High-temperature Bcc Phase Research Articles

Ab-initio study of point defects in Th and U alloy

Point defect formation energies are calculated along with several structural and elastic properties for the fcc (α) and bcc (β) Th crystal structures. Th-self defects and single uranium impurity defects are modeled in the fcc phase, whereas only Th self-defects are modeled in the high temperature bcc phase. Additionally, an analysis of several well known exchange-correlation functionals is given in regard to defect modeling performance. Overall, defect formation energies in the bcc phase were lower in energy compared to their defect equivalents in the fcc phase. In both phases, vacancies were found be the most stable, with the bcc vacancy being ∼0.8 eV lower in energy than the fcc vacancy, regardless of form of the exchange-functional. The most stable interstitial defects were in the octahedral and <110> dumbbell positions for the fcc and bcc phases, respectively. It was also found that the <110> and <111> dumbbell defects were unstable in the fcc phase, but not in the bcc phase. Overall, the choice of exchange-correlation functional was found to have almost a negligible effect on the calculated formation energies. The most notable difference between functionals was in the prediction of the vacancy defect formation energies, which may be attributed to differences in the way each functional handles exchange and correlation in regions of low electron density relative to the bulk of a material, such as in the internal surface of a vacancy or vacancy cluster.

Microstructure, compression properties, and oxidation behavior of Hf-25Ta-5Me alloys (Me is Mo, Nb, W, 0.5Mo + 0.5 W, Cr, or Zr)

Hf–Ta based alloys have recently been investigated as potential candidates for high-temperature structural applications. While most attentions have been given to the properties above ~1200 °C where the alloys are mainly single-phase BCC structures and have excellent oxidation performance due to formation of super-oxides, structural properties at lower temperatures are equally important for applications in which an alloy may experience a range of temperatures. In the present work, microstructure, phase composition, mechanical properties and oxidation behavior of six Hf-25Ta-5Me alloys (Me is Mo (HTM alloy), W (HTW), 0.5Mo + 0.5 W (HTMW), Cr (HTC) or Zr (HTZ), the compositions are in at.%) are reported at temperatures below the eutectoid transformation. The alloys were prepared by arc melting followed by hot isostatic pressing for 3 h at 1400 °C and 207 MPa. All the alloys display coarse grains of partially or fully transformed (by a eutectoid reaction) high-temperature BCC phase. The eutectoid regions consist of fine lamellae of Hf-rich HCP and Ta-rich BCC phases. The ternary alloys containing W or Cr also contained small amounts of a cubic Laves phase. At 25 °C, the HTW alloy was the strongest (yield stress σy = 1966 MPa) but brittle and HTZ was the weakest (σy = 1120 MPa) but ductile among the studied alloys. Other alloys showed intermediate behaviors. In general, the room temperature ductility of the alloys increased with decreasing σy. All alloys maintained high strength up to 800 °C, but displayed a noticeable strength decrease at 1000 °C. At 1000 °C, HTMW was the strongest alloy (σy = 468 MPa) and HTC was the weakest alloy (σy = 368 MPa). All alloys had excellent deformability at 1000 °C. Oxidation behavior of the alloys was studied at 800 °C and 1000 °C and compared with that of Hf–27Ta binary alloy. Although the ternary additions improved oxidation resistance, overall oxidation performance of the studied alloys at 800 °C and 1000 °C was poor.

Understanding the role of anharmonic phonons in diffusion of bcc metals

Diffusion in the high-temperature bcc phase of IIIB-IVB metals such as Zr, Ti, and their alloys is observed to be orders of magnitude higher than bcc metals of group VB-VIB, including Cr, Mo, and W. The underlying reason for this higher diffusion is still poorly understood. To explain this observation, we compare the first-principles-calculated parameters of monovacancy-mediated diffusion between bcc Ti, Zr, and dilute Zr- Sn alloys and bcc Cr, Mo, and W. Our results indicate that strongly anharmonic vibrations promote both the vacancy concentration and the diffusive jump rate in bcc IVB metals and can explain their markedly faster diffusion compared to bcc VIB metals. Additionally, we provide an efficient approach to calculate diffusive jump rates according to the transition state theory (TST). The use of standard harmonic TST is impractical in bcc IIIB/IVB metals due to the existence of ill-defined harmonic phonons, and most studies use classical or ab initio molecular dynamics for direct simulation of diffusive jumps. Here, instead, we use a stochastically sampled temperature-dependent phonon analysis within the transition state theory to study diffusive jumps without the need of direct molecular dynamics simulations. We validate our first-principles diffusion coefficient predictions with available experimental measurements and explain the underlying reasons for the promotion of diffusion in bcc IVB metals/alloys compared to bcc VIB metals.

Formation mechanism of nano-sized η and ω structures in β phase in ECP treated Cu-40Zn alloy

Two nano-scaled hexagonal distortions in high temperature BCC phase during cooling is commonly observed in many alloys systems. Although efforts have been made on studying the lattice softening of the BCC structure during cooling, the distortion mechanisms are less addressed. Thus, the formation of two hexagonal structures in the β precipitates in a Cu-40Zn alloy treated by ECP was thoroughly investigated. Results show that the β precipitates contain two kinds of nano-sized and diffuse atomic clusters one with a η structure obeying the Burgers OR and the other a ω structure obeying the Blackburn OR. They were each formed through a two-stepped atomic displacement. For the η structure, the first step is the atomic shuffle of each second 110β plane in the <11¯0>β direction and the second is a structure change mainly by a {1 1¯ 2} < 1¯11>β shear. For the ω structure, the first is an atomic shuffle on each second and third {112¯}β plane in the ± [111]β directions and then normal strains in three mutually perpendicular directions. The concomitant formation of the two structures minimizes the lattice distortion of single formation. The present results provide new information on the formation mechanism of the two hexagonal structures in a BCC matrix.

Melting Curve and Isostructural Solid Transition in Superionic Ice.

The phase diagram and melting curve of water ice is investigated up to 45GPa and 1600K by synchrotron x-ray diffraction in the resistively and laser heated diamond anvil cell. Our melting data evidence a triple point at 14.6GPa, 850K. The latter is shown to be related to a first-order solid transition from the dynamically disordered form of ice VII, denoted ice VII^{'}, toward a high-temperature phase with the same bcc oxygen lattice but larger volume and higher entropy. Our experiments are compared to abinitio molecular dynamics simulations, enabling us to identify the high-temperature bcc phase with the predicted superionic ice VII^{''} phase [J.-A. Hernandez and R. Caracas, Phys. Rev. Lett. 117, 135503 (2016).PRLTAO0031-900710.1103/PhysRevLett.117.135503].

Elinvar effect in β-Ti simulated by on-the-fly trained moment tensor potential

A combination of quantum mechanics calculations with machine learning techniques can lead to a paradigm shift in our ability to predict materials properties from first principles. Here we show that on-the-fly training of an interatomic potential described through moment tensors provides the same accuracy as state-of-the-art ab initio molecular dynamics in predicting high-temperature elastic properties of materials with two orders of magnitude less computational effort. Using the technique, we investigate high-temperature bcc phase of titanium and predict very weak, Elinvar, temperature dependence of its elastic moduli, similar to the behavior of the so-called GUM Ti-based alloys (Sato et al 2003 Science 300 464). Given the fact that GUM alloys have complex chemical compositions and operate at room temperature, Elinvar properties of elemental bcc-Ti observed in the wide temperature interval 1100–1700 K is unique.

Superioniclike Diffusion in an Elemental Crystal: bcc Titanium.

Recent theoretical investigations [A. B. Belonoshko etal. Nat. Geosci. 10, 312 (2017)1752-089410.1038/ngeo2892] revealed the occurrence of the concerted migration of several atoms in bcc Fe at inner-core temperatures and pressures. Here, we combine first-principles and semiempirical atomistic simulations to show that a diffusion mechanism analogous to the one predicted for bcc iron at extreme conditions is also operative and of relevance for the high-temperature bcc phase of pure Ti at ambient pressure. The mechanism entails a rapid collective movement of numerous (from two to dozens) neighbors along tangled closed-loop paths in defect-free crystal regions. We argue that this phenomenon closely resembles the diffusion behavior of superionics and liquid metals. Furthermore, we suggest that concerted migration is the atomistic manifestation of vanishingly small ω-mode phonon frequencies previously detected via neutron scattering and the mechanism underlying anomalously large and markedly non-Arrhenius self-diffusivities characteristic of bcc Ti.

Lattice dynamics and elasticity for \u03b5-plutonium

Lattice dynamics and elasticity for the high-temperature ε phase (body-centered cubic; bcc) of plutonium is predicted utilizing first-principles electronic structure coupled with a self-consistent phonon method that takes phonon-phonon interaction and strong anharmonicity into account. These predictions establish the first sensible lattice-dynamics and elasticity data on ε-Pu. The atomic forces required for the phonon scheme are highly accurate and derived from the total energies obtained from relativistic and parameter-free density-functional theory. The results appear reasonable but no data exist to compare with except those from dynamical mean-field theory that suggest ε-plutonium is mechanically unstable. Fundamental knowledge and understanding of the high-temperature bcc phase, that is generally present in all actinide metals before melting, is critically important for a proper interpretation of the phase diagram as well as practical modeling of high-temperature properties.

Electronic correlations determine the phase stability of iron up to the melting temperature.

We present theoretical results on the high-temperature phase stability and phonon spectra of paramagnetic bcc iron which explicitly take into account many-body effects. Several peculiarities, including a pronounced softening of the [110] transverse (T1) mode and a dynamical instability of the bcc lattice in harmonic approximation are identified. We relate these features to the α-to-γ and γ-to-δ phase transformations in iron. The high-temperature bcc phase is found to be highly anharmonic and appears to be stabilized by the lattice entropy.

Role of vibrational entropy in the stabilization of the high-temperature phases of iron

The phonon dispersions of the bcc and fcc phases of pure iron ({\alpha}-Fe, {\gamma}-Fe and {\delta}-Fe) at ambient pressure were investigated close to the respective phase transition temperatures. In the open bcc structure the transverse phonons along T1 [{\xi}{\xi}0] and T1 [{\xi}{\xi}2{\xi}] are of particularly low energy. The eigenvectors of these phonons correspond to displacements needed for the transformation to the fcc {\gamma}-phase. Especially these phonons, but also all other phonons soften considerably with increasing temperature. Comparing thermodynamic properties of the fcc and the two bcc phases it is shown that the high temperature bcc phase is stabilized predominantly by vibrational entropy, whereas for the stabilization of the fcc phase electronic entropy provides an equal contribution.

In-situ high-pressure X-ray diffraction on the Zn6Sc 1/1 periodic cubic approximant to a quasicrystal

The Zn 6 Sc 1/1 cubic approximant to a quasicrystal has been studied in-situ at high pressures by ­single-crystal X-ray diffraction. This phase can be described as a bcc packing of Tsai-type icosahedral clusters whose center is occupied by a disordered Zn 4 tetrahedron. At ambient pressure the Zn 6 Sc undergoes a structural phase transition at 159 K to a monoclinic superstructure in which the Zn 4 tetrahedra are orientationally ordered along the [1̄01] direction of the high-temperature bcc phase. In the pressure range up to 35 GPa, two new superstructures have been observed. The second phase corresponds to a four-fold pseudo cubic superstructure, i.e. a very large unit cell with a lattice parameter of about 5.5 nm. The resulting pressure-temperature phase diagram is different from that of Cd 6 Yb, which was reported by Watanuki et al. (2006).

Anomalous energy pathway of vacancy migration and self-diffusion in hcp Ti

An anomalous energy pathway with energetically equivalent double saddle points for vacancy mediated self-diffusion within an hcp-Ti basal plane is unveiled by density functional theory. Examination of migration pathway and phonon force constants suggests that the migrating atom tries to follow the bcc-hcp phase transition via the Burgers shear deformation. We propose that the formed energy local minimum with a bcc-like atomic environment between the two saddle points originates from the existence of high-temperature bcc phase and is a feature of Group IV hcp metals with bcc-hcp phase transition. Computed diffusion coefficients are in favorable accord with experiments for hcp Ti.

Inverse martensitic transformation in Zr nanowires

Like martensitic transformations MTs, inverse martensitic transformations IMTs are shear-dominant diffusionless transformations, but are driven by reduction in interfacial energies rather than bulk free energies, and exhibit distinctive behavior such as instantaneous initiation like spinodal decomposition and self-limiting lengthscale. Bulk Zr metal is known to undergo normal MT from the high-temperature bcc phase to the low-temperature hcp phase. Using molecular dynamics simulations we demonstrate that, unlike in the bulk, an IMT to the bcc structure can occur in 1 100-oriented hcp Zr nanowires at low temperatures, which is driven by the reduction in the nanowire surface energy. The bcc domains subsequently become distorted and transform into a new 1 ¯ 1 20-oriented hcp domain, leading to reorientation of the nanowire. This behavior has implications for the study of structural transformations at the nanoscale and surface patterning.

Positron annihilation studies of microstructural changes in cold-worked Fe–Ni-base aging alloys

Microstructural evolution of cold-worked fcc Fe–Ni–Ti(Al) aging alloys subjected to isochronal annealing has been investigated using positron annihilation. The stages corresponding to vacancy defect annealing, heterogeneous nucleation of γ′-phase particles and recrystallization have been clearly identified. It has been found that, due to strong interaction of vacancies with titanium atoms in the Fe–Ni–Ti alloy, low-temperature (450–700 K) segregation of titanium and formation of Ni 3Ti particles at dislocations are observed. The Ni 3Ti particles strongly pin the dislocations, leading to recrystallization retardation. At the same time, particles block positron trapping at dislocations. Decomposition of cold-worked Fe–Ni–Al alloy takes place over the same temperature range (800–900 K) as in the solution annealed state of this alloy. Precipitation of the Ni 3Al and high-temperature bcc-phase particles also leads to dislocation pinning and inhibiting recovery of the microstructure in cold-worked Fe–Ni–Al alloy.

Lattice dynamics and melting features of Li and Na

The high-pressure melting of Li and Na has been studied using ab initio calculations of the lattice dynamics. It has been shown that the recently discovered anomalous melting of Na is adequately explained by the phonon spectrum behavior and, accordingly, the thermal vibration amplitudes under compression. In a simple approach using the Lindemann criterion, the nonmonotonic behavior of the melting curve Tm(p) of Na has been quantitatively described within very wide pressure and temperature ranges, and, in particular, the melting temperature drop at p ∼ 1 Mbar down to values lower than those at normal pressure. This approach leads to a nonphysical discontinuity of the melting curve Tm(p) of Li near the bcc-fcc-liquid triple point. This is due to the “softness” of the phonon spectrum of the bcc phase of Li that is the necessary condition for the existence of the high-temperature bcc phase. The melting of Na and Li is used as an example to determine why the Lindemann criterion is efficient in some situations and is inapplicable in the other cases.

Calculations of high-pressure properties of beryllium: Construction of a multiphase equation of state

We describe the construction of a three-phase equation of state for elemental beryllium. The phases considered are: the ambient hcp phase, the high-temperature bcc phase, and the liquid. The free energies of the solid phases are constructed from cold, ion-thermal, and electron-thermal components derived from ab initio electronic structure-based calculations. We find that the bcc phase is unstable near ambient conditions and that even at high pressures at which the bcc phase is stable, the bcc-hcp energy barrier can be as small as a few hundred kelvins. The liquid free energy is based on a model of Chisolm and Wallace and is constrained by using the melt curve (determined by ab initio two-phase simulations) as a reference. The high-temperature plasma limit is addressed with an average-atom-in-jellium model. Comparisons to experimental results, both for the ambient hcp phase and for the phase diagram as a whole, are discussed.

The self-consistent ab initio lattice dynamical method

We describe a method for calculating temperature dependent phonon spectra self consistently from first principles. The method combines concepts from Born’s self-consistent phonon approach with ab initio calculations of accurate interatomic forces in a supercell. Test calculations on the high temperature bcc phase of Ti, Zr, Hf, Sc and Y, as representative examples, reproduce the observed high temperature phonon frequencies with good accuracy. By use of an embedded atom potential we demonstrate the method’s relevance in calculating approximate critical temperatures of solid–solid phase transitions for the hcp to bcc transition in Zr.

Entropy Driven Stabilization of Energetically Unstable Crystal Structures Explained from First Principles Theory

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 Born's interatomic self-consistent phonon approach with first principles calculations of accurate interatomic forces in a supercell. 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.

Experimental investigations on the electronic structure and the low-temperature stability of Cd-based quasicrystals and their 1/1 cubic approximants

Valence band spectra of icosahedral quasicrystals and their 1/1 cubic approximants in the Cd-Yb and Cd-Ca systems are investigated systematically. A sharp Fermi edge, indicative of sizable density of states at the Fermi level (E F ), is clearly observed for all the compounds and E F is located not at the bottom of the pseudogap but at its shoulder. In addition, a peak structure appears just below E F for the Cd-Ca system, which is also found for the Cd-Yb system when subtracting a Yb 4f derived doublet. Ca 2p-3d resonant photoemission spectroscopies on the Cd-Ca compounds reveal the existence of Ca 3d states at E F , indicating that the 3d states do contribute to the peak structure at E F , which is attributed to hybridization with the Cd sp states. The low-temperature structural properties of the Cd-based compounds are also reported. An occurrence of a structural phase transition at 110 K and 100 K for Cd6Yb and Cd6Ca, respectively, is well documented. The transitions are understood as a consequence of an orientational ordering of Cd4 tetrahedron located at the center of the icosahedral clusters. It is suggested that two orientations of the Cd4 tetrahedron alternatively occur along the [110] direction of the high temperature bcc phase.

Phase transformation analysis in titanium at nanosecond time resolution

Polycrystalline and mosaic bicrystalline titanium films were subjected to steep heating/cooling rate of 1011∕108Ks−1 by laser pulsing. The induced phase transformations were followed by imaging and diffraction with a dynamic transmission electron microscope on the time scale of nanoseconds. On heating the film up to near the melting point with a 6-ns laser pulse, the low-temperature hcp phase transformed to the high-temperature bcc phase, with a nucleation rate of 1025m−3s−1 and a crystal-growth velocity of about 1000ms−1. Quenching of molten Ti first produced the bcc phase, which in turn transformed to the hcp phase within a few microseconds. Thus, hcp-bcc transformations occur in Ti, even at the above high thermal rates. They are martensitic and not diffusion limited as claimed for transformations at low thermal rates.