Application of Finite Strain Landau Theory To High Pressure Phase Transitions

In this paper we explain how to set up what is in fact the only possible consistent construction scheme for a Landau theory of high pressure phase transitions that systematically allows to take into account elastic nonlinearities. 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 a both qualitatively as well as quantitatively satisfying description of recent high precision experimental data. Our nonlinear theory also allows to predict a number of additional elastic transition anomalies that are accessible to experiment.Comment: submitted to Phys. Rev. Let

Revealing the pure confinement effect in glass-forming liquids by dynamic mechanical analysis

Many molecular glass forming liquids show a shift of the glass transition Tg to lower temperatures when the liquid is confined into mesoporous host matrices. Two contrary explanations for this effect are given in literature: First, confinement induced acceleration of the dynamics of the molecules leads to an effective downshift of Tg increasing with decreasing pore size. Secondly, due to thermal mismatch between the liquid and the surrounding host matrix, negative pressure develops inside the pores with decreasing temperature, which also shifts Tg to lower temperatures. Here we present novel dynamic mechanical analysis measurements of the glass forming liquid salol in Vycor and Gelsil with pore sizes of d = 2.6, 5.0 and 7.5 nm. The dynamic complex elastic susceptibility data can be consistently described with the assumption of two relaxation processes inside the pores: A surface induced slowed down relaxation due to interaction with rough pore interfaces and a second relaxation within the core of the pores. This core relaxation time is reduced with decreasing pore size d, leading to a downshift of Tg in perfect agreement with recent DSC measurements

Finite strain Landau theory of high pressure phase transformations

The properties of materials near structural phase transitions are often successfully described in the framework of Landau theory. While the focus is usually on phase transitions, which are induced by temperature changes approaching a critical temperature T-c, here we will discuss structural phase transformations driven by high hydrostatic pressure, as they are of major importance for understanding processes in the interior of the earth. Since at very high pressures the deformations of a material are generally very large, one needs to apply a fully nonlinear description taking physical as well as geometrical nonlinearities (finite strains) into account. In particular it is necessary to retune conventional Landau theory to describe such phase transitions. In Troster et al (2002 Phys. Rev. Lett. 88 55503) we constructed a Landau-type free energy based on an order parameter part, an order parameter-(finite) strain coupling and a nonlinear elastic term. This model provides an excellent and efficient framework for the systematic study of phase transformations for a wide range of materials up to ultrahigh pressures

Antiferrodistortive phase transition in EuTiO3

X-ray diffraction, dynamical mechanical analysis and infrared reflectivity studies revealed an antiferrodistortive phase transition in EuTiO3 ceramics. Near 300K the perovskite structure changes from cubic Pm-3m to tetragonal I4/mcm due to antiphase tilting of oxygen octahedra along the c axis (a0a0c- in Glazer notation). The phase transition is analogous to SrTiO3. However, some ceramics as well as single crystals of EuTiO3 show different infrared reflectivity spectra bringing evidence of a different crystal structure. In such samples electron diffraction revealed an incommensurate tetragonal structure with modulation wavevector q ~ 0.38 a*. Extra phonons in samples with modulated structure are activated in the IR spectra due to folding of the Brillouin zone. We propose that defects like Eu3+ and oxygen vacancies strongly influence the temperature of the phase transition to antiferrodistortive phase as well as the tendency to incommensurate modulation in EuTiO3.Comment: PRB, in pres

Pathological rate matrices: from primates to pathogens

<p>Abstract</p> <p>Background</p> <p>Continuous-time Markov models allow flexible, parametrically succinct descriptions of sequence divergence. Non-reversible forms of these models are more biologically realistic but are challenging to develop. The instantaneous rate matrices defined for these models are typically transformed into substitution probability matrices using a matrix exponentiation algorithm that employs eigendecomposition, but this algorithm has characteristic vulnerabilities that lead to significant errors when a rate matrix possesses certain 'pathological' properties. Here we tested whether pathological rate matrices exist in nature, and consider the suitability of different algorithms to their computation.</p> <p>Results</p> <p>We used concatenated protein coding gene alignments from microbial genomes, primate genomes and independent intron alignments from primate genomes. The Taylor series expansion and eigendecomposition matrix exponentiation algorithms were compared to the less widely employed, but more robust, Padé with scaling and squaring algorithm for nucleotide, dinucleotide, codon and trinucleotide rate matrices. Pathological dinucleotide and trinucleotide matrices were evident in the microbial data set, affecting the eigendecomposition and Taylor algorithms respectively. Even using a conservative estimate of matrix error (occurrence of an invalid probability), both Taylor and eigendecomposition algorithms exhibited substantial error rates: ~100% of all exonic trinucleotide matrices were pathological to the Taylor algorithm while ~10% of codon positions 1 and 2 dinucleotide matrices and intronic trinucleotide matrices, and ~30% of codon matrices were pathological to eigendecomposition. The majority of Taylor algorithm errors derived from occurrence of multiple unobserved states. A small number of negative probabilities were detected from the Pad�� algorithm on trinucleotide matrices that were attributable to machine precision. Although the Padé algorithm does not facilitate caching of intermediate results, it was up to 3× faster than eigendecomposition on the same matrices.</p> <p>Conclusion</p> <p>Development of robust software for computing non-reversible dinucleotide, codon and higher evolutionary models requires implementation of the Padé with scaling and squaring algorithm.</p