Finite strain Landau theory of high pressure phase transformations

Schranz, W.; Tröster, A.; Koppensteiner, J.; Miletich, Ronald

doi:10.1088/0953-8984/19/27/275202

Cited by 13 publications

(10 citation statements)

References 30 publications

(40 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Ref. [34]), the anomalies observed for the individual elastic tensor components are quite pronounced: C 11 , C 12 , and C 33 exhibit a notable negative jump at P ¼ P c , while C 13 undergoes an upward jump. While these findings might have been anticipated from a qualitative comparison to the T-driven transition [35], they still await their verification in experiment.…”

Section: Application To Strontium Titanatementioning

confidence: 96%

Fully Consistent Finite-Strain Landau Theory for High-Pressure Phase Transitions

et al. 2014

View full text Add to dashboard Cite

Landau theory (LT) is an indispensable cornerstone in the thermodynamic description of phase transitions. As with structural transitions, most applications require one to consistently take into account the role of strain. If temperature drives the transition, the relevant strains are, as a rule, small enough to be treated as infinitesimal, and therefore one can get away with linearized elasticity theory. However, for transitions driven by high pressure, strains may become so large that it is absolutely mandatory to treat them as finite and deal with the nonlinear nature of the accompanying elastic energy. In this paper, we explain how to set up and apply what is, in fact, the only possible consistent Landau theory of high-pressure phase transitions that systematically allows us to take these geometrical and physical nonlinearities into account. We also show how to incorporate available information on the pressure dependence of elastic constants taken from experiment or simulation. We apply our new theory to the example of the high-pressure cubic-tetragonal phase transition in strontium titanate, a model perovskite that has played a central role in the development of the theory of structural phase transitions. Armed with pressure-dependent elastic constants calculated by density-functional theory, we give an accurate description of recent high-precision experimental data and predict a number of elastic transition anomalies accessible to experiments.

show abstract

Section: Application To Strontium Titanatementioning

confidence: 96%

Fully Consistent Finite-Strain Landau Theory for High-Pressure Phase Transitions

et al. 2014

View full text Add to dashboard Cite

show abstract

“…Individual components of the tensor of elastic compliances have been found to decrease in a non-linear fashion, which gives rise for unusual softening on compression affecting not only individual lattice directions but also bulk volume compressibility. This so-called elastic softening (Carpenter and Salje 1998a;1998b) was found to contribute over a wide pressure interval as exemplified for proper ferroelastic high-pressure transitions (Carpenter 2000;Tröster et al 2002;Schranz et al 2007).…”

Section: Introductionmentioning

confidence: 96%

The nonlinear anomalous lattice elasticity associated with the high-pressure phase transition in spodumene: a high-precision static compression study

Ullrich

Schranz²,

Miletich

2009

Phys Chem Minerals

View full text Add to dashboard Cite

The high-pressure behavior of the lattice elasticity of spodumene, LiAlSi 2 O 6 , was studied by static compression in a diamond-anvil cell. Investigations by means of single-crystal XRD and Raman spectroscopy within the hydrostatic limits of the pressure medium focus on the pressure ranges around 3.2 and 7.7 GPa, which have been reported previously to comprise two independent structural phase transitions. While our measurements confirm the well-established first-order C2/c-P2 1 /c transformation at 3.19 GPa (with 1.2% volume discontinuity and 0.81 GPa hysteresis), both unit-cell dimensions and the spectral changes observed in high-pressure Raman spectra give no evidence for structural changes related to a second phase transition. Monoclinic lattice parameters and unit-cell volumes at in total 59 different pressure points have been used to re-calculate the lattice-related properties of spontaneous strain, volume strain, and the bulk moduli as a function of pressure across the transition. A modified Landau free energy expansion in one order parameter has been developed and tested against these experimentally determined data. The Landau solution provides a much better reproduction of the observed anomalies than any equation-of-state fit to data sets truncated below and above P tr , thus giving Landau parameters of K 0 = 138.3(2) GPa, K' = 7.46(5),  V = 33.6(2) GPa, a= 0.486(3), b = -29.4(6) GPa and c = 551(11) GPa.

show abstract

“…[67] that a nonlinear and anharmonic extension of Landau theory coupled to finite strain is required once the external pressure becomes non-negligible in comparison to the elastic constants. It is only rather recently [29,30,[68][69][70] that such a nontrivial extension of LT has been constructed. Not unexpectedly, its backbone is the mathematically consistent incorporation of the pressure-dependence of elastic constants.…”

Section: Pressure-driven Phase Transitionmentioning

confidence: 99%

DFT study of the electronic properties and the cubic to tetragonal phase transition in RbCaF3

Ehsan

Tröster

Tran

et al. 2018

Phys. Rev. Materials

View full text Add to dashboard Cite

The structural, elastic, vibrational, and electronic properties of RbCaF 3 in the cubic and low-temperature tetragonal phases have been studied at the ab initio level with density functional theory. Using various exchange-correlation functionals of the generalized gradient approximation for structural properties like the CaF 6 octahedron rotational angle or ratio c/a of the tetragonal lattice constants, it is found that the best agreement with experiment is obtained with the PBEsol and Wu and Cohen (WC) functionals. The fundamental band gap is calculated to be direct and indirect in the tetragonal and cubic phases, respectively. The relation between the cubic and tetragonal phases is studied by monitoring the cubic zone boundary soft mode phonon R 15 as well as the c/a ratio and tilt angle. The results for the Born effective charge tensors are also reported in order to study the effect of the long-range Coulomb interactions. We also investigated the corresponding pressure driven phase transition at T = 0 K, which we observe to be of second order in contrast to the first-order character experimentally detected for the structurally similar high pressure transition at ambient temperature. Based on recently developed finite strain Landau theory, we offer a possible explanation for this peculiar change of character.

show abstract

Finite strain Landau theory of high pressure phase transformations

Cited by 13 publications

References 30 publications

Fully Consistent Finite-Strain Landau Theory for High-Pressure Phase Transitions

Fully Consistent Finite-Strain Landau Theory for High-Pressure Phase Transitions

The nonlinear anomalous lattice elasticity associated with the high-pressure phase transition in spodumene: a high-precision static compression study

DFT study of the electronic properties and the cubic to tetragonal phase transition in RbCaF3

Contact Info

Product

Resources

About