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First-principles calculations based on density-functional theory in the pseudo-potential approach have been performed for the total energy, crystal structure and cell polarization for SrTaO

Fil: Bastidas Briceno, Ruby Carolina. Universidad Nacional de La Plata. Facultad de Ingenieria. Departamento de Ciencias Basicas; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - La Plata. Instituto de Fisica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Fisica La Plata; Argentina

Montmorillonite (MMT) clays are 2:1 layered structures which in natural state may allocate different hydrated cations such as M-nH2O (M= Na, Ca, Fe, etc) in its interlayer space. Depending on the capability for ion sorption, these materials are interesting for environmental remediation. In this work we experimentally study the Co sorption in a natural Na-MMT using UV-visible spectrometry and XRD on semi-oriented samples, and then analyze the sorption ability of this clay by means of ab initio calculation performed on pristine MMT. The structural properties of Na-MMT and Co-adsorbed MMT, and the hyperfine parameters at different atomic sites were analyzed and compared with the experimental ones for the first, and for the case of the hyperfine parameters, presented for the first time for the last. The theoretical predictions based on total energy considerations confirm that Co incorporation replacing Na is energetically favorable. Also, the basal spacing d experimentally obtained is well reproduced., Facultad de Ciencias Exactas, Instituto de Física La Plata, Facultad de Ingeniería

CaCu 3 (Ti 4− x Hf x )O 12 ceramics ( x = 0.04, 0.1 and 0.2) were prepared by conventional synthesis (CS) and through reactive sintering (RS), in which synthesis and sintering of the material take place in one single step. The microstructure and the dielectric properties of Hf-doped CCTO (CCTOHf) have been studied by XRD, FE-SEM, AFM, Raman and impedance spectroscopy (IS) in order to correlate the structure, microstructure and the electrical properties. Samples prepared by reactive sintering show slightly higher dielectric constant than those prepared by conventional synthesis in the same way than the pure CCTO. Dielectric constant and dielectric losses decrease slightly increasing Hf content. For CCTOHf ceramics with x > 0.04 for CS and x > 0.1 for RS, a secondary phase HfTiO 4 appears. As expected, the reactive sintering processing method allows a higher incorporation of Hf in the CCTO lattice than the conventional synthesis one.

Mixed perovskites Ca1− x Sr x HfO 3 with x ≅ 0.25, 0.50 and 0.75 have been prepared for the first time by the high temperature solid state reaction method. The crystalline structures of these perovskites were investigated by X-Ray Diffraction (XRD) technique. The samples were irradiated with thermal neutrons to produce the 181 Hf- 181 Ta Perturbed Angular Correlation spectroscopy (PACs) probe. A static asymmetric and disordered electric field gradient interaction was used to fit the time spectra. The behaviour of the quadrupole frequency measured at room temperature with composition is discussed.

Estudios recientes sobre la transicion de fase en SrZrO3 haciendo uso entre otras tecnicas de Difraccion de Rayos X y de Neutrones, junto con espectroscopias de correlacion angular o espectroscopia Raman, ponen de manifiesto que el diagrama de fases de estos compuestos no es simple, ni esta claramente definido. Las temperaturas de transicion proporcionadas, son fuertemente dependientes de la historia termica del material. En este trabajo, presentamos por primera vez el estudio de la estabilidad de fase en funcion del proceso termico haciendo uso de Espectroscopia de Impedancia. En este trabajo nos centraremos en las transiciones de fase Pnma® Imma (Segundo orden) y Imma ® I4/mcm (primer orden), previamente establecidas a 750o C y 840o C respectivamente.

In order to study how the Hf replacement by Ti affects the crystalline structure of SrHfO3 pure perovskite, X-ray diffraction (XRD) studies and hyperfine characterizations of SrHf1−xTixO3 for the compositions x=0.25, 0.50 and 0.75 are reported. The structure at room temperature (RT) was determined by XRD. Hyperfine electric quadrupole interaction at Ta probes was determined by perturbed angular correlation spectroscopy. For every sample, spin precession curves were measured from RT to 1000 °C, in 50 °C steps. From the data fit it was determined that for x=0.25 the compound is orthorhombic (Pnma) at RT and undergoes one first-order and one second-order phase transitions at 550 and 750 °C, respectively. For x=0.50 the compound is in the orthorhombic (Cmcm) phase at RT and undergoes a second-order phase transition at about 250 °C. For x=0.75, the compound is cubic ( Pm 3 ¯ m ) from RT on. Also, comparison with other perovskite-type compound studies is performed.

Previous studies using perturbed angular correlation (PAC) spectroscopy in the PbZr1−xTixO3 (PZT) family of compounds show that whereas PbZrO3 is characterized by a single probes site with a very well-defined hyperfine interaction, in PZT with x⩾0.1 the probes occupy two distributed sites. In this work, we investigate the Zr-rich region of the PZT phase diagram from x=0.02 up to x=0.08 using PAC in order to correlate the hyperfine parameters with the antiferroelectric–ferroelectric phase transition reported to occur at x=0.05. Two static electric quadrupole interactions, one of them fairly distributed, were detected over the whole Ti concentration range, and an abrupt change in the hyperfine parameters for 0.02

The electronic structure of pure and Ta-doped $\mathrm{ZrSi}{\mathrm{O}}_{4}$ in the tetragonal $I{4}_{1}/amd$ phase with and without defects has been studied using the ab initio full-potential linear augmented plane wave plus local orbitals method. From the determined charge densities, the electric field gradient tensor at native Zr sites and at Ta impurities localized on cation sites of $\mathrm{ZrSi}{\mathrm{O}}_{4}$ were derived and compared to experimental data obtained using hyperfine techniques. The effects of the Ta probe atom, including its different charge states on the lattice, are investigated. In addition, different types of defects, such as O or Si vacancies, Ta replacing Si, and Ta enclosed in microstructures of $\mathrm{Si}{\mathrm{O}}_{2}$ phases, are examined. The combination of experiments and theory enables us to identify the different interactions observed in Ta-doped $\mathrm{ZrSi}{\mathrm{O}}_{4}$ and to elucidate the role played by different defects.

In this paperwe present the study of the glassy systems of formula: xMgO(1−x)(0.5V2O5·0.5MoO3)2TeO2,with (0 b x b 1). The aim of the work is to understand the relationship between in the induced changes in the glassy matrix by the incorporation of MgO in a vanadium–tellurite glass and the electrical response of the material. It has been found that the incorporation of MgO in the glassy matrix raises the glass transition temperature. The whole system's electrical behavior is explained by the small polaron hopping, in good agreement with the variable range polaron hopping model. In this matrix, an ionic transport by Mg2+ is not allowed. The study gives an opportunity to understand how to tune in the middle-range glassy structural order and, as a direct implication, how to control the electrical conduction process., Instituto de Física La Plata

The necessity of producing materials with better performances than those observed in ferroelectric perovskites has induced the investigation of new oxides, especially those belonging to the Aurivillius family which exhibit better performance than PZT in non-volatile ferroelectric memories (FeRAM). In this contribution a Raman analysis of Bi2-xTexSrNb2-xHfxO9 (x = 0.10) is carried out to investigate the vibrational spectra and the ferro-paraelectric phase transition of these compounds.

The Aurivillius type oxide Bi1.9Te0.1SrNb1.9Hf0.1O9 has been studied by Perturbed Angular Correlations spectroscopy using 181Ta probes. The spin precession curves were measured from room temperature up to 873 K. Two sites are occupied by probes and the temperature dependence of both indicates a continuous phase transition at about 625 K. One site is ordered while the other is disordered. This situation is analyzed in terms of simple models already applied to perovskites. The transition temperature of the solid solution Bi2−xTexSrNb2−xHfxO9 (with 0 ≤ x ≤ 0.5 ) shows a strong dependence on composition.

The study by x-ray diffraction and perturbed angular correlation spectroscopy of Sr1?xBaxHfO3 compounds for x = 0.12, 0.25, 0.5, 0.75 and 0.88 is presented. The hyperfine parameters are analysed in terms of ionic radii, ionic or covalent bonds, and cation?oxygen distances. A simple explanation of the behaviour of these parameters with composition is provided.

The necessity to produce materials with better performances than those observed in ferroelectric perovskites has generated the creation of new oxides, especially those belonging to the Aurivillius family. In the last few years much attention has been paid to the study of these materials, and this has opened up new fields due to their basic and applied properties. In this contribution a Raman analysis and a hyperfine study by perturbed angular correlations spectroscopy of Bi1.75Te0.25SrNb1.75Hf0.25O9 were carried out to reveal information about the lattice and the electronic structure. By the use of these techniques, it was observed that the ferroelectric to paraelectric phase transition at about 570 K is driven by a soft mode, and the broadening of the dielectric constant as a function of temperature previously observed at TC is connected to disorder in the Bi/Te–O layer.

En este trabajo se presenta las temperaturas de transicion TC a la estructura cubica, en la familia de compuestos SrXBa1-XHfO3 donde x es igual a 0.12, 0.25, 0.50, 0.75 y 0.88, determinadas por medidas de la Correlacion Angular Perturbada y usando al tantalio como sonda. El interes es estudiar como la sustitucion de estroncio por bario modifica dicha temperatura. El BaHfO3 es cubico a temperatura ambiente. En cambio, el SrHfO3 presenta una transicion estructural de tetragonal a cubica cuando TC1 . 1400 K. Por debajo de esta temperatura y hasta TC2 . 1000 K los octaedros de oxigeno estan rotados uno con respecto al consecutivo, en un angulo . alrededor del eje z de la red tetragonal que disminuye a cero a medida que T�¨TC. Esta rotacion esta relacionada con la interaccion del estroncio con el oxigeno, ya que el radio ionico del cation rSr (. 1.13 A) permite un mayor acercamiento entre ambos que el bario al oxigeno, pues rBa (. 1.35 A). Entonces, en los compuestos SrXBa1-XHfO3 se espera que haya una competencia entre la interaccion Ba-O, separados por 2.9502 A y la interaccion Sr-O separados por una distancia menor, 2.9089 A en las fases cubicas de los respectivos compuestos puros.

The hyperfine quadrupole interaction at probes in sites with cubic point group symmetry was measured in many perovskite-type compounds. This interaction is commonly associated to the presence of oxygen vacancies close to probes. The effect of this point defect on 181 Ta probe in BaTi x Hf 1 m x O 3 for x = 0.70, 0.50, 0.30, 0.10, 0.05, and 0.01, is studied. The lattice constant of these oxides at room temperature were measured using XRD technique. The quadrupole parameters corresponding to probe-defect interaction were obtained by means of Perturbed Angular Correlation (PAC) spectroscopy as functions of both, composition and temperature. A static, asymmetric and distributed quadrupole interaction was fitted to all PAC data. This interaction was observed to be strongly composition dependent. These results and those corresponding to compositions 0.75 h x < 1 were compared to the ones obtained using the point charge method for the calculation of the electric field gradient. The proposed model took into accou...

Using powder X-Ray Diffraction and Perturbed-Angular-Correlation spectroscopy, the crystal structure and the hyperfine interaction at 181 Ta probe in Sr 0.75 Ba 0.25 HfO 3 have been studied. A tetragonal (I4/mcm) to cubic (Pm &3macr;m) phase transition was observed. A two-phase field region, where the tetragonal and cubic phases coexist, was found between 673 and 923 K. The spin precession curves were measured from room temperature up to 1373 K. A static, asymmetric and disordered electric field gradient model was used to fit these time spectra. The hyperfine parameters corresponding to the tetragonal structure changed as the temperature increases: y T Q diminishes, m T is almost constant and i T diminishes. This interaction was observed to be unique up to 673 K. Above this temperature, a second interaction appeared and these two phases coexist up to 923K. Above this temperature, the hyperfine parameters corresponding to the cubic structure was only observed. The tetragonal to cubic transformation is char...

We report the crystal structure together with the electric field gradient (EFG) tensor at the Hf site in Sr 0.5 Ba 0.5 HfO 3 as a function of temperature. High-temperature X-ray diffraction data show a second-order tetragonal-to-cubic phase transition at 700 K. The hyperfine interaction measured at 181 Ta probe corresponds to a static, asymmetric and disordered EFG. The hyperfine parameters V zz and η also display evident changes close to 673 K confirming the phase transition observed by XRD. The line width of the quadrupole interaction is relatively small compared with other perovskite-type compounds.

The temperature dependence of the hyperfine parameters in a powder sample of the Sr0.88Ba0.12HfO3 compound has been investigated for the first time using perturbed angular correlation spectroscopy. The time spectra were measured as a function of the temperature from 293 to 1273 K. Activated 181Ta nuclei were used as hyperfine probes at the Hf sites. The analysis of the time spectra indicates the presence of two different surroundings for the Ta probes. The most populated site (f 1≈75% at laboratory temperature) was fitted with the usual static quadrupole hyperfine interactions found in most perovskite-type compounds. The resulting quadrupole frequency is ω Q ≈24 Mrad/s at this temperature. This frequency continuously decreases to nearly 9 Mrad/s at 1273 K. Its line width temperature dependence displays three regions and the changes observed probably correspond to phase transitions. The other site has a large and temperature independent quadrupole frequency ω Q ≈120 Mrad/s that reversibly transforms into the first at high temperatures and probably originates from some defect in the structure.

The electric field gradients in perovskite SrHfO 3 and BaHfO 3 powder samples were investigated by means of Perturbed Angular Correlation spectroscopy, using implanted 111 In hyperfine probes. The measurements cover the temperature ranges from 22 to 893 K for SrHfO 3 and from 293 to 875 K for BaHfO 3 , respectively. In both compounds, three quadrupole interactions were established. The largest fraction showing a pronounced dynamic interaction is assigned to 111 In/ 111 Cd probe atoms on substitutional Hf sites in both compounds. For SrHfO 3 , the temperature dependence of the dynamic interaction was associated to the Pnma↔Imma phase transition for SrHfO 3 at about 700 K. We discuss the results in relation to those obtained for 111 In/ 111 Cd-probes in PbZrO 3 and BaTiO 3 , and for 181 Hf/ 181 Ta-probes in AHfO 3 (A=Ca, Sr, Ba).

(a) Institute of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark(b) Department of Physics and Astronomy, Northwestern University, Evanston,IL 60208, USA(c) Departamento de Fisica, Universidad Nacional de La Plata, La Plata 1900, Argentina(d) Instituto de Fisica de Liquidos y Sistemas Biolo´gicos, Grupo Fisica del So´lido,Casilla de Correo 565, La Plata 1900, Argentina(Received August 14, 1998)Parameter-free calculations based on the density-functional theory are used to examine high-pres-sure phases of solids, mainly semiconductors. For the elemental semiconductors, as represented bySi, the diamond!b-tin!Imma sequence is examined, and for III–V semiconductors the optimi-zation of the structural parameters of the Cmcm and Imm2 phases is described. The structuralenergy differences are in several cases very small, and in some too small to allow a safe structureprediction on the basis of the calculations. In that context we also discuss ways to go beyond thelocal density approximation (LDA). We show that the predicted high-pressure phases may be sig-nificantly affected by inclusion of (generalized) gradient corrections (GGA). Elemental Zn (h.c.p.)is further taken as an example where we find that the simple LDA leads to poor results.

ABO3 perovskites display several physical properties determined by the characteristics of A and B cations. These compounds have cubic structure at high temperature. Lower symmetry cells that are distorted cubes are found at low temperature. Defects modify the properties of these compounds. Under standard conditions oxygen vacancies are produced. Cation substitution also alters the characteristics of perovskites. These materials have been studied by Perturbed Angular Correlation (PAC) spectroscopy and other hyperfine techniques. In this way abundant information is available to determine charge distributions close to probes. In the cubic phase perturbations were detected that are produced by the interaction of probes with defects. To show up these effects we analyze the quadrupole interaction at 181Ta in several compounds: ABO3 with A=Ca, Sr and Ba, BaTi1−x Hf x O3 and PbZr1−x Ti x O3 for 0⩽x⩽1. Three different quadrupole interactions were found and are interpreted in terms of distinct probe-oxygen vacancy configurations.

The temperature dependence of the hyperfine parameters in SrHfO3 powder samples has been investigated by means of Perturbed Angular Correlation spectroscopy using implanted 111In probes. Three quadrupole interactions have been established, with the largest fraction showing a pronounced dynamic interaction. We assign this fraction to 111In / 111Cd probe atoms on substitutional Hf sites. The temperature dependence of the dynamic interaction has been associated to the Pnma↔Imma phase transition at ∼700 K. We discuss the results in relation to those obtained for 181Hf / 111Ta-probes in AHfO3 (A=Ba, Sr, Ca) and for 111In / 111Cd-probes in PbZrO3 and BaTiO3.

Zone-center TO phonon frequencies and eigenvectors of cubic ${\mathrm{SrHfO}}_{3}$ are determinated, by calculating atomic forces, in the framework of the local density approximation to density functional theory to sense the presence of possible lattice instabilities. The results are compared with parallel calculations made on ${\mathrm{SrTiO}}_{3}$. An unstable zone-center phonon mode is obtained for both ${\mathrm{SrHfO}}_{3}$ and ${\mathrm{SrTiO}}_{3},$ but with quite different displacement patterns. As in ${\mathrm{SrTiO}}_{3}$, an unstable mode suggests the presence of a temperature-dependent ``soft'' mode in ${\mathrm{SrHfO}}_{3}$ which should be further confirmed by experimental measurements.

In this paper, the hyperfine quadrupole interaction at the Zr-Ti site of (PZT) polycrystalline samples is studied for the first time. Powders for x = 0, 0.1, 0.2, 0.4, 0.6, 0.8, 0.9 and 1 were prepared and characterized by XRD. The lattice constants and space groups were obtained as functions of Ti concentration. PAC analyses were done for ferroelectric PZT for x = 0.9 and 0.8 as a function of temperature, and for x = 0.6 at RT. Also antiferroelectric was analysed. Low-concentration nuclei were used as probes. In the ferroelectric and paraelectric phases of PZT compounds two sites were occupied by probes. For each site the quadrupole frequency, asymmetry and relative distribution width parameters were obtained as functions of temperature above and below the Curie temperature. For only one site was detected with a static quadrupole interaction below and a nuclear spin-relaxation process above it. Furthermore, the temperature dependence of the hyperfine parameters, the possible origin of both quadrupole interactions in PZT and the perturbation that characterizes the cubic phases of and compounds are discussed.

Samples of PbZr 0.52 Ti 0.48 O 3 (PZT) were fabricated by the Sol-Gel method and characterized by X-ray diffraction analysis. The Rietveld method was used to obtain lattice parameters and grain sizes as a function of the annealing temperature. A powder sample previously annealed at 873 K was irradiated to activate the 181 Ta probe. Then, Perturbed Angular Correlation (PAC) spectra were measured at RT and temperatures above 873 K to study the thermal behaviour on samples capsulated in SiO 2 tubes. The hyperfine parameters observed as a function of temperature show changes in this PZT compound that would correspond to thermal evolution of defects. Furthermore, the reaction of PZT with the substrate was observed at 1173 K, obtaining at this temperature the hyperfine parameters corresponding to SiZrO 4 . At this temperature no trace of the PZT was left.

Fil: Forker, M.. Centro Brasileiro de Pesquisas Fisicas; Brasil. Ministerio da Ciencia, Tecnologia e Inovacoes; Brasil

The SrMO 3 compounds with M = Ru, Zr 6 Hf display similar structures. They are orthorhombic at room temperature (RT) and transform into tetragonal (14/mcm) and cubic (Pm3m) at higher temperatures. These structures are characterized by rotations of the quasi-rigid oxygen octahedron through different axes. As temperature increases the rotation axes changes at the transition temperature but the M-O distances remain almost constant (1%) in the whole temperature range. The crystallographic study of the tetragonal to cubic transformation shows that it occurs by the rotation Φ(T c )→0 of the rigid oxygen octahedron about the c axis. This transition is of second order and can be described by Φ(T) ∼ Φ 0 (T C -T) β . βis the critical exponent and was fitted to 1/2, 1/4 and 1/8 for M = Hf, Zr and Ru, respectively. The electronic structure of these compounds should follows such changes and can be studied through the measurement of the quadrupole interaction as a function of temperature. In this contribution these results obtained by Perturbed Angular Correlations spectroscopy (PAC) for SrZrO 3 are discussed.

A combination of experiments and ab initio quantum-mechanical calculations has been applied to examine electronic, structural, and hyperfine interactions in pure and Ta-doped zirconium dioxide in its monoclinic phase (m-ZrO₂). From the theoretical point of view, the full-potential linear augmented plane wave plus local orbital (APW + lo) method was applied to treat the electronic structure of the doped system including the atomic relaxations introduced by the impurities in the host in a fully self-consistent way using a supercell approach. Different charge states of the Ta impurity were considered in the study and its effects on the electronic, structural, and hyperfine properties are discussed. Our results suggest that two different charge states coexist in Ta-doped m-ZrO₂. Further, ab initio calculations predict that depending on the impurity charge state, a sizeable magnetic moment can be induced at the Ta-probe site. This prediction is confirmed by a new analysis of experimental data.

A systematic high-resolution and high-statistics time-differential perturbed-angular-correlations study of the temperature dependence, from 77 to 1373 K, of the electric-field-gradient (EFG) tensor at $^{181}\mathrm{Ta}$ in ${\mathrm{HfO}}_{2}$ is presented. Three interactions were detected. One that was observed previously corresponds to the monoclinic structure, while the other two interactions have a reversible behavior with temperature and probably belong to equilibrium defect structures. The three components of the EFG tensor ${V}_{\mathrm{xx}}$, ${V}_{\mathrm{yy}}$, and ${V}_{\mathrm{zz}}$ corresponding to the monoclinic structure have different temperature behavior and are analyzed in terms of known models.

In order to determine the microscopic role of cation A in ABO 3 perovskites the hyperfine interaction in the Sr 1 xBaxHfO3 system using Perturbed Angular Correlation spectroscopy (PAC) is studied. As a previous result the compositions x = 0.50 and 0.25 are shown. The PAC spectra were obtained in the temperature range from 20 to 1000°C. In both compounds a phase transition to higher symmetry structure was observed at T400 and 200°C, respectively. This structure is proposed to be cubic in both compositions. The results are compared with those obtained in SrHfO 3 and BaHfO 3 .

The electronic and structural properties of pure and Ta-doped monoclinic ${\text{HfO}}_{2}$ have been examined by means of ab initio density-functional calculations. The full-potential linear augmented plane wave plus local orbital $(\text{APW}+\text{LO})$ method was used here to treat the electronic structure of the doped system including the atomic relaxations introduced by impurities. The effects of reducing the Ta concentration were simulated by means of periodic arrangements of supercells of increasing size, all containing a single Ta atom. The structural relaxations were calculated for two differently charged impurity states and the electrical-field gradients (EFG) at the site of the Ta impurity were derived. The EFGs, as well as the relaxations, depend on the charge state of the impurity. The analysis was carried out by combining time-dependent perturbed angular correlation experimental results and the theoretical $\text{APW}+\text{LO}$ calculations.

The alkali metals, which under ambient conditions are simple in the sense that their electronic structures are free-electron like and the their crystal structures are of high symmetry (body centered cubic), transform to surprisingly complex structures when pressure is applied. The experimentally determined pressure sequence for lithium up to 50 GPa is $bcc\ensuremath{\rightarrow}fcc\ensuremath{\rightarrow}hR1\ensuremath{\rightarrow}cI16$. In the present work the (non)linear optical properties of these Li phases are examined in order to gain better insight into the electronic properties. We propose that the comparison of optical experiments (performed on samples in a diamond anvil cell) with calculations like those presented here can be used to distinguish between various high-pressure phases and thus be a supplement to x-ray diffraction and Raman scattering techniques.

The fast-slow coincidence technique has been used for the first time to measure the electron half-life, obtaining a very simple way for extracting noise background from real signals. In this paper we present a 986h measurement for the channel e − → γ + ν , realized in a laboratory practically without any cosmic-ray shielding and with common low-resolution BaF 2 scintillators, obtaining a period of T e > 3.15 × 10 21 yr. This result is analized in comparision with previous reports obtained in ultra-low background, massive and high resolution Ge detectors located thousand meters underground. So, an extrapolation of the limit that would be obtained under such conditions is evaluated.

The question concerning the driving mechanism (displacive or order disorder) of the paraelectric--ferroelectric phase transition in ${\mathrm{BaTiO}}_{3}$ is investigated by means of the study of the electric field gradient tensor at the $\mathrm{Ti}$ site. A comparison of recent NMR results close to the critical temperature ${T}_{c}$ versus first-principle calculations of displacive and off-site $\mathrm{Ti}$ order--disorder type structures are accomplished. At a temperature just below ${T}_{c}$ the calculated ${V}_{zz}$ for the displacive-type structure describes well the experimental value, while the calculated order--disorder static ${V}_{zz}$ value is far away from it.

The electric-field gradient at the halide site is calculated in several compounds of Cl, Br, and I. The ab initio full-potential linear-augmented plane-wave method is employed with the generalized gradient approximation for exchange and correlation effects. The nuclear quadrupole moments of ${}^{35}\mathrm{Cl},$ ${}^{79}\mathrm{Br},$ and ${}^{127}\mathrm{I}$ are obtained by comparison of available experimental nuclear quadrupolar resonance data to the calculated electric-field gradients. The values of $|{Q(}^{35}\mathrm{Cl})|=0.0855\mathrm{b},$ $|{Q(}^{79}\mathrm{Br})|=0.330\mathrm{b},$ and $|{Q(}^{127}\mathrm{I})|=0.721\mathrm{b}$ are derived with $\ensuremath{\sim}3%$ statistical uncertainty. These values are in agreement with recent values derived by other methods, and thus confirm the validity of the present methodology for the determination of electric-field gradients in solids.