Theory of elastic phase transitions in metals at high pressures. Application to vanadium (original) (raw)
Melting curve and phase diagram of vanadium under high-pressure and high-temperature conditions
Physical Review B, 2019
We report a combined experimental and theoretical study of the melting curve and the structural behavior of vanadium under extreme pressure and temperature. We performed powder x-ray diffraction experiments up to 120 GPa and 4000 K, determining the phase boundary of the bcc-to-rhombohedral transition and melting temperatures at different pressures. Melting temperatures have also been established from the observation of temperature plateaus during laser heating, and the results from the density-functional theory calculations. Results obtained from our experiments and calculations are fully consistent and lead to an accurate determination of the melting curve of vanadium. These results are discussed in comparison with previous studies. The melting temperatures determined in this study are higher than those previously obtained using the speckle method, but also considerably lower than those obtained from shock-wave experiments and linear muffin-tin orbital calculations. Finally, a high-pressure high-temperature equation of state up to 120 GPa and 2800 K has also been determined.
Landau theory for the phase transitions of interstitial hydrogen in strained vanadium
Physical Review B, 2014
A special version of the Landau theory of phase transitions has been developed, capturing the order-disorder phase transition in the bulk and elastically strained vanadium-hydrogen system. The equations for the solubility isotherms are obtained and the influence of biaxial strain on the critical temperature is determined. The critical temperature is found to change exponentially with strain. The calculated solubility isotherms agree well with experimental data for temperatures below, as well as above, the critical temperature. The influence of elastic strain on the solubility isotherm is analyzed and noticeable deviations from Sieverts' law, even at the extremely low concentrations, are obtained.
Phase Transitions, 2007
We use a combination of diamond anvil cell techniques and large volume (multi-anvil press, piston cylinder) devices to study the synthesis, structure and properties of new materials under high pressure conditions. The work often involves the study of structural and phase transformations occurring in the metastable regime, as we explore the phase space determined as a function of the pressure, temperature and chemical composition. The experimental studies are combined with first principles calculations and molecular dynamics simulations, as we determine the structures and properties of new phases and the nature of the transformations between them. Problems currently under investigation include structural studies of transition metal and main group nitrides, oxides and oxynitrides at high pressure, exploration of new solid-state compounds that are formed within the C-N-O system, polyamorphic lowto high-density transitions among amorphous semiconductors such as a-Si, and transformations into metastable forms of the element that occur when its ''expanded'' clathrate polymorph is compressed.
Elasticity of the superconducting metals V, Nb, Ta, Mo, and W at high pressure
Physical Review B, 2008
First-principles calculations have been performed for V, Nb, Ta, Mo, and W. The recently discovered bcc→ rhombohedral transition for vanadium ͓Phys. Rev. Lett. 98, 085502 ͑2007͔͒ was confirmed as the mechanical instability of c 44 was found at P = 80 GPa. Furthermore, the c 11 , c 12 , and c 44 constants for the group-V elements showed erratic behaviors whereas the constants for the group-VI elements were monotonically increasing with pressure. The metals were analyzed with Fermi surface calculations, showing shrinking nesting vectors with pressure for V, Nb, and Ta but were not seen for Mo and W. From electronic topological transition contributions, a critical energy closely situated to the Fermi level for vanadium could be the reason why the elastic constants of V and Nb were difficult to reproduce at ambient pressure.
Phonon triggered rhombohedral lattice distortion in vanadium at high pressure
Scientific Reports, 2016
In spite of the simple body-centered-cubic crystal structure, the elements of group V, vanadium, niobium and tantalum, show strong interactions between the electronic properties and lattice dynamics. Further, these interactions can be tuned by external parameters, such as pressure and temperature. We used inelastic x-ray scattering to probe the phonon dispersion of single-crystalline vanadium as a function of pressure to 45 GPa. Our measurements show an anomalous high-pressure behavior of the transverse acoustic mode along the (100) direction and a softening of the elastic modulus C 44 that triggers a rhombohedral lattice distortion occurring between 34 and 39 GPa. Our results provide the missing experimental confirmation of the theoretically predicted shear instability arising from the progressive intra-band nesting of the Fermi surface with increasing pressure, a scenario common to all transition metals of group V. Although body-centered-cubic (bcc) metals have one of the simplest crystal structures in the periodic table, they display a rich variety of physical properties and thus provide an important benchmark for the validation of modern first-principle theory 1. In particular, the lattice dynamics of bcc transition metals have attracted great scientific attention. The Kohn anomaly in the phonon dispersion of bcc transition metals, and its dependence upon pressure and temperature, has been a challenge for first principle calculations to capture 2,3. The strong differences displayed by the phonon dispersion of the various elements of group V (vanadium, niobium and tantalum) suggest that there is a profound dependence of the phonon energies on the electronic structure and the topology of the Fermi surface 4,5. The high superconducting temperature (T c = 9.25 K for Nb and T c = 5.3 K for V) and its notable increase with pressure have also been suggested to be due to electron-phonon coupling and Fermi-surface properties 6-8. The stability at high pressure of the bcc structure is speculated to critically hinge on the topology of the Fermi surface as well, and an intra-band nesting is theoretically predicted to give rise to shear phonon instabilities 9. Focusing on vanadium, calculations of shear instabilities arising from phonon softening 9 have prompted the reinvestigation of the structural stability of V under high pressure. X-ray powder diffraction showed a transition from the bcc to a rhombohedral phase at 69 GPa 10 and subsequent calculations have confirmed the nature of the rhombohedral distortion-even though different transition pressures were proposed 5,11-13. Interestingly, under hydrostatic conditions the transition is hindered, and non-hydrostaticity helps in overcoming the energy barrier associated with the structural phase change 14. Irrespective of the exact pressure at which the transition occurs, the bulk of theoretical work points towards a common mechanism: the progressive intra-band nesting at the Fermi surface that eventually leads to an electronic topological transition (ETT) with a concomitant transverse acoustic phonon mode softening. Specifically, at a critical pressure, parts of the 3rd electronic, partially occupied, conduction band of d symmetry move into the close vicinity of the Fermi level. The nesting vector, already responsible for the Kohn anomaly in the transverse acoustic phonon mode along the (ξ, 0, 0) direction at ξ = 0.25 at ambient pressure 8 , reduces to zero and the ETT takes place, with instability in the shear elastic constant C 44 9. This anomalous softening of the elastic response causes an energy gain that counterbalances the standard elastic strain energy
Physical Review B
We study pressure-induced structural evolution of vanadium diselenide (VSe 2), a 1T polymorphic member of the transition metal dichalcogenide (TMD) family, using synchrotron-based powder x-ray diffraction (XRD) and first-principles density functional theory (DFT). Our XRD results reveal anomalies at P ∼ 4 GPa in the c/a ratio, V-Se bond length, and Se-V-Se bond angle, signaling an isostructural transition. This transition is followed by a first-order structural transition from the 1T (space group P3m1) phase to a 3R (space group R3m) phase at P ∼ 11 GPa due to sliding of adjacent Se-V-Se layers. Both the transitions at ∼4 and 11 GPa are cognate with associated changes in the Debye-Waller factors not reported so far. We present various scenarios to understand the experimental results within DFT and find that the 1T to 3R transition is captured using spinpolarized calculations with Hubbard correction (U eff = U −J = 8 eV), giving a transition pressure of ∼9 GPa, close to the experimental value.
Physical Review B, 2005
The structural transitions occurring between the high-pressure phases of alkali metals are described by displacive mechanisms. The different structures are associated with critical instabilities of the ambient-pressure body-centered-cubic structure. Unifying mechanisms are found for the transitions occurring in ͑Li and Na͒ and ͑K, Rb and Cs͒, respectively. The RbIII-RbIV-RbV and CsIII-CsIV phase sequences are interpreted as reflecting the hybridization process of the sand d-wave functions, which induces a deformation of the atomic shells, allowing a closer packing of the KIII, RbIV, and RbV structures. The RbIII and CsIII structures are proposed to represent commensurate approximations of incommensurately modulated structures locking in at the RbV and CsIV phases.
Structure, elastic moduli, and thermodynamics of sodium and potassium at ultrahigh pressures
2000
The equations of state at room temperature as well as the energies of crystal structures up to pressures exceeding 100 GPa are calculated for Na and K . It is shown that the allowance for generalized gradient corrections (GGA) in the density functional method provides a precision description of the equation of state for Na, which can be used for the calibration of pressure scale. It is established that the close-packed structures and BCC structure are not energetically advantageous at high enough compressions. Sharply non-monotonous pressure dependences of elastic moduli for Na and K are predicted and melting temperatures at high pressures are estimated from various melting criteria. The phase diagram of K is calculated and found to be in good agreement with experiment. 64.30.+t, 64.70.Kb, 71.25.Pi The theoretical and experimental studies of the matter properties at ultra-high pressures arouse a great interest in the connection with the possibility to obtain phases with uncommon properties as well as geophysical and astrophysical applications. As an example, the problem of metallic hydrogen can be mentioned 1 . In the high pressure studies the alkali metals can be conveniently used as model objects. This is due, first, to their high compressibility and, second, to the variety of physical phenomena occurring in their compression and numerous structural and electron phase transitions (see, e.g. 2-9 ). For heavy alkali metals it is the famous s−d isostructural FCC-FCC transition (see, e.g., 10 and references therein) as well as the transitions to uncommon distorted phases at higher pressures 11 . Recently it was supposed, basing on the electron structure calculations, that lithium can transform at high enough pressures into "exotic" phases similar to that of hydrogen 12 . Thus, further theoretical investigations of structural properties of alkali metals at ultra-high pressures seem to be interesting and important.
High pressure phase transformations revisited
Journal of Physics: Condensed Matter, 2018
High pressure phase transformations play an important role in the search for new materials and material synthesis, as well as in geophysics. However, they are poorly characterized, and phase transformation pressure and pressure hysteresis vary drastically in experiments of different researchers, with different pressure transmitting media, and with different material suppliers. Here we review the current state, challenges in studying phase transformations under high pressure, and the possible ways in overcoming the challenges. This field is critically compared with fields of phase transformations under normal pressure in steels and shape memory alloys, as well as plastic deformation of materials. The main reason for the above mentioned discrepancy is the lack of understanding that there is a fundamental difference between pressure-induced transformations under hydrostatic conditions, stressinduced transformations under nonhydrostatic conditions below yield, and strain-induced transformations during plastic flow. Each of these types of transformations has different mechanisms and requires a completely different thermodynamic and kinetic description and experimental characterization. In comparison with other fields the following challenges are indicated for high pressure phase transformation: (a) initial and evolving microstructure is not included in characterization of transformations; (b) continuum theory is poorly developed; (c) heterogeneous stress and strain fields in experiments are not determined, which leads to confusing material transformational properties with a system behavior. Some ways to advance the field of high pressure phase transformations are suggested. The key points are: (a) to take into account plastic deformations and microstructure evolution during transformations; (b) to formulate phase transformation criteria and kinetic equations in terms of stress and plastic strain tensors (instead of pressure alone); (c) to develop multiscale continuum theories, and (d) to couple experimental, theoretical, and computational studies of the behavior of a tested sample to extract information about fields of stress and strain tensors and concentration of high pressure phase, transformation criteria and kinetics. The ideal characterization should contain complete information which is required for simulation of the same experiments.