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Brody, Edward M.; Cummins, H. Z.

doi:10.1103/physrevb.9.179

Cited by 70 publications

(13 citation statements)

References 23 publications

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“…2 (Rehwald et al 1972); in KCN the elastic constant c 44 vanishes at the transition, and the soft subspaces are two-dimensional (Haussühl 1973;Knorr et al 1985). We remark that the actual situation may be quite complex; e.g., in the ferroelectric KDP the z component of the electric dipole moment couples linearly to the ε 12 shear deformation (Brody & Cummins 1974). Consequently, although caused by the ordering of hydrogen-bonding protons, the transition becomes ultimately an elastic phase transformation with vanishing shear modulus c 66 .…”

Section: Introductionmentioning

confidence: 92%

“…Hence the resulting critical behaviour in three dimensions is classical, even if the optical modes have their origin in short-range interactions that would by themselves allow for non-classical critical fluctuations. In KDP, there is a linear coupling of the polarization to the shear ε 12 (Brody & Cummins 1974). In LaP 5 O 14 , a Raman-active optical phonon coupled to ε 13 drives the transition (Fox et al 1976).…”

Section: Linear Coupling Of An Optical To An Acoustic Phononmentioning

confidence: 99%

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Continuous elastic phase transitions in pure and disordered crystals

Schwabl

Täuber

1996

Phil. Trans. R. Soc. Lond. A

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We review the theory of second-order (ferro-)elastic phase transitions, where the order parameter consists of a certain linear combination of strain tensor components, and the accompanying soft mode is an acoustic phonon. In threedimensional crystals, the softening can occur in one-or two-dimensional soft sectors. The ensuing anisotropy reduces the effect of fluctuations, rendering the critical behaviour of these systems classical for a one-dimensional soft sector, and classical with logarithmic corrections in case of a two-dimensional soft sector. The dynamical critical exponent is z = 2, and as a consequence the sound velocity vanishes as c s ∝ |T − T c | 1/2 , while the phonon damping coefficient is essentially temperature-independent. Even if the elastic phase transition is driven by the softening of an optical mode linearly coupled to a transverse acoustic phonon, the critical exponents retain their mean-field values. Disorder may lead to a variety of precursor effects and modified critical behaviour. Defects that locally soften the crystal may induce the phenomenon of local order parameter condensation. When the correlation length of the pure system exceeds the average defect separation n −1/3 D , a disorder-induced phase transition to a state with non-zero average order parameter can occur at a temperature T c (n D ) well above the transition temperature T 0 c of the pure crystal. Near T 0 c , the order-parameter curve, susceptibility, and specific heat appear rounded. For T < T c (n D ) the spatial inhomogeneity induces a static central peak with finite q width in the scattering cross section, accompanied by a dynamical component that is confined to the very vicinity of the disorder-induced phase transition. † Present address:

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Section: Introductionmentioning

confidence: 92%

Section: Linear Coupling Of An Optical To An Acoustic Phononmentioning

confidence: 99%

Continuous elastic phase transitions in pure and disordered crystals

Schwabl

Täuber

1996

Phil. Trans. R. Soc. Lond. A

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“…An analogous relation was reported for the KDP crystal ( Figure 44). It was shown that the high value of dielectric permittivity is [90,91], UPW (f $ 10 6 Hz) [92,93] and PR (f $ 10 5 Hz) [87] experiments. [90,91], UWP [92,93] and PR [82,87].…”

Section: Phase Transitions 739mentioning

confidence: 98%

Ferroelastic crystals and their nonlinear elastic properties observed in frequency range from gigahertz to milihertz

Wiesner

2009

Phase Transitions

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The experiments reported in this article have been performed to unify the results of earlier and recent determinations of parameters describing the elastic properties of Rb 4 LiH 3 (SO 4 ) 4 , LiCsSO 4 (LCS) and KH 2 PO 4 crystals measured by different experimental methods. The above crystals undergo a second-order phase transition, incommensurate phase transition (PT) and a first-order but close to second-order phase transition, respectively. To investigate the elastic properties of the crystals in the frequency range from 10 À1 to 10 10 Hz, five experimental methods were applied: dynamic mechanical analysis, piezoelectric resonance, composite oscillator bar, ultrasonic wave propagation and Brillouin light scattering. The results of the experiments allowed identification of the processes contributing to the elastic response of the crystals investigated. Moreover, for the LCS crystal a model of the incommensurate PT was presented.

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“…In ultrasonic pulse propagation experiments where hence 4=w(&)"' ( 7 ) Taking real and imaginary parts of Eq. (7) gives the phase velocity u = w/q' and the attenuation a = 4".…”

Section: The Equation Of Motion Givesmentioning

confidence: 99%

“…(7) to arrive at q', q" values as functions of T , w for various parameter choices. It is helpful in gaining insight into the possible central peak effects to look at the weak coupling limit which occurs away from T, at low frequencies where WT'(O) Q 1 and 4" Q 4.…”

Section: The Equation Of Motion Givesmentioning

confidence: 99%