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Register a new userEntropy driven stabilization of energetically unstable crystal structures explained from first principles theory
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Added by
Petros Souvatzis Dr
Publication date
2008
fields
Physics
and research's language is
English
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Conventional methods to calculate the thermodynamics of crystals evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the body-centered cubic (bcc) crystal structure when it appears as a high-temperature phase of many metals. A method for calculating temperature dependent phonon spectra self consistently from first principles has been developed to address this issue. The method combines concepts from Borns inter-atomic self-consistent phonon approach with first principles calculations of accurate inter-atomic forces in a super-cell. The method has been tested on the high temperature bcc phase of Ti, Zr and Hf, as representative examples, and is found to reproduce the observed high temperature phonon frequencies with good accuracy.
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We demonstrate the accurate calculation of entropies and free energies for a variety of liquid metals using an extension of the two phase thermodynamic (2PT) model based on a decomposition of the velocity autocorrelation function into gas-like (hard sphere) and solid-like (harmonic) subsystems. The hard sphere model for the gas-like component is shown to give systematically high entropies for liquid metals as a direct result of the unphysical Lorentzian high-frequency tail. Using a memory function framework we derive a generally applicable velocity autocorrelation and frequency spectrum for the diffusive component which recovers the low frequency (long time) behavior of the hard sphere model while providing for realistic short time coherence and high frequency tails to the spectrum. This approach provides a significant increase in the accuracy of the calculated entropies for liquid metals and is compared to ambient pressure data for liquid sodium, aluminum, gallium, tin, and iron. The use of this method for the determination of melt boundaries is demonstrated with a calculation of the high pressure bcc melt boundary for sodium. With the significantly improved accuracy available with the memory function treatment for softer interatomic potentials, the 2PT model for entropy calculations should find broader application in high energy density science, warm dense matter, planetary science, geophysics, and material science.
Lattice dynamical methods used to predict phase transformations in crystals typically deal with harmonic phonon spectra and are therefore not applicable in important situations where one of the competing crystal structures is unstable in the harmonic approximation, such as the bcc structure involved in the hcp to bcc martensitic phase transformation in Ti, Zr and Hf. Here we present an expression for the free energy that does not suffer from such shortcomings, and we show by self consistent {it ab initio} lattice dynamical calculations (SCAILD), that the critical temperature for the hcp to bcc phase transformation in Ti, Zr and Hf, can be effectively calculated from the free energy difference between the two phases. This opens up the possibility to study quantitatively, from first principles theory, temperature induced phase transitions.
Glasses are solid materials whose constituent atoms are arranged in a disordered manner. The transition from a liquid to a glass remains one of the most poorly understood phenomena in condensed matter physics, and still no fully microscopic theory exists that can describe the dynamics of supercooled liquids in a quantitative manner over all relevant time scales. Here we present such a theoretical framework that yields near-quantitative accuracy for the time-dependent correlation functions of a supercooled system over a broad density range. Our approach requires only simple static structural information as input and is based entirely based on first principles. Owing to this first-principles nature, the framework offers a unique platform to study the relation between structure and dynamics in glass-forming matter, and paves the way towards a systematically correctable and ultimately fully quantitative theory of microscopic glassy dynamics.
The standard formulation of thermostatistics, being based on the Boltzmann-Gibbs distribution and logarithmic Shannon entropy, describes idealized uncorrelated systems with extensive energies and short-range interactions. In this letter, we use the fundamental principles of ergodicity (via Liouvilles theorem), the self-similarity of correlations, and the existence of the thermodynamic limit to derive generalized forms of the equilibrium distribution for long-range-interacting systems. Significantly, our formalism provides a justification for the well-studied nonextensive thermostatistics characterized by the Tsallis distribution, which it includes as a special case. We also give the complementary maximum entropy derivation of the same distributions by constrained maximization of the Boltzmann-Gibbs-Shannon entropy. The consistency between the ergodic and maximum entropy approaches clarifies the use of the latter in the study of correlations and nonextensive thermodynamics.
Phonon lifetime calculations from first principles usually rely on time consuming molecular dynamics calculations, or density functional perturbation theory (DFPT) where the zero temperature crystal structure is assumed to be dynamically stable. Here a new and effective method for calculating phonon lifetimes from first principles is presented, not limited to crystal structures stable at 0 K, and potentially much more effective than most corresponding molecular dynamics calculations. The method is based on the recently developed self consistent lattice dynamical method and is here tested by calculating the bcc phase phonon lifetimes of Li, Na, Ti and Zr, as representative examples.
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