Soft Mode Condensation Research Articles

Theoretical study of structural phase transition and soft mode behavior in moganite

Changes in the structure and lattice dynamics of the moganite during crystal expansion were studiedusing ab initio calculations within the framework of density functional theory. The results obtained shed light onmany anomalies in the temperature behavior of this crystal, such as the presence of a phase transition, soft modecondensation, elastic anomalies and negative thermal expansion. Comparison of the structural and dynamicproperties of moganite and quartz opens up new possibilities for their identification in natural samples of mixedcomposition.

Structural-Stability Study of AntiperovskiteNa3OClforNa-Rich Solid Electrolyte

The structural phase transition of the high-symmetry cubic phase of antiperovskite $\mathrm{Na}$${}_{3}$$\mathrm{O}\mathrm{Cl}$ is investigated by computing the phonon band structures of 14 different polymorphs with distinct types of $\mathrm{O}\mathrm{Na}$${}_{6}$ octahedral tilting. The resulting $P$-$T$ phase diagram shows that, at high temperature and low pressure, the high-symmetry cubic structure with $Pm\overline{3}m$ symmetry is the most stable phase. At low temperature and high pressure, on the other hand, the monoclinic structure with $P{2}_{1}/m$ symmetry becomes the most stable phase. In between those two, there is a region in the phase diagram where the orthorhombic structure with $Bmmb$ symmetry is the most stable phase. To improve upon the quasiharmonic results, we do additional calculations in the framework of the self-consistent phonon (SCP) theory, including lattice anharmonicity by using cubic and quartic interatomic force constants (IFCs). This is particularly important for the high-symmetry cubic phase. We find that by decreasing the temperature, the frequency of the soft phonon at the $M$ and $R$ symmetry points gradually shifts to lower values. From these results, we can infer that a phase transition occurs around 166--195 K upon soft-mode condensation. Due to the proximity of the soft-mode frequencies at both symmetry points $R$ and $M$, we expect a cubic-to-orthorhombic phase transition to be realized via simultaneous condensation of the two octahedral tilting modes.

Pressure–Temperature Phase Diagram of Multiferroic TbFe2.46Ga0.54(BO3)4

The pressure–temperature phase diagram of the multiferroic TbFe2.46Ga0.54(BO3)4 was studied for hydrostatic pressures up to 7 GPa and simultaneously with temperatures up to 400 K by the Raman spectroscopy technique. The structural phase transition from the R32 phase to the P3121 phase was determined by observing the condensation of soft modes and the appearance of new lines. An increase in pressure leads to an increase in the temperature of the structural phase transition. These phases are stable over the entire investigated temperature and pressure range. No other phases have been found.

Фазовая диаграмма и особенности поведения мягких мод в твердых растворах со структурой хантита TbFe-=SUB=-3-x-=/SUB=-Ga-=SUB=-x-=/SUB=-(BO_3)-=SUB=-4-=/SUB=-

The Raman spectra of four crystals of TbFe3-хGax (BO3) 4 solid solutions (x from 0 to 0.54) were studied in the temperature range from 8 to 350 K. The temperatures of structural phase transitions were determined. The observed spectral behavior is characteristic to condensation and restoration of soft modes. Soft modes are associated with a structural phase transition from the R32 phase to the P3121 phase. The Compositions-Temperature phase diagram was constructed

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The Raman spectra of four crystals of TbFe3-хGax (BO3) 4 solid solutions (x from 0 to 0.54) were studied in the temperature range from 8 to 350 K. The temperatures of structural phase transitions were determined. The observed spectral behavior is characteristic to condensation and restoration of soft modes. Soft modes are associated with a structural phase transition from the R32 phase to the P3121 phase. The Compositions-Temperature phase diagram was constructed

New Phase Transitions Driven by Soft Phonon Modes for CsPbBr3: Density Functional Theory Study

New phase transitions driven by the soft mode condensation from the Pm3m structure to related subgroup variants are predicted for CsPbBr3 from DFT calculations, performed by Raouia Ben Sadok and co-workers (see article number 2000289). The Pb2+ cation has only a small contribution to the structural distortions, which leaves an important role to Br– and Cs+ displacements in the structure stabilization. The ferroelectric distortion is found less favorable than the antiferrodistortive one, where the out-of-phase rotations of the PbBr6 octahedra may determine more stable structures than the in-phase rotations. Nevertheless, the polar structure Pmc21 appears to be a candidate as ground state. All predicted structures show semiconductor character, with the band gap increasing when increasing the Pb–Br bond length and the angle of rotation of the PbBr6 octahedra. The optical dielectric constant and Born effective charges show low sensitivity to unit cell volume.

Antiferromagnetic order in CeCoIn5oriented by spin-orbital coupling

An incommensurate spin-density wave (Q phase) confined inside the superconducting state at high basal plane magnetic field is an unique property of the heavy-fermion metal CeCoIn5. The neutron scattering experiments and the theoretical studies point out that this state come out from the soft mode condensation of magnetic resonance excitations. We show that the fixation of direction of antiferromagnetic modulations by a magnetic field reported by Gerber et al. [Nat. Phys. 10, 126 (2014)], is explained by spin-orbit coupling. This result, obtained on the basis of quite general phenomenological arguments, is supported by the microscopic derivation of the χ z z susceptibility dependence on the mutual orientation of the basal plane magnetic field and the direction of modulation of spin polarization in a multiband metal.

Phenomenological approach of the phase transitions in ABX3-type crystals

Perovskite ABX3-type crystals undergo ferroelastic phase transitions at different temperatures. We suggest a three components order parameter model to describe the successive phase transitions due to condensation of several soft modes. The thermodynamical potential models and phase diagrams of the expansion coefficients are suggested for an adequate Landau-type description of the phase transitions in ABX3. We study the pressure–temperature phase diagrams and the temperature dependence of elasticity of CsPbX3 (X=Cl, Br).

Raman spectroscopic study of the lattice dynamics in the Rb2KMoO3F3 oxyfluoride

The lattice dynamics of the Rb2KMoO3F3 oxyfluoride has been studied by Raman spectroscopy in the temperature range 7–400 K. A phase transition has been revealed at T ≈ 185 K with decreasing temperature. Anomalies of the frequencies and Raman line half-widths have been analyzed. No condensation of soft lattice modes has been found. The character of changes in the Raman spectra of the Rb2KMoO3F3 oxyfluoride shows that the phase transition is related to variations in the [MoO3F3]3− molecular octahedron.

Analysis of Structures and Order Parameters in Antiferroelectric PbHfO3 Using Neutron Diffraction

We performed structural analysis of PbHfO 3 between 10 and 500 K in the room-temperature antiferroelectric phase and the cubic phase using powder neutron diffraction. Disordered arrangements of Pb atoms were not detected in the cubic phase in contrast to the results of X-ray diffraction. This indicates that Pb atoms have an electron-density distribution that spreads out more widely than the expected distribution in isolated Pb ions. The simple concept of order parameters in soft-mode condensation, that is, all atomic shifts show proportional temperature dependences, was not observed in the antiferroelectric phase of PbHfO 3 . However, physical properties, such as lattice distortion, show the temperature dependences predicted on the basis of a phenomenological theory as if the simple concept were applicable over the entire temperature range.

Lattice dynamics of cubic SrZrO 3

Using density functional perturbation theory, the optical dielectric constant, Born effective charges and phonon dispersion curves of cubic SrZrO 3 have been calculated. The obtained dispersion curves show a soft phonon branch spreading from R to M points of the cubic Brillouin zone. An analysis based on the symmetry relationships indicates that the experimentally observed low-symmetry phases of SrZrO 3 can be considered as results of the soft mode condensation at R and M points.

Composition dependence of the diffuse scattering in the relaxor [formula omitted]– [formula omitted] ( [formula omitted] and 0.10)

We have measured the neutron diffuse scattering in the relaxor ( 1 - x ) Pb ( Mg 1 / 3 Nb 2 / 3 ) O 3 – x PbTiO 3 single crystals with x = 0 % and 10% around (1 1 0) and (1 0 0) to study the effect of Ti substitution on polar nanoregions (PNR). Both the x = 0 % and 10% samples exhibit weak diffuse scattering extending along [1 1 0] at (1 1 0) above 500 K. In addition, we observed strong diffuse scattering below T = 500 K , which extends along [ 1 1 ¯ 0 ] at (1 1 0) and [ 1 ± 1 0 ] at (1 0 0) . The correlation length ξ derived from the low- T diffuse scattering indicates that the average size of the PNR is enlarged by the substitution of Ti ++ for ( Mg 1 / 3 Nb 2 / 3 ) ++ . For PMN–10% PT, the high- T diffuse scattering, which extends along the longitudinal direction at 650 K, expands along the transverse direction on cooling. This change can be understood in terms of the soft mode condensation. As the temperature decreases below 500 K, the weak high- T diffuse scattering becomes almost isotropic, and the low- T diffuse scattering extending along the transverse direction becomes dominant.

Characteristics of the premartensitic transition in the Ni50.5Mn24.5G25 single crystals

The characteristics of premartensitic transition on nearly stoichiometric Ni 505Mn245Ga25 single crystals have been investigated systematic ally by various methods, such as the ac magnetic susceptibility, resistance, mag netostriction, premartensitic transition strain and magnetization measurement. T he premartensitic transition strain in free samples was reported, and the enhanc ed premartensitic transition strain with an external magnetic field applied alon g the different directions was investigated. A large magnetostriction up to 505ppm in the [001] direction of the parent phase is obtained in a pulse magnetic field of about 80kA/m applied along the [010] direction at the premartensitic t ransition point, which is over five times larger than that in the parent phase. Based on the soft mode condensation and characteristic of the crystal growth, th e mechanism of the premartensitic transition strain was analyzed. The effect of magnetic field intervened premartensitic transition strain is attributed to the competition between the crystal lattice deformation induced by the enhancing mag netoelastic coupling and the intrinsic deformation originated from the soft-mode condensation. We found that the premartensitic transition further generated the anisotropy between two crystallographic directions of [001] and [010], which is proved by the magnetization measurement. Furthermore, the resulting strain prop erties, such as the largest magnetostriction, the saturated premartensitic trans ition strain and saturated field, have been discussed in detail.

Crystal Structure and Order Parameters in the Phase Transition of Antiferroelectric PbZrO3

X-ray and neutron diffraction and dielectric measurements were performed for the antiferroelectric phase of PbZrO 3 . The antiferroelectric Σ 3 (TO) and the R 25 superlattice-reflection intensities, and the pseudo-tetragonal lattice distortion of the perovskite sublattice showed the same temperature dependence below room temperature, showing a saturation below about 60 K. Above room temperature, however, they showed rather different temperature dependences. These temperature dependences can be well described by the free energy based on a group theoretical method, which includes a quantum effect. The atomic shifts do not necessarily conform to a simple concept of order parameter in soft mode condensation. However the antiferroelectric phase transition can be understood by the phenomenological theory for coupled order parameters if applied over the whole temperature region.

Pressure-Induced Phase Transitions in ScF 3 Crystal--Raman Spectra and Lattice Dynamics

New pressure-induced phases are found in normally cubic ScF 3 crystal using polarizing microscopy and micro-Raman spectroscopy. Their supposed space groups are R 3 ¥ c, Z = 2 and Pnma, Z = 4. Using ab initio model cubic phase was shown to be stable at ambient pressure down to T = 0 K, while hydrostatic pressure brings one of the phonon branches down to negative squared frequencies. R 5 soft mode condensation results in the rhombohedric distortion of the cubic lattice with cell volume doubling. Calculated squared frequencies of the high pressure phase are positive, their number and values agree with experimental results.

Nonlinear dielectric spectroscopy in the smectic-A-smectic-C(*)(alpha) phase transition.

We performed nonlinear dielectric spectroscopy to study the dynamic properties near the smectic-A-smectic-C(*)(alpha) phase transition point of an antiferroelectric liquid crystal 4-(1-methyl-heptyloxycar- bonyl)phenyl 4-octylcarbonyloxybiphenyl-4-carboxylate (MHPOCBC). A Landau-type theory was developed in order to analyze the experimentally obtained frequency dispersions. From the experimental and theoretical results we successfully obtained the temperature dependence of the relaxation frequency of the soft mode in both the smectic-A and smectic-C(*)(alpha) phases, which gave direct evidence that the transition is brought about by soft mode condensation. Significant features of this transition are also discussed.

Observation of the soft-mode condensation in the Sm-A-Sm-C(*)(alpha) phase transition by nonlinear dielectric spectroscopy.

We have theoretically and experimentally studied the nonlinear dielectric response under large orientational fluctuations near the Sm-A-Sm-C(*)(alpha) phase transition point in a chiral smectic liquid crystal. The third-order nonlinear dielectric response due to the fluctuations was observed in the vicinity of the transition point. By using it, we have successfully observed the soft-mode condensation inducing the Sm-A-Sm-C(*)(alpha) phase transition.

Neutron diffuse scattering from polar nanoregions in the relaxorPb(Mg1/3Nb2/3)O3

We have studied the diffuse scattering in the relaxor $\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}$ (PMN) using triple-axis neutron scattering techniques. The diffuse scattering first appears around the Burns temperature ${T}_{d}\ensuremath{\approx}620\mathrm{K},$ indicating that its origin lies within the polar nanoregions (PNR's). While the relative intensities of the diffuse scattering around (101), (200), and (300) are consistent with those previously reported by Vakhrushev et al., they are, surprisingly, entirely different from those of the lowest-energy transverse-optic (TO) phonon. This observation led Naberezhnov et al. to claim that this TO mode could not be the ferroelectric soft mode. However, a recent neutron study by Gehring et al. has unambiguously shown that the lowest-energy TO mode does soften on cooling and that the relative intensities are similar to those of ${\mathrm{PbTiO}}_{3}.$ If the diffuse scattering in PMN originates from the condensation of a soft TO mode, then the atomic displacements of the PNR must satisfy the center-of-mass condition. But, the atomic displacements determined from diffuse scattering intensities do not fulfill this condition. To resolve this contradiction, we propose a simple model in which the total atomic displacement consists of two components ${\ensuremath{\delta}}_{c.m.}$ and ${\ensuremath{\delta}}_{\mathrm{shift}}.$ Here ${\ensuremath{\delta}}_{c.m.}$ is created by the soft-mode condensation and thus satisfies the center-of-mass condition. On the other hand, ${\ensuremath{\delta}}_{\mathrm{shift}}$ represents a uniform displacement of the PNR's along their polar direction relative to the surrounding (unpolarized) cubic matrix. Within the framework of this model, we can successfully describe the neutron diffuse scattering intensities observed in PMN.

Premartensitic phenomena and other phase transformations in Ni–Mn–Ga alloys studied by dynamical mechanical analysis and electron diffraction

Ni–Mn–Ga ferromagnetic ordered shape memory alloys are known to exhibit phonon softening and soft mode condensation into a premartensitic phase prior to the martensitic transformation itself. In the present work, this unique behaviour of Ni–Mn–Ga system has been studied as a function of electron concentration (i.e., alloy composition) and a region on the phase transformations diagram which corresponds to the stability of the intermediate phase has been determined, being completely in the ferromagnetic zone. The results were mainly obtained by means of dynamical mechanical analysis and transmission electron microscopy. The two types of lattice instability which might occur in the parent phase driving it to either the soft mode condensed intermediate phase or to the martensitic phase are discussed in this work, together with precursor phenomena and the intermartensitic transformation observed in alloys with the highest electron concentration.

The cubic-to-monoclinic phase transition in (NH4)3ScF6 cryolite: A Raman scattering study

This paper reports on a Raman study of the cubic-to-monoclinic phase transition in (NH4)3ScF6 cryolite. We observed sharp anomalies in the frequencies and half-widths of the Raman lines corresponding to internal vibrations of the ScF 6 3+ ions and to lattice vibrations; no soft lattice mode condensation was revealed. It is concluded that the phase transition studied is related primarily to the orientational ordering of these ions.