Computational thermodynamics and the kinetics of martensitic transformation

To assist the science-based design of alloys with martensitic microstructure, a multicomponent database kMART (kinetics of MARtensitic Transformation) encompassing the components Al, C, Co, Cr, Cu, Fe, Mn, Mo, N, Nb, Ni, Pd, Re, Si, Ti, V, and W has been developed to calculate the driving force for martensitic transformation. Built upon the SSOL database of the Thermo-Calc software system, a large number of interaction parameters of the SSOL database have been modified, and many new interaction parameters, both binary and ternary, have been introduced to account for the heat of transformation, T ₀ temperatures, and the composition dependence of magnetic properties. The critical driving force for face-centered cubic (fcc) → body-centered cubic (bcc) heterogeneous martensitic nucleation in multicomponent alloys is modeled as the sum of a strain energy term, a defect-size-dependent interfacial energy term, and a composition-dependent interfacial work term. Using our multicomponent thermodynamic database, a model for barrierless heterogeneous martensitic nucleation, a model for the composition and temperature dependence of the shear modulus, and a set of unique interfacial kinetic parameters, we have demonstrated the efficacy of predicting the fcc → bcc martensitic start temperature (M _s ) in multicomponent alloys with an accuracy of ± 40 K over a very wide composition range.     

Composition and non-equilibrium crystallization in partially devitrified co-rich soft magnetic nanocomposite alloys

The body-centered cubic (bcc) phase tends to preferentially nucleate during solidification of highly undercooled liquid droplets of binary alloy systems, including Fe–Co, Fe–Ni and Fe–Cr–Ni. We investigate a similar tendency during the partial devitrification of Co-rich amorphous precursors of composition (Co_1?xFe_x)₈₈Zr₇B₄Cu₁ by identifying the structure and composition of the nanocrystalline grains. The Co:Fe ratio of the bcc nanocrystals varies linearly with the Co:Fe ratio of the amorphous precursor, and can lie well within the single-phase face-centered cubic (fcc) region of the Fe–Co phase diagram at the crystallization temperature. Classical nucleation theory therefore suggests several potential explanations for the preferential nucleation of bcc phase from an amorphous precursor, including: (i) a reduced amorphous/bcc interface energy as compared to the close-packed phases; (ii) a lower strain of precipitation for bcc nuclei as compared to close-packed fcc and hexagonal close-packed nuclei; and (iii) stabilization of the bcc phase by dissolved glass-formers such as Zr and B.     

Mechanisms of martensitic phase transformations in body-centered cubic structural metals and alloys: Molecular dynamics simulations

Two different mechanisms of the stress-induced martensitic phase transformation at the crack tip in body-centered cubic (bcc) structural metals and alloys have been studied by molecular dynamics simulations. For cracks with 〈1 0 0〉 crack fronts, the bcc (B2) to face-centered cubic (fcc) (L1₀) phase transformation along the Bain stretch occurs. Whereas for cracks with 〈1 1 0〉 crack fronts, either the bcc (B2) to fcc (L1₀) or the bcc (B2) to hexagonal close-packed (hcp) transformation is the candidate. We have found that the combination of local stress and crystal orientation plays an important role in the mechanism of the martensitic transformation. Thus a simple way to determine the mechanism of the martensitic transformation is developed. The complicated deformation behaviors at the crack tip in bcc iron and B2 NiAl are discussed in terms of this method.     

Nucleation of Ni–Fe alloy near the spinodal

In molecular dynamics simulations, “non-classical” nucleation around the spinodal in Fe–Ni alloys is observed by controlling the composition. With increasing Fe concentration, metastable body-centered cubic (bcc) clusters are formed during pre-crystallization under the influence of the spinodal, and then grow into face-centered cubic (fcc)-ordered critical nuclei. When the composition reaches 75 at.% Fe, this transformation is suppressed and the bcc, rather than fcc, symmetry dominates the structure of critical nuclei, a typical nucleation behavior near the spinodal. Further increase in the Fe concentration depresses nucleation below the spinodal temperature. As a consequence, two transient bcc phases characterized by high and low densities appear upon reaching the critical size.     

The effect of melt-spinning processing parameters on crystal structure and magnetic properties in Fe–Mn–Ga alloys

We have succeeded to fabricate body-centered cubic (bcc) single phase of Fe–Mn–Ga alloys using melt-spinning technique. Heusler type L2₁ structure of Fe₂MnGa alloy are predicted to have half-metallic properties, however bulk Fe₂MnGa alloys crystallize into face-centered cubic (fcc) lattice with small admixture of bcc phase. By changing either ejection temperature or rotation speed of melt-spinning processing parameters, fcc or bcc lattice can be obtained from same precursor ingot. For stoichiometric Fe₂MnGa as-spun alloy, super-lattice diffraction peaks indicative of L2₁ structure are observed from XRD measurements. The as-spun bcc alloys transform into ferromagnetic hexagonal lattice by thermal annealing.     

Application of classical nucleation theory to phase selection and composition of nucleated nanocrystals during crystallization of Co-rich (Co,Fe)-based amorphous precursors

Classical steady-state nucleation theory is applied to Co-rich Fe,Co-based alloys to provide a rationale for experimental observations during the nanocrystallization of Co-rich (Co,Fe)₈₉Zr₇B₄ and (Co,Fe)₈₈Zr₇B₄Cu₁ amorphous precursors. The amorphous precursor free energy is estimated using density functional theory. This simple theory suggests: (i) strain or interface energy effects could explain a tendency for a body-centered cubic (bcc) phase to form during crystallization. Dissolved glass formers (Zr,B) in crystalline phases may also contribute; (ii) similar face-centered cubic (fcc) and hexagonal close-packed (hcp) free energies could explain the presence of some hcp phase after crystallization even though fcc is stable at the crystallization temperature; (iii) nanocrystal compositions vary monotonically with the Co:Fe ratio of the amorphous precursor even when multiple phases are nucleating because nucleation is not dictated by the common tangency condition governing bulk phase equilibria; and (iv) Fe-enrichment of the bcc phase can be attributed to a relatively small free energy difference between the amorphous and bcc phases for high Co-containing alloys.     

First-principles calculations of the structural and thermodynamic properties of bcc,fcc and hcp solid solutions in the Al–TM (TM = Ti,Zr and Hf) systems: A comparison of cluster expansion and supercell methods

The thermodynamic properties of solid solutions with body-centered cubic (bcc), face-centered cubic (fcc) and hexagonal close-packed (hcp) structures in the Al–TM (TM = Ti, Zr and Hf) systems are calculated from first-principles using cluster expansion (CE), Monte-Carlo simulation and supercell methods. The 32-atom special quasirandom structure (SQS) supercells are employed to compute properties at 25, 50 and 75 at.% TM compositions, and 64-atom supercells have been employed to compute properties of alloys in the dilute concentration limit (one solute and 63 solvent atoms). In general, the energy of mixing (Δ_mE) calculated by CE and dilute supercells agree very well. In the concentrated region, the Δ_mE values calculated by CE and SQS methods also agree well in many cases; however, noteworthy discrepancies are found in some cases, which we argue originate from inherent elastic and dynamic instabilities of the relevant parent lattice structures. The importance of short-range order on the calculated values of Δ_mE for hcp Al–Ti alloys is demonstrated. We also present calculated results for the composition dependence of the atomic volumes in random solid solutions with bcc, fcc and hcp structures. The properties of solid solutions reported here may be integrated within the CALPHAD formalism to develop reliable thermodynamic databases in order to facilitate: (i) calculations of stable and metastable phase diagrams of binary and multicomponent systems, (ii) alloy design, and (iii) processing of Al–TM-based alloys.     

Microstructures,tensile properties and serrated flow of AlxCrMnFeCoNi high entropy alloys

Microstructures and mechanical properties of dual-phase Al_xCrMnFeCoNi (x=0.4, 0.5, 0.6, at.%) alloys were investigated. Thermomechanical processing leads to a microstructural evolution from cast dendritic structures to equiaxed ones, consisting of face-centered cubic (fcc) and body-centered cubic (bcc) phases in the two states. The volume fraction of bcc phase increases and the size of fcc grain decreases with increasing Al content, resulting in remarkably improved tensile strength. Specifically, the serrated flow occurring at the medium temperatures varies from type A+B to B+C or C as the testing temperature increases. The average serration amplitude of these Al-containing alloys is larger than that of CoCrFeNiMn alloy due to the enhanced pinning effect. The early small strain produces low-density of dislocation arrays and bowed dislocations in fcc grains while the dislocation climb and shearing mechanism dominate inside bcc grains. The cross-slip and kinks of dislocations are frequently observed and high-density-tangled dislocations lead to dislocation cells after plastic deformation with a high strain.     

Empirical design of single phase high-entropy alloys with high hardness

We collect the available basic properties of nearly 100 high-entropy alloys (HEAs) with a single face centered cubic (fcc) or body centered cubic (bcc) phase. HEAs crystallizing in the fcc structure are mainly composed of the late 3d elements (LTM-HEAs), whereas HEAs consisting of the early (refractory) transition elements and the LTM-HEAs containing an increased level of bcc stabilizer form the bcc structure. Guided by the solid solution theory, we investigate the structure and hardness of HEAs as a function of the valence electron concentration (VEC) and the atomic size difference (δ). The fcc structure is found for VEC between 7.80 and 9.50, whereas the structure is bcc for VEC between 4.33 and 7.55. High strength is obtained for an average valence electron number VEC ∼ 6.80 and for an average atomic size difference δ ≈ 6%. Based on these empirical correlations, one can design the high-entropy alloys with desired hardness.     

Review on ω Phase in Body-Centered Cubic Metals and Alloys

An to phase with a primitive hexagonal crystal structure has been found to be a common metastable phase in body-centered cubic(bcc) metals and alloys.In general,to phase precipitates out as a high density of nanoscale particles and can obviously strengthen the alloys;however,coarsening of the co particles significantly reduces the alloy ductility.The co phase has coherent interfacial structure with its bcc matrix phase,and its lattice parameters are a_ω =2~(1/2)×a_(bcc) and C_ω= 3~(1/2)/2 ×a_(bcc).The common {112}(11 l)-type twinning in bcc metals and alloys can be treated as the product of theω→ bcc phase transition,also known as the ω-lattice mechanism.The ω phase's behavior in metastable β-type Ti alloys will be briefly reviewed first since the ω phase was first found in the alloy system,and then the existence of the ω phase in carbon steels will be discussed.Carbon plays a crucial role in promoting the ω formation in steel,and the ω phase can form a solid solution with various carbon contents.Hence,the martensitic substructure can be treated as an α-Fe matrix embedded with a high density of nanoscale ω-Fe particles enriched with carbon.The recognition of the ω phase in steel is expected to advance the understanding of the relationship between the microstructure and mechanical properties in bcc steels,as well as the behavior of martensitic transformations,twinning formation,and martensitic substructure.     

The isotropic shear modulus of multicomponent Fe-base solid solutions

A critical analysis of the available experimental data for the effect of alloying elements on the isotropic shear modulus of bcc (body-centered cube) Fe–X (X=Al, Be, C, Co, Cr, Ge, Ir, Mn, Ni, Pt, Re, Rh, Ru, Si and V) solid solutions is carried out. The total effect of a solute on the shear modulus is decomposed into two contributions: the electronic (or chemical) and the volumetric. A systematic trend of the electronic contribution is demonstrated as a function of electron-to-atom (e/a) ratio and the ground-state electronic configuration of the solute atom. Based on the demonstrated trend, we predict the chemical contribution of the shear modulus of Cu, Mo, N, Nb, Ti and W in ferromagnetic α-Fe (bcc), and that of Ti and V in paramagnetic γ-Fe [face-centered cube (fcc)]. These along with the corresponding volumetric contributions enable us to predict the total effect of a solute on the shear modulus in α-Fe and γ-Fe. In the case of γ-Fe, we derive the chemical and volumetric contributions of Ni and Pt from the experimental shear modulus data of paramagnetic Fe–Ni and Fe–Pt alloys while those of C, Co, Cr, Mn, Mo, N and Si are derived from the shear modulus of paramagnetic Fe–Ni–X alloys. In the case of Al, Be, Cu, Ge, Ir, Nb, Re, Rh , Ru and W, the total effect on the shear modulus is calculated by assuming that the electronic contribution to the shear modulus in γ-Fe is the same as in α-Fe. To calculate the isotropic shear modulus of multicomponent bcc and fcc solid solutions, we propose linear superposition laws. The proposed relationships are validated using the experimental data of a large number of multicomponent alloys having austenitic, ferritic, and lath martensitic microstructures. It is demonstrated that for all three microstructures, in most cases the shear modulus can be predicted with an accuracy of ±3% in multicomponent solid solutions. It is also found that the high dislocation density in lath martensite accounts for a decrease in shear modulus by about 5% compared to the ferritic counterpart. We also demonstrate that the temperature dependence of shear modulus in multicomponent bcc and fcc solid solutions is similar to that of pure α- and γ-Fe, respectively, for up to about 800 K.     

MnFeNiCuPt and MnFeNiCuCo high-entropy alloys designed based on L10 structure in Pettifor map for binary compounds

Quinary exact equi-atomic MnFeNiCuPt and MnFeNiCuCo alloys were investigated to examine their formation of high-entropy alloys (HEAs) by focusing on an L1₀ structure from Pettifor map for binary compounds with 1:1 stoichiometry. The MnFeNiCuPt alloy was practically selected through computer-assisted alloy design under conditions of ≤ 20 at% noble metals, and the condition that the L1₀ structure appears as frequently as possible in the constituent binary equi-atomic compositions comprised of 78 elements. MnFeNiCuCo was selected by substituting Pt with Co from the MnFeNiCuPt alloy as the second candidate. X-ray diffraction and observations by scanning electron microscopy (by energy dispersive spectroscopy for composition analysis) revealed that as-prepared MnFeNiCuPt and MnFeNiCuCo alloys were formed into HEAs with dual fcc structures containing dendrites of ∼10 μm in width. The MnFeNiCuPt and MnFeNiCuCo alloys annealed at 1373 K for 43.2 ks and subsequently quenched in water formed single fcc phases and dual fcc phases, respectively. The annealed MnFeNiCuPt and MnFeNiCuCo alloys were subsequently cooled in a furnace and formed single L1₂ ordered phases and dual fcc phases, respectively. These phases, experimentally observed in the annealed samples, could be partially explained by thermodynamic calculations using Thermo-Calc with SSOL4 and SSOL5 databases for solid solutions. The MnFeNiCuPt and MnFeNiCuCo alloys exhibit soft magnetism with saturation magnetization of 0.23 and 0.43 T, respectively, with coercivity values of ∼1 kA m⁻¹. An alloy design for HEAs based on digitalized crystallographic data of these samples could lead to the discovery of new HEAs.     

The microstructure and properties of rapidly quenched Ti-rich Ti-Ni binary alloys with shape memory effects

The structure, phase composition, and martensitic transformations in binary titanium-rich Ti-Ni alloys with shape memory effects, produced by ultrarapid quenching using melt jet spinning, have been studied using electron microscopy, X-ray diffraction, and measurements of some physicomechanical properties in a wide temperature range. The alloys with a Ti content that exceeded the stoichiometric composition by 5% and more can be produced in an amorphous state. The alloys with a smaller deviation from the stoichiometry, as well as the Ti₅₀Ni₅₀ alloy, are crystallized in a submicrocrystalline state and undergo a B2 → B19’ martensitic transformation at temperatures above room temperature. They have high strength and plastic properties and demonstrate narrow-hysteresis shape-memory effects.     

Calculations of energies of mixing of atoms in α- and γ-phases of Fe-Ni alloys by ab initio modeling method

Ab initio calculations of the total energy, energy of mixing, and magnetic moments of atoms in the binary Fe-Ni alloys with the bcc and fcc lattices are carried out in the whole range of concentrations. With increasing atomic fraction of Ni x, the energy of mixing E _mix ^γ passes the maximum, intersects the zero value, and reaches the minimum in the range of negative values. The energy of mixing of the bcc alloys in the range of nickel concentrations x = 0?0.32 is positive, which indicates that these alloys tend to clustering. The difference between the free energies of the fcc and bcc phases is calculated; the calculation result is close to the thermodynamic data of Kaufman and Cohen for 0 K.     

Alloy design for high-entropy alloys based on Pettifor map for binary compounds with 1:1 stoichiometry

Pettifor map for binary compounds with 1:1 stoichiometry was utilized as an alloy design for high-entropy alloys (HEAs) with exact or near equi-atomicity in multicomponent systems. Experiments started with selecting GuGd binary compound with CsCl structure from Pettifor map, followed by its extensions by selecting the binary compounds with the same CsCl structure to CuDyGdTbY equi-atomic quinary alloy and to Cu₄GdTbDyY and Ag₄GdTbDyY quinary alloys and Cu₂Ag₂GdTbDyY senary alloy in sequence. X-ray diffraction revealed that CuDyGdTbY alloy was formed into a HEA with mixture of bcc, fcc and hcp structures, whereas the Cu₂Ag₂GdTbDyY HEA was a single CsCl phase. The results suggest a potential of Pettifor map for the development of HEAs by utilizing its information of crystallographic structures. The further analysis was performed for composition diagrams of multicomponent systems corresponding to simplices in a high dimensional space. The present results revealed that a strategy of equi-mole of compounds instead of conventional equi-atomicity also works for the development of HEAs.     

一种粉末冶金铁素体钢中的双组态结构(英文)

采用混合预合金粉末和球磨粉末的方法,制备一种具有双组态结构的铁素体合金钢,其名义成分为Fe-14Cr-3W-0.42Ti-0.32Y。其微观组织与成分相同但是采用全球磨粉末成形的铁素体钢有明显的区别。通过热锻、空冷之后,该合金具有铁素体晶粒和马氏体晶粒混合构成的双组态结构。通过微观组织研究发现了在该合金中发生了局部的αbcc→γfcc→α'bcc相变。同时,这种双组态结构能够较好地均衡合金的强度和韧性。     

Microstructure and Properties of Aluminum-Containing Refractory High-Entropy Alloys

A new metallurgical strategy, high-entropy alloying (HEA), was used to explore new composition and phase spaces in the development of new refractory alloys with reduced densities and improved properties. Combining Mo, Ta, and Hf with “low-density” refractory elements (Nb, V, and Zr) and with Ti and Al produced six new refractory HEAs with densities ranging from 6.9 g/cm³ to 9.1 g/cm³. Three alloys have single-phase disordered body-centered cubic (bcc) crystal structures and three other alloys contain two bcc nanophases with very close lattice parameters. The alloys have high hardness, in the range from H _v = 4.0 GPa to 5.8 GPa, and compression yield strength, σ _0.2 = 1280 MPa to 2035 MPa, depending on the composition. Some of these refractory HEAs show considerably improved high temperature strengths relative to advanced Ni-based superalloys. Compressive ductility of all the alloys is limited at room temperature, but it improves significantly at 800°C and 1000°C.     

Theoretical study of phase stability in Ni-Al and Ni-Ti alloys

The thermodynamic stability of the bcc and fcc based ordered phases in Ni-Ti and Ni-AI has been studied with a highly accurate first-principles electronic structure method. The occurrence of a martensitic transformation in Ni-AlB2 ordered intermetallic alloys is discussed with relation to the existence of intermediate structures between bcc and fcc based phases. It is shown that closely related ordered structures can exist on fcc and bcc lattices in the composition range where the transformation occurs. The Ni-rich side of the Ni-Al phase diagram has been computed, and a comparison with a recent assessment is made. In addition, the rather unusual appearance of the NiTi B2 ordered structure in the phase diagram is discussed. This paper was presented at the International Phase Diagram Prediction Symposium sponsored by the ASM/MSD Thermodynamics and Phase Equilibria Committee at Materials Week, October 21–23,1991, in Cincinnati, Ohio. This symposium was organized by John Morral, University of Connecticut, and Philip Nash, Illinois Institute of Technology.     

Theoretical study of phase stability in Ni-Al and Ni-Ti alloys

The thermodynamic stability of the bcc and fcc based ordered phases in Ni-Ti and Ni-AI has been studied with a highly accurate first-principles electronic structure method. The occurrence of a martensitic transformation in Ni-AlB2 ordered intermetallic alloys is discussed with relation to the existence of intermediate structures between bcc and fcc based phases. It is shown that closely related ordered structures can exist on fcc and bcc lattices in the composition range where the transformation occurs. The Ni-rich side of the Ni-Al phase diagram has been computed, and a comparison with a recent assessment is made. In addition, the rather unusual appearance of the NiTi B2 ordered structure in the phase diagram is discussed. This paper was presented at the International Phase Diagram Prediction Symposium sponsored by the ASM/MSD Thermodynamics and Phase Equilibria Committee at Materials Week, October 21–23,1991, in Cincinnati, Ohio. This symposium was organized by John Morral, University of Connecticut, and Philip Nash, Illinois Institute of Technology.     

A direct method for the crystallography of martensitic transformation and its application to TiNi and AuCd

A simple and straightforward method to obtain a complete set of twining planes and habit planes of martensitic crystals by using the crystallographic data is proposed under the bulk strain energy minimization hypothesis. This method can also be used to obtain the diffraction pattern corresponding to martensitic transformation forming the invariant planes. Applications to the cubic→trigonal and cubic→monoclinic martensitic transformation are presented. The results well explain the morphological differences between R-phase in TiNi and ζ′₂ martensite in AuCd.