Pressure-induced ferroelastic instability and lattice dynamics of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Cs</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">HgCl</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>crystals within the semiempirical rigid-ion model

Kityk, A. V.; Shchur, Ya.; Zadorozhna, A. V.; Trach, I.; Girnyk, I.; Martynyuk-Lototska, I.; Vlokh, O. G.

doi:10.1103/physrevb.58.2505

Cited by 13 publications

(8 citation statements)

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“…However, the scenario of structural PTs in Cs 2 HgCl 4 appears to be even more intriguing. Another type of lattice instability, also related to the soft TO and TA modes of the same 3 symmetry, is realized in Cs 2 HgCl 4 via the direct second-order ferroelastic PT at hydrostatic pressures above 140 MPa [28]. It is again caused by a lowering of the soft optic branch (B 3g symmetry in the BZ center), but this time preferably at the point as sketched in figure 3(e) (left panel).…”

Section: Phenomenological Descriptionmentioning

confidence: 90%

“…Cs 2 HgCl 4 exhibits a very rich sequence of structural PTs into both C and IC phases (see table 1) which have been intensively studied in the past by various experimental techniques, among which are the structural analysis [21], dielectric [22], optics and acoustics [23,24], resonance [25,26] and heat capacity [27] methods. A ferroelastic instability induced by the hydrostatic pressure and lattice dynamics associated with it in the high temperature phase of Cs 2 HgCl 4 were explored in [28][29][30]. However, most of these investigations had been performed prior to the comprehensive structural studies of all the low temperature phases in Cs 2 HgCl 4 crystals provided later by Bagautdinov et al [15][16][17][18].…”

Section: Phasementioning

confidence: 99%

“…somewhat higher compared to the one if the bilinear interaction between the soft TO and TA modes would be ignored. To give a more transparent view on such an interaction one may construct a Lagrangian using the free energy F, given by (7), as the potential energy [28]:…”

Section: Phenomenological Descriptionmentioning

confidence: 99%

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Soft-mode-driven lattice instabilities in Cs₂HgCl₄crystal: phenomenological treatment and far-infrared spectroscopy of the structurally modulated phases

Shchur

Kamba

Parasyuk

et al. 2012

J. Phys.: Condens. Matter

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This paper reports a comprehensive phenomenological description and experimental infrared (IR) investigations of the soft-mode-driven lattice instabilities into various commensurately and incommensurately modulated phases of Cs(2)HgCl(4) crystals. Our theoretical analysis shows that the lattice instabilities along the a and c crystallographic directions are related to low-frequency transverse optical (TO) phonon branches of Σ(2) and Λ(3) symmetry, respectively, which merge together in the center of the Brillouin zone at the point of B(3g) symmetry. As the temperature decreases both branches fall down, leading first to the direct condensation of the soft TO Σ(2) mode in the symmetric Σ direction (k is parallel to a*). On the other hand, coupling of the TO and transverse acoustic (TA) modes of Λ(3) symmetry causes, at somewhat lower temperatures, a series of frozen modulated commensurate and incommensurate states developing along the symmetric Λ direction (k is parallel to c*). Polarized far-infrared (FIR) reflectivity spectra (15-600 cm(-1)) of Cs(2)HgCl(4) crystals were measured in a broad temperature region, 10-297 K. Despite a rich sequence of structurally modulated phases existing above 163 K we observed rather moderate temperature evolution of IR spectra where only a few new modes of different polarizations have been activated. However, the commensurately modulated phases occurring below 163 K made an essential impact on the spectra of all three polarizations. The process of activation of both the Raman- and the IR-active phonons in the structurally modulated phases is subjected to the phenomenological analysis.

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Section: Phenomenological Descriptionmentioning

confidence: 90%

Section: Phasementioning

confidence: 99%

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Soft-mode-driven lattice instabilities in Cs₂HgCl₄crystal: phenomenological treatment and far-infrared spectroscopy of the structurally modulated phases

Shchur

Kamba

Parasyuk

et al. 2012

J. Phys.: Condens. Matter

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“…15,16) According to the AC calorimetry measurement, Cs 2 HgCl 4 undergoes seven phase transitions at T IC = 219, T C = 193, T C1 = 182.5, T C2 = 177, T C3 = 173.0, T C4 = 163.5 and T C5 = 120 K, 7) although the number and the temperatures of the phase transitions are not consistent necessarily with the other methods. 4, 6, 10) A crystallographic study 3) showed that the symmetry of the N phase above T IC is centrosymmetric Pnma with displaceishimaru@staff.chem.tsukuba.ac.jp mic anomalies due to phase transitions at 163.0±0.6, 172.2±1.0, 177.3±0.9, 183.1±0.6 and 219.5±0.8 K in good agreement with the phase transition temperatures of T C4 , T C3 , T C2 , T C1 and T IC , respectively, previously determined by the AC calorimetry measurement.…”

Section: Dta Thermograms On Heating Displayed Endother- §1 Introductionmentioning

confidence: 97%

Studies on¹³³Cs NMR Spectra and Spin-Lattice Relaxation Times in Incommensurate Cs₂HgCl₄

2000

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133 Cs NMR spectra and the spin-lattice relaxation times, T 1 , in Cs 2 HgCl 4 crystals were measured in the ranges of 160-361 K and 160-371 K, respectively. The central lines of the spectra show small splittings characteristic of the incommensurate (IC) phase. The splitting increases with decreasing temperature. The critical exponent ζ of T 1 at the phase transition from normal (N) to IC phase was determined to be 0.615±0.025 in the high-temperature side of the transition, which is in good agreement with the three-dimensional XY model predicting the one-dimensional modulation wave in the IC phase. The frequency dependence of T 1 in the IC phase can be explained by the fluctuations of phason with a small gap, 0-5 MHz, and amplitudon. ment disorders in HgCl 2− 4 complex anions and one of the crystallographically inequivalent two Cs cations. It has been presumed that the ferroelectric commensurate (C) phase below T C without centrosymmetry have a point symmetry mm2, 4) but detailed studies on structures below T C have not been reported. 35 Cl NQR, 12) dielectric and Raman scattering 8) measurements revealed a different result that the IC phase appears between T IC and T C1 . 12) From the optical polarization measurement, the low-temperature phase immediately below T C1 is anticipated to be a ferroelastic C phase analogous to that in Cs 2 MBr 4 (M=Cd, Hg). §2. Experimental Cs 2 HgCl 4 crystals were grown by cooling a molten mixture containing stoichiometric amounts of CsCl (purity 99.9%) and HgCl 2 (purity 99.9%) purchased from Wako Pure Chemical Industries, Ltd. The crystalline powder obtained was dried in vacuo and then sealed in glass tubes with nitrogen gas for differential thermal analysis (DTA) and NMR measurements.DTA was measured between 120 and 300 K to confirm the phase transitions reported previously. The sample temperature was determined within ±0.2 K using a chromel-constantan thermocouple. The measurement of 133 Cs NMR T 1 was performed with a Bruker MSL-300 spectrometer at frequency of 39.4 MHz in the range 160-371 K and also with a Bruker MSL-400 spectrometer at 52.5 MHz in 196-215 K. 133 Cs NMR spectra were recorded by a Bruker MSL-300 using a saturated CsCl aqueous solution as a standard of frequency shift. The sample temperature was controlled within ±0.5 K by Bruker VT-1000 temperature controller and determined by a copper-constantan thermocouple with the same accuracy. The uncertainty in the T 1 measurement is estimated to be within 5%. §3. Results DTA thermograms on heating displayed endother- §1. IntroductionMany compounds belonging to the A 2 BX 4 family with the pseudo-hexagonal β-K 2 SO 4 type structure (P nma) form incommensurate (IC) phases at low temperatures. We reported lattice dynamics in IC phases of Cs 2 MBr 4 (M=Cd and Hg) studied by 133 Cs NMR. 1) The critical exponents obtained at the phase transitions from normal to incommensurate (N-IC) phase correspond to the three-dimensional XY and the mean field models for Cd and Hg compounds, respectively. This difference seems to be expl...

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“…A clear correlation between the softening of the B 3g optical mode and the falling down of the B 1u acoustic branch may be easily explained within the phenomenological Landau-Ginzburg theory. The quasi-harmonic contribution to the free-energy density function may be written as follows [7,29]:…”

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confidence: 99%

Phonon dynamics simulation of TlH₂PO₄ crystal

Shchur

2011

Physica Status Solidi (b)

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Lattice dynamics of TlH 2 PO 4 crystal was simulated within the atomistic semi-empirical approach in high-temperature Pbcn and ferroelastic P2 1 /b phases. Phonon dispersion relations, partial density of phonon states, dispersion of mean square displacements and isotropic temperature factors were calculated. Using both the lattice dynamics simulation and phenomenological Landau-Ginzburg analysis it was shown that the ferroelastic phase transition occurs due to the bilinear interaction between the soft B 3g optical and transverse acoustic TA Y (k jj b 3 ) phonon modes. The oxygen-hydrogen interactions within the shorter O 1 -H 1 ÁÁÁO 2 hydrogen bonds play the key role at the ferroelastic phase transition.

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Pressure-induced ferroelastic instability and lattice dynamics ofCs2HgCl4crystals within the semiempirical rigid-ion model

Cited by 13 publications

References 1 publication

Soft-mode-driven lattice instabilities in Cs₂HgCl₄crystal: phenomenological treatment and far-infrared spectroscopy of the structurally modulated phases

Soft-mode-driven lattice instabilities in Cs₂HgCl₄crystal: phenomenological treatment and far-infrared spectroscopy of the structurally modulated phases

Studies on¹³³Cs NMR Spectra and Spin-Lattice Relaxation Times in Incommensurate Cs₂HgCl₄

Phonon dynamics simulation of TlH₂PO₄ crystal

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Pressure-induced ferroelastic instability and lattice dynamics ofCs2HgCl4crystals within the semiempirical rigid-ion model

Cited by 13 publications

References 1 publication

Soft-mode-driven lattice instabilities in Cs2HgCl4crystal: phenomenological treatment and far-infrared spectroscopy of the structurally modulated phases

Soft-mode-driven lattice instabilities in Cs2HgCl4crystal: phenomenological treatment and far-infrared spectroscopy of the structurally modulated phases

Studies on133Cs NMR Spectra and Spin-Lattice Relaxation Times in Incommensurate Cs2HgCl4

Phonon dynamics simulation of TlH2PO4 crystal

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Product

Resources

About

Soft-mode-driven lattice instabilities in Cs₂HgCl₄crystal: phenomenological treatment and far-infrared spectroscopy of the structurally modulated phases

Soft-mode-driven lattice instabilities in Cs₂HgCl₄crystal: phenomenological treatment and far-infrared spectroscopy of the structurally modulated phases

Studies on¹³³Cs NMR Spectra and Spin-Lattice Relaxation Times in Incommensurate Cs₂HgCl₄

Phonon dynamics simulation of TlH₂PO₄ crystal