J . Phys. Chem. 1987, 91, 1067-1073
1067
Vibrational Spectra of Magneslum-Sodium-Borate Glasses. 1. Far-Infrared Investigation of the Cation-Site Interactions E. I. Kamitsos,* G. D. Chryssikos,+and M. A. Karakassides Theoretical and Physical Chemistry Institute, The National Hellenic Research Foundation, 48, Vas. Constantinou Avenue, Athens 1 1 6/35. Greece (Received: August 8, 1986)
,
Far-infrared spectra of compositions probing the whole glass-forming region of the ternary system xMg0.yNa20.B203have been studied to elucidate the glass-formingand/or -modifying properties of MgO. Mg2+and Na+ motions give characteristic absorptions in the far-infrared region appearing at 300-450 and 170-230 cm-I, respectively. The cation dependence of the peak frequency of the cation-motion band was modeled through a Born-Mayer-type potential. Thus, the cation-oxygen site interactions were associated with an effective ionic charge, qeff,calculated from cation-motionfrequencies. The compositional dependence of qeff,related to Mg2+-oxygensite interactions, was found to exhibit a nonlinear behavior, which may originate in part from magnesium-oxygen covalent contributions. The main character of the Mg*+-oxygen site interactions was found to be ionic in all cases studied here. The integrated intensity of the cation-motion bands was shown to be proportional to qcf?. This indicates that the effective charge and the integrated intensity constitute new sensitive probes of the degree of ionic character of the cation-site interactions.
Introduction Structure and properties of oxide glasses strongly depend on the nature and the concentration of the constituent oxides. The ability of certain oxides to form glasses, i.e. network formers, has been first examined by Zachariasen1V2who showed that cations of network formers are highly charged, have small ionic radii, and are usually 3- or 4-coordinated to oxygen atoms. Oxides such as B203,Si02,Pz05,GeOz, and hZO3are typical network formers. Oxides that alone do not form glass serve to change the properties of the glass when added to it and are called network modifiers. Cations of such oxides have large ionic radii and are typically thought to occupy octahedral oxygen sites. Typical modifiers are N a 2 0 , K 2 0 , R b 2 0 , and Cs20. The distinction between the two classes of oxides is not very strict in the sense that there are oxides of cations such as Li’, Mg2+, A13+, Sn4+, and Y3+ which may act either as network formers or as network modifiers, depending on the specific glass composition. Glass-forming properties of such oxides are associated with a tetrahedral configuration of oxygens around the cation, while the network-modifying character is associated with an octahedral type g e ~ m e t r y . ~ . ~ The existence of Mg2+ in both tetrahedral and octahedral coordination was assumed to account for “anomalies” observed in the compositional dependence of several physical properties of magnesium-alkali-~ilicate~~~ and magnesium-phosphate7-” glass systems. It should be noted that, on the basis of subsequent X-ray emission spectra, Kanazawa and co-workers found that the coordination of magnesium in the latter system remains octahedral and thus, a different explanation should be advanced to account for the “phosphate anomaly”.10s12 Kim and Bray originally studied the coordination of magnesium in magnesiumsodium-borate glasses by IlB NMR.13 They found a reduction in the fraction of boron atoms in 4-coordination, N,, for glasses containing more than 15 mol % MgO. This was attributed to the glass-forming properties of MgO, which presumably enters the network as MgO, tetrahedra. Konijnendijk measured the Raman spectra of several glasses in this system and observed that replacing NazO by MgO resulted in a tendency toward the formation of connected BO, tetrahedra and boroxol rings.’, Subsequent ESR work by Kawazoe and co-worker~’~ on Cu2+ doped glasses of composition xR20-yMg0-(100- x - y ) B 2 0 3(R = Na, K) showed that, for x + y 6 15, Mg2+ causes the formation of boroxol and diborate groups. For x + y 3 15, boroxol rings *Author to whom correspondence should be addressed.
‘Onleave from the Chemistry Department, Brown University, Providence, R I 02912.
and pyroborate ions are formed. For such compositions, Mg2+ was assumed to be 4-coordinated (Mg042-)by oxygens of pyroborate ions, in accordance to the suggestion of Kim and Bray.I3 However, later X-ray emission studies on the same system showed that Mg2+ ions appear to be 6-co0rdinated.’~~” It is evident that clarification of the role of MgO and similar oxides, exhibiting both glass-modifying and -forming properties, requires further investigation. It has been shown that far-infrared spectroscopy is a useful probe of the interactions of cations with their local environments in a variety of ionic Exarhos and Risen21,zzshowed that the metal cation-oxygen interactions in metaphosphate glasses give rise to a far-IR absorption, assigned to the vibration of the cation in its oxygen cage. Subsequently, cation-motion vibrations were observed in the far-IR spectra of various other glass composition^,^^-^^ and they proved to give
(1) Zachariasen, W. H. J . Am. Chem. SOC.1932, 54, 3841. (2) Zachariasen, W. H. J . Chem. Phys. 1935, 3, 162. (3) Bishop, S. G.; Bray, P. J. Phys. Chem. Glasses 1966, 7 , 73. (4) Nelson, B. N.; Exarhos, G. J. J . Chem. Phys. 1979, 71, 2739. (5) Weyl, W. A,; Marboe, E. C. The Constitution of Glasses, Wiley-Intersciences: New York, 1964; Vol. 11, Part I, p 523. (6) Brauda, F.; Buri, A.; Caferra, D.; Marotta, A. J . Non-Cryst. Solids 1983, 54, 193. (7) Kordes, E.; Vogel, W.; Feterowsky, R. 2.Electrochem. 1953, 57, 282. (8) Kordes, E.; Nieder, R. Glasstech. Ber. 1968, 4 1 , 41. (9) Elyard, C. A,; Bayuton, P. L.; Rawson, H. Glasstech. Ber. Sonderband, 32K 1959, 36. (10) Kanazawa, T. J . Non-Cryst. Solids 1982, 52, 187. (11) Bogomolora, L. D.; Jachklu, V. A.; Lazukin, V. N.; Parlushkina, T. K.; Shmuckler, V. A. J . Non-Crysr. Solids 1978, 28, 375. (12) Isozaki, K.; Hosono, H.; Kokumai, H.; Kawazoe, H.; Kanazawa, T.; Gohshi, Y . J . Mater. Sci. Lett. 1981, 16, 2318. (13) Kim, K. S.; Bray, P. J. Phys. Chem. Glasses 1974, 15, 47. (14) Konijnendijk, W. L. Phys. Chem. Glases 1976, 17, 205. (1 5) Kawazoe, H.; Kokumai, H.; Hosono, H.; Kanazawa, T. J . Non-Cryst. Solids 1980, 38/39, 717. (16) Kawazoe, H.; Kokumai, H.; Kanazawa, T.; Gohshi, Y . J . Phys. Chem. Solids 1981, 42, 519. (17) Kawazoe, H. J . Non-Cryst. Solids 1980, 42, 281. (18) Edgell, W. F.; Lyford, J.; Wright, R.; Risen, W. M., Jr ; Watts, A. J . Am. Chem. SOC.1970, 92, 2240. (19) Tsatsas, A. T.; Reed, J. W.; Risen, W. M., Jr. J . Chem. Phys. 1971, 55, 3260. (20) Tsatsas, A. T.; Stearns, R. W.; Risen, W. M., Jr. J . Am. Chem. SOC. 1972, 94, 5247. (21) Exarhos, G. J.; Risen, W. M., Jr. Chem. Phys. Lett. 1971, 10, 484. (22) Exarhos, G. J.; Risen, W. M., Jr. Solid State Commun. 1972, 11,755.
0022-3654187 I209 1- 1067$01 S o l 0 0 1987 American Chemical Societv
Kamitsos et al.
1068 The Journal of Physical Chemistry, Vol, 91, No. 5, 1987
Na20
TABLE I: Compositions of Glasses xMg0.yNa20.B203Studied in This Work along with Cation-Motion Frequencies and qe(t Values
sample
vMg2+,
Y
cm-'
4eff
6
0 0.12 0.22 0.32 0.42 0.56
0.1 1 0.11 0.1 1 0.1 1 0.1 1 0.1 1
288 299 312 327 346
1.39 1.44 1 .so 1.58 1.67
7 8 9 10 11 12
0 0.10 0.20 0.30 0.44 0.57
0.23 0.23 0.23 0.23 0.23 0.23
286 304 322 348 365
1.38 1.46 1.55 1.68 1.76
13 14
0 0.05
IS
0.15
16 17
0.25 0.39
0.28 0.28 0.28 0.28 0.28
315 320 334 355
1.52 1.54 1.61 1.71
18 19 20 21 22 23
0 0.10 0.20 0.34 0.47 0.67
0.33 0.33 0.33 0.33 0.33 0.33
327 342 354 369 388
1.58 1.65 1.71 1.78 1.87
24
0
0.43
25 26 27 28
0 0.14 0.27 0.47
0.53 0.53 0.53 0.53
352 375 386
1.70 1.81 1.86
29 30 31 32
0.80 0.90 1.oo 1.20
0 0 0 0
355 368 388 415
1.71 1.77 1.87 2.00
I 2 3 4
5
Figure 1. Glass formation region of the system xMg0.yNa20-B20,. The binary and ternary glasses studied in this work are indicated: for exact compositions see Table I.
valuable information for understanding glass properties such as transport and glass transition p h e n ~ m e n a . ~ ~ , ~ ~ Recently, Nelson and Exarhos4 demonstrated that studies of the cationsite interactions, in the far-IR, can be used to distinguish between metal cations exhibiting predominantly covalent and cations exhibiting mainly ionic interactions with their oxygen sites. On this basis, we have applied far-IR spectroscopy to the system xMg0.yNaZ0.B2O3 ( x + y = 0.53) in an effort to investigate the glass-forming and/or -modifying properties of Mg0.30 This preliminary work showed that the frequency of the Mg2+-motion band changes in a nonlinear manner with composition, indicating a similar trend in the Mg2+-oxygen site interactions. In this work we extend this far-IR study over the whole glass-forming region of the ternary magnesium-sodium-borate system to investigate the generality of the aforementioned behavior and its relation to the coordination of magnesium. Thus, the far-IR spectra of 32 compositions including binary and ternary glasses as well as analogous crystalline compounds have been measured and analyzed. It has been shown that the Mg2+-motion bands can be well separated from those originating from similar Na+ motions, while band frequencies were used as probes of the interaction forces beween cations and their oxygen environments. Using a simplified Born-Mayer potential we showed that it is possible to relate the frequency of the cation-motion band to the product of charges of cation and anionic-oxygen sites. This effective charge was then used as an indication of the degree of the ionic character of the metal-oxygen interactions. It was shown that the magnesium-oxygen interactions are predominantly ionic in character. Substitution of MgO for NazO along parallels with a constant (MgO N a 2 0 ) / B 2 0 , ratio revealed minima in qefr. Thus, although these interactions were found to remain primarily ionic, it appears that at certain compositions some covalent character cannot be neglected. This study demonstrates the high
+
(23)
Rouse, G. B.; Gordon, J. M.; Risen, W. M., Jr. J . Non-Cryst. Solids
1979, 33, 83.
(24) Paeglis, A. U. Ph.D. Thesis, Brown University, 1979. (25) Windisch, C. F. Ph.D. Thesis, Brown University, 1982. (26) Kamitsos, E. I.; Risen, W. M., Jr. J . Non-Cryst. Solids 1984, 65, 333. (27) Rao, C. N. R.;Randhawa, H. S.; Reddy, N. V. R.; Chakravarty, D. Spectrochim. Acta, Part A 1975, 31, 1283. Rao, C. N. R. J . Mol. Struct. 1973, 19, 493. (28) Exarhos, G . J.; Miller, P. J.; Risen, W. M., Jr. SolidState Commun. 1975, 17, 29. (29) Exarhos, G. J.; Miller, P. J.; Risen, W. M., Jr. J . Chem. Phys. 1974, 60, 4145. (30) Kamitsos, E. I.; Karakassides, M . A,; Chryssikos. G. D. Solid State Commun., 1986, 60, 885.
"\a+.
X
no.
cm-' 160
175
200
210
225 236
sensitivity and usefulness of far-IR spectroscopy in probing subtle changes of the ionic character of the metal-oxygen interactions. A complete structural model to account for the observed trends will be presented in the following paper.
Experimental Section Reagent grade powders of anhydrous BZO3, MgO, and Na2C03 were used for the preparation of 5-g glass batches. Appropriate amounts of the materials were thoroughly mixed and melted in Pt crucibles in an electric furnace. Melting temperatures in the range of 900-1 100 OC and melting times of ca. 15-20 min were adequate to obtain clear and homogeneous glasses. Glass fibers drawn from the melt with a Pt wire were used without any further heat treatment. Thus, 32 glass samples were prepared within the phase diagram reported by Kim and Bray,I3 on the basis of Imaoka's r e ~ u l t s , ~and ' are shown in Figure 1. Their compositions are given in Table I. The compositions were selected in such a way as to form diagonals with constant N a 2 0 / B 2 0 3ratio and parallels with constant (MgO N a 2 0 ) / B 2 0 3ratio. Besides the compositions inside this phase diagram, we were able to prepare glasses with compositionsoutside Imaoka's diagram by melting at higher temperatures, ca. 1400 O C , and cooling the melt faster. Thus, by dipping part of the Pt crucible in cold water under a flow of dry NZ,it was possible to prepare the new ternary glasses 23 and 28 and to extend the forming region of the binary magnesium-borate system, Le. x = 0.80-1.20. Preparation of the samples for far-IR measurements required grinding in a vibrating mill and dispersing the powder in lowdensity polyethylene. The mixture was melted between two glass plates at ca. 100 "C to give 0.5-mm-thick plate-shaped samples containing about 15 wt % glass. Far-infrared spectra were recorded on a Fourier-transform Bruker 113V vacuum infrared
+
(31) Imaoka, M J Ceram Assoc Jpn 1961, 69, 282
Cation-Site Interactions in Mg0.Na20.B203
CM-1 Figure 2. Far-infrared absorption spectra of binary yNa20.B203 glasses (a) and binary xMgO.B2O3 glasses (b) including the crystalline magnesium pyroborate compound (b).
spectrometer. The Hg source and the 3.5-pm mylar beam splitter were employed. Each spectrum is the average of 32 scans at 4-cm-’ resolution.
Results It is useful to consider first the far-IR spectra of the binary yNaz0.B203glasses, shown in Figure 2a, for several compositions. Each spectrum is dominated by a broad band with both frequency and intensity increasing withy. These bands are assigned to the vibrations of the Na+ cations in their oxygen sites. The frequency of such far-IR cation-motion bands is strongly dependent on cation mass, charge, and r a d i ~ s .These ~ parameters are expected to remain essentially constant within the sodium-borate binary system, and thus, the systematic shift of the Na+ band to higher frequencies may reflect a progressive increase of the oxygen-cage charge density. Such an increase is easily explained since increasing the amount of alkali oxide in borate glasses is known to induce formation of tetraborate, diborate, and finally nonbridging oxygen-containing groups32 that participate in the formation of oxygen cages (sites) with increasing charge density. The asymmetry observed in the low-frequency side of the Na+-motion band does not necessarily indicate the existence of an asymmetric distribution of sites available to the cations. Indeed, in the same region of the far-IR spectrum, one may expect the Occurrence of the low-energy “boson” peak, which is universal for glasses and similar in nature to the low-frequency Raman scattering peak.33,34 In addition, this far-IR absorption region may be affected by particle size dependent light scattering. Since the origin of the asymmetry cannot be known with accuracy, it should be considered as contributing to the experimental error in either reading peak position or evaluating the integrated intensity of the cation-motion band. The spectra of the binary magnesium-borate glasses, xMgO-B2O3, are shown in Figure 2b, where the spectrum of crystalline magnesium-pyroborate, 2MgO-B2O3,is also included for comparison. The spectra of glasses show a broad band at ca. 400 cm-I, assigned to Mg2+ motion. This band constitutes the envelope of the optical phonon spectrum of the crystal and is consistent with the assignment of the cation far-IR band in glasses (32) For a review article on borate glass structure see: Griscom, D. L. Borate Glass: Structure, Properties and Applications, Pye, L. D., Frechette, V. D., Kreidl, N. K., Eds.; Plenum: New York, 1978. (33) Stolen, R. H. Phys. Chem. Glasses 1970, I Z , 83. (34) Malinovsky, V. K.; Sokolov, A. P. Solid State Commun. 1986, 57, 757.
The Journal of Physical Chemistry, Vol. 91, No. 5, 1987 1069
-5 00
300
3 00
100 5 0 0 C M-1
I00
Figure 3. Far-infrared absorption spectra of ternary xMgO. 0.1 1Na20.B203glasses (a) and corresponding difference far-infrared spectra (b). x MgO~0.53Na20.B203 x= 0.47
IO0
3 00
100
CM-I Figure 4. Far-infrared absorption spectra of ternary xMgO0.53Na20.B2O3glasses (a) and corresponding difference spectra (b).
to a density of coupled oscillator pseudo-phonon statesz9 Again, a systematic increase in band frequency and intensity is observed upon increasing x. It is interesting to note that bands in the region of 400 cm-’ have also been observed in the spectra of crystalline magnesium germanate and silicate compounds35 and very recently in the spectrum of MgA1B0,.j6 In all these cases magnesium is known to be 6-coordinated by oxygens and, thus, the band in this region was taken as originating from the same characteristic vibration of MgO, octahedra. Moreover, far-IR studies of solutions of magnesium salts in amide solvents and of magnesium complexes, where Mg2+ is 6-coordinated, gave bands around 390 cm-I .27J7 (35) Tarte, P. Acad. R. Belg. Mem. Cl. Sci. 1965, 35, 1-248. (36) Tarte, P.; Cahay, R.; Rulmont, A,; Werging, G. Spectrochim. Acta, Part A 1985, 41, 1215.
1070 The Journal of Physical Chemistry, Vol. 91, No. 5, 1987
Taking into consideration these reports and also the fact that the far-IR spectra of binary magnesium-borate glasses are similar in band frequency to that of crystalline magnesium-pyroborate, where Mgz+ is 6-coordinated,16we can assume an octahedral-type coordination of magnesium in these glasses as well. Representative spectra of ternary glasses are shown in Figures 3a and 4a, along two diagonals with constant Naz0/B2O3ratio. (See paragraph at end of text regarding supplementary material.) Addition of MgO to each yNa20.B203binary glass causes the growth of a second band, in the 300-450-cm-' region, which is thus assigned to vibrations of Mgz+ cations in their sites. Understanding the nature of these sites, and consequently the glass-forming and/or -modifying properties of Mg2+ cations, requires the knowledge of the frequencies at the absorption maxima of the magnesium cation-motion bands. As illustrated in Figures 3a and 4a, it is possible to directly deduce these frequencies only from the spectra of high magnesium content glasses. For glasses of low magnesium content, the Mg2+-motion band overlaps with the Na+-motion band and, thus, it is not possible to accurately define frequencies in these cases. However, it is reasonable to assume at this point that, along each diagonal, the Na+-motion band remains approximately the same in peak frequency and intensity. This is a legitimate assumption to make because Na+ is a strong modifying cation and thus, for a constant Na20/BZO3ratio, the number and type of sites available to Na+ cations are approximately the same, since they strongly depend on the value of this ratio. Under the above made assumption, we can subtract the spectrum of each binary yNa20.B2O3glass from the spectra of the corresponding xMg0~yNaZ0.B2O3 glasses of the same diagonal. Thus, utilizing appropriate software, we obtained the difference far-IR spectra shown in Figures 3b and 4b. For each ternary composition the Mg2+-motion band is obtained with peak frequency and intensity strongly dependent on the MgO content. The fact that these bands appear quite well shaped, especially on the low-frequency side, where the Na+-motion band was located, indicates the validity of the above made assumption. The frequencies of the Mgz+-motion bands, obtained from the difference spectra, are summarized in Table I and plotted in Figure 5 as a function of MgO mole fraction. These frequencies are accurate to within f 4 cm-' for the high magnesium content glasses and to within ca. f7 cm-' for the low content glasses. The frequencies of the Naf-motion bands are also plotted in Figure 5. They exhibit a clear sigmoidal behavior with a breaking point at about 20 mol % N a 2 0 . A similar but not as clear behavior is shown by the Mg2+ frequencies, viewed along each diagonal. The position of the break points seems to depend on the specific diagonal that is the N a 2 0 / B 2 0 3ratio. While there surely are similarities between the Na+- and Mg2+-motion bands, there is a clear difference along each parallel. That is, the Na+-motion bands are expected to retain the same sigmoidal behavior along each parallel under the assumption made earlier. However, the Mg*+-motion band frequencies show well-defined minima in each parallel, depicted by the broken lines in Figure 5b. They become quite shallow for the fourth parallel and disappear in the last two parallels, of high modifier content. Interestingly enough all minima are situated on the same diagonal, namely that of y = 0.23, and are observed at different values of MgO content. Thus, it seems that this change in the behavior of the Mg2+-motion band frequency is not related to the MgO content in a way as simple as that suggested by Kim and Bray,13 i.e. that MgO participates in network formation for contents greater than 15 mol 9 MgO. Although an interpretation for this locus (Le. y = 0.23) will be presented later, it is interesting to note that it falls between the two lobes of the glass-forming diagram (Figure 1). Furthermore, it seems that this same diagonal constitutes the boundary of the regions marked as I1 and I1 111 in Kawazoe's et al. ESR study of the Mg0.K20.B,03 glass system.I5 Thus, it appears that
+
(37) Rao, C. N. R.; Bhujle, V. V.; Goel, A,; Bhat, U. R.; Paul, A. J . Chem. Sot., Chem. Commun. 1973,161.
Kamitsos et al.
2Y25
a
01
02
03
GL
b
05 32
01
c2 VgO
03
04
7
35
mol f r a c t i o r -----+
Figure 5. Plot of the cation-motion frequency vs. composition for y N a 2 0 - B 2 0 3binary glasses (a), and for x M g 0 y N a 2 0 . B 2 0 , ternary glasses (b). Unnumbered points in part a are taken from unpublished results of our laboratory.
this diagonal has a pronounced importance related to the structural changes under investigation, and this is reflected in the specific shape of the glass-forming region. Observation of the original spectra of the ternary glasses (Figures 3a, 4a, 7a, and 8a) shows two additional differences between the Mg2+-and the Na+-motion bands. Despite the fact that magnesium and sodium have nearly the same mass, the Mg2+-peakfrequency is much higher than that of the Na+ bands. In addition, the corresponding intensity of the Mg2+ band is much greater than that of the Na+ band. This is well demonstrated by spectra of glasses containing the same number of Mg2+ and Na+ cations, i.e. the spectra of samples 3, 11, and 23. The compositional dependence of the frequency and intensity of the Mgzf-motion band will be discussed in the following section.
Discussion 1 . Compositional Dependence of the Cation-Motion Band Frequency. Observation of vibrations of cations in their anionic sites provides a direct measurement of the forces of interaction between cations and their oxygen sites. Understanding the variation with composition of the frequency as well as the intensity of the cation-motion band requires a consideration of all factors affecting the cation-site interactions. For a detailed description of such interactions, a modified Rittner potential has been previously used for anionic polymeric systems.Ig Such a potential contains the well-known Coulombic term, the charge-induced dipole and the induced dipole-induced dipole terms, as well as the van der Waals and the Born-Mayer repulsion terms. It was recently shown by Nelson and Exarhos4 that, for glasses where the cation-site interactions are predominantly ionic, a simplified
The Journal of Physical Chemistry, Vol. 91, No. 5, 1987 1071
Cation-Site Interactions in Mg0.Na20.B203 type of the Born-Mayer potential can be successfully applied to describe the cation-site interaction dependence on cation parameters. The Born-Mayer-type potential considers only the electrostatic attraction and the repulsive parts as the main contributions to the lattice energy of ionic crystals. van der Waals and polarization terms are completely ignored. Using the simplified Bom-Mayer potential, the potential energy per molecule can be written as38
where qc and q A are the charge of cation and anion, respectively, r is the separation of the ions, z is the number of nearest neighbors of an ion, X and p are empirical constants, and (Y is the Madelung constant. Crystallographic studies in various crystalline sodium-borate compounds have shown that the number of nearest oxygen neighbors of a sodium cation varies from 5 to 8. Thus, coordination numbers of 5 and 6 are reported for a-Na20a3B203,39 6, 7, and 8 for P-Na20.3B203$0and 6 and 7 for Na20.B203!' In the glassy state is is then reasonable to assign an average of six nearest neighbor oxygen atoms around a Na+ cation and to approximate this oxygen environment as nearly ~ c t a h e d r a l . ~ ~ Magnesium cations are also six-coordinated according to Kanazawa and co-w~rkers.'~-''Additional evidence for 6-coordination of Mg2+ comes from the similarities between the spectra of magnesium-borate glasses and crystalline magnesium-borate compounds, as discussed in the previous section. Assuming an octahedral type arrangement of oxygen atoms around each cation, we can rewrite eq 1 in terms of the equilibrium internuclear distance ro, and the change in internuclear distance Ar, as follows:42
Differentiating U with respect to Ar and approximating the products of (Ar)2 by zero, we obtain
dU = X exp[ d(Ar)
-:] [
expl:]
- expl-:]
- Ar
]
(3)
P
Expanding the exponentials in brackets in eq 3 in Taylor series and collecting terms gives
The force constant for a simple harmonic oscillator under the influence of a potential U can now be obtained:
The minimum of the potential energy occurs at r = to, where the first derivative of U equals zero:
Combining eq 5 and 6 gives ~~
(7) At the minimum of the potential well (r = ro), the simple, harmonic oscillator relationship gives f = 472c2wJ
(8)
where c is the speed of light, p is the reduced mass, and v is the frequency of oscillation in cm-I. The only infrared allowed stretching mode of a cation in an octahedral site is the TI, mode, with reduced mass given by p = mmo/m 2mo. Here m and mo are the masses of cation and oxygen, respectively. If we assume that the cation vibrations are effectively decoupled from the vibrations of the boron-oxygen network, then the reduced mass can be approximated by the mass of the oscillating cation, m. The dependence of the cation-motion frequency on cation parameters can now be derived from eq 7 and 8. Replacing p by m and qCqA by qcqA/4?rto, where to is the permitivity of free space, we obtain in the SI system
+
v2=
[ -1
%[
8?r3c2to mzrO ; - 2 ]
(9)
Equation 9 gives the peak frequency of the cation-motion band as a function of cation charge and mass (qc,m), as well as of size (ro,z) and charge (qA) of the cation-containing oxygen environment. The fact that the Mg2+-peakfrequencies are higher than those of Na+ frequencies can be easily explained on the basis of differences in cation charge. To further check the validity of the ionic approach used here, we investigate whether eq 9 can give reasonable values for the pseudo-Madelung constant a by using the far-IR experimental values for frequencies v. The values of the various other parameters are taken as follows: Frequency maxima equal to 41 5 and 230 cm-' were taken as representative of the Mg2+- and Na'site interactions, respectively. These frequencies were measured in binary samples of the highest modification (1 .20Mg0.B203 and 0.53Na20.B203),where the strongest possible ionic character is assumed and, thus, the charges qc = qA can be taken as 2e and l e for Mg2+ and Na+, respectively. Values of the repulsion parameter p have been reported for various crystalline compounds, including alkali halides and alkali and alkaline-earth 0xides.4~ We use the value p = 0.333 A, reported by Morris for alkali and alkaline-earth oxides.44 The equilibrium internuclear distance, ro, is taken as the sum of the Pauling ionic radii, ro = rNa++ r02= 2.35 A, for the case of Na+. The value of ro for Mg2+ is taken from the recent statistical work of Nord and Kierkegaard."5 They reported that 90% of the examined crystalline magnesium compounds had Mg2+ in octahedral sites. Thus, the average value of ro = 2.091 8,for this coordination is used here. The calculated values of the pseudo-Madelung constant a, through eq 9, are then 1.7 13 from the magnesium data and 2.39 1 from the sodium data. Considering that the Madelung constant for rocksalt crystals (z = 6) is a = 1.7456,38and taking into account the various approximations made above, one finds that the calculated values of a are satisfactory. A measured Mg2+-peakfrequency corresponds obviously to a set of the previously defined parameters qc, qA, ro, z. It would be misleading to think of these parameters as independent and attribute a change in cation-motion frequency to the change of one of them alone. For example, a change in the product qCqA would probably affect ro and cause a distortion in the cationoxygen polyhedra, thus slightly affecting coordination z, as well. On the other hand, Mg2+ coordination is known not to deviate much from z = 6.45 Even if a change in coordination occurs, ro is expected to change only by some hundredths of an angstrom.45 Thus, it is justified to assume ro and z constant and compile all
(38) Kittel, C.Introduction to Solid State Physics; Wiley: New York,5th
ed.,p 88. (39) (40) (41) (42)
Krogh-Moe, J. Acta Crystallogr., Sect. E 1974, 30, 747. Krogh-Moe, J. Acta Crystallogr., Sect. E 1972, 28, 1571. Krogh-Moe, J. Actu Crystallogr., Sect. E 1974, 30, 578. Mitra, S.J.; Joshi, K. K. Physica 1960, 26, 284.
(43) Tosi, M. P. Solid State Phys. 1964, 16, 1 . (44) Morris, D. C. J . Phys. Chem. Solids 1958, 5 , 264. Proc. R. Soc. London, Ser. A 1957, 242, 116. (45) Nord, A. G . ; Kierkegaard, P. Chim. Acra 1984, 24, 151.
1072 The Journal of Physical Chemistry, Vol. 91, No. 5, 1987
compositional effects to an effective charge qeff,defined by qeff = (qCqA)'l2. Changes in qeffcould be viewed to reflect changes in the ionic charge density that characterizes the Mg2+-site interactions. They may indicate either a change in the site ionic charge localization (the interaction remaining in this case simply ionic) or a change of the degree of covalent contribution to this interaction. The calculated values of qeff(in units of e) by eq 9 for the Mg2+-containing oxygen sites are given in Table I. These qeffvalues are not to be taken as absolute, but rather as indicating the relative magnitude and trend as a function of composition. Since qEffis proportional to the cation-motion frequency, u, its compositional dependence will be the same as that of u. Thus, the substitution of MgO for N a 2 0 , along parallels with low oxide content, results in changes in qeffin a nonlinear manner. For the composition parallels having higher modifier content the effect is less pronounced or completely absent. Thus, for such compositions the ionic character of the Mg2+-oxygen site interactions remains essentially the same, i.e. almost independent of the sodium content. 2. Compositional Dependence of the Cation-Motion Band Integrated Intensity. As discussed earlier, the intensity of the cation-motion band shows a distinct difference between Mg2+ and Na'. The cation dependence of the far-IR band has been studied by Exarhos et al.29 in binary alkali and alkaline earth metaphosphate glasses. They found a linear relationship between the integrated intensity ( A ) and u2, the cation-motion frequency squared. The explanation of this behavior was based on the Whalley and Bertie theory46that treats the vibrational spectra of orientationally disordered crystals and gives the integrated absorbance as follows: 7r M2U* (A)= - -
3 f
where u is the frequency (cm-I) of the cation vibration, f is the mass weighted force constant, and A4 is the derivative of the dipole moment with respect to a mass weighted longitudinal displacement. Thus, the linear variation of ( A ) with u2 was explained in binary phosphate glasses by using eq 10, implying that M / f 'IS a con~tant.~~ The above equation can be simplified, if a simple harmonic oscillator relationship for the force constant (eq 8) and a dipole ~ the mass moment in the form 1.1 = qr are a ~ s u m e d . Then, weighted force constant is 4.rr2c2u2,and the mass weighted derivative of the dipole moment is q/m'I2. Here q and m are the cation charge and mass, respectively. Then eq 10 can be rewritten as
Thus, a linear dependence of ( A ) on q2 is predicted. It would be interesting to investigate whether this linear relationship is exhibited by our experimental data on binary as well as ternary glasses. Instead of plotting ( A ) vs. calculated qef:, we prefer to plot experimental ( A ) values vs. experimental u2 values, since u is proportional to qeff. Absorbances of cation-motion bands cannot be given in absolute values, due to the great experimental difficulties involved with such measurements. The procedure used here in measuring ( A ) is the following. The far-IR spectrum of vitreous B 2 0 3 was measured under the same sample preparation and instrumental conditions as the spectra of the rest of the glasses. This far-IR B 2 0 3spectrum was used as a background for the spectra of the binary borate glasses. The total area confined between the background and the cation motion band was then measured and normalized to the same number of cation oscillators to give the integrated absorbance ( A ) . For the spectra of the ternary glasses, the same procedure was followed to determine the total absorbance due to both Na+ and Mg+ motions. From this value, the absorbance of the corresponding binary sodium-borate glass was (46) Whalley, E.; Bertie, J. E. J . Chem. Phys. 1967, 46, 1264
Kamitsos et al.
32
a
Figure 6. The linear dependence of the integrated absorption, ( A ) , of the cation motion band, on cation vibration frequency squared, u2, for the system xMgOyNa20.B20,.
subtracted to give the Mg2+-motionabsorbance. All these values were then normalized to the same number of cation oscillators to give ( A ) . The measured integrated absorbance, ( A ) ,has been plotted in Figure 6 vs. u2 for several binary and ternary glass systems. Considering the large experimental error in ( A ) ,ca. lo%, all data in Figure 6 can be described reasonably well with a single straight line, of correlation factor 0.96 and intercept close to zero on both axes. The linear dependence of ( A ) on u2 is exhibited by the two binary borate glass systems studied here, as well as by the more complex ternary glasses4' The linear dependence of ( A ) on qef;, born out in Figure 6, emphasizes the importance of the ionic character of the cationsite interactions on the frequency and even more on the integrated intensity of the cation-absorption peak. Additional experimental evidence of the effect of the ionic character on both ( A ) and u is provided by the characteristic result reported by Nelson and E x a r h o ~ .Thus, ~ Pb2+ and Hg2+ have nearly the same mass; however, the cation motion peak of lead in metaphosphate glass is about 15 cm-' higher than that of the mercury metaphosphate glass. Moreover, the absorbance of the Pb2+band is about four times as much as that of the Hg2+band. These differences in frequency and absorbance were attributed to differences in the degree of the ionic character between metal and oxygen. Indeed, Pb-0 is predominantly ionic, while the Hg-O bond has a considerable degree of covalent character, resulting in a consequent reduction of the degree of the ionic ~ h a r a c t e r . ~ This is directly reflected in a reduction of both frequency and intensity of the Hgz+-motion band in the far-IR. Conclusions The cation-site interactions in magnesium-sodium borate glasses have been studied by measuring the cation-motion bands in the far-IR in an effort to elucidate the glass-modifying and/or -forming properties of MgO in a borate glass matrix. The Mg2+-motion band was observed between 300 and 450 cm-I, while the motion of Na+ cations in their sites occurs at lower frequencies, i.e. in the range of 170-230 cm-'. The peak position for the Mg2+-motionband, in comparison with the far-IR spectra (47) Similar results have been obtained from the study of other binary and ternary glasses. They will be presented in a future publication.
J . Phys. Chem. 1987, 91, 1073-1079 of Mg-containing crystals, suggests a six-coordination of Mg2+ ions. Both Na+- and Mg2+-motion bands were found to upshift in frequency and grow in intensity upon increasing the cation content in binary glasses. In ternary glass systems with constant amount of total modifier the frequency of the Mg2+ band was found to exhibit a nonlinear behavior. The cation dependence of the far-IR frequency maxima was successfully modeled via a Born-Mayer ionic potential. Thus, an effective ionic charge of the cation-site interactions defined by qeff= (qcqA)'/' was calculated from the experimental cation-motion frequencies. The same quantity, qeff,squared was demonstrated to scale with the integrated cation-motion band intensity ( A ) . Thus, the latter becomes another very sensitive probe for the ionic cation site interactions. The slope of the plot of ( A ) vs. vz appears the same for all binary and ternary systems studied so far and may be of universal value. The composition dependence of qeff was taken to indicate changes in the ionic charge density relevant to the cation-site interactions. In the case of Na+ such changes can only be viewed within the frame of purely ionic interactions. However, the observed minima in qeff,related to Mgz+-oxygen site interactions, may as well originate from covalent contributions. Even if these
1073
observed reductions in qcffare solely due to partial covalency, between magnesium and oxygen, the character of the magnesium-oxygen site interactions was found in all cases to be primarily ionic. Understanding the changes in qeff,on the basis of the nature of the oxygen sites, requires structural knowledge of the boronoxygen network which will be addressed in the following paper. Acknowledgment. The authors are grateful to Professor C. A. Nicolaides of the National Hellenic Research Foundation for his support throughout this work. G.D.C. thanks Professors W. M. Risen of Brown University and C. A. Nicolaides for making his collaboration to this work possible. This project has been financially supported by the National Hellenic Research Foundation. Registry No. MgO, 1309-48-4. Supplementary Material Available: Figures 7 and 8 showing far-infrared absorption spectra of ternary xMg0yNa20.B20, glasses, with y = 0.23 (Figure 7) and y = 0.33 (Figure 8) (2 pages). Ordering information is available on any current masthead page.
Vibrational Spectra of Magnesium-Sodium-Borate Glasses. 2. Raman and Mid-Infrared Investigation of the Network Structure E. I. Kamitsos,* M. A. Karakassides, and G. D. Chryssikost Theoretical and Physical Chemistry Institute, The National Hellenic Research Foundation, 48, Vas. Constantinou Avenue, Athens 116/35, Greece (Received: August 12, 1986)
Raman and infrared spectra of glasses in the system xMg0.yNa20.B2O3 have been measured and analyzed in order to elucidate the role of MgO in such glasses. It was shown that for compositions x y = 0.33, 0.53, and 0.67 the presence of Mg2+ cations causes mainly the destruction of diborate groups in favor of boroxol rings, tetraborate groups, pyroborate, and metaborate units. Similar borate groups were found in glass compositions x + y = 1.O, originating from the destruction of orthoborate and di-triborate groups. These Raman and IR results were expressed in terms of melt equilibria between the various borate groups and proved useful in providing a structural interpretation for the compositional dependence of the Mg2+motion band, observed in the far-infrared, as reported in part 1 of this work.
+
Introduction Metal oxides such as Li20, MgO, Alz03, and S n 0 2 can act either as glass network formers or as network modifiers, depending on the specific glass composition.' The glass-forming properties of such oxides are associated with a tetrahedral configuration of oxygen atoms around the metal cation, while a network modifying character is manifested by an octahedral oxygen arrangement. The existence of Mg2+cations in tetrahedral and/or octahedral coordination has been frequently assumed to account for "anomalies" observed in the compositional dependence of physical properties of various magnesium containing oxide g l a s s e ~ . ~ - ~ The coordination of magnesium in the MgO-Na2O-B2O3 glass system has been studied by "B N M R , ESR, Raman, and X-ray emission technique^,^-^ which gave contradictory results as for the coordination and the exact role of Mg2+ in this system. The type of interactions of Mg2+cations with their local oxygen environments depends on the nature of such oxygen sites. Since it was demonstrated that interactions of metal cations with their environments (in a variety of ionic systems including ionic can be effectively probed by far-infrared spectros-
* Author to whom correspondence should be addressed. 'On leave from the Chemistry Department, Brown University, Providence, RI 02912.
copy, we applied this technique to the Mg0-Na20-B203 glass system in order to elucidate the effect of Mg0.'4*15 The fre(1) Nelson, B. N.; Exarhos, G. J. J . Chem. Phys. 1979, 71, 2739. (2) Weyl, W. A.; M a r k , E. C. The Constitution of Glasses, Vol. 111, Part I; Wiley-Interscience: New York, 1964. (3) Kordes, E.; Nieder, R. Glastech. Ber. 1968, 41, 41. (4) Bogomolova, L. D.; Jachkin, V. A.; Lazukin, V. V.; Parlushkina, T. K.; Shmuckler, V. A. J . Non-Cryst. Solids 1978, 28, 375. (5) Branda, F.; Buri, A,; Caferra, D.; Marotta, A. J . Non-Cryst. Solids 1983, 54, 193. (6) Kim, K. S.; Bray, P. J. Phys. Chem. Glasses 1974, 15, 47. (7) Kawazoe, H.; Kokumai, H.; Hosono, H.; Kanazawa, T. J . Non-Cryst. Solids 1980, 39/39, 717. (8) Konijnendijk, W. L. Phys. Chem. Glasses 1976, 17, 205. (9) Kawazoe, H.; Kokumai, H.; Kanazawa, T. J. Phys. Chem. Solids 1981, 42, 519. (10) Edgell, W. F.; Lyford, L.; Wright, R.; Risen, W. M., Jr.; Watts, A. J . Am. Chem. SOC.1970, 92, 2240. (1 1) Tsatsas, A. T.; Reed, J. W.; Risen, W. M., Jr. J . Chem. Phys. 1971, 55, 3260. (12) Exarhos, G. J.; Risen, W. M., Jr. Chem. Phys. Letr. 1971, 10, 484. (13) Exarhos, G. J.; Miller, P. J.; Risen, W. M., Jr. J . Chem. Phys. 1974, 60,4145, and references therein. (14) Kamitsos, E. I.; Karakassides, M. A.; Chryssikos, G. D. Solid Stare Commun. 1986, 60, 885. (15) Kamitsos, E. I.; Chryssikos, G. D.; Karakassides, M. A. J . Phys.
Chem., preceding article in this issue.
0022-365418712091- 1073$01.50/0
0 1987 American Chemical Society
