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Short-range order in a NASIGLAS sample by X-ray diffraction
Volume 14I, number 1,2
CHEMICAL PHYSICS LETI-ERS
30 October 1987
SHORT-RANGE ORDER IN A NASIGLAS SAMPLE BY X-RAY DIFFRACTION G. ENNAS, A. MUSINU, G. PICCALUGA, G. PINNA Diparfimento di Scienze Chimiche, Universitd di Cagliari, 09100 Cagliari, Italy
and M. MAGINI Divisione Chimicu-TIB, ENEA. CRE-Casaccia, Rome, Italy
Received 18 May 1987; in final form 2 I August 1987
X-ray diffraction measurements have been performed on NASIGLAS and LISIGLAS glasses of the same molar ratios. The difference curve, calculated by subtracting the radial distribution function of the LISIGLAS sample from that of the NARIGLAS sample, displays peaks from the distribution of nearest-neighbour atoms around Na+ atoms. A quantitative analysis showed that the Na+ environment is not a regular polyhedron; the Na+ coordination number is significantly lower than that obtained in the corresponding crystalline counterparts (NARICON). The possible connection of this result with the different conductivity of NASIGLAS and NASICON samples is discussed.
1. Introduction In 1976 Goodenough, Kafalas and Hong [ 1 ] demonstrated that some crystalline compounds with the composition Na, +xZrzSixP3_-x0,2 (NASICON) are among the best sodium conductors. These materials have been tested in high-power batteries (sodiumsulfur cells) and have also proved useful for lowpower electrochemical devices such as microbatteries, displays and sensors. Two main problems hamper the use of NASICON [2]: (a) a structural transition is observed for many compositions in the temperature range 100-200°C that may produce electrical and mechanical anomalies; (b) in sintered NASICON free z1-0~ almost invariably appears as a second phase, leading to poor mechanical properties. To prevent this inconvenience, NASICON compounds with a reduced ZrOz content have been proposed [ 3 1, corresponding to the stoichiometry Na, +xZr2--x,3SixP3_-x0,~_zx,~.With the aim of achieving improved mechanical properties, isotropic conductivity, and the absence of a phase change, vitreous forms of the two mentioned NASICON compositions have been prepared. These materials, called
NASIGLAS by analogy, were obtained by quenching [ 41 and by gel precursor techniques [ 2,5]. The gelling method is particularly attractive, since it allows preparations of samples in different physical forms from amorphous to highly crystalline states. Conducting and structural properties of various NASICON and NASIGLAS materials may then be compared for samples of the same composition. Crystalline monoclinic NASICON, obtained by sintering the gel precursor at the highest temperatures (1200-1250°C) has been shown to have the best conducting properties. On lowering the sintering temperature to 6OO”C, less ordered NASICON forms are obtained up to the glassy form; the conductivity values are reduced accordingly. Two structural effects might explain this behaviour. The first calls for long-range order variations produced by the crystal-to-glass transition; the second is connected with short-range modificiations, particularly regarding the coordination of charge carrier ions. The first point has been widely investigated by Colomban [6,7] using DCS, X-ray diffraction and vibrational spectroscopy. These studies have led to the conclusion that NASICON is a super-
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ionic conductor, in which strong coupling between the motion of conducting cations and dynamic orientational motion of tetrahedral SiO., (or PO_,) in the lattice occurs, similarly to that observed in plastic superionic conductors [ 8 1. The dynamic disorder is a maximum at high temperatures for materials with the lowest static disorder. Thus periodicity and a highly crystallized state favour dynamic disorder. As regards the second point, the role of Na+ ion coordination has not yet been examined, probably because of the difficulty in determining the order around the Na’ ions in glassy samples. This problem has been considered by some of us in an X-ray diffraction study of sodium borate glasses [9]. A comparison of the radial distribution functions of L&O-B203 and Na20-B203 glasses having the same molar ratios suggested a possible distribution of nearest neighbour atoms around Na+ ions. In the present paper the applicability of the same method to the study of Na+ coordination in NASIGLAS is examined. To this end, two glasses were prepared, a NASIGLAS sample and a corresponding LISIGLAS. The stoichiometry adopted was 2Mez0-ZrO?3Si02 (that is NadZrSi,Olo), which represents the final member of the reduced ZrO, composition.
2. Experimental and data treatment The samples were prepared using amounts of reagent grade SiOz, ZrOa, Na2C03 (or Li,C03) (Carlo Erba) according to the selected composition. The starting materials were mixed and ground for 40 min in an agate ball mill, melted, kept at 1873 K for 2 h and at I923 K for 40 min, then cast in cold water and dried at 373 K. Chemical analyses indicated possible variations of the compositions within l-2%; in any case, the different precision in the determination of the various species suggested the use of nominal compositions in the calculations. Nominal compositions (in wt% of the oxides) and densities (determined by an electronic Westphal balence) are reported in table 1, together with the reference names used in the text (NASIG and LISIG). Powdered samples were used for X-ray measurements carried out in an atmosphere of N2 to prevent the action of C02. The 19-29X-ray diffractometer used and the procedure for data handling have been 144
30 October 1987
Table 1 Density and composition (in wt%) of the investigated glasses. Extended and short reference names, used in the text, are given in column 1 Glass
d(gcm-‘)
Me*0
SiO*
Zr02
NASIGLAS (NASIG) LlSIGLAS (LISIG)
2.8686 2.1554
29.00 16.56
42.16 49.63
28.84 33.92
described in detail elsewhere [ 10,l 1 1. Data from t?=2” to 19=67”, corresponding tos (s=4x sin 0/A) from 0.3 to 16.3 A-‘, were collected using MO Ku radiation. A narrow scanning step (At9=O. 1) was used to reveal the formation of any free ZrO, crystalline phase. Usually in our experimental apparatus, monochromatization is achieved by reflection of the X-ray diffracted beam on a curved quartz crystal. In the present case, as Zr atoms produce high intensity fluorescence radiation, which passes through the monochromator pass-band, and extra Zr filter was placed on the incident beam. A strong reduction in the diffracted intensities resulted; as a consequence 50000 counts per point were collected by five repeated runs, to avoid the risk of some instrumental drift over long angular scannings. During the data collection counting rate variations did not exceed 2%. Diffracted intensities were corrected for background, absorption, polarization, and were normalized by semi-empirical techniques [ 121. From the normalized intensities, I,,, the structure functions i(s) were obtained according to i(s) =I,, - ,t, &f?(S) 3
(1)
where Ze,,are normalized intensities, ni are stoichiometric coefficients of the assumed unit andf;( s) are the scattering factors of the species. The radial distribution functions, D(r), were then evaluated by Fourier transfomation: Small D(r)
=42r2po + F
I
si(s) M(s) sin(sr) d.s,
bin
(2) where p. is the average electronic bulk density and M(s) is a modification function of the form
Volume 14I, number 1,2
30 October 1987
CHEMICAL PHYSICS LETTERS
[ CndXo)12exp( -ks2), [CkfXs)12
k=0.005.
In the assumed unit the coefficient 1 was assigned to the Si atom.
3. Results and discussion The structure functions, reported fig. 1, are characteristic of amorphous systems and do not suggest the presence of a massive crystalline phase separation. The radial curves, given in fig. 2, display three dominant peaks and, on the whole, look very similar. They are very different from those obtained from glasses containing, more silica and/or lighter metal atoms, where atomic distributions reflect the predominance of the silicate matrix with respect to the incorporated cations. Here, on the contrary, the presence of a considerable amount of heavy Zr atoms contributes significantly to the total scattered intensity (it is known that the contribution of each pair interaction is proportional to the atomic scattering factors). Thus, while the first peak, centered at about 1
1
,tA-'10"
I
I
I
I
8 i(skM(5)
:. 8% :i
:
t.
*:
i
,i’? i?.._. :;j
:::..
::
*
.v
.5’* .:
I
b :
? ’
i ./ s
Fig. 1. Experimental structure functions: (a) NASIG, (b) LISIG.
r,A 0
I
1
I
I
,
1
2
3
4
5
Fig. 2. Experimental radial distribution functions: ~ --LISIG.
NASIG;
1.63 A, is the usual Si-0 peak found in other silicate glasses [ 13- 151, the second well defined peak falling at 2.10 8, can be ascribed to Zr-0 interactions, on the grounds of ionic radii and crystallographic results [ 16,171. Furthermore, the third unusually prominent peak between 3.45 and 3.55 A is likely to be produced by zirconium second shell interactions. In addition to the abovementioned peaks, other humps appear between 2.60 and 3.10 A which may be due to traces of O-O interactions in the coordination polyhedra of Si and Zr. Peaks coming from nearest neighbour coordination of Na and Li atoms are not observable in the total radial curves. However, a comparison of the NASIG and LISIG distribution curves shows that the right side of the Zr-0 peak is higher in the NASIG system. This happens in the region around 2.40 A where Na +-0 distances are expected; the phenomenon can thus be considered as mainly due to Na+-0 interactions. Going to higher r values increases the electronic density (and hence the parabolic term 4rrr*po) and this explains the difference between the two radial curves. Given the small scattering power of the Li+ ion, Li+-0 distances are almost unobservable, even if higher values of the LISIG radial function around the Si-0 peak may be partly due to Li+-0 contributions. To obtain detailed information about short-range 145
Volume I4 1, number 1,2 order,
a quantitative
CHEMICAL PHYSICS LETTERS determination
of atomic
30 October 1987
coor-
dination was carried out. Given the good resolution of Si-0 and Zr-0 peaks, the coordination of Si and Zr was evaluated through a simulation of those peaks directly in the total radial curves. The theoretical peaks were calculated by Fourier transforming the pair contributions to the structure functions, defined as
where ri_o is the average distance between i (i= Si, Zr) and 0 atoms, Q,~ the associated root mean square deviation, and Ni_o the average coordination number of the ith atom. The theoretical peaks were matched to the experimental curves by continuous adjustments of the above parameters. Li+-0 interactions were neglected in the LISIG sample on account of their small weight in comparison with the Si-0 and Zr-0 contributions. In the NASIG glass, the right-hand side of the Zr-0 peak came out unresolved; in fact, Na+-0 interactions cannot be neglected here and they were accounted for by subtracting the theoretical Nat-O contributions (see later) from the experimental radial distribution curve. The theoretical and experimental curves reported in fig. 3 show excellent agreement. The best fit parameters are given in table 2. The differences between the parameter values in the two samples are within the uncertainty limits (about 2% for distances and 10% for coordination numbers) discussed elsewhere [ 9,18,19]. The calculations thus indicate that the framework of the glasses is built up from the same basic units present in the crystals [ 16,171, i.e. SiO, tetrahedra and ZxQ octahedra. The Na+ coordination cannot be deduced from an analysis of the total radial curve because of the small contribution from Na+-0 interactions. A difference method was applied, which has been described in
r.A t
0
I
2
1
3
Fig. 3. (a) Experimental (...) and simulated (-) radial distribution functions for the LISIG sample. (b) Experimental (...) radial distribution function for the NASIG sample; simulated distribution around Na+ ions ( - - - ): difference of the two above radial function (A); simulation of the difference curve (-).
detail in previous studies [ 13-l 51 on metal ion coordination in various glass networks. The main assumption of this method is that the networks of SiO, and Zr06 units are almost identical in sodium and lithium glasses of the same composition. Thus, if the D(r) of LISIG is subtracted from that of NASIG, the contributions to the radial function from the glassy network are cancelled. The difference curve should exhibit as positive peaks the Na+-surrounding atom contributions, weakly perturbed by
Table 2 Structural parameters (r, u, N are the distance, root mean square deviation, and coordination number, respectively) obtained for Si-0 and Zr-0 first coordination sphere Glass
k.
uSi-
hi-0
rxl-o
~zr-0
f&O
NASIG
1.61 1.61
0.01 0.01
3.7 4.0
2.09 2.09
0.10 0.10
6.7 6.5
LISIG
146
1
I
1
I
AD(r)
91’ k.10"
.“* * .
. . -
. . . .
0
1
30 October 1987
CHEMICAL PHYSICS LETTERS
Volume 14I, number I,2
2
3
,
4
Fig. 4. Difference of the experimental radial functions of NASIG and LISIG (...); simulated nearest-neighbour radial distribution around Na’ ions (-).
the small Li+-surrounding atom contributions. The difference curve given in fig. 4 shows a positive double peak falling between 2.40 and 2.70 A, where Na+-0 distances are expected. The negative region on the left-hand side of this peak may be ascribed to Li+-0 pairs; in any case it is evident that the Lit-O peak is much less important than the Na+-0 one and mingles with the small spurious ripples at low r. A preliminary observation of the Na+-0 peak indicates that the local Na+ ion environment is well defined, as recently observed by EXAFS in silicate glasses [ 201, but the coordination polyhedron is not regular. Therefore analysis of the peak, based on the method already described for Si-0 and Zr-0 pairs, was carried out by introducing two different Na+-0 contributions in the calculations. The fitting of the synthetic curve to the left-hand side of the experimental peak was emphasised in the simulation, since the right-hand side of the experimental D(r) is not
completely resolved, The synthetic D(r) from the best fit is given as a solid line in fig. 4; the parameters used in this calculation are reported in table 3. The total coordination number of Na+ ions came out to about 4. If we look at the crystalline structures of some compounds in the NASICON family [ 16,17,2 11, we find that the Na+ coordination number is significantly higher than that obtained in the NASIGLAS system investigated here (6-8 against 3.8). The different coordination should have important effects on the mobility of Na+ ions, so it becomes essential to assess the reliability of the present result. In this connection the following observations are in order: (A) The assumed structural identity of NASIG and LISIG cannot be verified. In silicate glasses isostructurality is not complete because of the different aptitude of Li+ and Na+ cations to coordinate nonbridging oxygens [ 221. However, confining ourselves to an analysis of Nat first coordination shell only, the structural identity of the two glasses needs to be fulfilled within a very small distance range (r< 2.8 A). Since this range comprises contributions from the rigid units (Si04, ZQ,) of the glassy network, the assumption is likely to be realistic. In this connection, the observed similarity of NASIG and LISIG D( r)s in the low r region supports the validity of the difference method, as does the strong similarity of the structure fuctions at medium-high s. (B) The precision of the method is strongly dependent on the accuracy of the experimental work: the preparation procedure, the alignment of the Xray apparatus, the counting statistics, and the treatment of the experimental data must be kept rigorously constant. Fig. 2 shows that systematic errors have been minimized and, moreover, that they are very similar in both cases; spurious ripples at low r are in fact small and display the same behaviour. Therefore, despite the experimental difficulties and
Table 3 Structural parameters (r, u, Nare the distance, root mean square deviation, and coordination number, respectively) obtained for Na+-0 interactions Glass NASIG
2.33
0.02
2.3
2.64
0.04
1.5
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CHEMICAL PHYSICS LETTERS
a possible light effect due to Li+ ions, only minor peaks appear in the region 0- 1.5 A of the difference curve of fig. 4, ensuring that systematic errors have not seriously affected the real difference peaks. (C) The structural parameters reported in table 3 display a strong inner consistency. In fact, the decrease in the coordination number in going from crystal to glass is correctly coupled with shorter average Na+-0 distance and smaller oNa+_. values. On the whole, the present analysis suggests that the coordination of Na+ions can be determined with enough accuracy with the difference method, even if from only one case it is impossible to evaluate the associated error. In conclusion, Na+ ions in NASIG seem to be bound to the framework of Si04 and Zr06 units more strongly than in crystals and this fact might be connected with the decreased mobility of Nat in the amorphous compound. Keeping in mind this picture of Na+ coordination, a reasonable hypothesis suggests that the peak at about 3.5 8, in the difference curve is a real one, indicative of second shell interactions of Na+ ions with Si or Zr atoms. Following this hypothesis, an analysis of the peak showed that its area is consistent with about one Na+-Si and two Na+-Zr contributions, that is, with a second coordination number close to that of the first coordination number. On the whole the results obtained seem promising and open a way to investigate the environment of charge carrier ions in NASIGLAS obtained by different preparation methods, or having different network composition, or different Na+ content.
Acknowledgement This research has been performed under contract ENEA-UniversitB di Cagliari No. 794, 5-2-87. Calculations were performed at the Centro di Calcolo Elettronico of the University of Cagliari.
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References [ 1] J.B. Goodenough, H.Y.P. Hong and J.A. Kafalas, Mat. Res. Bull. 11 (1976) 203.
[ 21 J.P. Boilot and Ph. Colomban, J. Mat. Sci. Letters 4 (1985) 22.
[ 31 U. von Alpen, M.F. Bell and H.H. Hofer, Solid State Ionics 314 (1981) 215. [4] S. Susman, C.J. Delbecq and J. A. McMillan, Solid State Ionics 9/10 (1983) 667. [ 51J.P. Boilot, Ph. Colomban and N. Blanchard, Solid State Ionics 9/10 (1983) 639. [ 61 Ph. Colomban, Solid State lonics 21 (1986) 97. [ 71 Ph. Colomban, Dynamics of molecular crystals (Elsevier, Amsterdam), to be published. [S] E.I. Cooper and C.A. Angell, Solid State Ionics 18/19 (1986) 570. [ 91 G. Paschina, G. Piccaluga and M. Magini, J. Chem. Phys. 81 (1984) 6201. [IO] G. Licheri, G. Piccaluga and G. Pinna, J. Chem. Phys. 64 (1976) 2437. [ I1 ] R. Caminiti, G. Licheri, G. Piccaluga, G. Pinna and M. Magini, Rev. Inorg. Chem. 1 (1979) 333. [ 121 A. Habenschuss and F.H. Spedding, J. Chem. Phys. 70 (1979) 2197. [ 131 M. Magini, A.F. Sedda, G. Licheri, G. Paschina, G. Piccaluga, G. Pinna and G. Cocco, J. Non-Cryst. Solids 65 (1984) 145. [ 141 A. Corrias, M. Magini, M. de Moraes, A.F. Sedda, A. Musinu, G. Paschina and G. Piccaluga, J. Chem. Phys. 84 (1986) 5769. [ 151 A. Musinu, G. Piccaluga and M. Magini, to be published, [ 161 W.H. Baur, J.R. Dygas, D.H. Whitemore and J. Faber, Solid StateIonics 18119(1986) 935. [17] J.J. Didisheim, E. Prince and B.J. Wuensch, Solid State Ionics 1809 (1986) 944. [ 181 G. Paschina, G. Piccaluga, G. Pinna and M. Magini, J. Chem. Phys. 78 (1983) 5745. [ 191 G. Licheri, A. Musinu, G. Paschina, G. Piccaluga, G. Pinna and A. Magistris, J. Chem. Phys. 85 (1986) 500. [20] G.N. Greaves, J.Non-Cryst. Solids 71 (1985) 203. [ 211 J.P. Boilot, G. Collin and Ph. Colomban, Mat. Res. Bull., to be published. [22] R. Dupree, D. Holland and D.S. Williams, J. Non-Cryst. Solids81 (1986) 185.
CHEMICAL PHYSICS LETI-ERS
30 October 1987
SHORT-RANGE ORDER IN A NASIGLAS SAMPLE BY X-RAY DIFFRACTION G. ENNAS, A. MUSINU, G. PICCALUGA, G. PINNA Diparfimento di Scienze Chimiche, Universitd di Cagliari, 09100 Cagliari, Italy
and M. MAGINI Divisione Chimicu-TIB, ENEA. CRE-Casaccia, Rome, Italy
Received 18 May 1987; in final form 2 I August 1987
X-ray diffraction measurements have been performed on NASIGLAS and LISIGLAS glasses of the same molar ratios. The difference curve, calculated by subtracting the radial distribution function of the LISIGLAS sample from that of the NARIGLAS sample, displays peaks from the distribution of nearest-neighbour atoms around Na+ atoms. A quantitative analysis showed that the Na+ environment is not a regular polyhedron; the Na+ coordination number is significantly lower than that obtained in the corresponding crystalline counterparts (NARICON). The possible connection of this result with the different conductivity of NASIGLAS and NASICON samples is discussed.
1. Introduction In 1976 Goodenough, Kafalas and Hong [ 1 ] demonstrated that some crystalline compounds with the composition Na, +xZrzSixP3_-x0,2 (NASICON) are among the best sodium conductors. These materials have been tested in high-power batteries (sodiumsulfur cells) and have also proved useful for lowpower electrochemical devices such as microbatteries, displays and sensors. Two main problems hamper the use of NASICON [2]: (a) a structural transition is observed for many compositions in the temperature range 100-200°C that may produce electrical and mechanical anomalies; (b) in sintered NASICON free z1-0~ almost invariably appears as a second phase, leading to poor mechanical properties. To prevent this inconvenience, NASICON compounds with a reduced ZrOz content have been proposed [ 3 1, corresponding to the stoichiometry Na, +xZr2--x,3SixP3_-x0,~_zx,~.With the aim of achieving improved mechanical properties, isotropic conductivity, and the absence of a phase change, vitreous forms of the two mentioned NASICON compositions have been prepared. These materials, called
NASIGLAS by analogy, were obtained by quenching [ 41 and by gel precursor techniques [ 2,5]. The gelling method is particularly attractive, since it allows preparations of samples in different physical forms from amorphous to highly crystalline states. Conducting and structural properties of various NASICON and NASIGLAS materials may then be compared for samples of the same composition. Crystalline monoclinic NASICON, obtained by sintering the gel precursor at the highest temperatures (1200-1250°C) has been shown to have the best conducting properties. On lowering the sintering temperature to 6OO”C, less ordered NASICON forms are obtained up to the glassy form; the conductivity values are reduced accordingly. Two structural effects might explain this behaviour. The first calls for long-range order variations produced by the crystal-to-glass transition; the second is connected with short-range modificiations, particularly regarding the coordination of charge carrier ions. The first point has been widely investigated by Colomban [6,7] using DCS, X-ray diffraction and vibrational spectroscopy. These studies have led to the conclusion that NASICON is a super-
0 009-26 14/87/.$ 03.50 0 Elsevier Science Publishers B.V.
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ionic conductor, in which strong coupling between the motion of conducting cations and dynamic orientational motion of tetrahedral SiO., (or PO_,) in the lattice occurs, similarly to that observed in plastic superionic conductors [ 8 1. The dynamic disorder is a maximum at high temperatures for materials with the lowest static disorder. Thus periodicity and a highly crystallized state favour dynamic disorder. As regards the second point, the role of Na+ ion coordination has not yet been examined, probably because of the difficulty in determining the order around the Na’ ions in glassy samples. This problem has been considered by some of us in an X-ray diffraction study of sodium borate glasses [9]. A comparison of the radial distribution functions of L&O-B203 and Na20-B203 glasses having the same molar ratios suggested a possible distribution of nearest neighbour atoms around Na+ ions. In the present paper the applicability of the same method to the study of Na+ coordination in NASIGLAS is examined. To this end, two glasses were prepared, a NASIGLAS sample and a corresponding LISIGLAS. The stoichiometry adopted was 2Mez0-ZrO?3Si02 (that is NadZrSi,Olo), which represents the final member of the reduced ZrO, composition.
2. Experimental and data treatment The samples were prepared using amounts of reagent grade SiOz, ZrOa, Na2C03 (or Li,C03) (Carlo Erba) according to the selected composition. The starting materials were mixed and ground for 40 min in an agate ball mill, melted, kept at 1873 K for 2 h and at I923 K for 40 min, then cast in cold water and dried at 373 K. Chemical analyses indicated possible variations of the compositions within l-2%; in any case, the different precision in the determination of the various species suggested the use of nominal compositions in the calculations. Nominal compositions (in wt% of the oxides) and densities (determined by an electronic Westphal balence) are reported in table 1, together with the reference names used in the text (NASIG and LISIG). Powdered samples were used for X-ray measurements carried out in an atmosphere of N2 to prevent the action of C02. The 19-29X-ray diffractometer used and the procedure for data handling have been 144
30 October 1987
Table 1 Density and composition (in wt%) of the investigated glasses. Extended and short reference names, used in the text, are given in column 1 Glass
d(gcm-‘)
Me*0
SiO*
Zr02
NASIGLAS (NASIG) LlSIGLAS (LISIG)
2.8686 2.1554
29.00 16.56
42.16 49.63
28.84 33.92
described in detail elsewhere [ 10,l 1 1. Data from t?=2” to 19=67”, corresponding tos (s=4x sin 0/A) from 0.3 to 16.3 A-‘, were collected using MO Ku radiation. A narrow scanning step (At9=O. 1) was used to reveal the formation of any free ZrO, crystalline phase. Usually in our experimental apparatus, monochromatization is achieved by reflection of the X-ray diffracted beam on a curved quartz crystal. In the present case, as Zr atoms produce high intensity fluorescence radiation, which passes through the monochromator pass-band, and extra Zr filter was placed on the incident beam. A strong reduction in the diffracted intensities resulted; as a consequence 50000 counts per point were collected by five repeated runs, to avoid the risk of some instrumental drift over long angular scannings. During the data collection counting rate variations did not exceed 2%. Diffracted intensities were corrected for background, absorption, polarization, and were normalized by semi-empirical techniques [ 121. From the normalized intensities, I,,, the structure functions i(s) were obtained according to i(s) =I,, - ,t, &f?(S) 3
(1)
where Ze,,are normalized intensities, ni are stoichiometric coefficients of the assumed unit andf;( s) are the scattering factors of the species. The radial distribution functions, D(r), were then evaluated by Fourier transfomation: Small D(r)
=42r2po + F
I
si(s) M(s) sin(sr) d.s,
bin
(2) where p. is the average electronic bulk density and M(s) is a modification function of the form
Volume 14I, number 1,2
30 October 1987
CHEMICAL PHYSICS LETTERS
[ CndXo)12exp( -ks2), [CkfXs)12
k=0.005.
In the assumed unit the coefficient 1 was assigned to the Si atom.
3. Results and discussion The structure functions, reported fig. 1, are characteristic of amorphous systems and do not suggest the presence of a massive crystalline phase separation. The radial curves, given in fig. 2, display three dominant peaks and, on the whole, look very similar. They are very different from those obtained from glasses containing, more silica and/or lighter metal atoms, where atomic distributions reflect the predominance of the silicate matrix with respect to the incorporated cations. Here, on the contrary, the presence of a considerable amount of heavy Zr atoms contributes significantly to the total scattered intensity (it is known that the contribution of each pair interaction is proportional to the atomic scattering factors). Thus, while the first peak, centered at about 1
1
,tA-'10"
I
I
I
I
8 i(skM(5)
:. 8% :i
:
t.
*:
i
,i’? i?.._. :;j
:::..
::
*
.v
.5’* .:
I
b :
? ’
i ./ s
Fig. 1. Experimental structure functions: (a) NASIG, (b) LISIG.
r,A 0
I
1
I
I
,
1
2
3
4
5
Fig. 2. Experimental radial distribution functions: ~ --LISIG.
NASIG;
1.63 A, is the usual Si-0 peak found in other silicate glasses [ 13- 151, the second well defined peak falling at 2.10 8, can be ascribed to Zr-0 interactions, on the grounds of ionic radii and crystallographic results [ 16,171. Furthermore, the third unusually prominent peak between 3.45 and 3.55 A is likely to be produced by zirconium second shell interactions. In addition to the abovementioned peaks, other humps appear between 2.60 and 3.10 A which may be due to traces of O-O interactions in the coordination polyhedra of Si and Zr. Peaks coming from nearest neighbour coordination of Na and Li atoms are not observable in the total radial curves. However, a comparison of the NASIG and LISIG distribution curves shows that the right side of the Zr-0 peak is higher in the NASIG system. This happens in the region around 2.40 A where Na +-0 distances are expected; the phenomenon can thus be considered as mainly due to Na+-0 interactions. Going to higher r values increases the electronic density (and hence the parabolic term 4rrr*po) and this explains the difference between the two radial curves. Given the small scattering power of the Li+ ion, Li+-0 distances are almost unobservable, even if higher values of the LISIG radial function around the Si-0 peak may be partly due to Li+-0 contributions. To obtain detailed information about short-range 145
Volume I4 1, number 1,2 order,
a quantitative
CHEMICAL PHYSICS LETTERS determination
of atomic
30 October 1987
coor-
dination was carried out. Given the good resolution of Si-0 and Zr-0 peaks, the coordination of Si and Zr was evaluated through a simulation of those peaks directly in the total radial curves. The theoretical peaks were calculated by Fourier transforming the pair contributions to the structure functions, defined as
where ri_o is the average distance between i (i= Si, Zr) and 0 atoms, Q,~ the associated root mean square deviation, and Ni_o the average coordination number of the ith atom. The theoretical peaks were matched to the experimental curves by continuous adjustments of the above parameters. Li+-0 interactions were neglected in the LISIG sample on account of their small weight in comparison with the Si-0 and Zr-0 contributions. In the NASIG glass, the right-hand side of the Zr-0 peak came out unresolved; in fact, Na+-0 interactions cannot be neglected here and they were accounted for by subtracting the theoretical Nat-O contributions (see later) from the experimental radial distribution curve. The theoretical and experimental curves reported in fig. 3 show excellent agreement. The best fit parameters are given in table 2. The differences between the parameter values in the two samples are within the uncertainty limits (about 2% for distances and 10% for coordination numbers) discussed elsewhere [ 9,18,19]. The calculations thus indicate that the framework of the glasses is built up from the same basic units present in the crystals [ 16,171, i.e. SiO, tetrahedra and ZxQ octahedra. The Na+ coordination cannot be deduced from an analysis of the total radial curve because of the small contribution from Na+-0 interactions. A difference method was applied, which has been described in
r.A t
0
I
2
1
3
Fig. 3. (a) Experimental (...) and simulated (-) radial distribution functions for the LISIG sample. (b) Experimental (...) radial distribution function for the NASIG sample; simulated distribution around Na+ ions ( - - - ): difference of the two above radial function (A); simulation of the difference curve (-).
detail in previous studies [ 13-l 51 on metal ion coordination in various glass networks. The main assumption of this method is that the networks of SiO, and Zr06 units are almost identical in sodium and lithium glasses of the same composition. Thus, if the D(r) of LISIG is subtracted from that of NASIG, the contributions to the radial function from the glassy network are cancelled. The difference curve should exhibit as positive peaks the Na+-surrounding atom contributions, weakly perturbed by
Table 2 Structural parameters (r, u, N are the distance, root mean square deviation, and coordination number, respectively) obtained for Si-0 and Zr-0 first coordination sphere Glass
k.
uSi-
hi-0
rxl-o
~zr-0
f&O
NASIG
1.61 1.61
0.01 0.01
3.7 4.0
2.09 2.09
0.10 0.10
6.7 6.5
LISIG
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1
I
1
I
AD(r)
91’ k.10"
.“* * .
. . -
. . . .
0
1
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CHEMICAL PHYSICS LETTERS
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2
3
,
4
Fig. 4. Difference of the experimental radial functions of NASIG and LISIG (...); simulated nearest-neighbour radial distribution around Na’ ions (-).
the small Li+-surrounding atom contributions. The difference curve given in fig. 4 shows a positive double peak falling between 2.40 and 2.70 A, where Na+-0 distances are expected. The negative region on the left-hand side of this peak may be ascribed to Li+-0 pairs; in any case it is evident that the Lit-O peak is much less important than the Na+-0 one and mingles with the small spurious ripples at low r. A preliminary observation of the Na+-0 peak indicates that the local Na+ ion environment is well defined, as recently observed by EXAFS in silicate glasses [ 201, but the coordination polyhedron is not regular. Therefore analysis of the peak, based on the method already described for Si-0 and Zr-0 pairs, was carried out by introducing two different Na+-0 contributions in the calculations. The fitting of the synthetic curve to the left-hand side of the experimental peak was emphasised in the simulation, since the right-hand side of the experimental D(r) is not
completely resolved, The synthetic D(r) from the best fit is given as a solid line in fig. 4; the parameters used in this calculation are reported in table 3. The total coordination number of Na+ ions came out to about 4. If we look at the crystalline structures of some compounds in the NASICON family [ 16,17,2 11, we find that the Na+ coordination number is significantly higher than that obtained in the NASIGLAS system investigated here (6-8 against 3.8). The different coordination should have important effects on the mobility of Na+ ions, so it becomes essential to assess the reliability of the present result. In this connection the following observations are in order: (A) The assumed structural identity of NASIG and LISIG cannot be verified. In silicate glasses isostructurality is not complete because of the different aptitude of Li+ and Na+ cations to coordinate nonbridging oxygens [ 221. However, confining ourselves to an analysis of Nat first coordination shell only, the structural identity of the two glasses needs to be fulfilled within a very small distance range (r< 2.8 A). Since this range comprises contributions from the rigid units (Si04, ZQ,) of the glassy network, the assumption is likely to be realistic. In this connection, the observed similarity of NASIG and LISIG D( r)s in the low r region supports the validity of the difference method, as does the strong similarity of the structure fuctions at medium-high s. (B) The precision of the method is strongly dependent on the accuracy of the experimental work: the preparation procedure, the alignment of the Xray apparatus, the counting statistics, and the treatment of the experimental data must be kept rigorously constant. Fig. 2 shows that systematic errors have been minimized and, moreover, that they are very similar in both cases; spurious ripples at low r are in fact small and display the same behaviour. Therefore, despite the experimental difficulties and
Table 3 Structural parameters (r, u, Nare the distance, root mean square deviation, and coordination number, respectively) obtained for Na+-0 interactions Glass NASIG
2.33
0.02
2.3
2.64
0.04
1.5
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a possible light effect due to Li+ ions, only minor peaks appear in the region 0- 1.5 A of the difference curve of fig. 4, ensuring that systematic errors have not seriously affected the real difference peaks. (C) The structural parameters reported in table 3 display a strong inner consistency. In fact, the decrease in the coordination number in going from crystal to glass is correctly coupled with shorter average Na+-0 distance and smaller oNa+_. values. On the whole, the present analysis suggests that the coordination of Na+ions can be determined with enough accuracy with the difference method, even if from only one case it is impossible to evaluate the associated error. In conclusion, Na+ ions in NASIG seem to be bound to the framework of Si04 and Zr06 units more strongly than in crystals and this fact might be connected with the decreased mobility of Nat in the amorphous compound. Keeping in mind this picture of Na+ coordination, a reasonable hypothesis suggests that the peak at about 3.5 8, in the difference curve is a real one, indicative of second shell interactions of Na+ ions with Si or Zr atoms. Following this hypothesis, an analysis of the peak showed that its area is consistent with about one Na+-Si and two Na+-Zr contributions, that is, with a second coordination number close to that of the first coordination number. On the whole the results obtained seem promising and open a way to investigate the environment of charge carrier ions in NASIGLAS obtained by different preparation methods, or having different network composition, or different Na+ content.
Acknowledgement This research has been performed under contract ENEA-UniversitB di Cagliari No. 794, 5-2-87. Calculations were performed at the Centro di Calcolo Elettronico of the University of Cagliari.
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