This work generalizes our previous works on fcc-bcc martensitic transformations to the larger family of transformations in the fcc-bcc-hcp system and to fcc-fcc mechanical twinning. The analytical expressions of the atomic displacements and lattice distortions are calculated directly from the orientation relationships without any adjustment of free parameter; the unique assumption is that the atoms are hard-spheres that cannot interpenetrate themselves. The habit planes are predicted on the simple criterion that they are unrotated by the distortion, and the results are compared to experimental observations published in literature. It is shown that shuffle is required for transformations implying the hcp phase because the hcp primitive Bravais lattice contains two atoms, instead of one for the fcc and bcc phases. A simple encoding of the lattice distortions and shuffles permits to attribute a groupoid structure to the transformations in the fcc-hcp-bcc system. The analytical expressions of the intermediate states are given and could be used to calculate activation energies. The martensitic distortion occurs in one-step, without shearing, and its accommodation generates orientation gradients in the parent phase, independently of its glide modes. The concept of reversibility is detailed on the basis of crystallographic and morphological arguments. The possibility to apply this approach to diffusion-limited martensitic transformations is discussed.
From our previous models of martensitic transformation, the continuous matrices of atomic displacements and lattice deformations from face-centred-cubic (fcc) to body centred-cubic (bcc) phases are calculated in agreement with different possible final orientation relationships, such as Bain, Pitsch and Kurdjumov-Sachs (KS). The angular distortion introduced in the calculations appears a natural order parameter of transition. The distortion corresponding to KS is the only one that respects the parallelism of a dense direction and of a dense plane of both the fcc and bcc phases. This paper gives…
The Burgers distortion is a two-stage transition between body centered cubic (BCC) and hexagonal close-packed (HCP) structures. Refractory metal elements from the Sc and Ti columns of the periodic table (BCC/HCP elements) form BCC structures at high temperatures but transition to HCP at low temperatures via the Burgers distortion. Elements of the V and Cr columns, in contrast, remain BCC at all temperatures. The energy landscape of BCC/HCP elements exhibits an alternating slide instability, while the normal BCC elements remain stable as BCC structures. This instability is verified by the prese…
The dynamical model of forming of martensitic crystals for the bcc-hcp transition is offered. It is shown that all macroscopic morphological characters (the habit plane, the macroshear and the orientational relationship) are expressed through elastic moduluses Cij of an initial bcc phase.
We have performed molecular dynamic simulations of a Martensitic bcc->hcp transformation in a homogeneous system. The system evolves into three Martensitic variants, sharing a common nearest neighbor vector along a bcc <111> direction, plus an fcc region. Nucleation occurs locally, followed by subsequent growth. We monitor the time-dependent scattering S(q,t) during the transformation, and find anomalous, Brillouin zone-dependent scattering similar to that observed experimentally in a number of systems above the transformation temperature. This scattering is shown to be related to the elastic …
The pressure induced bcc to hcp transition in Fe has been investigated via ab-initio electronic structure calculations. It is found by the disordered local moment (DLM) calculations that the temperature induced spin fluctuations result in the decrease of the energy of Burgers type lattice distortions and softening of the transverse $N$-point $TA_1$ phonon mode with $[\bar{1}10]$ polarization. As a consequence, spin disorder in an system leads to the increase of the amplitude of atomic displacements. On the other hand, the exchange coupling parameters obtained in our calculations strongly decre…
Beryllium (Be) is an important material with wide applications ranging from aerospace components to X-ray equipments. Yet a precise understanding of its phase diagram remains elusive. We have investigated the phase stability of Be using a recently developed hybrid free energy computation method that accounts for anharmonic effects by invoking phonon quasiparticles. We find that the hcp to bcc transition occurs near the melting curve at 0<P<11 GPa with a positive Clapeyron slope of 41 K/GPa. The bcc phase exists in a narrow temperature range that shrinks with increasing pressure, explaining the…
The summary of the models offered by the author revealing features of the physical mechanisms controlling processes of martensite crystal formation is resulted. The rapid growth of a cooling martensite crystal is considered as a self-organized process controlled by the quasi-longitudinal lattice displacement waves (DW). It is shown, that processes of the heterogeneous nucleation and wave growth have the genetic connection in case of spontaneous fcc-bcc martensitic transformation. The exposition of strain martensite formation is considered in the context of a cryston model.
Martensitic transformation in steels is responsible for their very high strength and has thus been studied for more than one century since the first works of Martens. However, there is not yet simple physical theory. A rigorous classification of the crystallographic subgroupoids (packets) of the KS variants and the continuity between the KS, NW and Pitsch variants are introduced to represent the crystallographic intricacy associated to the martensite transformation. From this analysis, a new simple theory based on Pitsch distortion is proposed. The distortion respects the hard sphere packing o…
Many structural transformations involve a group-nonsubgroup relationship between the initial and transformed phases, and hence are beyond the purview of conventional Landau theory. We utilize a systematic and robust methodology to describe such reconstructive martensitic transformations by coupling group-theoretical arguments to first-principles calculations. In this context we (i) use a symmetry-based algorithm to enumerate transformation paths, (ii) evaluate the energy barriers along these transformation paths using all-electron first principles calculations, (iii) deduce the full set of pri…
Under high pressures, phase transition, as well as deformation twins, are constantly reported in many BCC metals, whose interactions are of fundamental importance to understand strengthen mechanism of these metals under extreme conditions. However, the interactions between twins and phase transition in BCC metals are remain largely unexplored. In this work, interactions between coherent twin boundaries and $α\to ε$ phase transition of iron are investigated using both non- equilibrium molecular dynamics simulations and nudge elastic band method. Mechanisms of both twin-assisted phase transition…
Molecular dynamics simulations are performed to investigate the structural phase transition in body-centered cubic (bcc) single crystal iron under high strain rate loading. We study the nucleation and growth of the hexagonal-close-packed (hcp) and face-centered-cubic (fcc) phases, and their crystal orientation dependence. Results reveal that the transition pressures are less dependent on the crystal orientations ($\mathtt{\sim}$14 GPa for loading along [001], [011], and [111] directions). However, the pressure interval of mixed phase for [011] loading is much shorter than loading along other o…
This book is the first monograph in the scientific literature, dedicated to the FCC-BCC transformation in iron-based alloys, in which the dynamical approach is used for the explanation of the martensite growth stage. The rapid growth of a cooling martensite crystal is considered as a self-organized process controlled by the quasi-longitudinal lattice displacement waves (DW). The regime of the DW initial excitation is rigid. DW have the frequencies ~$10^{10} sec^{-1}$ from the hypersound band and the amplitudes providing the level of deformation ~$10^{-3}$. The conditions that are necessary for…
Refractory high entropy alloys containing elements from the Ti, V and Cr columns of the periodic table form body centered cubic (BCC) structures. Elements from the Ti column are noteworthy because they take the BCC structure at high temperature but undergo a shear instability and transform to the hexagonal (HCP) structure at low temperature. We show that the instability of these elements impacts the properties of the HEAs that contain them. In particular, the shear moduli are greatly reduced, causing increased dynamic contributions to lattice distortion. Relatively large size differences betwe…
We employed a recently developed semi-empirical Zr potential to determine the diffusivities in the hcp and bcc Zr via molecular dynamics simulation. The point defect concentration was determined directly from MD simulation rather than from theoretical methods using T=0 calculations. We found that the diffusion proceeds via the interstitial mechanism in the hcp Zr and both the vacancy and interstitial mechanisms give contribution in diffusivity in the bcc Zr. The agreement with the experimental data is excellent for the hcp Zr and for the bcc Zr it is rather good at high temperatures but there …
Motivated by the disagreement between recent diffusion Monte Carlo calculations and experiments on the phase transition pressure between the ambient and beta-Sn phases of silicon, we present a study of the HCP to BCC phase transition in beryllium. This lighter element provides an oppor- tunity for directly testing many of the approximations required for calculations on silicon and may suggest a path towards increasing the practical accuracy of diffusion Monte Carlo calculations of solids in general. We demonstrate that the single largest approximation in these calculations is the pseudopotenti…
Ab-initio calculations for the structural properties of Zr-Nb alloys at different values of the niobium concentration are done at zero temperature. Different cases for Zr-Nb alloys with unit cells having BCC and HCP structures are considered. Optimal values of the lattice constants are obtained. Critical value for the niobium concentration corresponding to the structural transformation HCP \rightarrow BCC at zero temperature is determined. Electronic densities of states for two different structures with niobium concentrations 12.5% and 25% having HCP and BCC structures, accordingly, are studie…
Nanoprecipitates form during nucleation of multiphase equilibria in phase segregating multicomponent systems. In spite of their ubiquity, their size-dependent physical chemistry, in particular at the boundary between phases with incompatible topologies, is still rather arcane. Here we use extensive atomistic simulations to map out the size-temperature phase diagram of Cu nanoprecipitates in α-Fe. The growing precipitates undergo martensitic transformations from the body-centered cubic (BCC) phase to multiply-twinned 9R structures. At high temperatures, the transitions exhibit strong first-orde…
The coexistence pressure of two phases is a well-defined point at fixed temperature. In experiment, however, due to non-hydrostatic stresses and a stress-dependent potential energy barrier, different measurements yield different ranges of pressure with a hysteresis. Accounting for these effects, we propose an inequality for comparison of the theoretical value to a plurality of measured intervals. We revisit decades of pressure experiments on the bcc - hcp transformations in iron, which are sensitive to non-hydrostatic conditions and sample size. From electronic-structure calculations, we find …
New interatomic potentials describing defects, plasticity and high temperature phase transitions for Ti are presented. Fitting the martensitic hcp-bcc phase transformation temperature requires an efficient and accurate method to determine it. We apply a molecular dynamics (MD) method based on determination of the melting temperature of competing solid phases, and Gibbs-Helmholtz integration, and a lattice-switch Monte Carlo method (LSMC): these agree on the hcp-bcc transformation temperatures to within 2 K. We were able to develop embedded atom potentials which give a good fit to either low or…
There has been a long debate on the stable phase of iron under the Earth's inner core conditions. Because of the solid-liquid coexistence at the inner core boundary, the thermodynamic stability of solid phases directly relates to their melting temperatures, which remains considerable uncertainty. In the present study, we utilized a semi-empirical potential fitted to high-temperature ab initio data to perform a thermodynamic integration from classical systems described by this potential to ab initio systems. This method provides a smooth path for thermodynamic integration and significantly redu…
Structural stability of paramagnetic (PM) body-centered cubic (bcc) Fe under pressure is investigated based on first-principles phonon calculations. Spin configurations of the PM phase are approximated using a binary special quasi-random structure (SQS) with a supercell approach. The behavior of phonon modes can be associated with pressure-induced phase transitions to the face-centered cubic (fcc) and hexagonal close-packed (hcp) structures as follows: For the PM phase, it is found that the low-frequency transverse mode at the N point (N$_4^-$ mode), which corresponds to a bcc-hcp phase transi…
High-entropy alloys (HEAs), and even medium-entropy alloys (MEAs), are an intriguing class of materials in that structure and property relations can be controlled via alloying and chemical disorder over wide ranges in the composition space. Employing density-functional theory combined with the coherent-potential approximation to average over all chemical configurations, we tune free energies between face-centered-cubic (fcc) and hexagonal-close-packed (hcp) phases in Fe$_{x}$Mn$_{80-x}$Co$_{10}$Cr$_{10}$ systems.~Within Fe-Mn-based alloys, we show that the martensitic transformation and chemic…
We use first principles molecular dynamics simulations coupled to the thermodynamic integration method to study the hcp-bcc transition and melting of beryllium up to a pressure of 1600~GPa. We derive the melting line by equating solid and liquid Gibbs free energies, and represent it by a Simon Glatzel fit $T_m= 1564~\text{K} (1 + P/(15.6032 ~\text{GPa}))^{0.383}$, which is in good agreement with previous two-phase simulations below 6000~K. We also derive the hcp-bcc solid-solid phase boundary and show the quasiharmonic approximation underestimates the stability of the hcp structure, predicting…
The effect of the film thickness and temperature on structural phase transformations in infinite films of bcc zirconium with (001) crystallographic orientation is studied by the molecular dynamics method with a many-body potential of interatomic interaction obtained within the embedded atom model. It is shown that the mechanism, sequence and final structures of phase transitions in bcc Zr films essentially depend on the film thickness. The films with (001) surface up to 6.1 nm thick experience an orientational transition into the bcc (110) phase through an intermediate metastable fcc phase, an…
The martensitic transformation is a fundamental physical phenomenon at the origin of important industrial applications. However, the underlying microscopic mechanism, which is of critical importance to explain the outstanding mechanical properties of martensitic materials, is still not fully understood. This is because for most martensitic materials the transformation is a fast process that makes in situ studies extremely challenging. Noble solids krypton and xenon undergo a progressive pressure induced fcc to hcp martensitic transition with a very wide coexistence domain. Here, we took advant…
We determine from first-principles the Curie temperature Tc for bulk Co in the hcp, fcc, bcc, and tetragonalized bct phases, for FeCo alloys, and for bcc and bct Fe. For bcc-Co, Tc=1420 K is predicted. This would be the highest Curie temperature among the Co phases, suggesting that bcc-Co/MgO/bcc-Co tunnel junctions offer high magnetoresistance ratios even at room temperature. The Curie temperatures are calculated by mapping ab initio results to a Heisenberg model, which is solved by a Monte Carlo method.
We investigate the temperature and pressure dependences of the electrical resistivity for bcc and hcp Fe using the low-order variational approximation and theoretical transport spectral functions calculated from first principles linear response linear-muffin-tin-orbital method in the generalized-gradient approximation. The calculated values are in close agreement with available experimental data, and show strong increase with temperature and decrease with pressure. We also discuss the behavior of the electrical resistivity for the bcc -> hcp phase transition.
The electronic structures of rare-earth elements in the HCP structure, and Europium in the BCC structure, are calculated by use of density-functional theory, DFT. Simulation of X-ray photoemission spectroscopy (XPS) and bremsstrahlung isochromatic spectroscopy (BIS) are made within DFT by imposing that f-electrons are excited by a large photon energy, either by removing from the occupied states in XPS, or by adding to the unoccupied f-states in BIS. The results show sizable differences in the apparent position of the f-states compared to the f-band energy of the ground states. This result is f…
Materials with an allotropic phase transformation can result in the formation of microstructures where grains have orientation relationships (ORs) determined by the transformation history. These microstructures influence the final material properties. In zirconium alloys, there is a solid-state body centred cubic (BCC) to hexagonal close packed (HCP) phase transformation, where the crystal orientations of the HCP phase can be related to the parent BCC structure via the Burgers orientation relationship (BOR). In the present work, we adapt a reconstruction code developed for steels which uses a …
The structural and electronic properties of Rutherfordium, the newest group IV B element, have been evaluated by first principles density functional theory in scalar relativistic formalism with and without spin-orbit coupling and compared with the known experimental and theoretical properties of its homologue Hf. It is found that it will crystallize in the hexagonal close packed structure with metallic character. However, under pressure, it will have different sequence of phase transitions than Hf: hcp\rightarrow bcc instead of hcp\ rightarrow ω\rightarrow bcc.
We present a coarse molecular-dynamics (CMD) approach for the study of stress-induced structural transformations in crystals at finite temperatures. The method relies on proper choice of a coarse variable (order parameter, observable), which parameterizes the changes in effective free energy during the transformation. Results are reported for bcc-to-hcp lattice transitions under pressure. We explore coarse-variable space to reconstruct an effective free-energy landscape quantifying the relative stability of different metastable basins and locate the onset, at a critical pressure, of the bcc-to…
The martensitic transformation is one of the most important phenomena in metals science due to its essential contribution to the strength of steels and most engineering alloys. Yet the basic, atomistic mechanisms leading to martensite nucleation and twin morphology are not yet known. A detailed picture in this regard is required if the strengthening effects of martensite are to be properly understood. This work presents molecular dynamics (MD) simulations of the martensitic transformation using a model fcc/bcc semi-coherent interface with Nishiyama-Wasserman orientation relationship. Significa…
Using ab-initio density functional theory we study the role of interstitial hydrogen on the energetics of the phase transformation of iron from bcc to hcp along Bain's pathway. The impurity creates an internal stress field that can be released through a tetragonal distortion of the lattice, promoting the bcc (ferromagnetic) $\rightarrow$ fcc (frustrated antiferromagnetic) $\rightarrow$ hcp (ferromagnetic) transition. The transformation between crystal systems is accompanied by a drastic magnetic reorganization and sudden variations of the unit cell volume, that can be one of the reasons for em…
We have studied the effect of ageing within the miscibility gap on the electric, magnetic and thermodynamic properties of a non-stoichiometric Heusler Cu-Al-Mn shape-memory alloy, which undergoes a martensitic transition from a $bcc$-based ($β$-phase) towards a close-packed structure ($M$-phase). Negative magnetoresistance which shows an almost linear dependence on the square of magnetization with different slopes in the $M$- and $β$-phases, was observed. This magnetoresistive effect has been associated with the existence of Mn-rich clusters with the Cu$_2$AlMn-structure. The effect of an appl…
The behavior of metals at high pressure is of great importance to the fields of shock physics, geophysics, astrophysics, and nuclear materials. In order to further understand the properties of metals at high pressures we studied the equation of state of aluminum using first-principles techniques up to 2500 GPa, pressures within reach of the planned L.L.N.L. National Ignition Facility. Our simulations use density-functional theory and density-functional perturbation theory in the generalized gradient approximation at 0K. We found core overlaps to become relevant beyond pressures of 1200 GPa. Th…
We have used a tight-binding model that is fit to first-principles electronic-structure calculations for titanium to calculate quasi-harmonic phonons and the Gibbs free energy of the hexagonal close-packed (hcp) and omega crystal structures. We show that the true zero-temperature ground-state is the omega structure, although this has never been observed experimentally at normal pressure, and that it is the entropy from the thermal population of phonon states which stabilizes the hcp structure at room temperature. We present the first completely theoretical prediction of the temperature- and pr…
We have studied the body-centered cubic (bcc), face-centered cubic (fcc) and hexagonal close-packed (hcp) phases of Fe alloyed with 25 at. % of Ni at Earth's core conditions using an ab initio local density approximation + dynamical mean-field theory (LDA+DMFT) approach. The alloys have been modeled by ordered crystal structures based on the bcc, fcc, and hcp unit cells with minimum possible cell size allowing for the proper composition. Our calculations demonstrate that the strength of electronic correlations on the Fe 3d shell is highly sensitive to the phase and local environment. In the bc…
We present a unifying description for the martensitic transformation of steel that accounts for important experimentally observable features of the transformation namely, the Neumann bands, the interfacial (habit) plane between the transformed and untransformed phases and their orientation relationship (OR). It is obtained through a simple geometric minimization of the total distance traveled by all the atoms from the austenite (FCC or $γ$) phase to the martensite (BCC or $α$) phase, without the need for any explicit energy minimization. Our description unites previously proposed mechanisms bu…
A class of Fe-Mn-Si-based alloys exhibits a reversible martensitic transformation between the $γ$ phase with a face-centered cubic~(fcc) structure and an $ε$ phase with a hexagonal close-packed (hcp) structure. During the deformation-induced $γ$--$ε$ transformation, we identified a phase that is different from the $ε$ phase. In this new phase, the electron diffraction spots are located at the 1/3 positions that correspond to the $\{$0002$\}$ plane of the $ε$ (hcp) phase with 2H structure, which suggests long-period stacking order (LPSO). To understand the stacking pattern and explore the possi…
Magnetic and transport properties of near-stoichiometric metastable FexMnyGaz alloys (46<x<52, 17<y25, 26<z<30) with face-centered cubic (FCC), body-centered cubic (BCC), and two-phase (FCC+BCC) structures are investigated. The experimental results are analyzed in terms of first-principles calculations of stoichiometric Fe2MnGa alloy with the L21, L12, and the tetragonally distorted L21 structural orderings. It is shown that the pure BCC and FCC phases have distinct magnetic and transport properties. Two-phase Fe2MnGa alloys have magnetic and transport properties typical of the mixed BCC and F…
In this paper the phonon self energy produced by anharmonicity is calculated using second order many body perturbation theory for all bcc, fcc and hcp transition metals. The symmetry properties of the phonon interactions are used to obtain an expression for the self energy as a sum over irreducible triplets, very similar to integration in the irreducible part of the Brillouin zone for one particle properties. The results obtained for transition metals shows that the lifetime is on the order of 10^10 s. Moreover the Peierls approximation for the imaginary part of the self energy is shown to be …
The crystal structure of iron in the Earth's inner core remains debated. Most recent experiments suggest a hexagonal-close-packed (hcp) phase. In simulations, it has been generally agreed that the hcp-Fe is stable at inner core pressures and relatively low temperatures. At high temperatures, however, several studies suggest a body-centered-cubic (bcc) phase at the inner core condition. We have examined the crystal structure of iron at high pressures over 2 million atmospheres (>200GPa) and at high temperatures over 5000 kelvin in a laser-heated diamond cell using microstructure analysis combin…
Observation of hexagonal close-packed water ice at conditions in ice giant planetary interiors
CEA DAM DIF（法国原子能委员会达姆-迪费中心）；Université Paris-Saclay, CEA, Laboratoire Matière en Conditions Extrêmes（巴黎萨克雷大学、法国原子能委员会极端条件物质实验室）；Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie (IMPMC), Sorbonne Université, CNRS UMR 7590, MNHN（索邦大学矿物学、材料物理与宇宙化学研究所（IMPMC），CNRS UMR 7590，自然历史博物馆）；European Synchrotron Radiation Facility（欧洲同步辐射装置）
The equation of state, structural behavior and phase stability of α-uranium have been investigated up to 1.3 TPa using density functional theory, adopting a simple description of electronic structure that neglects the spin-orbit coupling and strong electronic correlations. The comparison of the enthalpies of Cmcm (alpha-U), bcc, hcp, fcc, and bct predicts that the aplpha-U phase is stable up to a pressure of ~285 GPa, above which it transforms to a bct-U phase. The enthalpy differences between the bct and bcc phase decrease with pressure, but bcc is energetically unfavorable at least up to 1.3…
Our earlier Monte Carlo simulations of metastable supercooled-liquid and glass phases of Lennard-Jones atoms found several distinct signatures for identifying the glass transition boundary; i.e., the density, enthalpy, and pair distribution function dependences on temperature and pressure are different for the two phases (F. F. Abraham, J. Chem. Phys., 72, 359 (1980)). In this extension of that study, we base our analysis on the Ackland-Jones (A-J) method for determining the local crystal packing about each atom (G. Ackland & A. Jones, PRB 73, 054104 (2006)). It focuses on the angular distribu…
We apply a simple dynamical density functional theory, the phase-field crystal (PFC) model of overdamped conservative dynamics, to address polymorphism, crystal nucleation, and crystal growth in the diffusion-controlled limit. We refine the phase diagram for 3d, and determine the line free energy in 2d, the height of the nucleation barrier in 2d and 3d for homogeneous and heterogeneous nucleation by solving the respective Euler-Lagrange (EL) equations. We demonstrate that in the PFC model, the body-centered cubic (bcc), the face-centered cubic (fcc), and the hexagonal close packed structures (…
Transformation-mediated twinning governs plasticity in body-centered cubic nanocrystals under extreme loading
University of West Bohemia in Pilsen（西波希米亚大学）；University of Helsinki（赫尔辛基大学）；National Centre for Nuclear Research（国家核研究中心）；Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）
We have calculated the ground state electronic structure of He under pressure from 0 to 1500 GPa using both all-electron full-potential and pseudopotential methods based on the density functional theory (DFT). We find that throughout this pressure range, pseudopotentials yield essentially the same energy-volume curve for all of bcc, fcc, and hcp configurations as does the full-potential method, a strong indication that pseudopotential approximation works well for He both as the common element in some giant planets and as detrimental impurities in fusion reactor materials. The hcp lattice is al…
Ab initio High-Pressure Phase Diagrams of Al-Mg Alloys in the Low Solute Concentration Limit
University College London（伦敦大学学院）；AWE Nuclear Security Technologies（阿韦核安全技术公司）；London Centre for Nanotechnology, University College London（伦敦大学学院纳米技术研究中心）；Dipartimento di Fisica Ettore Pancini, Università di Napoli Federico II（那不勒斯费德里科二世大学埃托雷·潘奇尼物理系）
We use first-principles techniques to re-examine the suggestion that transitions seen in high-P experiments on Mo are solid-solid transitions from the bcc structure to either the fcc or hcp structures. We confirm that in the harmonic approximation the free energies of fcc and hcp structures become lower than that of bcc at P > 325 GPa and T below the melting curve, as reported recently. However, we show that if anharmonic effects are fully included this is no longer true. We calculate fully anharmonic free energies of high-T crystal phases by integration of the thermal average stress with resp…
