- Email: [email protected]
Cryogenic EXAFS investigations of the short-range structural environment of gallium in PbO–Ga2O3 glasses
Journal of Non-Crystalline Solids 256&257 (1999) 119±123
www.elsevier.com/locate/jnoncrysol
Cryogenic EXAFS investigations of the short-range structural environment of gallium in PbO±Ga2O3 glasses Jong Heo a
a,* ,
Yong Gyu Choi a, Vladimir A. Chernov
b
Non-Crystalline Materials Laboratory, Department of Materials Science and Engineering, Pohang University of Science and Technology, San 31, Hyoja-dong, Nam-gu, Pohang, Kyungbuk 790-784, South Korea b Siberian Synchrotron Radiation Center, Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russian Federation
Abstract Gallium K-edge extended X-ray absorption ®ne structure (EXAFS) spectra of PbO±Ga2 O3 glasses were recorded at liquid-nitrogen temperature (77 K) to understand the coordination scheme of gallium in these glasses. Four oxygens were found to be bonded to each Ga, forming GaO4 tetrahedra with an average bond distance of 1.855±1.862 A. Assuming a non-Gaussian distribution of Ga±O bond distances provided better results with a smaller R-factor com pared to the Gaussian counterpart. Two-subshell ®tting indicated that oxygens with Ga±O bond distance of 1.87 A are bonded to three cations, while the shorter Ga±O bonded oxygens are two-coordinated. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Infrared, Raman and nuclear magnetic resonance (NMR) spectroscopic studies are consistent with the hypothesis that most gallium ions in PbO±Ga2 O3 glass are in four-fold coordination by oxygens [1±3]. Quantitative analysis by X-ray and neutron diraction studies showed less than 10% of the total gallium ions are surrounded by six oxygens [4]. A recent extended X-ray absorption ®ne structure (EXAFS) analysis also proved the existence of a four-fold coordination scheme of gallium, with a negligible amount of six-fold coordination [5]. On the other hand, the average Ga± in glasses were O bond lengths of 1.858 0.003 A normally found for crystals longer than the 1.83 A, with a similar coordination scheme. These long
* Corresponding author. Tel.: +82-562 279 2147; fax: +82-562 279 2399; e-mail: [email protected]
Ga±O bonds seemed to be associated with the three-coordinated oxygens. However, since the room-temperature EXAFS spectra provided only an average of Ga±O distances for each glass, no quantitative information on the distribution of the bond lengths could be obtained. The present study, therefore, aimed at detailed analyses of the oxygen coordination around gallium in binary PbO±Ga2 O3 glasses using the Ga K-edge EXAFS spectra recorded at liquid-nitrogen temperature (77 K). 2. Experimental procedure All spectra for glass samples were recorded at liquid-nitrogen temperature. The two end points of the Fourier transform, kmin and kmax , were ÿ1 , respectively. Non3.0 1.0 and 14.5 2.0 A linear least-squares ®ttings were carried in R-space (Fourier transformed spectra) within the range of
0022-3093/99/$ - see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 3 9 3 - 2
120
J. Heo et al. / Journal of Non-Crystalline Solids 256&257 (1999) 119±123
where the Ga±O correlated partial dis0.9±2.2 A, tribution peak is located. Detailed description on the sample preparation and EXAFS measurements are provided elsewhere [5]. 3. Methods of ®ttings and results Experimental Ga K-edge EXAFS spectra in Kspace for three glasses recorded at 77 K are shown in Fig. 1. A larger amplitude and more regular variation of EXAFS oscillations were found for ÿ1 in contrast to those recorded at room k > 12 A temperature [5]. In the case of a PbGa2 O4 crystal, the room temperature EXAFS spectrum had an
Fig. 1. k3 -weighted Ga K-edge v k spectra of three glasses with the composition: (a) 70PbO±30Ga2 O3 ; (b) 75PbO±25Ga2 O3 ; (c) 80PbO±20Ga2 O3 ; (d) a crystalline standard of PbGa2 O4 . Solid lines and dotted lines represent the spectra recorded at liquidnitrogen and room temperatures, respectively.
ÿ1 for adequate signal to noise ratio at k 14:5 A measurements and therefore, the spectrum was not recorded at 77 K. Three dierent ®tting models were used to attain the most reasonable ®tting of the Ga±O partial correlation peak. The ®rst model (Model I) assumed a Gaussian distribution of Ga± O bond lengths. Four independent ®tting variables were used: the energy origin shift (E0 ); Ga±O bond distance (RGa±o ); coordination number (N) of oxygens around Ga and the EXAFS-type Debye± Waller factor (r2 ). Two additional ®tting variables used in Model II were the third (C3 ) and the fourth (C4 ) cumulants. This expansion on cumulants was used as a convenient way to express the disorder independent of the model chosen for the atomic distribution function [6]. The presence of a certain order of non-Gaussian distributions of Ga±O bond distances could be corrected by introducing these higher order cumulants [7]. In Model III, ®ttings with two dierent Ga±O distances in the GaO4 tetrahedra were attempted using seven ®tting variables. After the coordination number N I of oxygens with a longer bond distance was calculated, the other N II was obtained simply by subtracting N I from four. Results of each ®tting are listed in Table 1, along with the variables used for the calculation. The R-factor, calculated by normalizing the dierences between experimental and theoretical values against the magnitude of experimental values, provides a measure of goodness of ®t. The R-factor is the smallest for Model II for all glasses (Table 1). The cumulant ®tting scheme of Model II seems to take the best `snapshot' of distribution of oxygens around Ga, judged by the R-factor and coincidence of the ®tted values with the structural information obtained from other investigations (Table 2). On the other hand, the R-factor of Model I is the largest of all. Furthermore, Ga±O bond lengths obtained from Model I diered from those obtained from the previous room temperature EXAFS and neutron scattering analyses [4,5,8]. In addition, oxygen coordination numbers which were smaller than four for Model I, increased to approximately four for Model II. We suggest that the amplitude envelope of the Ga±O correlation peak should be analyzed by assuming a non-Gaussian distribution of Ga±O bond lengths
a
0.015 1.874 (0.008) 3.68 (0.49) 675 (114)
0.003 1.851 (0.016) 4.06 (0.45) 917 (68) ÿ3.85 (1.66) 3.67 (710) 1.822 (0.08) 1.10 316 (841)
0.005 1.868 (0.016) 2.90 (0.74) 471 (274)
0.008 1.867 (0.005) 3.59 (0.47) 197 (55)
0.005 1.857 (0.012) 3.95 (0.33) 285 (79) ÿ1.01 (2.16) 1.34 (721)
Model II
70PbO±30Ga2 O3 Model I
Model III
Model I
Model II
PbGa2 O4
1.817 (0.06) 1.54 10 (523)
0.006 1.871 (0.013) 2.46 (0.68) 6.8 (321)
Model III 0.009 1.864 (0.008) 3.86 (0.36) 274 (61)
0.004 1.855 (0.009) 4.08 (0.38) 350 (112) ÿ1.02 (3.18) 1.20 (821)
Model II
75PbO±25Ga2 O3 Model I
1.821 (0.06) 1.62 10 (497)
0.006 1.873 (0.014) 2.38 (0.54) 4.1 (317)
Model III
0.011 1.846 (0.007) 3.80 (0.42) 196 (83)
0.002 1.862 (0.006) 4.00 (0.31) 314 (87) 1.90 (1.86) 2.33 (519)
Model II
80PbO±20Ga2 O3 Model I
1.824 (0.05) 1.84 6.2 (352)
2.16 (0.73) 10 (442)
0.006 1.876
Model III
2 in model III only for glasses. Values in the parentheses are the estimated uncertainties. E0 shifts are within ÿ2±6 eV in all cases. Upper limit of r2 was set to 10ÿ4 A
N(II) 2 ) r2 (II) (10ÿ5 A
RGa±O (II) (A)
4 ) C4 (10ÿ5 A
3 ) C3 (10ÿ4 A
2 ) r2 (I)(10ÿ5 A
N(I)
R-factor RGa±O (I) (A)
Variable
Table 1 Fitting variables and results of each model used to ®t the Ga±O pair correlation peak in Ga K-edge EXAFS taken at a liquid-nitrogen temperature (77 K) for glasses and room temperature for the PbGa2 O4 crystal a
J. Heo et al. / Journal of Non-Crystalline Solids 256&257 (1999) 119±123 121
122
J. Heo et al. / Journal of Non-Crystalline Solids 256&257 (1999) 119±123
Table 2 unit in PbO±Ga2 O3 glasses Average Ga±O bond lengths in A Composition
Source EXAFS
70PbO±30Ga2 O3 75PbO±25Ga2 O3 80PbO±20Ga2 O3 a b c
1.856 1.858 1.861
a
RT [5]
EXAFS LN2 (Model I, this study)
EXAFS LN2 (Model II, this study)
Neutron scattering [4]
1.867 1.864 1.846
1.857 1.855 1.862
1.86
b
Neutron scattering [8] 1.8587
c
1.8602
k-range: 3±12 A ÿ1 , without higher order cumulants. Single-shell ®tting, R-range: 0.9±2.2 A, Value for 50PbO±50GaO1:5 (mol%) composition. Value for 67PbO±33Ga2 O3 (mol%) composition.
in glasses, especially when an EXAFS spectrum is recorded at a cryogenic temperature (Fig. 2). Model III assumes two dierent sets of Ga±O and the other at bond distances, i.e. one at 1.820 A 1.860 A. Results of analyses showed that the longer Ga±O distances in glasses were 1.873 A, while the shorter ones were within 1.820 A. The coordination number for a longer Ga±O subshell was in the range of 2.16±2.46 and tended to increase with increasing Ga2 O3 concentration. However, the R-factor calculated from Model III was larger than that calculated from Model II. This dierence again shows that the ®tting, by assuming a non-Gaussian distribution of the Ga± O distance, can represent the most reasonable Ga environment among the three models used for the analysis.
4. Discussion From the results of calculations based on the three dierent structural models, the following nearest-neighbor environment of Ga can be proposed. Ga in the glasses have four oxygens to form GaO4 tetrahedra as based on the calculated coordination number of 4.00 from Model II. This tetrahedral coordination scheme was also veri®ed in previous investigations [3±5]. The Ga±O bond on average, length forming tetrahedra is 1.858 A, which is again comparable to those reported previously. However, there seems to be a nonGaussian distribution of Ga±O bond lengths and a single averaged bond distance can misrepresent the
Fig. 2. Magnitude of the Fourier transforms of k3 -weighted v k spectra for: (a) 70PbO±30Ga2 O3 ; (b) 75PbO±25Ga2 O3 ; (c) 80PbO±20Ga2 O3 glasses recorded at liquid-nitrogen temperature; (d) the standard crystal PbGa2 O4 at room temperature. Solid lines and dots denote data are from the experimental and those ®tted with model II, respectively. The phase shifts were not corrected and only the nearest-neighboring peak was ®tted.
J. Heo et al. / Journal of Non-Crystalline Solids 256&257 (1999) 119±123
real structure. An accurate description of the detailed distribution is dicult at present. However, it is clear that Ga±O bond distances cannot be explained either by a single average number or by only two distinct numbers, and there is a degree of non-Gaussian distribution. It has been suggested that oxygens exist bonded to three cations in these heavy metal oxide glasses [4,5,9]. The presence of three-coordinated oxygens was proposed mainly because of the formation of GaO4 tetrahedra in Ga2 O3 . In other words, if all the Ga2 O3 forms GaO4 tetrahedra, which seems to be the case for these glasses [2±5], there will not be enough oxygens available. Formation of threecoordinated oxygens is, therefore, necessary to compensate this oxygen de®ciency. Ga±O bond lengths are between 1.81 and 1.87 in a PbGa2 O4 crystal [10]. Speci®cally, oxygens A bonded to three cations have a Ga-O bond dis while those bonded to two tance of 1.83±1.87 A As a Ga have shorter Ga±O distances of 1.82 A. result, the Ga±O bond lengths are asymmetrically distributed in the PbGa2 O4 crystal. In glasses, an average Ga±O bond distance from the room temperature EXAFS [5] and Model II of the current This length is considanalysis was about 1.86 A. erably longer than the Ga±O distance of two coordinated oxygens. In addition, Model II, considering the presence of long Ga±O bonds, i.e., the non-Gaussian distribution, provided the most reasonable ®ttings. This non-Gaussian distribution of oxygens around Ga seems to be evidence of two- and three-coordinated oxygens in glasses similar to the case of PbGa2 O4 crystal. In addition, in Fig. 2 which is due to there is a peak at 3.13 A the Ga±Ga bond length as reported for the PbGa2 O4 crystal and PbO±Ga2 O3 glasses [4]. Model III, considering two distinct Ga±O bond lengths, is consistent with assuming that more than two out of four oxygens bonded to Ga have a Ga± and they are most probably O distance of 1.87 A connected to three cations. On the other hand, the remaining oxygens are located at a distance of and form two-coordinated oxygens. 1.82 A
123
Therefore, the two-subshell calculation, as in Model III, can provide an idea of how many of those oxygens forming GaO4 tetrahedra are bonded to three cations, even though calculations using Model II may describe the overall structure more precisely. 5. Conclusions Short-range order structural parameters around Ga in PbO±Ga2 O3 glasses were analyzed from the Ga K-edge EXAFS spectra recorded at a liquidnitrogen temperature. Four oxygens were found to be bonded to each gallium, forming GaO4 tetrahedra with an average bond distance of 1.855± A model assuming a non-Gaussian 1.862 A. distribution of Ga±O bond distance provided the best ®t with the smallest R-factor compared to the other models. Models with two distinct Ga±O bond distances have approximately 60% of oxygens bonded to Ga as three-coordinated and this amount decreases with decreasing Ga2 O3 concentration. References [1] A.A. Kharlamov, R.M. Almeida, J. Heo, J. Non-Cryst. Solids 202 (1996) 233. [2] F. Miyaji, S. Sakka, J. Non-Cryst. Solids 134 (1991) 77. [3] F. Miyaji, K. Tadanaga, T. Yoko, S. Sakka, J. Non-Cryst. Solids 139 (1992) 268. [4] F. Miyaji, T. Yoko, J. Jin, S. Sakka, T. Fukunaga, M. Misawa, J. Non-Cryst. Solids 175 (1994) 211. [5] Y.G. Choi, J. Heo, V.A. Chernov, J. Non-Cryst. Solids 221 (1997) 199. [6] G. Bunker, Nucl. Instrum. and Meth. 207 (1983) 437. [7] E.D. Crozier, J.J. Rehr, R. Ingalls, in: D.C. Koningsberger, R. Prins (Eds.), X-Ray Absorption: Principles, Applications, Techniques of EXAFS, SEXAFS and XANES, Wiley, New York, 1988. [8] A.C. Hannon, J.M. Parker, B. Vessal, J. Non-Cryst. Solids 196 (1996) 187. [9] J.C. Lapp, Bull. Am. Ceram. Soc. 71 (1992) 1543. [10] Von K.-B. Plotz, H. Muller-Buschbaum, Z. Anorg. Allg. Chem. 488 (1982) 38.
www.elsevier.com/locate/jnoncrysol
Cryogenic EXAFS investigations of the short-range structural environment of gallium in PbO±Ga2O3 glasses Jong Heo a
a,* ,
Yong Gyu Choi a, Vladimir A. Chernov
b
Non-Crystalline Materials Laboratory, Department of Materials Science and Engineering, Pohang University of Science and Technology, San 31, Hyoja-dong, Nam-gu, Pohang, Kyungbuk 790-784, South Korea b Siberian Synchrotron Radiation Center, Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russian Federation
Abstract Gallium K-edge extended X-ray absorption ®ne structure (EXAFS) spectra of PbO±Ga2 O3 glasses were recorded at liquid-nitrogen temperature (77 K) to understand the coordination scheme of gallium in these glasses. Four oxygens were found to be bonded to each Ga, forming GaO4 tetrahedra with an average bond distance of 1.855±1.862 A. Assuming a non-Gaussian distribution of Ga±O bond distances provided better results with a smaller R-factor com pared to the Gaussian counterpart. Two-subshell ®tting indicated that oxygens with Ga±O bond distance of 1.87 A are bonded to three cations, while the shorter Ga±O bonded oxygens are two-coordinated. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Infrared, Raman and nuclear magnetic resonance (NMR) spectroscopic studies are consistent with the hypothesis that most gallium ions in PbO±Ga2 O3 glass are in four-fold coordination by oxygens [1±3]. Quantitative analysis by X-ray and neutron diraction studies showed less than 10% of the total gallium ions are surrounded by six oxygens [4]. A recent extended X-ray absorption ®ne structure (EXAFS) analysis also proved the existence of a four-fold coordination scheme of gallium, with a negligible amount of six-fold coordination [5]. On the other hand, the average Ga± in glasses were O bond lengths of 1.858 0.003 A normally found for crystals longer than the 1.83 A, with a similar coordination scheme. These long
* Corresponding author. Tel.: +82-562 279 2147; fax: +82-562 279 2399; e-mail: [email protected]
Ga±O bonds seemed to be associated with the three-coordinated oxygens. However, since the room-temperature EXAFS spectra provided only an average of Ga±O distances for each glass, no quantitative information on the distribution of the bond lengths could be obtained. The present study, therefore, aimed at detailed analyses of the oxygen coordination around gallium in binary PbO±Ga2 O3 glasses using the Ga K-edge EXAFS spectra recorded at liquid-nitrogen temperature (77 K). 2. Experimental procedure All spectra for glass samples were recorded at liquid-nitrogen temperature. The two end points of the Fourier transform, kmin and kmax , were ÿ1 , respectively. Non3.0 1.0 and 14.5 2.0 A linear least-squares ®ttings were carried in R-space (Fourier transformed spectra) within the range of
0022-3093/99/$ - see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 3 9 3 - 2
120
J. Heo et al. / Journal of Non-Crystalline Solids 256&257 (1999) 119±123
where the Ga±O correlated partial dis0.9±2.2 A, tribution peak is located. Detailed description on the sample preparation and EXAFS measurements are provided elsewhere [5]. 3. Methods of ®ttings and results Experimental Ga K-edge EXAFS spectra in Kspace for three glasses recorded at 77 K are shown in Fig. 1. A larger amplitude and more regular variation of EXAFS oscillations were found for ÿ1 in contrast to those recorded at room k > 12 A temperature [5]. In the case of a PbGa2 O4 crystal, the room temperature EXAFS spectrum had an
Fig. 1. k3 -weighted Ga K-edge v k spectra of three glasses with the composition: (a) 70PbO±30Ga2 O3 ; (b) 75PbO±25Ga2 O3 ; (c) 80PbO±20Ga2 O3 ; (d) a crystalline standard of PbGa2 O4 . Solid lines and dotted lines represent the spectra recorded at liquidnitrogen and room temperatures, respectively.
ÿ1 for adequate signal to noise ratio at k 14:5 A measurements and therefore, the spectrum was not recorded at 77 K. Three dierent ®tting models were used to attain the most reasonable ®tting of the Ga±O partial correlation peak. The ®rst model (Model I) assumed a Gaussian distribution of Ga± O bond lengths. Four independent ®tting variables were used: the energy origin shift (E0 ); Ga±O bond distance (RGa±o ); coordination number (N) of oxygens around Ga and the EXAFS-type Debye± Waller factor (r2 ). Two additional ®tting variables used in Model II were the third (C3 ) and the fourth (C4 ) cumulants. This expansion on cumulants was used as a convenient way to express the disorder independent of the model chosen for the atomic distribution function [6]. The presence of a certain order of non-Gaussian distributions of Ga±O bond distances could be corrected by introducing these higher order cumulants [7]. In Model III, ®ttings with two dierent Ga±O distances in the GaO4 tetrahedra were attempted using seven ®tting variables. After the coordination number N I of oxygens with a longer bond distance was calculated, the other N II was obtained simply by subtracting N I from four. Results of each ®tting are listed in Table 1, along with the variables used for the calculation. The R-factor, calculated by normalizing the dierences between experimental and theoretical values against the magnitude of experimental values, provides a measure of goodness of ®t. The R-factor is the smallest for Model II for all glasses (Table 1). The cumulant ®tting scheme of Model II seems to take the best `snapshot' of distribution of oxygens around Ga, judged by the R-factor and coincidence of the ®tted values with the structural information obtained from other investigations (Table 2). On the other hand, the R-factor of Model I is the largest of all. Furthermore, Ga±O bond lengths obtained from Model I diered from those obtained from the previous room temperature EXAFS and neutron scattering analyses [4,5,8]. In addition, oxygen coordination numbers which were smaller than four for Model I, increased to approximately four for Model II. We suggest that the amplitude envelope of the Ga±O correlation peak should be analyzed by assuming a non-Gaussian distribution of Ga±O bond lengths
a
0.015 1.874 (0.008) 3.68 (0.49) 675 (114)
0.003 1.851 (0.016) 4.06 (0.45) 917 (68) ÿ3.85 (1.66) 3.67 (710) 1.822 (0.08) 1.10 316 (841)
0.005 1.868 (0.016) 2.90 (0.74) 471 (274)
0.008 1.867 (0.005) 3.59 (0.47) 197 (55)
0.005 1.857 (0.012) 3.95 (0.33) 285 (79) ÿ1.01 (2.16) 1.34 (721)
Model II
70PbO±30Ga2 O3 Model I
Model III
Model I
Model II
PbGa2 O4
1.817 (0.06) 1.54 10 (523)
0.006 1.871 (0.013) 2.46 (0.68) 6.8 (321)
Model III 0.009 1.864 (0.008) 3.86 (0.36) 274 (61)
0.004 1.855 (0.009) 4.08 (0.38) 350 (112) ÿ1.02 (3.18) 1.20 (821)
Model II
75PbO±25Ga2 O3 Model I
1.821 (0.06) 1.62 10 (497)
0.006 1.873 (0.014) 2.38 (0.54) 4.1 (317)
Model III
0.011 1.846 (0.007) 3.80 (0.42) 196 (83)
0.002 1.862 (0.006) 4.00 (0.31) 314 (87) 1.90 (1.86) 2.33 (519)
Model II
80PbO±20Ga2 O3 Model I
1.824 (0.05) 1.84 6.2 (352)
2.16 (0.73) 10 (442)
0.006 1.876
Model III
2 in model III only for glasses. Values in the parentheses are the estimated uncertainties. E0 shifts are within ÿ2±6 eV in all cases. Upper limit of r2 was set to 10ÿ4 A
N(II) 2 ) r2 (II) (10ÿ5 A
RGa±O (II) (A)
4 ) C4 (10ÿ5 A
3 ) C3 (10ÿ4 A
2 ) r2 (I)(10ÿ5 A
N(I)
R-factor RGa±O (I) (A)
Variable
Table 1 Fitting variables and results of each model used to ®t the Ga±O pair correlation peak in Ga K-edge EXAFS taken at a liquid-nitrogen temperature (77 K) for glasses and room temperature for the PbGa2 O4 crystal a
J. Heo et al. / Journal of Non-Crystalline Solids 256&257 (1999) 119±123 121
122
J. Heo et al. / Journal of Non-Crystalline Solids 256&257 (1999) 119±123
Table 2 unit in PbO±Ga2 O3 glasses Average Ga±O bond lengths in A Composition
Source EXAFS
70PbO±30Ga2 O3 75PbO±25Ga2 O3 80PbO±20Ga2 O3 a b c
1.856 1.858 1.861
a
RT [5]
EXAFS LN2 (Model I, this study)
EXAFS LN2 (Model II, this study)
Neutron scattering [4]
1.867 1.864 1.846
1.857 1.855 1.862
1.86
b
Neutron scattering [8] 1.8587
c
1.8602
k-range: 3±12 A ÿ1 , without higher order cumulants. Single-shell ®tting, R-range: 0.9±2.2 A, Value for 50PbO±50GaO1:5 (mol%) composition. Value for 67PbO±33Ga2 O3 (mol%) composition.
in glasses, especially when an EXAFS spectrum is recorded at a cryogenic temperature (Fig. 2). Model III assumes two dierent sets of Ga±O and the other at bond distances, i.e. one at 1.820 A 1.860 A. Results of analyses showed that the longer Ga±O distances in glasses were 1.873 A, while the shorter ones were within 1.820 A. The coordination number for a longer Ga±O subshell was in the range of 2.16±2.46 and tended to increase with increasing Ga2 O3 concentration. However, the R-factor calculated from Model III was larger than that calculated from Model II. This dierence again shows that the ®tting, by assuming a non-Gaussian distribution of the Ga± O distance, can represent the most reasonable Ga environment among the three models used for the analysis.
4. Discussion From the results of calculations based on the three dierent structural models, the following nearest-neighbor environment of Ga can be proposed. Ga in the glasses have four oxygens to form GaO4 tetrahedra as based on the calculated coordination number of 4.00 from Model II. This tetrahedral coordination scheme was also veri®ed in previous investigations [3±5]. The Ga±O bond on average, length forming tetrahedra is 1.858 A, which is again comparable to those reported previously. However, there seems to be a nonGaussian distribution of Ga±O bond lengths and a single averaged bond distance can misrepresent the
Fig. 2. Magnitude of the Fourier transforms of k3 -weighted v k spectra for: (a) 70PbO±30Ga2 O3 ; (b) 75PbO±25Ga2 O3 ; (c) 80PbO±20Ga2 O3 glasses recorded at liquid-nitrogen temperature; (d) the standard crystal PbGa2 O4 at room temperature. Solid lines and dots denote data are from the experimental and those ®tted with model II, respectively. The phase shifts were not corrected and only the nearest-neighboring peak was ®tted.
J. Heo et al. / Journal of Non-Crystalline Solids 256&257 (1999) 119±123
real structure. An accurate description of the detailed distribution is dicult at present. However, it is clear that Ga±O bond distances cannot be explained either by a single average number or by only two distinct numbers, and there is a degree of non-Gaussian distribution. It has been suggested that oxygens exist bonded to three cations in these heavy metal oxide glasses [4,5,9]. The presence of three-coordinated oxygens was proposed mainly because of the formation of GaO4 tetrahedra in Ga2 O3 . In other words, if all the Ga2 O3 forms GaO4 tetrahedra, which seems to be the case for these glasses [2±5], there will not be enough oxygens available. Formation of threecoordinated oxygens is, therefore, necessary to compensate this oxygen de®ciency. Ga±O bond lengths are between 1.81 and 1.87 in a PbGa2 O4 crystal [10]. Speci®cally, oxygens A bonded to three cations have a Ga-O bond dis while those bonded to two tance of 1.83±1.87 A As a Ga have shorter Ga±O distances of 1.82 A. result, the Ga±O bond lengths are asymmetrically distributed in the PbGa2 O4 crystal. In glasses, an average Ga±O bond distance from the room temperature EXAFS [5] and Model II of the current This length is considanalysis was about 1.86 A. erably longer than the Ga±O distance of two coordinated oxygens. In addition, Model II, considering the presence of long Ga±O bonds, i.e., the non-Gaussian distribution, provided the most reasonable ®ttings. This non-Gaussian distribution of oxygens around Ga seems to be evidence of two- and three-coordinated oxygens in glasses similar to the case of PbGa2 O4 crystal. In addition, in Fig. 2 which is due to there is a peak at 3.13 A the Ga±Ga bond length as reported for the PbGa2 O4 crystal and PbO±Ga2 O3 glasses [4]. Model III, considering two distinct Ga±O bond lengths, is consistent with assuming that more than two out of four oxygens bonded to Ga have a Ga± and they are most probably O distance of 1.87 A connected to three cations. On the other hand, the remaining oxygens are located at a distance of and form two-coordinated oxygens. 1.82 A
123
Therefore, the two-subshell calculation, as in Model III, can provide an idea of how many of those oxygens forming GaO4 tetrahedra are bonded to three cations, even though calculations using Model II may describe the overall structure more precisely. 5. Conclusions Short-range order structural parameters around Ga in PbO±Ga2 O3 glasses were analyzed from the Ga K-edge EXAFS spectra recorded at a liquidnitrogen temperature. Four oxygens were found to be bonded to each gallium, forming GaO4 tetrahedra with an average bond distance of 1.855± A model assuming a non-Gaussian 1.862 A. distribution of Ga±O bond distance provided the best ®t with the smallest R-factor compared to the other models. Models with two distinct Ga±O bond distances have approximately 60% of oxygens bonded to Ga as three-coordinated and this amount decreases with decreasing Ga2 O3 concentration. References [1] A.A. Kharlamov, R.M. Almeida, J. Heo, J. Non-Cryst. Solids 202 (1996) 233. [2] F. Miyaji, S. Sakka, J. Non-Cryst. Solids 134 (1991) 77. [3] F. Miyaji, K. Tadanaga, T. Yoko, S. Sakka, J. Non-Cryst. Solids 139 (1992) 268. [4] F. Miyaji, T. Yoko, J. Jin, S. Sakka, T. Fukunaga, M. Misawa, J. Non-Cryst. Solids 175 (1994) 211. [5] Y.G. Choi, J. Heo, V.A. Chernov, J. Non-Cryst. Solids 221 (1997) 199. [6] G. Bunker, Nucl. Instrum. and Meth. 207 (1983) 437. [7] E.D. Crozier, J.J. Rehr, R. Ingalls, in: D.C. Koningsberger, R. Prins (Eds.), X-Ray Absorption: Principles, Applications, Techniques of EXAFS, SEXAFS and XANES, Wiley, New York, 1988. [8] A.C. Hannon, J.M. Parker, B. Vessal, J. Non-Cryst. Solids 196 (1996) 187. [9] J.C. Lapp, Bull. Am. Ceram. Soc. 71 (1992) 1543. [10] Von K.-B. Plotz, H. Muller-Buschbaum, Z. Anorg. Allg. Chem. 488 (1982) 38.