NMR and infrared study of cation motion in vitreous and polycrystalline TlPO3

Journal of Non-Crystalline Solids 24 (1977) 51-59 © North-Holland Publishing Company

NMR AND INFRARED STUDY OF CATION MOTION IN VITREOUS AND POLYCRYSTALLINE TIPO3 L.W. PANEK *, G.J. EXARHOS **, P.J BRAY and W.M.RISEN Departments of Physics and Chemistry, Brown University, Providence, Rhode Island 02912, USA

The activation energy for T1+ conduction in TIPO3 glass is obtained from analysis of temperature-dependent motional narrowing for T1205 NMR spectra and determinations of the localized far infrared (FIR) vibrational frequency for TI+. Use is made of the phenomenological equation of Hendrickson and Bray to analyze the NMR data, yielding E a = 1.19 eV; the measured FIR T1+ vibrational frequency of 80 cm -1 yields E a = 1.09 eV. No significant ionic conduction is observed in polycrystalline TIPO3. Differential scanning calorimeter measurements yield a glass transition temperature T~ of 96°C and the onset of crystallization tempera~ • . mteraction . . as . a functxon of frequency ture of 132oC. Measurements of the T12 0 5 chemmal shift indicate that (1) the TI+ sites in both polycrystalline and glassy T1PO3 are ionic, the sites in the polycrystal being slightly more ionic than in the glass; (2) the chemical shift interaction is anisotropic in the glass and isotropic in the polycrystal; and (3) distributions in the values of the principal components of the chemical shift tensor exist in the glass, corresponding to a variety of T1-O bond lengths and bond strengths.

1. Introduction

The role of thallium in glass has been likened to the role played by the alkali cations, since the T1÷ cation, almost exclusively, is present in the oxide glasses containing thallium. Alkali-metaphosphate glasses have been studied using far infrared (FIR) techniques [1]; cation vibrational frequencies which depend on the cation mass have been determined and can be used to obtain activation energies for ionic conduction in the glass [2]. The FIR spectrum for thallium cations in glassy T1PO3 is expected to be similar to the spectra for the alkali-metaphosphate glasses. The short-range structure of both glassy and crystalline T1PO3 is expected to be the same, being similar to the alkali-metaphosphate glasses. The alkali-metaphosphate glasses consist of long chains of PO4 tetrahedra sharing two vertices with adjacent tetrahedra through bridging oxygen atoms. Each tetrahedron has two bridging oxygen atoms and two non-bridging oxygen atoms, the latter presumed to * Based on work performed in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Brown University. Present address: Department of Science, Widener College, Chester, Pennsylvania 19013, USA. ** Present address: Department of Chemistry, Harvard University, Cambridge, Massachusetts 02/38, USA. 51

52

L. W. Panek et al. / N M R and IR study o f cation motion

carry the negative charge. Alkali cations act to cross-link the chains through ionic interactions with the non-bridging oxygens. Nuclear magnetic resonance (NMR) studies have been carried out using the T12°3 and T12°s resonances in a variety of glass systems [3-7]. Both nuclei have spin I = !2 and large magnetic moments, yielding strong NMR signals, and since thallium has 81 electrons, both the chemical shift and exchange interactions will be large, providing information about the thallium environment. Motional narrowing of the NMR linewidth has been observed f o r the lighter alkali cations and can be used to obtain activation energies for the cation motion. Motional narrowing, previously unobserved for thallium cations, is reported here for glassy T1PO3 and is used to calculate the activation energy for the thermally activated cation motion.

2.

Experimental

Glassy T1PO3 was prepared from thermal dehydration of T1H2PO4. The dihydrogen phosphate was heated in a porcelain crucible at a temperature of c. 1000°C for 2 h to form a clear bubble-free melt. The melt was quenched to room temperature between two stainless steel blocks to form clear, colorless glass discks used for FIR measurements. Cylindrical glass slugs (9 mm dia. X 20 mm long) formed in a carbon mold were used to obtain the NMR motional narrowing data. Polycrystalline T1PO3 was prepared by slow cooling of the melt employing the Bridgman technique. A quartz tube containing liquid TIPO3 was passed through a 60 cm cylindrical tube furnace with a 5°C/cm gradient from 550 to 250°C over a period of 48 h. The resulting polycrystalline sample was powdered in a dry nitrogen atmosphere and sealed in a glass tube. This sample will be referred to as the polycrystal throughout the paper. The Raman spectrum of the polycrystal revealed no trace of the glassy phase. Phase transition data were determined from differential scanning calorimeter (DSC) tracings on 10 mg samples at a nominal heating rate of 20°C/min. A Perkin-Elmer DSC-2 was used to measure the glass transition temperature Tg, and the glass crystallization temperature Tcry s. Raman spectra were obtained using a Cary 82 Raman spectrometer with a Spectra Physics Ar + Model 164 laser, confirming the polymetaphosphate strucutre and the absence of the crystalline phase in the glass. The sample preparation and equipment used to obtain the FIR spectrum are described elsewhere [ 1]. T12°3 and T12°s NMR line shapes were obtained at room temperature for the frequencies' 8, 10, 12, 14, 16, and 26.5 MHz, and temperature-dependent T12°s linewidths were measured at 16 MHz using the same methods and equipment described elsewhere [4,8].

L. 1t/. Panek et al, / NMR and IR study o f cation motion

53

3. Results

3.1. FIR and DSC measurements The presence of alkali cations in metaphosphate glasses manifests itself as an intense broad band in the FIR spectra of such glasses [1]. The bandwidth and resonance frequency of this localized cation vibration in the glass are known to shift markedly with cation mass and charge. As shown in fig. 1, the localized cation vibrational band is observed at 80 cm - l in the FIR spectrum of glassy T1PO3. Its bandwidth at half maximum is 80 cm -1. The weak feature at c. 155 cm -1 is the first overtone of the T1+ vibration at 80 c m - l ; similar weak features of the proper frequency were observed in vitreous RbPO3 and CsPO3. The broad absorption beginning around 300 cm - l is common to all metaphosphate glasses and is ascribed to chain backbone vibrations. The DSC measurements yielded a Tg of 96°C; the onset of crystallization occurred at about 132°C. 3.2. Calculation o f activation energy from FIR data Exarhos et al. [2] have shown that the activation energies for ionic conduction in inorganic oxide glasses are related to the cation-motion vibrational frequencies obtained from the FIR spectra of the glasses. Upon consideration of the pseudofree ion approach of Rice and Roth [9], a closely related formalism was developed

.~

/z

f=

HI

H2

H3

I~

Acs

dr I

:~H

Hi=Ho(~_--~) I

I

1

I

IOO

200

300

400

(J.) (cm-I)

ACS= H o (or3- o])

Fig. 1. Far infrared absorption spectrum of glassy TIPO 3. Fig. 2. Powder pattern for the chemical shift interaction (solid line), and the effect of dipolar broadening (dashed line).

54

L. 1t:.Panek et al. / NMR and IR study o f cation motion

using the vibrational energetics for the ion and its site. The basic form of the equation is E a = ½(/.t/2p2),

(I)

where ~t is the reduced mass, l the ion motion distance to its next site and v is the ion site vibrational frequency. For the motion of a cation/a ~ M, where M is the cation mass. This relationship was shown to yield values for E a of a number o f metaphosphate and silicate glasses which are in good agreement with those observed for conductance. The cation-motion frequency for T1÷ motion in vitreous T1PO3 was found to be 80 cm -1 in the FIR spectrum discussed above, and its mass is known. The site-tosite distance can be estimated from the crystal structure of RbPO3, as it was for vitreous RbPO3, because the radii of the TI+ and Rb ÷ ions are the same. For RbPO3, the ionic radius of Rb ÷ is 1.47 A and lo is 4.23 A, so lo is also taken as 4.23 A for vitreous T1PO3. Thus, the value o f E a found with eq. (1) is 1.09 eV. 3.3. TI 2°5 N M R chemical shift measurements

In general, the chemical shift interaction yields an absorption spectrum, termed a powder pattern, as illustrated by the solid curve in fig. 2. The locations of the two shoulders H1 and//3, and the divergence //2, are given in terms of the principal components of the chemical shift tensor o (ol, a2 and a3). The magnetic dipoledipole, pseudodipole and exchange interactions act to smooth out the features of the powder pattern as illustrated by the dashed curve in fig. 2. The relative amount of broadening is expressed by the ratio Acs/2o, where Acs =Ha - HI = (2rrvo/7)(o3 - o l )

(lOll < < 1)

(2)

and 2o is the width of the broadening function (assumed to be gaussian). The derivative of the absorption is observed experimentally, and may or may not exhibit the structure of the powder pattern as illustrated in fig. 3, depending on the value of the ratio Acs/2O that characterizes the spectrum. Whenever resolved structure is present, as in fig. 3b, it is relatively easy to determine the values of the oi's from computer simulations. However, when the spectrum is structureless as in fig. 3a the task is more difficult. Baugher and Bray [3] have shown that whenever resolved structure is absent, the values of o3-o~ and 2o (the broadening width) can be determined by fitting the experimental linewidths as a function of operating frequency to the empirical equation W - - = 1 + 0.225 (Acs/2O) 2, 2o

0 ~< (Acs/2O) ~< 1,

(3)

where W is the linewidth. (W is defined as the separation, measured along the frequency axis, of the positive and negative extrema in the derivative of the line shape.) Equation (3) applies only to structureless spectra resulting from excessive

55

L. W. Panek et al. / NMR and IR study o f cation motion TIPO 3 gla s.s

J TIPO 3 crystal

Fig. 3. Computer simulations of the derivatives of a chemical shift powder pattern for two values of the ratio Acs/2O. Fig. 4. Experimental line-shape derivative of T12°s for glassy and polycrystalline T1PO3 at vo = 16 MHz and room temperature. dipolar, pseudo-dipolar or exchange broadening and not from distributions in the values o f the components o f the chemical shift tensor (el'S). The values o f Aes/2tr obtained from eq. (3) must be less than 1 to be consistent with the assumptions used to obtain the equation. Values of Acs/2O greater than 1 indicate that a distribution in the oi's is responsible for the lack o f structure in the spectra. Slightly asymmetric and structureless absorption derivatives resembling those observed for T12°s in previous studies [3,4] were observed at all frequencies for the glass. The polycrystal yielded structureless and symmetric absorption derivatives. Examples o f the experimental spectra are given in fig. 4, and the experimental linewidths as a function of the operating frequency are given in fig. 5. The linewidths for the glass were fitted to eq. (3); the results are given in table 1 with the values o f Acs/2tl calculated for Vo = 26.5 MHz using the results of the least-squares fit. This value o f Acs/2O = 3.3 corresponds to a line shape with a clearly resolved Table 1 Results of least-squares fit of the linewidths to eq. (3) and the NMR measurements of Oiso.

TIPO3 glass TIPO3 crystal

2a ((3)

a3

1.86 -

5.6 × 10 - 4 -

-

-

0"1

Oiso at 16 MHz

ACs/2O at 26.5 MHz

(0.9 -+0.5) × 10 - 4 (4.3 +-0.5) × 10 - 4

3.3 -

56

L. W. Panek et al. / NMR and IR study o f cation motion

6

• TIPO3 Glass

//~

5 1.9

4

,.J

I

a

i

,b ,2

I

,.

I

26.

Frequency(MHz) Fig. 5. T1205 linewidths as a function of frequency for both glassy and polycrystalline T1PO 3.

shoulder. Since no shoulder is observed, the results are inconsistent, and eq. (3) is not applicable. Consequently, the lack of resolved structure is not due to large broadening effects, but instead substantial distributions in the values of the oi's must be present in the glass as observed in other thallium glasses [3,4]. The isotropic chemical shift [4] Ois O = 1(O 1 + 02 -I- 0"3)

(4)

was measured at 16 MHz for both the glass and the polycrystal using a reference solution of thallium acetate and water: the results are given in table 1. Since for the case of axial symmetry Ho(1 -Oiso) is the field about which the first moment of the line shape vanishes, Oiso was calculated from the experimental line shape for the glass. In the polycrystal, Oiso was measured using the zero crossing of the symmetric line-shape derivative. A positive shift indicating an ionic environment was observed in both the glass and the polycrystal, with the polycrystal environment being slightly more ionic than that for the glass. The shifts are similar to those obtained for thallium borate glasses of low thallium content (less than 10 mol % TI20) [4].

3.4. NMR motional narrowing of the T12°5 resonance Thelinewidth of the T12°5 resonance at 16 MHz in glassy T1PO3 was measured as a function of the temperature between 25 and 170°C. It was found that glassy T1PO3

57

L.W. Panek et al. / NMR and IR study o f cation motion

IO

~e O m t. Z

"i

4

1

1

300

1

1

i

i

340 380 TEMPERTURE ( K * )

i

i

420

i

i

460

Fig. 6. Tl20Slmewid~s ~ a ~nctionoftemperatureforglassy ~PO3atl6 MHz. crystallizes readily for temperatures greater than 130°C, and thus measurements had to be made quickly, using solid slugs to retard the surface crystallization process. The presence of crystalline T1PO3 in the glassy sample at elevated temperatures is readily detectable since the linewidth in polycrystalline T1PO3, which does not narrow in this temperature range, is much larger than the motionally narrowed resonance in the glass. The two resonances are clearly distinguishable, and it is easy to confirm that motional narrowing only in the glass is being observed. The T12°s linewidth for T1PO3 glass is plotted as a function of temperature in fig. 6. The linewidth decreases dramatically with temperature in the region 90-130°C. This variation was analyzed using the phenomenological equation of Hendrickson and Bray [8]. A least-squares fit to this equation, which takes into account contributions to W, due to magnetic field inhomogeneity was carried out using all the linewidth measurements *. The solid line in fig. 6 represents the leastsquares fit, which was obtained with the following parameters: E a = 1.19 eV, and B = 2.25 × 10 -~s kHz. The parameter B is a phenomenological parameter which indicates the range of the activated cation motion and is related to the spin-lattice relaxation time for the activated ions [8]. 4. Discussion Although the short-range shucture of T1P03 glass and polycrystal are believed to be similar, the NMR measurements presented above indicate differences in the thai* The least-squares fit was carried out by S.A. Feller, using the computer program of Hendrickson [10].

58

L.W. Panek et al. / NMR and IR study o f cation motion

lium environments for the glass and the polycrystal. The chemical shift interaction has an anisotropic contribution in the glass, indicated by the strong frequency dependence of the linewidth. The linewidths for the polycrystal, on the other hand, have no frequency dependence and only an isotropic contribution. The results of the least-squares fit to eq. (3) for the glass indicate that there must be a distribution in the oi's. The values of Oiso for the glass and polycrystal indicate an ionic environment for thallium in both, although the T1÷ environments in the polycrystal are slightly more ionic than those in the glass. The thallium enviroments in the glass can be expected to be slightly different from the crystal, as is observed, since the random glass structure will produce a variety of T1-O bond lengths and bond strengths. Such a distribution in T1-O bond lengths and bond strengths can account for the observation of an isotropic chemical shift, a more covalent value for Oiso and distributions in the chemical shift parameters for the glass. The lack of an anisotropic contribution to the linewidth for the polycrystal is also expected since the thallium cations are in sites of high symmetry. For both the polycrystal and the glass the broadening of the spectra due to magnetic dipoledipole, pseudo-dipolar and exchange effects is almost identical. This is indicated by the fact that the average T12°s linewidth in the polycrystal (1.8 G) is almost exactly the same as the zero field linewidth predicted for the glass (2o = 1.86 G) from the least-squares fit to eq. (3). Thus, although the thallium sites in the glass are slightly more covalent than in the crystal, both sites are essentially ionic and only small changes in the ionicity are being observed. The fact that motional narrowing is observed in the glass and not in the polycrystal indicates that the thallium atoms are more loosely bound in the random glass network than in the rigid crystal structure. The activation energies of 1.19 eV (NMR) and 1.09 eV (vibrational calculation) agree well and are relatively large. The small value of the parameter B indicates long-range motion for the thallium ions: values o f B > 10 -3 kHz correspond to local ion motion and values <10 - a kHz correspond to long-range motion [8]. The ions, via site-to-site hopping, move throughout the open glass network of PO4 tetrahedra. Motional narrowing is observed in T1PO3 glass but not in the thallium silicate, thallium germanate and thallium borate glass sytems investigated up to 300°C [4]. The mobility of the T1÷ ions in the phosphate glass may arise from either of two effects: (1) distributions in the character of the thallium ions may yield some ions with relatively low activation energies, or (2) the network structure of the phosphate glass may be sufficiently loose or open to permit long-range motion of the large thallium ions. 5. Conclusion

The observation of motional narrowing and the chemical shift contributions to the TI 2°s linewidths of TIPO3 glass and polycrystal indicate a difference in the thai-

L.W. Panek et aL / NMR and lR study o f cation motion

59

lium sites between the glass and the polycrystal. There exist variations in the thallium sites in the glass that are responsible for the distributions observed in the chemical shift parameters. The thallium environment is ionic in both the glass and polycrystal, being slighly more ionic in the polycrystal. Distributions in the character of the T1-O bonds in the glass may enable thallium ions to be thermally activated at modest temperatures. On the other hand, it may be the loose or open network in glassy T1PO3 that is primarily responsible for the thermally activated cation motion and not the small difference in the T1-O bonds between the glass and polycrystal.

Acknowledgements This research was supported by the Materials Science Program, Brown University, NSF Grant No. 73-06515 A02, and the Materials Science Program, Harvard University, NSF Grant No. DMR-72-03020.

References [1] G.J. Exarhos, P.J. Miller and W.M. Risen, J. Chem. Phys. 60 (1974) 4145. [2] G.J. Exarhos, P.J. Miller and W.M. Risen, Solid State Commun. 17, (1975) 29. [3] J.F. Baugher and P.J. Bray, Phys. Chem. Glasses 10 (1969) 77. [4] L.W. Panek and P.J. Bray, J. Chem. Phys. 66 (1977). [5] N. Nachtrieb and R.K. Momii, Reactivity of Solids (Wiley New York, 1969) p. 675. [6] Von L. Kolditz and E. Wahner, Z. Anorg. AUg.Chem. 400, (1973) 161. [7] K. Otto and M.E. Milberg, J. Am. Ceram. Soc. 50 (1967) 513. [8] J.R. Hendrickson and P.J. Bray, J. Mag. Res. 9 (1973) 341. [9] M.J. Rice and W.L. Roth, Solid State Chem. 4, (1972) 294. [10] J.R. Hendrcikson, Ph.D. Thesis, Brown University (1973).