okano, M. Suzuki, K. Imura, N. Fukada, A. Hirakt, J. Non-Cryst. Solids 59–60 (1983) 969. [3] S.R. Ovshinsky, Phys. Rev. Lett. 36 (1976) 1469. [4] M. Suzuki, S. Okano, S. Machi, H. Yamakawa, in: Proceedings of the Material Research Society Symposium, Vol. 11986, Materials Research Society, Pittsburgh, PA, 1986, p. 375. [5] N.F. Mott, E.A. Davis, Electronic Processes in Non-Crystalline Materials, Clarendon Press, Oxford, 1979 (Chapter 9). [6] N.F. Mott, Philos. Mag. 22 (1970) 7. [7] N.F. Mott, Philos. Mag. 22 (1970) 903. [8] V.A. Twaddell, W.C. Lacourse, D.D. Machenzie, J. Non-Cryst. Solids 8–10 (1972) 831. [9] N.F. Mott, Philos. Mag. 32 (1975) 961. [10] Z.H. Khan, M.M. Malik, M. Zulfequar, M. Husain, J. Mater. Sci. Technol. 48 (1997) 13. [11] J.C. Philips, M.F. Trope, Solids State Commun. 34, 153 (1983) 43, 203 [12] W.H. Zarcharia Sen, J. Am. Chem. Soc. 54 (1932) 3841. [13] J.R. Chelikowsky, J.C. Philips, Phys. Rev. 17 (1978) 2453. [14] L. Pauling, The Nature of the Chemical Bond, 3rd Edition, Cornell University Press, Ithaca, NY, 1960, p. 188. [15] L.J. Zhenhua, Non-Cryst. Solids 127 (1991) 298.