Energetics of the fcc ($γ$) - bcc ($α$) lattice transformation by the Bain tetragonal deformation is calculated for both magnetically ordered and paramagnetic (disordered local moment) states of iron. The first-principle computational results manifest a relevance of the magnetic order in a scenario of the $γ$ - $α$ transition and reveal a special role of the Curie temperature of $α$-Fe, $T_C$, where a character of the transformation is changed. At a cooling down to the temperatures $T < T_C$ one can expect that the transformation is developed as a lattice instability whereas for $T > T_C$ it follows a standard mechanism of creation and growth of an embryo of the new phase. It explains a closeness of $T_C$ to the temperature of start of the martensitic transformation, $M_s$.
Several experimental techniques are used for phase identification and microstructure characterization of austempered vermicular cast irons (XRD, SEM, TEM and Mossbauer spectroscopy). Acicular structures were found to be composed by ferrite and austenite with average sizes compatible with those reported for bainitic ferrite in steels and Austempered Ductile Iron. An assessment of the free energy change involved in the austenite to bainite transformation assuming a plate-like nucleation shape for bainite gave an average characteristic length close to the observed from statistical length distribu…
The effects of tensile stresses on isothermal bainitic transformation were studied in the case of a 35MV7 steel. The modification of transformation kinetics and the presence of transformation plasticity is shown in a first step. Furthermore the effect of stress on the morphological modifications of the ferrite laths is illustrated. The role of the stress on these changes is analysed.
The effects of magnetism on the Bain transformation of $α$-phase FeNi systems are investigated by using the full potential linearized augmented plane wave (FLAPW) method based on the generalized gradient approximation (GGA). We found that Ni impurity in bcc Fe increases the lattice constant in ferromagnetic (FM) states, but not in the nonmagnetic (NM) states. The shear modulus $G$ and Young's modulus $E$ of bcc Fe are also increased by raising the concentration of nickel. All the compositions considered show high shear anisotropy and the ratio of the bulk to shear modulus is greater than 1.75 …
This article provides a rigorous proof of a conjecture by E.C. Bain in 1924 on the optimality of the so-called "Bain strain" based on a criterion of least atomic movement. A general framework that explores several such optimality criteria is introduced and employed to show the existence of optimal transformations between any two Bravais lattices. A precise algorithm and a GUI to determine this optimal transformation is provided. Apart from the Bain conjecture concerning the transformation from face-centred cubic to body-centred cubic, applications include the face-centred cubic to body-centred…
The effect of finish rolling temperature (FRT) on the austenite- () to-bainite () phase transformation is quantitatively investigated in high-strength C-Mn steels. In particular, the present study aims to clarify the respective contributions of the conditioning during the hot rolling and the variant selection (VS) during the phase transformation to the inherited texture. To this end, an alternative crystallographic reconstruction procedure, which can be directly applied to experimental electron backscatter diffraction (EBSD) mappings, is developed by combining the best features of the existing…
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…
The diversity of mesostructures formed in steel at cooling from a high-temperature austenite ("gamma") phase is determined by the interplay of shear reconstructions of crystal lattice and diffusion of carbon. Combining first-principles calculations with large-scale phase-field simulations we demonstrate a decisive role of magnetic degrees of freedom in the formation of energy relief along the Bain path of "gamma"-"alpha" transformation and, thus, in this interplay. We show that there is the main factor, namely, the magnetic state of iron and its evolution with temperature which controls the ch…
Exploiting Landau's theory of phase transformations, defining an original order parameter and using the phenomenological transformation temperatures, it is reported that it is possible to describe in a global approach the conditions for the formation of each phase (ferrite, bainite, martensite) from austenite during cooling in steel. It allowed to propose a new rigorous classification of the different thermodynamic conditions controlling each phase tranformation. In a second step, the approach predicts naturally the effect of cooling rate on the bainite start temperature. Finally perspectives …
Exchange interactions in α- and γ-Fe are investigated within an ab-initio spin spiral approach. We have performed total energy calculations for different magnetic structures as a function of lattice distortions, related with various cell volumes and the Bain tetragonal deformations. The effective exchange parameters in γ-Fe are very sensitive to the lattice distortions, leading to the ferromagnetic ground state for the tetragonal deformation or increase of the volume cell. At the same time, the magnetic-structure-independent part of the total energy changes very slowly with the tetragonal defo…
Kinetics of polymorphous "gamma"-"alfa" transformation in Fe is studied numerically within a model taking into account both lattice and magnetic degrees of freedom, based on first-principle calculations of the total energy for different magnetic states. It is shown that magnetoelastic phenomena, namely, a strong sensitivity of the potential relief along the Bain deformation path to the magnetic state, are crucial for the picture of the transformation. With the temperature increase, a scenario of the phase transformation evolves from a homogeneous lattice instability at T<Ms (Ms is the temperat…
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…
Despite of the appearance of numerous new materials, the iron based alloys and steels continue to play an essential role in modern technology. The properties of a steel are determined by its structural state (ferrite, cementite, pearlite, bainite, martensite, and their combination) that is formed under thermal treatment as a result of the shear lattice reconstruction "gamma" (fcc) -> "alpha" (bcc) and carbon diffusion redistribution. We present a review on a recent progress in the development of a quantitative theory of the phase transformations and microstructure formation in steel that is ba…
The prediction of the atomistic structure and properties of crystals including defects based on ab-initio accurate simulations is essential for unraveling the nano-scale mechanisms that control the micromechanical and macroscopic behaviour of metals. Density functional theory (DFT) can enable the quantum-accurate prediction of some of these properties, however at high computational costs and thus limited to systems of ~1,000 atoms. In order to predict with quantum-accuracy the mechanical behaviour of nanoscale structures involving from thousands to several millions of atoms, machine learning i…
We report high pressure structural phase transformation sequence in a layered Iron-based superconducting compound FeSe0.3Te0.7 to 31 GPa at room temperature. The ambient pressure PbO type tetragonal phase (Space Group - P4/nmm) transforms to a monoclinic phase (Space group - P21/m) at a pressure of 7.3 \pm 0.9 GPa. This monoclinic phase is similar to the one observed below 100 K at ambient pressure. On further increase of pressure above 12 GPa, a transformation to an amorphous phase is observed that is completed by 20 GPa. The amorphous phase is found to be stable to the highest pressure of 31…
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…
We report the discovery of a new allotrope of iron by first principles calculations. This phase has $Pmn2_1$ symmetry, a six-atom unit cell (hence the name Fe$_6$), and the highest magnetization density (M$_s$) among all known crystalline phases of iron. Obtained from the structural optimizations of the Fe$_3$C-cementite crystal upon carbon removal, $Pmn2_1$ Fe$_6$ is shown to result from the stabilization of a ferromagnetic FCC phase, further strained along the Bain path. Although metastable from 0 to 50 GPa, the new phase is more stable, at low pressures, than the other well-known HCP and FC…
The room temperature magnetoelectric effect was observed in epitaxial iron garnet films that appeared as magnetic domain wall motion induced by electric field. The films grown on gadolinium-gallium garnet substrates with various crystallographic orientations were examined. The effect was observed in (210) and (110) films and was not observed in (111) films. Dynamic observation of the domain wall motion in 400 V voltage pulses gave the value of domain wall velocity in the range 30-50 m/s. The same velocity was achieved in magnetic field pulse about 50 Oe.
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…
The reduction of iron ore with carbon-carriers is one of the largest sources of greenhouse gas emissions in the industry, motivating global activities to replace the coke-based blast furnace reduction by hydrogen-based direct reduction (HyDR). Iron oxide reduction with hydrogen has been widely investigated both experimentally and theoretically. The process includes multiple types of chemical reactions, solid state and defect-mediated diffusion (by oxygen and hydrogen species), several phase transformations, as well as massive volume shrinkage and mechanical stress buildup. In this work, a chem…
This thesis investigates a transformation path between the Th3P4-type and the spinel-type structures of hafnium (IV) and titanium (IV) nitride, M3N4 (M = Hf, Ti) with computational methods. For both compounds, the Th3P4-type was synthesized experimentally at high-pressure conditions and was quenched to ambient conditions. Computations reveal that while at high pressure Th3P4-type structures are favored by enthalpy, at low pressure the Th3P4-type is only meta-stable. The spinel-type is energetically more favorable at zero pressure than the Th3P4- type in both systems. However, even the spinel-t…
The data of different authors on the thermal conductivity of wustite Fe1-xO, magnetite F3O4, hematite Fe2O3 and pure iron are systematized. The generalized values are described by piecewise smooth functions containing as varying parameters the temperatures of magnetiv and polymorphic (for iron) transformations as well as the thermodynamic stability boundary (for wustite). At polymorphic transformation a finite break of the thermal conductivity function is envisaged, at othet critical points only a break of its temperature derivative is acceptable. The proposed formulas are presented in two for…
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…
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.
Using classical molecular dynamics simulations, we study austenite to ferrite phase transformation in iron, focusing on the role of interface morphology. We compare two different morphologies; a \textit{flat} interface in which the two phases are joined according to Nishiyama-Wasserman orientation relationship vs. a \textit{ledged} one, having steps similar to the vicinal surface. We identify the atomic displacements along a misfit dislocation network at the interface leading to the phase transformation. In case of \textit{ledged} interface, stacking faults are nucleated at the steps, which hi…
The phonon dispersions of the bcc and fcc phases of pure iron (α-Fe, γ-Fe and δ-Fe) at ambient pressure were investigated close to the respective phase transition temperatures. In the open bcc structure the transverse phonons along T1 [ξξ0] and T1 [ξξ2ξ] are of particularly low energy. The eigenvectors of these phonons correspond to displacements needed for the transformation to the fcc γ-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 temp…
We investigate the topology of the spin-polarized charge density in bcc and fcc iron. While the total spin-density is found to possess the topology of the non-magnetic prototypical structures, in some cases the spin-polarized densities are characterized by unique topologies; for example, the spin-polarized charge densities of bcc and high-spin fcc iron are atypical of any known for non-magnetic materials. In these cases, the two spin-densities are correlated: the spin-minority electrons have directional bond paths with deep minima in the minority density, while the spin-majority electrons fill…
Iron oxides and oxyhydroxides are challenging to model computationally as competing phases may differ in formation energies by only several kJ/mol, they undergo magnetization transitions with temperature, their structures may contain partially occupied sites or long-range ordering of vacancies, and some loose structures require proper description of weak interactions such as hydrogen bonding and dispersive forces. If structures and transformations are to be reliably predicted under different chemical conditions, each of these challenges must be overcome simultaneously, while preserving a high …
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 …
Precise control of crystallography and magnetism in focused-ion-beam transformed iron-nickel thin films
CEITEC BUT, Brno University of Technology（布尔诺理工大学欧洲技术与创新卓越中心）；Institute of Applied Physics, TU Wien（维也纳工业大学应用物理研究所）；Institute of Physical Engineering, Brno University of Technology（布尔诺理工大学物理工程学院）
The combination of multiple functionalities in a single material is an appealing strategy for the de-velopment of smart materials with unique features. In this work, we present the preparation of thermoresponsive magnetic nanoparticles and their one-dimensional assembly into transient micro-filaments. The material is based on 9.4 nm iron oxide nanoparticles grafted with poly(N-n-propylacrylamide) via multiphosphonic acid anchoring sites. The hybrid nanoparticles present a low critical solution temperature (LCST) transition between 21 °C and 28 °C, depending on the pH and the ionic strength. Wh…
Huge deformations of the crystal lattice can be achieved in materials with inherent structural instability by epitaxial straining. By coherent growth on seven different substrates the in-plane lattice constants of 50 nm thick Fe70Pd30 films are continuously varied. The maximum epitaxial strain reaches 8,3 % relative to the fcc lattice. The in-plane lattice strain results in a remarkable tetragonal distortion ranging from c/abct = 1.09 to 1.39, covering most of the Bain transformation path from fcc to bcc crystal structure. This has dramatic consequences for the magnetic key properties. Magneto…
The dynamic observation of domain wall motion induced by electric field in magnetoelectric iron garnet film is reported. Measurements in 800 kV/cm electric field pulses gave the domain wall velocity ~45 m/s. Similar velocity was achieved in magnetic field pulse about 50 Oe. Reversible and irreversible micromagnetic structure transformation is demonstrated. These effects are promising for applications in spintronics and magnetic memory.
We extend the solid-state nudged elastic band method to handle a non-conserved order parameter - in particular, magnetization, that couples to volume and leads to many observed effects in magnetic systems. We apply this formalism to the well-studied magneto-volume collapse during the pressure-induced transformation in iron - from ferromagnetic body-centered cubic (bcc) austenite to hexagonal close-packed (hcp) martensite. We find a bcc-hcp equilibrium coexistence pressure of 8.4 GPa, with the transition-state enthalpy of 156 meV/Fe at this pressure. A discontinuity in magnetization and coheren…
Phonon densities of states (DOS) of bcc $α$-$^{57}$Fe were measured from room temperature through the 1044K Curie transition and the 1185K fcc $γ$-Fe phase transition using nuclear resonant inelastic x-ray scattering. At higher temperatures all phonons shift to lower energies (soften) with thermal expansion, but the low transverse modes soften especially rapidly above 700K, showing strongly nonharmonic behavior that persists through the magnetic transition. Interatomic force constants for the bcc phase were obtained by iteratively fitting a Born-von Kármán model to the experimental phonon spec…
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 (T$_1$) 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.
Diagonal flipping of a rhombus consisting of two triangles sharing a common edge with atoms (ions) in vertices of the triangles is considered as an elementary act of the polymorphic transformation in metals. The estimation of the energy threshold for the diagonal flipping has been carried out for various combination of rhombus vertices occupation by Fe, Cr, and Mn atoms. The energy threshold has been calculated in the framework of Morse interatomic pair potential. Numerical coefficients for the approximation of the pair potential function have been scaled by experimental values of the sublimat…
The known data on the heat capacity of magnetite (Fe3O4), hematite (Fe2O3) and iron (Fe) at different temperatures are approximated by formulas containing phase transition temperatures as varying parameters. This allows to take into account the effect of phase transition shifts, for example, due to impurities, lattice defects, grain sizes or high cooling rates. For this purpose, the entire target temperature range from 0 C to 1300 C is divided by phase transition temperatures into separate intervals. The conjugation of the approximating functions between the intervals at the magnetic transitio…
The orbital and spin magnetic properties of iron inside transforming metallic and semiconducting 1D carbon nanotube hybrids are studied by means of local x-ray magnetic circular dichroism (XMCD) and bulk superconducting quantum interference device (SQUID) measurements. Nanotube hybrids are initially ferrocene filled single-walled carbon nanotubes (SWCNT) of different metallicities. After a high temperature nanochemical reaction ferrocene molecules react with each other to form iron nano clusters. We show that the ferrocenes molecular orbitals interact differently with the SWCNT of different me…
We provide evidence that high-pressure high-temperature (2.5 GPa and 1040 K) treatment of mixtures of iron with fullerene powders leads to the complete transformation of iron into iron carbide Fe$_3$C. The comparison of the magnetic properties (Curie temperature and magnetic moment) of the here studied samples and those for the ferromagnetic polymer Rh-C$_{60}$ indicates that the main ferromagnetic signal reported in those samples is due to Fe$_3$C and not related to the ferromagnetism of carbon as originally interpreted. Taking into account the results obtained in this study the original pape…
In this manuscript the theory and phenomena associated with the Little Effect are introduced as the spin induced orbital dynamics of confined fermions under strong magnetic and thermal environments. This Little Effect is considered in details for the electron transfer reactions associated with redox processes of Cu-Ag alloy within deionized water and for the orbital dynamics during the iron catalyzed covalent bond rearrangements associated with amorphous carbon conversion to diamond. Furthermore, prolong extreme conditions of 74,000 amps, 403 V, strong Lorentz compression, and thermal stresses…
Electronic-Entropy-Driven Phase Transitions in Compressed Iron Oxides
University of Manchester（曼彻斯特大学）；University of Oxford（牛津大学）；Center for Advanced Systems Understanding（高级系统理解中心）；Helmholtz Zentrum Dresden-Rossendorf（德累斯顿-罗森多夫亥姆霍兹中心）；TU Dresden（德累斯顿工业大学）
Majorana quasi-particles may arise as zero-energy bound states in vortices on the surface of a topological insulator that is proximitized by a conventional superconductor. Such a system finds its natural realization in the iron-based superconductor FeTe$_{0.55}$Se$_{0.45}$ that combines bulk $s$-wave pairing with spin helical Dirac surface states, and which thus comprises the ingredients for Majorana modes in absence of an additional proximitizing superconductor. In this work, we investigate the emergence of Majorana vortex modes and lattices in such materials depending on parameters like the …
By combining DFT-based computational analysis and symmetry constraints in terms of group-subgroup relations, we analysed the formation of the native crystalline structure of loellingite FeAs$_2$. We showed that the ground state of the material exhibits the ordered patterns of the electronic localization which are mainly associated with iron $3d_{x^2 - y^2}$ orbitals and can be characterized in terms of nematic-like ordering. The ordering is the result of the close interplay of the lattice and the electron degrees of freedom. In a structural aspect, it pursues an energy quest to select the orth…
The nature of the phase separation in KxFe2-ySe2 single crystals is not well understood. Here, temperature dependent SEM images provide compelling evidence that phase separation corresponds to a nucleation and growth process rather than a spinodal decomposition. The superconducting phase is the remnant of high temperature phase after iron vacancy order-disorder transition. Three-dimension (3D) spatial distribution of superconducting phase in the iron vacancy ordered matrix was revealed by using focused ion beam scanning electron microscopy (FIB-SEM). Our results clearly show that superconducti…
Thermodynamic properties and structural aspects of the non-stoichiometric wüstite Fe 1-z O, and its modifications-the so-called pseudo-phases-as functions of composition z and equilibrium temperature are reviewed from 1960 to present (159 references). The focus is first put on the complexity of the equilibrium phase diagram. The first order transition W $\rightleftharpoons$ W' is specified on the boundary iron/ wüstite close to 1185 K. Transitions correlated to the modifications Wi at T(W) > 1185 K and W'j at 1185K < T(W') < T(W) (i and j =1,2,3) are reexamined. Structural determinations based…
The magnetic and electronic structures of Fe4O5 have been investigated at ambient and high pressures via a combination of representation analysis, density functional theory (DFT+U) calculations, and Mössbauer spectroscopy. A few spin configurations corresponding to the different irreducible representations have been considered. The total-energy calculations reveal that the magnetic ground state of Fe4O5 corresponds to an orthogonal spin order. Depending on the magnetic propagation vector k two spin ordered phases with minimal energy differences are realized. The lowest energy magnetic phase is…
