J. Phys. Chem. B 2000, 104, 1191-1197
1191
Structure and Properties of NaCl and the Suzuki Phase Na6CdCl8 Michael Chall* and Bjo1 rn Winkler Institut fu¨ r Geowissenschaften der Christian-Albrechts UniVersita¨ t, Olshausenstrasse 40, D-24098 Kiel, Germany
Peter Blaha and Karlheinz Schwarz Institut fu¨ r Physikalische und Theoretische Chemie, Technische UniVersita¨ t Wien, A-1060 Vienna, Austria ReceiVed: July 19, 1999; In Final Form: NoVember 3, 1999
Ab initio band structure calculations based on density functional theory were performed for NaCl, CdCl2, and the Suzuki phase Na6CdCl8. For Na6CdCl8 the structural parameters and physical properties, such as molar volume and the magnitude of the free internal coordinate and electric field gradients, together with their pressure dependence, were obtained. These results are compared to calculations for NaCl and CdCl2 to investigate the hypothesis that Na6CdCl8 can only exist as precipitates in a stabilizing surrounding NaCl matrix. From the present calculations it follows that the lattice parameters of NaCl and the Suzuki phase are identical within the accuracy of the calculations, and that therefore no “clamping” of the Suzuki phase occurs. However, it is found that Na6CdCl8 is only metastable with respect to the decomposition into solid sodium chloride and cadmium chloride. Calculations for NaCl were also used to evaluate the quality of different exchange-correlation functionals (LDA, GGA-PW91, GGA-PBE96), where the best results are obtained when the GGA-PBE96 is used. The NaCl calculations suggest that the bulk modulus of the B2 phase reported in the literature is too large, mainly due to a lack of data for the molar volume at ambient pressure.
Introduction When alkali metal halides are doped with divalent cations, one usually observes, after a certain threshold is exceeded, the precipitation of additional phases. These precipitates often have a cubic structure closely related to that of NaCl.1 Such precipitates are generally called Suzuki phases, after Kazuo Suzuki who first described them in NaCl:Cd. The structure of the Suzuki phases is shown in Figure 1. Characteristic for Suzuki phases, M6N0X8, is the high concentration of ordered cation vacancies, 0. In most cases M stands for an alkali metal, such as Na or Li, and N represents divalent cations like Cd, Mn, Mg, etc. In most Suzuki phases X denotes a halide ion (F, Cl, Br), but it is interesting to note that isostructural compounds also exist in oxidic systems, e.g., Mg6MnO8.2 Although a considerable number of investigations have been devoted to the study of Suzuki phases,3,4 numerous questions concerning their stability, structure, and physical properties remain unanswered. Most of these questions could easily be answered experimentally, provided pure phases rather than precipitates were available. However, to the best of our knowledge, it has not yet been possible to obtain pure Na6CdCl8, let alone to grow single crystals, and it was claimed that this is impossible.5 One interesting question is whether or not hypothetical singlephase Suzuki crystals would behave similarly as Suzuki precipitates in a NaCl-type matrix, or require some kind of “clamping”. However, single-phase data would be a necessary prerequisite to answer such questions. This gap can ideally be filled with ab initio studies, which can provide reliable data for the structure and physical properties of ideal perfect crystals. With such methods one can obtain reference data to determine deviations from ideal behavior induced by the surrounding
Figure 1. (100) plane of the Suzuki structure (after Suzuki1). The light gray circles represent Na, the darker ones Cd, the squares vacancies, and the larger circles the Cl anions. The arrows indicate the direction of the anion displacement δ (at low pressures).
matrix. Furthermore, such calculations can provide numerical values for physical and structural properties which are difficult or even impossible to obtain experimentally. Finally, it is possible to determine the pressure dependence of the calculated properties. Currently most modern ab initio calculations on threedimensionally periodic structures are based on density functional theory, and this is also the approach employed here. To investigate the influence of the approximation used for the exchange-correlation functional, we tested three different functionals.
10.1021/jp9924528 CCC: $19.00 © 2000 American Chemical Society Published on Web 01/21/2000
1192 J. Phys. Chem. B, Vol. 104, No. 6, 2000
Chall et al.
TABLE 1: Results Obtained for NaCla method
a0 (Å)
GGA-PBE GGA-PW91 LDA exptl HFg HF + P91h
5.691(2) 5.694(1) 5.464(0) 5.5975b 5.80 5.54
GGA-PBE GGA-PW91 LDA exptl HF + P91h
3.517(1) 3.516(1) 3.372(1) 3.41
V0 (cm3/mol)
K0 (GPa)
B1 Structure 27.75(3) 25.1(3) 27.79(1) 24.5(1) 24.56(0) 32.2(0) 26.15b 23.68c 29.4 22.3 25.6 30.1 B2 Structure 26.19(2) 26.0(1) 26.18(1) 25.6(1) 23.09(1) 34.5(1) 36.2(42)f 23.8 33.8
K1
pt (GPa)
4.44(4) 4.46(1) 4.71(1) 5.38d
24.6(1) 24.2(1) 24.0(1) 26.6(5)e 28.9
4.41(1) 4.45(1) 4.58(2) 4f
a
The errors are derived from the fit of the data with eq 3, except for the error of pt, which was graphically estimated from Figure 4. b Extrapolation of the room temperature (RT) value8 to 7 K using thermal expansion data.9 c RT data derived by ultrasonic measurements.39 d RT data derived by ultrasonic measurements.40 e RT data.12 f RT data; K was assumed to be equal to 4.38 g Hartree-Fock 1 calculations.6 h Hartree-Fock + correlation calculations.7
As the quality of the results calculated for the Suzuki phase cannot be evaluated by comparison with experimental data, it is necessary to use another reference. Ab initio calculations are computationally rather expensive, and thus it is desirable for this purpose to use a similar but small structure, which for obvious reasons was chosen to be NaCl in the present study. Hence, we first compared for NaCl the calculated and experimental compressibility, the corresponding pressure derivative, the lattice parameter, and the phase transition pressure from the B1 phase into the B2 phase. After having found the calculations to reproduce the experimental data satisfactorily, we computed the unknown properties for the Suzuki phase. An estimation of the thermodynamical stability of Na6CdCl8 with respect to NaCl and CdCl2 would require very accurate and precise calculations of cadmium chloride. For reasons explained below, this was impossible in the present study. However, approximate calculations were carried out to determine the relative stability to a first approximation. In the following, we first give some further introductory remarks on the compounds NaCl, Na6CdCl8, and CdCl2. Then we present the results obtained for these substances. Finally the results are discussed in the last section. NaCl. NaCl is one of the simplest structures, and therefore, it served often as a “test system” for computational studies.6,7 One of the primary test criteria is the lattice parameter a0 at ambient pressure and 0 K. Surprisingly, the low-temperature lattice parameter has not been precisely measured directly, but only indirectly by dilatometry. As a consequence, calculations have been compared to a variety of different a0-values. The most recent high-precision lattice parameter determination at room temperature is from Swanson and Fuyat (1953).8 The temperature-induced dilatation of NaCl has been measured by Meincke and Graham (1965)9 down to 7 K. From a combination of these data one finds a ) 5.5975 Å (Table 1). We recently determined a0 ) 5.5951(3) Å by neutron and synchrotron powder diffraction.10 At high pressures between 20 and 30 GPa, depending on temperature, NaCl undergoes a phase transformation from the F-centered B1 phase with NaCl structure to the primitive B2 phase with CsCl structure.11 With decreasing temperature, the phase transition occurs less readily. Hence, the “brackets”, i.e., the difference in the phase transition pressure, pt, between the
transition from the B1 phase into the B2 phase and Vice Versa, widen, thus decreasing the accuracy of the measured transition pressures. Hence, the direct determination of transition pressures at low temperatures is impossible. Therefore, transition pressures at low temperatures can only be inferred by an extrapolation from the high-temperature data. At room temperature the most recent measured transition pressure is 26.6 GPa.12 Na6CdCl8. It has been mentioned above that in most cases the Suzuki phase exists only as precipitates in a NaCl-type matrix. Although Suzuki1 reports to have “fortunately” obtained a single crystal of Na6CdCl8, extensive later attempts to reproduce this result failed.5 Therefore, the structure and properties of single crystals could not be studied, making it difficult to determine the influence of mesoscopic phenomena, such as the particle size or the strain imposed by the surrounding matrix. In fact, only very few crystallographic studies have been conducted on Na6CdCl8. The first structure determination is due to Suzuki.1 Using film techniques, he determined the space group as Fm3hm and the lattice parameter to be exactly twice that of NaCl. In the Suzuki structure, the positions of all cations and one-quarter of the anions are fixed by symmetry. The remaining Cl(2) atoms are located between a Cd and a vacancy. They are displaced from the midpoint by a small amount δ, which Suzuki1 determined to be 0.028 (in fractional coordinate units), corresponding to 0.3 Å. The only two other structural determinations of δ resulted in the values 0.01413 and 0.020.14,15 In summary, no satisfactory structure determination of Na6CdCl8 is available. The first computational study of Suzuki phases was conducted by Sors and Lilley.15 They used force-field calculations based on empirical potentials and found δ ) 0.023. In contrast to the work of Sors and Lilley15 modern ab initio calculations, such as those presented here, are capable of providing accurate information on the structure and a large variety of physical properties and thereby can overcome the lack of experimental data. CdCl2. Strictly speaking, the structure of CdCd2 is unknown. The most recent structural “determination” dates back to 193016 and was based on the comparison of a few estimated intensities derived from Laue and oscillation photographs. In this study the space group could not be determined, and the simplest structural model was accepted as it gave “reasonable results”. As precise data are not available a reasonable structural model of van-der-Waals-bounded layers of face-sharing CdCl6 octahedra has been assumed here. It should be realized that the experimental investigation of CdCl2 is not straightforward, as the compound is highly hygroscopic. A full geometry optimization would be computationally too expensive with the approach employed here. Hence, we restrict ourselves to the determination of the total energy of CdCl2 in the structure suggested in the literature.16 We optimized this structure with respect to the position of the chlorine atom. This yields an upper bound for the true total energy of CdCl2. Electric Field Gradients. We computed electric field gradient (EFG) tensors, which can experimentally be determined by nuclear magnetic resonance (NMR). Structural information can be obtained from NMR measurements in which the interaction between the nuclear quadrupole moment, eQ, and the local electric field gradient, eq ) Vzz, is determined in terms of the quadrupole coupling constant, QCC, given by
QCC ) eVzzQ/h
(1)
The EFG depends on the nonspherical charge distribution around the nuclei, and its deviation from axial symmetry is defined by
Structure and Properties of NaCl and Na6CdCl8
J. Phys. Chem. B, Vol. 104, No. 6, 2000 1193
the asymmetry parameter η
η ) (Vxx - Vyy)/Vzz
(2)
which varies between 0 (axial symmetry) and 1. Here we follow the same conventions as in the work of Schwarz et al.17 From DFT calculations EFGs can be determined to about 10% and asymmetry parameters to about 0.1 of the experimental values.18 In Na6CdCl8 there is a nonvanishing EFG at the Na and Cl(2) positions. The Na on Wyckoff position 24d has point symmetry mmm, and hence η does not vanish. In contrast to this, the asymmetry parameter of the Cl on position 24e does vanish, because the point symmetry of this position is 4mm, and hence the representation quadric of the EFG tensor is a rotational ellipsoid. Computational Approach The calculations presented here are based on density functional theory (DFT),19,20 using either the standard local density approximation (LDA) or one of two formulations of a generalized gradient approximation (GGA). For NaCl we tested in detail the effect of the exchangecorrelation functional, namely, the LDA21 and GGAs in the formulations of Perdew and Wang (PW9122) and of Perdew, Burke, and Ernzerhof (PBE9623). All Na6CdCl8 calculations were performed with the GGA-PBE96. For DFT calculations, one of the most accurate schemes is the full-potential, linearized augmented plane wave, FP-LAPW, method, in which the unit cell is divided into spheres centered at the atomic positions and an “interstitial” region. In the latter the basis set consists of plane waves, which are augmented by atomic-like solutions (numerical radial functions multiplied with spherical harmonics) inside the spheres. The potential within the sphere is not restricted to have spherical symmetry, as in the older “muffin-tin” calculations, but is allowed to be general; i.e., a “full potential” without any shape approximation is used. A recent in-depth summary can be found in the book by Singh.24 It is well known that DFT calculations will in general give structural parameters to within 1-2% of the experimental data. In the present study, the FP-LAPW package, WIEN97,25 has been used. WIEN97 is maintained at the Vienna University of Technology and includes the possibility to employ “local orbitals” 26 and to calculate residual forces on atoms.27,28 The calculation of the EFGs is based on the work of Blaha et al.;29 a more detailed description can be found in Schwarz et al.17 The precision, maximum accuracy, and convergence behavior of FP-LAPW calculations are controlled by only a few parameters. For the expansion of the charge density (potential) in the interstitial region, a Fourier series with |G| e 12 was used. For the wave functions inside the atomic spheres angular momentum components up to l ) 12 were included. For the sampling of reciprocal space 20 k-points in the irreducible wedge of the Brillouin zone were used in the calculations of NaCl and 4 k-points for the calculations of the Suzuki phase. The plane wave cutoff for the wave function, RmtKmax, was about 9.510.5 Rydberg. In the present calculations no “empty spheres” are required. The radii of all spheres were kept constant throughout the calculations. The sphere radii (rMT(Na) ) rMT(Cl) ) rMT(Cd) ) 2.0 au) were chosen so that even at the highest compression the spheres did not overlap. The applicability of the current approach to Cd-containing compounds has been demonstrated recently.30 Results NaCl. B1 Phase. The total energy, E, calculated using the LDA as a function of the lattice parameter, a, is shown in Figure
Figure 2. Change of the total energy per formula unit of NaCl as a function of the lattice parameter (circles). The energy is minimal (Etot ) -16 926.45 eV) for a lattice parameter a0 ) 5.464 Å. The line is a fit to the data with eq 3.
2. Similar data were acquired using the other two exchangecorrelation potentials. Each data set was fitted with a transformed third-order Birch-Murnaghan equation of state:31
E(V) ) c1 +
{(
)[( ) ( ) ()] () ()}
9c2V0K0 K1 V0 2 V0 2/3 -1 +3 4 4 V V V0 4/3 V0 1 V0 4/3 + 3 V 2 V V
2/3
(3)
Here, c1 is an arbitrary offset and c2 a conversion factor. If E is measured in eV, K0 in GPa, and V0 in Å3, c2 has the numerical value 1/160.2192. V0 is the volume per formula unit (pfu) at zero pressure, K0 is the adiabatic bulk modulus at zero pressure, and K1 ) dK0/dp, where p denotes the pressure. Noting that
∫
E ) - p dV
(4)
it is obvious that eq 3 is obtained from the third-order BirchMurnaghan equation of state:
[( ) ( ) ]{
V0 3 p(V) ) K0 2 V
7/3
-
V0 V
5/3
[( ) ]}
V0 3 1 + (K1 - 4) 4 V
2/3
-1
(5)
As the ground-state energy E0 equals E(V0), one finally finds the relationship
E0 ) c1 + c2(9/16)V0K0(K1 - 6)
(6)
The results of the fits to the three calculated data sets are summarized in Table 1. It is obvious that all calculations for the B1 phase give reasonable values for the lattice parameter. The LDA leads to an overestimation of ∼2%, whereas both forms of the GGA result in an underestimation of ∼1.7%. This corresponds to a deviation of ∼6% of V0 from the experimental value. The errors given in Table 1 are statistical estimates from the fits of the data with eq 3. These are much smaller than the systematic errors, which can be estimated from the comparison with experimental data. The compressibility K0 derived from the GGA calculations agrees within 6% with experiment. However, the LDA ap-
1194 J. Phys. Chem. B, Vol. 104, No. 6, 2000
Figure 3. Calculated isotherms for NaCl in the B1 phase (solid line) and B2 phase (dashed line). All calculated data are calibrated to the V0 calculated for the NaCl B1 phase. For comparison, some experimental data points are given.
proximation leads to a poorer result and deviates by more than +30%. The pressure derivative of K0, K1, was underestimated by all three approximations by ∼5%. However, the calculated GGA-PBE isotherm, shown in Figure 3, is in very good agreement with the experimental data. B2 Phase. The calculated data for the B2 phase were analyzed in the same way as the B1 data (Table 1). As the B2 phase is a high-pressure phase, no experimental data for the lattice parameter and the volume at p ) 0 are available. The calculated K0 for all three approximations is larger than for the B1 phase; i.e., the B2 phase is harder, as expected. The value calculated with the LDA comes closest to the experimental value, but as will be discussed below, the error of the experimental K0 is likely to be much larger than the given value of 10%. The GGA calculations result in an increase of K0 of ∼4% relative to the corresponding value of the B1 phase, while in the LDA the increase is 7%. This is much less than the experimentally determined change of 50% for the bulk modulus when the B1 phase is transformed into the B2 phase. B1-B2 Phase Transformation. From the p,V-data and the total energy, E, it is possible to calculate the enthalpy, H ) E + pV, as a function of the pressure for both phases. As the calculations correspond to a temperature of 0 K, the enthalpy equals the free energy. Hence, the stable phase at a given pressure can be directly calculated from the enthalpy difference between the two phases, ∆H, shown in Figure 4. The obtained phase transformation pressures, pt, listed in Table 1, are all 8-10% lower than the transition pressure observed at room temperature. Na6CdCl8. Structure and Pressure Dependence. Most allelectron ab initio techniques currently in use do not yet allow a full geometry optimization in the mixed space of internal coordinates and cell variables. The first part requires ab initio calculated atomic forces and the second the computation of the stress tensor, which is presently only available for pseudopotential plane wave codes.32 However, as the WIEN97 code allows the calculation of residual forces acting on the atoms using the formalism of Yu et al.27 and there is only one cell variable to relax, this was unproblematic in the present calculations.
Chall et al.
Figure 4. Calculated enthalpy difference between the B1 and B2 phases as a function of pressure. The arrows indicate the phase transformation pressures. Additionally, a recent experimental value (at room temperature) is given.12 The use of different exchange-correlation functionals has only minor influence on the predicted pt.
Figure 5. Calculated energies and forces as a function of the Cl(2) displacement δ at a constant lattice parameter. The forces (energies) were fitted with a polynomial of first (second) order to obtain the equilibrium displacement. Both independent fits give the same result within error.
Figure 5 shows the dependence of the residual force acting on the Cl on Wyckoff position 24e as a function of the x-coordinate for a fixed lattice constant of a ) 11.4 Å (21.5 au). Additionally, the dependence of the energy on the atomic position is displayed. For this lattice parameter, the force acting on the atom vanishes for δ ) 0.0154(6). In the investigated range, it depends linearly on the Cl(2) displacement. The minimal total energy obtained from the independent fit of the total energy with a polynomial of second order was found at the same δ-value within the errors of the fits. These results can be used to obtain the frequency of the Raman-active A1g-mode by expanding the change of the total energy in a power series and retaining only the quadratic term in a harmonic ansatz. Such a calculation gives a frequency νA1g
Structure and Properties of NaCl and Na6CdCl8
Figure 6. Calculated minimal energies as a function of the lattice parameter. The equilibrium lattice parameter is indicated.
) 207(1) cm-1 for the breathing mode around the divalent ion. This compares favorably with the experimental result33,34 of 220 cm-1. We calculated the total energy for eight force-free structures (Figure 6). A fit to the data with a Birch-Murnaghan equation of state yielded a compressibility of K0 ) 20.2(8) GPa, K1 ) 4.7(2), and an equilibrium lattice parameter at zero pressure and temperature of 11.39(1) Å. Hence, in summary, we predict a low-pressure, low-temperature structure of Na6CdCl8 with a ) 11.39(1) Å and δ ) 0.0154(6), corresponding to a Cd-Cl(2) distance of 2.67(5) Å. The knowledge of K0 and K1 allows the calculation of the pressure as a function of the lattice parameter. The pressures corresponding to the calculated lattice parameters, ranging from -2.5 to +39 GPa are indicated in Figure 6. The pressure dependence of the equilibrium Cd-Cl(2) distance and that of the Na-Cl(1) distance are compared in Figure 7. The former varies much less than the latter, so that this is the shorter bond below ca. 9.5 GPa while it becomes the longer bond at higher pressures. The relative displacement, δ, of the Cl(2) atoms from the x ) 1/4 position covers the range from -0.015 to +0.027, or +0.0153 if one considers positive pressures only (Figure 7). At ca. 9.5 GPa (corresponding to a ) 10.45 Å), the Cl(2) is located at x/a ) 0.25, i.e., δ ) 0. CdCl2. We calculated the total energy of CdCl2 using experimental lattice constants35 and the simplest structural model, i.e., the centrosymmetric space group R3hm with Cd at 000 and Cl at xxx. The only internal parameter x was optimized and found to coincide with the value of 0.25 reported in the literature.16 The minimal total energy per formula unit was found to be -88 697.43 eV. We did not optimize the structure with respect to the lattice parameters and did not test the alternative acentric structure as this would have been computationally too expensive. Thus, the calculated value is only an upper bound for the true total energy. Electric Field Gradients. It has been mentioned above that the only relevant EFG parameters are Vzz and η for Na and Vzz for Cl(2). The field gradients and the asymmetry parameter depend linearly on the Cl(2) displacement for a fixed cell parameter in both cases. The dependence of the EFG of Na on the lattice parameter is shown in Figure 8. We observe minima
J. Phys. Chem. B, Vol. 104, No. 6, 2000 1195
Figure 7. Pressure dependence of structural parameters in Na6CdCl8. The pressure-induced change in the relative Cl(2) displacement δ is shown in the inset. At p ≈ 9.5 GPa δ vanishes. Note that the relationship between δ and the lattice parameter is linear. The change in δ leads to changes in the Cd-Cl(2) and Na-Cl(1) bond lengths as a function of pressure. The positions of Cd, Na, and Cl(1) are fixed by symmetry; the position of Cl(2) is not.
Figure 8. Lower panel: Dependence of Vzz and η of Na on the lattice parameter. Upper panel: Dependence of Vzz of Cl(2) on the lattice parameter.
of Vzz and η at a lattice parameter of 10.45 Å, which corresponds to the above-mentioned pressure of 9.5 GPa. Above and below, there is a linear relationship for Vzz, but with different slopes. The dependence of η on the lattice parameter can be described with an arcus tangens-type function. From fits to the data with fixed positions of the minima at 10.45 Å, we derive minimal values of 0.23(4) for η and 0.041(8) × 1021 V/m2 for Vzz. Vzz of Cl(2) falls monotonically with increasing lattice parameter (Figure 8).
1196 J. Phys. Chem. B, Vol. 104, No. 6, 2000 Discussion NaCl. The results of our ab initio calculations given in Table 1 with parameters for a0, K0, K1, and pt illustrate the usual accuracy of modern ab initio methods. Comparison with older LDA calculations (a comprehensive list can be found in Apra` et al.7) also shows good agreement. Previous GGA results are not available, but the underbinding of the GGA calculations is a commonly observed behavior. The calculations for the NaCl B1 phase show that both forms of the GGA used here give results which are generally in better agreement with experimental data than the LDA results. There are only minor differences between the two formulations of the GGA. Although all approximations for the exchange-correlation functional reproduce the lattice parameter at zero pressure equally well, the results for the compressibility are much closer to the experimental values when a GGA is used. For the B2 phase, only the experimental value for K0 can be used for comparison. It is significantly larger than the values obtained from the GGA calculations. Nevertheless, we think that the better agreement of the LDA result with the experimental value is fortuitous for the following reason. The high experimental value for K0 may be due to an inherent problem in the analysis of the experimental data, since only high-pressure data are available. The curvature of the p(V)-curve is not known in the important region around V0, and consequently a fit will tend to overemphasize the linear contribution, leading to an overestimation of K0. This is apparent from Figure 3 where the experimental data of the B1 and B2 phases coincide within errors, which implies that it is rather unlikely that the bulk modulus of the B2 phase is larger by 50% in comparison to that of the B1 phase. Hence, our results are a strong indication for a significantly lower K0-value of the B2 phase. The calculated phase transformation pressures are all lower than the observed pt at room temperature. If one linearly extrapolates pt(T) to 0 K (Figure 3 from Li and Jeanloz12), the deviation is even larger, as this gives pt ≈ 29 GPa instead of 26.6 GPa. Nevertheless, on the basis of the results presented, we believe that the FP-LAPW method describes with sufficient accuracy the structural data and physical properties for NaCl. We shall now employ the same methodology to investigate the Suzuki phase Na6CdCl8 described above. Na6CdCl8. Our calculations indicate a zero pressure displacement δ ≈ 0.0154(6) of the Cl(2) atoms located between a Cd and a vacancy. The experimental values obtained from measurements on precipitates are 0.02014,15 and 0.014,13 and that for ansallegedssingle crystal is 0.028.1 Only the result of Toman13 is consistent with our findings. The differences between the suggested atomic positions are more than 0.1 Å. However, it has been pointed out by Sors and Lilley15 that the experimental data suffer from large experimental errors, due to thescompared to modern standardsscrude techniques employed (estimated intensities from X-ray photographs, very few reflections used, estimated overall displacement factors, etc.). We therefore conclude that the current results are probably more reliable than the older experimental data. To confirm this, we are currently optimizing the synthesis techniques and hope to clarify this point by new diffraction experiments in the near future. We have also predicted the compressibility of Na6CdCl8. As one would expect, this compound is softer than NaCl. The relative difference from the calculated compressibility of NaCl is -20%. The NaCl B1/B2 calculations showed that relative differences of compressibilities are computed rather accurately, although the absolute values are approximately 6% too high. If we assume that this overestimation of K0 applies also to the
Chall et al. Suzuki phase, we expect a compressibility of ∼19 GPa to be found in experimental investigations. Our calculations show that at zero pressure the Cl(2) located between a Cd and a vacancy is attracted by the Cd and displaced toward it. With increasing pressure the repulsive interaction becomes more important, and since the Na-Cl(1) distance decreases significantly more than the Cd-Cl(2) distance (Figure 7), the Cl(2) is effectively shifted back toward the vacancy, making δ negative. Thus, the first coordination polyhedron of the Na located next to the Cl(2) is distorted in one direction at zero pressure (δ > 0), becomes regular for δ ) 0, and then starts to distort in the other direction (δ < 0). These changes in the distortion of the coordination polyhedron of the Na are reflected in the anomalous behavior of its EFG. When the polyhedron becomes regular, Vzz and η do not vanish completely, which would be the case for cubic symmetry, since the next coordination shell still deviates from cubic symmetry. The lattice parameter of Na6CdCl8 is found to be, within the errors of the fits, exactly twice that of NaCl. Hence, at 0 GPa no misfit between both structures is expected. This then implies that the precipitates are not stabilized by mechanical “clamping” or some kind of elastic deformation. A comparison of the calculated total energies of NaCl, CdCl2, and Na6CdCl8 at 0 GPa indicates that the Suzuki phase is only metastable. Using the GGA-PBE formulation for the exchangecorrelation functional, we find energies per formula unit of -16 981.84 eV for NaCl and -88 697.43 eV for CdCl2. An upper limit for the total energy of the mechanical mixture of NaCl and CdCl2 corresponding to the composition of the Suzuki phase is thus -279 285.86 eV. This is already more stable by 5.53 eV than the total energy of Na6CdCl8 (-279 280.33 eV). Hence, the Suzuki phase is metastable with respect to its components NaCl and CdCl2. This is consistent with the difficulties experienced during sample synthesis. Acknowledgment. We acknowledge Professor Wulf Depmeier for initiating this research project and valuable discussion. M.C. is grateful for financial support from the Deutsche Forschungsgemeinschaft under Grant De412/18-1. B.W. is grateful for financial support from the Deutsche Forschungsgemeinschaft under Grant Wi1232. K.S. and P.B. were supported in part by the Austrian Science Foundation (SFB Project F1108). This work was also supported by the TMR network “Electronic Structure Calculations of Material Properties and Processes for Industry and Basic Sciences”. References and Notes (1) Suzuki, K. J. Phys. Soc. Jpn. 1961, 16, 67-78. (2) Porta, P.; Minelli, G.; Botto, I. L.; Baran, E. J. J. Solid State Chem. 1991, 92, 202-207. (3) Marco de Lucas, C.; Rodrı´guez, F.; Moreno, M. Phys. Status Solidi B 1994, 184, 247-265. (4) Guerrero, A. L.; Butler, E. P.; Pratt, P. L.; Hobbs, L. W. Philos. Mag. A 1981, 43, 1359-1376. (5) Bonanos, N.; Lilley, E. Mater. Res. Bull. 1979, 14, 1609-1615. (6) Prencipe, M.; Zupan, A.; Dovesi, R.; Apra`, E.; Saunders, V. R. Phys. ReV. B 1995, 51, 3391-3396. (7) Apra`, E.; Causa`, M.; Principe, M.; Dovesi, R.; Saunders, V. R. J. Phys.: Condens. Matter 1993, 5, 2969-2976. (8) Swanson, F. Natl. Bur. Stand. (U.S.), Circ. 539 1953, as cited in the JCPDS-ICDD Powder Diffraction File, Card 5-628. (9) Meincke, P. P. M.; Graham, G. M. Can. J. Phys. 1965, 43, 18531866. (10) Chall, M.; Knorr, K.; Winkler, B. Z. Kristallogr. Suppl. Issue 1999, 16, 147. (11) Bassett, W. A.; Takahashi, T.; Mao, H. K.; Weaver, J. S. J. Appl. Phys. 1968, 39, 319-325. (12) Li, X.; Jeanloz, R. Phys. ReV. B 1987, 36, 474-479. (13) Toman, K. Czech. J. Phys. B 1962, 12, 542-548.
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