Displacive Phase Transition Research Articles

Tungsten bronze type dielectrics in SrO-Sm2O3-TiO2-Nb2O5 system and their dielectric anomaly

The dielectric behavior and the features of the diffused phase transition of the SrpSm6−pTi8−pNb2+pO30(p=4,5) ceramics were investigated together with their structure. Both Sr5SmTi3Nb7O30 and Sr4Sm2Ti4Nb6O30 had tungsten bronze structure and weak ferroelectric nature. Though Sr5SmTi3Nb7O30 showed the diffused ferroelectrics phase transition, it was concluded that the transition was mainly the displacive ferroelectric phase transition. In Sr4Sm2Ti4Nb6O30, the Sr2+ ions and Sm3+ ions did not form an order structure and it showed a typical displacive ferroelectric phase transition. The dielectric anomaly was attributed to the different BO6 octahedral distortion.

Impact of radiation defects on the structural stability of pure zirconia

Optical spectroscopy and x-ray diffraction were used to study the behavior of polycrystalline samples of pure monoclinic zirconia irradiated by low energy ions. A microscopic model based on these experiments is proposed to explain the displacive phase transition observed in this material after irradiation. Defects, produced in the oxygen sublattice, induce important strain fields on a nanometric scale. This strain field can be handled as a secondary order parameter within the Landau theory approach, leading to a decrease of the phase transition temperature and thus quenching the high temperature tetragonal phase. The model also explains the consequences of the thermal annealing for restoring the ground state monoclinic structure.

Random-field quantum spherical ferroelectric model

We study a (quenched) random-field quantum model of an anharmonic crystal for displacive structural phase transitions in spherical approximation: the random-field quantum spherical (ferroelectric) model. For stationary ergodic random fields its behavior depends on the quantum parameter of the model and on the expectation and covariance of the field. If quantum fluctuations are small enough not to destroy the phase transition, then it can be suppressed when the field fluctuations are large. For the field of independent identically distributed random variables and the short-range interaction we obtain that the lower critical dimensionality dl=4 (dl=2 for the zero-field) and that it decreases for long-range interactions.

A neutron diffraction and Rietveld analysis of cooperative Li motion in beta-eucryptite

Li+ mobility and structural changes in the aluminosilicate beta-eucryptite have beenstudied by high-resolution powder neutron diffraction as a function of temperaturefrom 573 to 873 K. A Li split-atom model was used to describe the disorder ofLi+ ions in the structure. Analysis of the data shows two anomalies around 698 and 758 K. The firstanomaly is attributed to an M-point zone boundary transition reported in the literature,which is connected to the appearance of the incommensurate structure. The secondanomaly is attributed to a displacive phase transition of the framework and doubling in thea cell parameter.

Displacive phase transition in SrTiO3 thin films grown on Si(001)

Polarization dependent near and extended x-ray absorption fine-structure (XANES and EXAFS), in combination with x-ray diffraction, has been used to study the structure of SrTiO3 (STO) ultra thin films grown on Si(001). For the in-plane direction (200), the x-ray diffraction data indicate that all films (from 40 to 200 Å) are equally expanded. This is in contradiction to previous reports claiming that the growth is pseudomorphic and epitaxial (coherent), which would predict an inplane contraction. Even the thinnest films (40 Å) grow in a relaxed mode (not coherent) at the deposition temperature (700 °C). As the system is brought to room temperature, the films (now anchored to the substrate) are not allowed to compress as much as bulk STO. The residual film expansion is quantitatively explained by the differential thermal expansion of Si and STO. For the out-of-plane direction (002), the x-ray diffraction data indicate that STO films are expanded for the thinnest films, and relaxed for a thickness of 200 Å. The in-plane and out-of-plane EXAFS and XANES data show that the perpendicular expansion of the thinner films is accompanied by a displacive phase transition of SrTiO3 where the Ti atom moves toward the (002) direction. This ferroelectric-type behavior of the thinner films implies important potential applications in electronics.

A multisublattice magnetic phase induced by external field in a singlet magnet

The theory of magnetization in a longitudinal magnetic field is developed for an easy-plane multisublattice antiferromagnet with a singlet ground state and a strong single-ion anisotropy exceeding the magnitude of exchange interaction. The magnetic-field-induced phase transition from the singlet (magnetically dis-ordered) state to a multisublattice antiferromagnetic state represents a displacive magnetic phase transition. At T=0, this transition proceeds continuously and belongs to second-order phase transitions, while at T ≠0, the behavior changes to jumplike and the process becomes the first-order phase transition.

α–β Inversion in quartz from low frequency electrical impedance spectroscopy

The α–β phase transformation in quartz has been studied in the pressure range from 0.5 to 2.5 GPa by the use of the low frequency electrical impedance spectroscopy. The electrical conductivity data obtained at low frequencies exhibit a different slope on an Arrhenius plot ln(σ LFD ∗T) vs. 1/ T above and below T c, where T is the absolute and T c is the inversion temperature. The point where the slope changes, coincide with the T c, i.e. the temperature point of α–β inversion in quartz. The obtained inversion temperature T c from this method compares well with the previous measurements of T c using DTA and laser interferometry. The low frequency dispersion data in insulating materials with the ionic conductivity due to impurities may be a useful method for characterization of structural displacive phase transitions in quartz-like structures.

Simulations of minerals using density-functional theory based on atomic orbitals for linear scaling

The use of quantum mechanics methods within the formalism of density functional theory requires a method to represent the electron wave functions. We compare the use of strictly localized basis functions based on atomic orbitals with the use of plane waves for the study of mineral properties and behaviour. Strictly localized functions enable the computational resources to scale linearly with the size of the system, whereas plane-wave methods scale more as the cube power of the system size, and for this reason the use of localized functions will be preferred for studies of large sizes. We present test results obtained from studies of cation ordering in spinel, garnet and amphibole phases, the high-pressure displacive phase transition in cristobalite, and the intercalation of organic molecules into pyrophyllite. We conclude that the use of localized basis sets provides a useful route forward for quantum mechanical studies of large-scale mineral problems.

Structures and phase transitions of trigonal ZrMo2O8 and HfMo2O8.

This paper describes the structures, thermal-expansion properties and phase transitions of the trigonal forms of ZrMo(2)O(8) and HfMo(2)O(8). Both phases adopt a P(-)3m structure at room temperature and show positive thermal expansion. Both phases also undergo a displacive phase transition at high temperature (ZrMo(2)O(8) at 487 K and HfMo(2)O(8) at 463 K) to a higher-symmetry structure that has lower thermal expansion. The structure of the high-temperature alpha'-AMo(2)O(8) form (A = Zr and Hf) has been refined from powder diffraction data in space group P(-)3m1.

Novel phase transition in orthoenstatite

Single-crystal Brillouin scattering measurements on natural orthoenstatite [OEN] to 1350 °C at 1 atm show significant softening of the elastic moduli C 33 and C 55 ahead of a phase transition. To our knowledge, these are the first observations of acoustic mode-softening in orthoenstatite at high temperature and room pressure and could have important implications for Earth's mantle. The phase transition is rapid and shows some hysteresis in the observed transition temperature, T tr . Experiments performed on increasing and decreasing temperature bracket the transition temperature between 1090(10) °C ≤ T tr ≤ 1175(10) °C, and pronounced acoustic mode-softening is evident at temperatures above 900 °C. Backscattering measurements to T = 1350 °C show no evidence for additional transitions. OEN was recovered at room temperature. Our results are interpreted in terms of elastic softening ahead of a displacive phase transition. Before the displacive transition can occur, however, the elastic softening appears to trigger the observed reconstructive transition to the more-stable protoenstatite (or high clinoenstatite) structure. We suggest that the displacive phase transition would lead to a previously unreported pyroxene structure with Cmca symmetry.

Lattice Dynamics and Central-Mode Phenomena in the Dielectric Response of Ferroelectrics and Related Materials

In this review we describe and discuss recent results on the linear dielectric response of high-permittivity dielectric crystals and ceramics in the wide frequency range 102–1014Hz. Our attention is paid to materials which exhibit some interesting low-frequency polar-phonon anomalies in combination with some additional dielectric dispersion below the polar phonon region. The following compounds are discussed: microwave ceramics Bi1.5Zn1.0Nb1.5O7, antiferroelectric PbZrO3ceramics and AgNbO3crystals, ferroelectric LiNaGe4O9, LaBGeO5, Cd2Nb2O7and SrBi2Ta2O9crystals, incommensurate ferroelectric Sr2Nb2O7, Ba2NaNb5O15and BCCD crystals, dipolar-glass crystal of Rb1/2(ND4)1/2D2PO4, relaxor ferroelectric Pb(Sc1/2Ta1/2)O3and PLZT ceramics and PMN crystals, antiferroelectric PLZT 2/95/5 ceramics and relaxor-based PMN-PT, PZN-PT and BiScO3-PT crystals and ceramics. For these materials the polar phonon spectra are discussed together with their flow-frequency dielectric response and dispersion regions in between, in the 10–300 K or higher temperature range, depending on the existing phase transitions of interest. Some universal features of the disorder and anharmonicities are pointed out: central-mode phenomena near displacive phase transitions and polar nano-clusters which appear at rather high temperatures and remain present down to low temperatures if the material remains structurally disordered. The manifestation of the latter in the dielectric spectra consists in extreme broadening of the relaxation region on cooling which at low temperatures results in constant loss spectra (1/fnoise).

High pressure behavior, transformation and crystal structure of synthetic iron-free pigeonite

A single-crystal high pressure X-ray investigation was performed up to P = 6.5 GPa on a synthetic clinopyroxene of composition Ca0.15(1)Mg1.85(1)Si2.00(1)O6 [Di15En85, unit-cell parameters at room pressure: a = 9.6525(6)Å, b = 8.8461(2)Å, c = 5.2036(5)Å, β = 108.370(5)°, V = 421.68(4)Å3]. A first order P21/c-C2/c displacive phase transition was found at P = 5.1 GPa; the transition was revealed by the disappearance of the b reflections (h + k = odd) and by sharp changes in the unit-cell parameters. Reversals through the transformation show that, if present, hysteresis is smaller than 0.1 GPa. The volume variation has been described by a third-order Birch-Murnaghan equation of state with V0 = 421.68(8) Å3, KT0 = 102(2) GPa, and K′ = 8(1) for the low-symmetry phase (P21/c) and with V0 = 411.06(3) Å3 and KT0 = 108(2) GPa for the high-symmetry phase (C2/c), with K′ fixed to the value obtained for the low-symmetry form. The axial compressibility shows the following scheme: βb > βa ≅ βc > βasinβ for both phases. In comparison with pure clinoenstatite, Di15En85 shows a similar step in unit-cell parameters at the transition, the disappearence of hysteresis and a decrease of transition pressure and of bulk modulus.

Microscopic calculations of displacive (Elpasolite family) and order-disorder (Potassium selenate family) structural phase transitions

The critical temperatures and thermodynamic characteristics for the displacive phase transition O h 7 → O 4h 5 in crystals of the elpasolite family Rb2KBF6 (B = Sc, In, Lu) and for the successive phase transitions O 6h 4 → D 2h 16 → I → C2h/5 (I is the incommensurate phase) in crystals of the selenate potassium family have been calculated. The calculations were carried out using the effective Hamiltonian method. The Hamiltonian parameters for the elpasolite-like crystals were determined from ab initio calculations, and those for the crystals of the selenate potassium family were found using a small number of fitting parameters.

TheT-Xdependence of the isosymmetric displacive phase transition in synthetic Fe3+-Al zoisite: A temperature-dependent infrared spectroscopy study

We have studied three synthetic Al-Fe3+ zoisites with variable Fe3+-contents [Xps = 0.0, 0.035 (12), and 0.062 (23)] by means of temperature-dependent infrared powder spectroscopy. Spectra were recorded from -150 to 170 °C in steps of 20 °C in the lattice vibrational range 400 to 1200 cm-1. At -150 °C, a total of 34 bands could be identified in all samples. With increasing temperature, the bands broaden and generally shift smoothly to lower wave numbers. The maxima of bands at ~620 and ~909 cm-1 as well as the autocorrelation analysis of the spectral region 820 to 1050 cm-1 display linear but different temperature dependencies of the spectral properties at low and high temperatures. These changes in temperature dependence of the spectral properties marks the isosymmetric displacive phase transition between zoisite I and II. The transition temperatures Ttr are about 45 °C for Xps = 0.0 and = 0.035 (12), and about -35 °C for Xps = 0.062 (23) and suggest a negative correlation between Ttr and Xps. A combination with literature data yields a positive slope of 9.4 ± 2.0 MPa/K and a ΔS of 0.5 ± 0.1 J/(K·mol) for the zoisite I → zoisite II transition for a composition of about Xps = 0.035.

An Approach to Developing a Force Field for Molecular Simulation of Martensitic Phase Transitions between Phases with Subtle Differences in Energy and Structure

d,l-Norleucine is one of only a few molecules whose crystals exhibit a martensitic or displacive-type phase transformation where the emerging phase shows a topotaxial relationship with the parent phase. The molecular mechanism for such phase transformations, particularly in molecular crystals, is not well understood. Crystalline phases that exhibit displacive phase transitions tend to be very similar in structure and energy. Consequently, the development of a force field for such phases is challenging as the phase behavior is determined by subtle differences in their lattice energies and entropies. We report an approach for developing a force field for such phases with an application to d,l-norleucine. The proposed procedure includes calculation of the phase diagram of the crystalline phases as a function of temperature to identify the best force field. d,l-Norleucine also presents an additional problem since in the solid state it exists as a zwitterion that is unstable in vacuo and therefore cannot be characterized using high-level ab initio calculations in the gas phase. However, a stable zwitterion could be obtained using Onsager's reaction-field continuum model for a solvent (SCRF) using both Hartree-Fock and density functional theory. A number of force fields and the various sets of partial charges obtained from the SCRF calculations were screened for their ability to reproduce the crystal structures of the two known phases, alpha and beta, of d,l-norleucine. Selected parameter sets were then employed in free energy minimizations to identify the best set on the basis of a correct prediction of the alpha-beta phase transition. The Williams' nonbonded parameters combined with partial charges from SCRF-Polarized Continuum Model calculation were found to reproduce the structures of the phases accurately and also maintained their stability in extended molecular dynamics simulations in the Parrinello-Rahman constant stress ensemble. Moreover, we were also able to successfully simulate the phase transformation of the beta- to the alpha-phase. The identified force field should enable detailed studies of the phase transformations exhibited by crystals of d,l-norleucine and hence enhance our understanding of martensitic-type transformations in molecular crystals.

Phonon anomalies in displacive phase transitions by surface X-ray scattering

Phonon anomalies in displacive phase transitions have long been suspected to aid the nucleation of the new phase. In materials with strong but incomplete phonon softening, the crystal surface might additionally play an important role, since the enhanced softening of associated surface phonons effectively lowers the nucleation barrier. X-ray scattering under grazing angles is discussed with regard to experimental studies of such phase transitions between 2 and 3 dimensions, as in this geometry all x-ray techniques provide information from a controlled depth below the surface adjustable from nanometers to microns. However, the sensitivity to premonitory phonon softening varies greatly with the scattering technique employed. It is argued that soft modes confined to a narrow interval in q need not show up in the Debye-Waller factor while giving a strong signal in thermal diffuse scattering. Synchrotron radiation data from Ni 2 MnGa provide evidence for this behavior and confirm also the feasibility of depth-resolved studies of the [ζζ0] TA 2 phonon softening.

The P21/m? C2/m phase transition in synthetic amphibole Na NaMg Mg5 Si8 O22 (OH)2: thermodynamic and crystal-chemical evaluation

The P21/m↔C2/m displacive phase transition in the synthetic end-member amphibole Na NaMg Mg5 Si8 O22 (OH)2 has been studied by monitoring changes in unit-cell parameters and the intensities of superlattice reflections at 25–400 °C. This amphibole allows investigation of the effects of compositional variations at the A- and B-group sites upon the transition. Polynomial fitting of a 24 Landau potential to the evolution of the order parameter with T yielded a T c of 257 ± 3 °C, and Landau coefficients compatible with a second-order transition. Structure refinement of single-crystal data collected at 25, 140, 270 and 370 °C allowed modelling of the structural changes as a function of T and symmetry. Crystal-chemical analysis suggests that differences in T c in cummingtonites and in the crystal of this work depend mainly upon the relations between the aggregate ionic radii of the B- and C-group cations.

The high-temperature P2/c1?C2/c phase transition in Fe-free Ca-rich P21/c clinopyroxenes

An in situ, high-temperature, powder diffraction investigation was performed for iron-free clinopyroxenes with compositions Ca0.40Mg1.60Si2O6, Ca0.52Mg1.46Al0.05Si1.98O6, Ca0.59Mg1.41Si2O6 and Ca0.70Mg1.30Si2O6, up to 850 °C using synchrotron radiation (ESRF, Grenoble). In samples with compositions Ca0.52Mg1.46Al0.05Si1.98O6 and Ca0.59Mg1.41Si2O6, evidence of for the P21/c-C2/c displacive phase transition was seen in changes in lattice parameters at T ≈ 550 and 300 °C respectively. Landau modelling of the phase transition behaviour for the sample with composition Ca0.52Mg1.46Al0.05Si1.98O6 shows a tricritical behaviour [T c =547(16)]. Comparison with the transition behaviour in other samples with lower Ca contents along the join diopside–enstatite indicates that a decrease in T c , and a switch from first-order to tricritical behavior occurs with increasing Ca content. The change in the transition behaviour was related to an interaction with the antiphase domains at the nanoscale.

Phase transition from asymmetric to symmetric dimer structure on the Si(001) surface at high temperature.

The dimer configurations on the Si(001) surface at high temperatures have been investigated using the rocking curve of reflection high-energy electron diffraction. The Si(001) surface shows a displacive phase transition around 900 K, where a well-known asymmetric (tilted) dimer structure on the Si(001) at room temperature transforms to a symmetric dimer structure around 900 K. The metallic feature of the Si(001) surface above 900 K can be explained by the phase transition.

Displacive Character of the Paraelectric–Ferroelectric Phase Transition in K2ZnI4

The crystal structure of K 2 ZnI 4 is refined at 24 temperatures above and below the paraelectric–ferroelectric phase transition temperature by means of X-ray diffraction to reinvestigate the mechanism of the phase transition in more detail. The temperature dependence of the translation of K(1) and K(2) along the b -axis and the rotational angle of the ZnI 4 tetrahedron about the axis nearly parallel to the a -axis is obtained by the structural analyses. It is concluded that the mechanism of this phase transition is not the order–disorder type but the displacive one. The temperature variation of the anisotropic temperature parameter U 22 of K(1), K(2), I(1) and I(2) is coincident with the theoretical prediction for the displacive type phase transition proposed by Fujii and Matsubara [Prog. Theor. Phys. 78 (1987) 177].