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Register a new userTemperature driven $alpha$ to $beta$ phase-transformation in Ti, Zr and Hf from first principles theory combined with lattice dynamics
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Added by
Petros Souvatzis Dr
Publication date
2011
fields
Physics
and research's language is
English
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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.
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Contrary to previous studies that identified the ground state crystal structure of the entire R_3Co series (R is a rare earth) as orthorhombic Pnma, we show that Y_3Co undergoes a structural phase transition at T_t=160K. Single crystal neutron diffraction data reveal that at T_t the trigonal prisms formed by a cobalt atom and its six nearest-neighbor yttrium atoms experience distortions accompanied by notable changes of the Y-Co distances. The formation of the low-temperature phase is accompanied by a pronounced lattice distortion and anomalies seen in heat capacity and resistivity measurements. Density functional theory calculations reveal a dynamical instability of the Pnma structure of Y_3Co. In particular, a transversal acoustic phonon mode along the (00z) direction has imaginary frequencies at z<1/4. Employing inelastic neutron scattering measurements we find a strong damping of the (00z) phonon mode below a critical temperature T_t. The observed structural transformation causes the reduction of dimensionality of electronic bands and decreases the electronic density of states at the Fermi level that identifies Y_3Co as a system with the charge density wave instability.
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.
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.
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.
We have investigated the plastic deformation properties of non-equiatomic single phase Zr-Nb-Ti-Ta-Hf high-entropy alloys from room temperature up to 300 {deg}C. Uniaxial deformation tests at a constant strain rate of 10$^{-4}$ s$^{-1}$ were performed including incremental tests such as stress-relaxations, strain-rate- and temperature changes in order to determine the thermodynamic activation parameters of the deformation process. The microstructure of deformed samples was characterized by transmission electron microscopy. The strength of the investigated Zr-Nb-Ti-Ta-Hf phase is not as high as the values frequently reported for high-entropy alloys in other systems. We find an activation enthalpy of about 1 eV and a stress dependent activation volume between 0.5 and 2 nm$^3$. The measurement of the activation parameters at higher temperatures is affected by structural changes evolving in the material during plastic deformation.
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