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.     

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.     

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.     

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.     

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.     

The correlation of microstructural development and thermal stability of mechanically alloyed multicomponent Fe-Co-Ni-Zr-B alloys

The microstructural evolution of multicomponent Fe_70-x-yCo_xNi_yZr₁₀B₂₀ (x = 0, 7, 21; y = 7, 14, 21, 28) alloys during mechanical alloying (MA) has been studied using XRD, SEM and TEM. Mixtures of elemental and pre-alloyed powders have been transformed initially into the single supersaturated bcc α-Fe solid solution phase for the alloys investigated. Subsequently, an amorphous phase has been obtained in Co-free alloys and Co-containing alloys with high Ni/Co ratios of 1 and 3. However, no amorphous phase was detected in another Co-containing alloy with a lower Ni/Co ratio (e.g. 0.33). The thermal stability of the as-milled powders has been investigated by a combination of DSC and the Pendulum magnetometer experiments. The DSC studies provide information on the thermodynamics and kinetics of crystallization of amorphous structure as a function of alloying contents. The Pendulum magnetometer studies reveal the phase transformation from nanocrystalline bcc α-Fe solid solution to amorphous structure during MA and the thermomagnetization behavior of the as-milled powder.     

Effect of minor Cu content on microstructure and mechanical property of NiTiCu bulk alloys fabricated by crystallization of metallic glass powder

Ultrafine-grained Ni_50.2−xTi_49.8Cu_x (x = 0, 2.5, 5, and 7.5) bulk shape memory alloys were fabricated by sintering of metallic glass (MG) powder and crystallization of amorphous phase. Non-isothermal crystallization kinetic analysis reveals that the crystallization mechanism of the synthesized x = 5 MG powder is typical interface-controlled two dimensional growth of nuclei followed by volume diffusion-controlled three dimensional growth of nuclei. In contrast, the crystallization mechanism of the synthesized x = 7.5 MG powder is typical volume diffusion-controlled three dimensional growth of nuclei in whole crystallization process. Correspondingly to different crystallization mechanisms, the two sintered and crystallized (SCed) bulk alloys have the same crystallized phases of bcc B2, fcc NiTi₂ phases, and monoclinic B19′, but these phases display different morphologies and distributions. The SCed x = 5 bulk alloy has a microstructure of bcc B2 matrix surrounding fcc NiTi₂ phase region, while the SCed x = 7.5 bulk alloy possesses discontinuous bcc B2 phase region. Consequently, the different crystallization mechanisms and microstructures causes extreme high yield strength and large plasticity for the SCed x = 5 bulk alloy and low strength and no plasticity for the SCed x = 7.5 bulk alloy. Especially, the yield strength of the SCed x = 5 bulk alloy is at least two times of that of the counterpart alloy prepared by melt solidification. The results provide a method fabricating high performance bulk alloys by tailoring crystallization mechanism using powder metallurgy.     

Stability of Ti–B–N solid solutions and the formation of nc-TiN/a-BN nanocomposites studied by combined ab initio and thermodynamic calculations

The ab initio density functional theory (DFT) has been used to calculate the properties of binary face-centered cubic (fcc)(NaCl)– and fcc (ZnS)–TiN and BN, hexagonal-close-packed (hcp)–TiB₂, and ternary Ti_1−xB_xN and TiB_xN_1−x solution phases. In order to study the stability of the ternary fcc(NaCl)–Ti_1−xB_xN and of the nitrogen-deficient fcc(NaCl)–TiB_xN_1−x solution, their mixing energies and the phase stability diagrams were constructed over the entire range of compositions. The results show that the fcc(NaCl)–Ti_1−xB_xN should decompose by spinodal mechanism, whereas the substoichiometric fcc(NaCl)–TiB_xN_1−x should decompose via nucleation and growth. The relatively large lattice mismatch between the fcc(NaCl)–TiN and fcc(NaCl)–BN, and the high lattice instability of the fcc(NaCl)–BN with respect to fcc(ZnS)–BN, suggests that the spinodal decomposition will, in the later stages, be accompanied by transformation of the fcc(NaCl)–BN to a more stable phase.     

Solid-state reactions upon mechanical alloying of an Fe32Al68 binary mixture

The sequence of solid-state reactions that occur upon mechanical alloying of powder mixtures of Al and Fe taken in an atomic ratio of 68: 32 has been studied by the methods of X-ray diffraction analysis, M?ssbauer spectrometry, and Auger spectrometry. Upon the formation of a nanocrystalline state (<10 nm), there takes place a mutual penetration of Al atoms into Fe and Fe atoms into Al particles. The rate of consumption of the fcc Al is substantially higher than that of the bcc Fe. The process of the mechanical alloying (MA) was found to be two-stage. At the first stage, up to 2 at % Fe is dissolved in the fcc Al, and an amorphous Fe₂₅Al₇₅ phase is formed in the interfaces, whose amount reaches 70 at % at the finish of the initial stage. In the interfaces of the ??-Fe phase, a disordered bcc phase of composition Fe₆₆Al₃₄ is formed, which contains up to 12 at % Al segregates. At the second stage, the amorphous phase crystallizes into an orthorhombic intermetallic compound Fe₂Al₅. The residual ??-Fe, bcc Fe₆₆Al₃₄, and segregated Al form a bcc phase of composition Fe₃₅Al₆₅.     

Modeling of phase stability of the fcc phases in the Ni–Ir–Al system using the cluster/site approximation method coupling with first-principles calculations

A combined CSA (cluster/site approximation)/FP (first-principles) calculation approach was employed to investigate the phase stability and thermodynamic properties of the face-centered cubic (fcc) phases of the Ni–Ir–Al system. For the constituent binaries of the Ni–Ir–Al system, enthalpies of formation of the Ni_xIr_1−x, Ni_xAl_1−x and Ir_xAl_1−x fcc compounds were calculated by first-principles approach at x = 0.75, 0.5 and 0.25 at 0 K, respectively. The pair exchange energies of the Ni–Ir and Al–Ir systems in the CSA model were obtained from FP calculated enthalpies of formation, while those for the Ni–Al binary were adopted from previous work. Thermodynamic model parameters of the fcc phases for the Ni–Ir–Al ternary system were then obtained from the constituent binaries via extrapolation. The calculated isothermal section at 1573 K is in good agreement with the experimental data within the uncertainties of the calculations and experiments.     

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.     

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.     

Structure and properties of cast and splat-quenched high-entropy Al–Cu–Fe–Ni–Si alloys

The effect of the composition and cooling rate of the melt on the microhardness, phase composition, and fine-structure parameters of as-cast and splat-quenched (SQ) high-entropy (HE) Al–Cu–Fe–Ni–Si alloys was studied. The quenching was performed by conventional splat-cooling technique. The cooling rate was estimated to be ~10⁶ K/s. Components of the studied HE alloys were selected taking into account both criteria for designing and estimating their phase composition, which are available in the literature and based on the calculations of the entropy and enthalpy of mixing, and the difference between atomic radii of components as well. According to X-ray diffraction data, the majority of studied Al–Cu–Fe–Ni–Si compositions are two-phase HE alloys, the structure of which consists of disordered solid solutions with bcc and fcc structures. At the same time, the Al_0.5CuFeNi alloy is single-phase in terms of X-ray diffraction and has an fcc structure. The studied alloys in the as-cast state have a dendritic structure, whereas, after splat quenching, the uniform small-grained structure is formed. It was found that, as the volume fraction of bcc solid solution in the studied HE alloys increases, the microhardness increases; the as-cast HE Al–Cu–Fe–Ni–Si alloys are characterized by higher microhardness compared to that of splat-quenched alloys. This is likely due to the more equilibrium multiphase state of as-cast alloys.     

Molecular dynamics study of the α–γ phase transition in Fe induced by shear deformation

Using classical molecular dynamics simulation and the Meyer–Entel interaction potential, we study phase transitions in a biphasic body-centered cubic (bcc)/face-centered cubic Fe crystallite under an applied shear strain. Our results show a strong temperature dependence. At low temperatures, both homogeneous and heterogeneous nucleation of the bcc phase is observed. At higher temperatures, but still below the equilibrium transition temperature, the bcc phase only grows by interface motion. Above the transition temperature, the bcc phase transforms homogeneously to the close-packed phase. In all cases studied, the unstrained system is stable and does not transform.     

Atomic-scale compositional characterization of a nanocrystalline AlCrCuFeNiZn high-entropy alloy using atom probe tomography

We have studied a nanocrystalline AlCrCuFeNiZn high-entropy alloy synthesized by ball milling followed by hot compaction at 600 °C for 15 min at 650 MPa. X-ray diffraction reveals that the mechanically alloyed powder consists of a solid-solution body-centered cubic (bcc) matrix containing 12 vol.% face-centered cubic (fcc) phase. After hot compaction, it consists of 60 vol.% bcc and 40 vol.% fcc. Composition analysis by atom probe tomography shows that the material is not a homogeneous fcc–bcc solid solution but instead a composite of bcc structured Ni–Al-, Cr–Fe- and Fe–Cr-based regions and of fcc Cu–Zn-based regions. The Cu–Zn-rich phase has 30 at.% Zn α-brass composition. It segregates predominantly along grain boundaries thereby stabilizing the nanocrystalline microstructure and preventing grain growth. The Cr- and Fe-rich bcc regions were presumably formed by spinodal decomposition of a Cr–Fe phase that was inherited from the hot compacted state. The Ni–Al phase remains stable even after hot compaction and forms the dominant bcc matrix phase. The crystallite sizes are in the range of 20–30 nm as determined by transmission electron microscopy. The hot compacted alloy exhibited very high hardness of 870 ± 10 HV. The results reveal that phase decomposition rather than homogeneous mixing is prevalent in this alloy. Hence, our current observations fail to justify the present high-entropy alloy design concept. Therefore, a strategy guided more by structure and thermodynamics for designing high-entropy alloys is encouraged as a pathway towards exploiting the solid-solution and stability idea inherent in this concept.     

Martensitic transformation and magnetic properties in Ni–Fe–Ga–Co magnetic shape memory alloys

Ni–Fe–Ga–Co is a promising system for magnetic shape memory alloy applications, due to its good ductility, mobile twin boundaries and high transformation temperatures. Unlike previous studies which focused on compositions with a Ga content of 27 at.%, here the martensitic transformation and magnetic properties over a large composition range of Ni_54−xFe₂₀Ga₂₆Co_x, Ni_54−xFe₁₉Ga₂₇Co_x, Ni_56−xFe₁₇Ga₂₇Co_x and Ni_54−xFe₁₈Ga₂₈Co_x (x = 0, 2, 4) are investigated. The martensitic transformation temperature T_m and the Curie temperature T_c can be tailored in a wide range by changing composition and heat treatment. A coupling of martensitic and magnetic transformations at ∼90 °C is found for Ni₅₂Fe₁₇Ga₂₇Co₄. Additionally, the effect of thermal cycling on the martensitic transformation of single- and two-phase Ni–Fe–Ga–Co alloys is discussed. Furthermore, an intermediate face-centered cubic phase induced by powderization and transformed into a body-centered cubic phase by aging is reported. The saturation magnetization is significantly decreased by powderization, while recovered by the subsequent aging.     

Correlation between composition and phase transformation temperatures in Ni–Mn–Ga–Co ferromagnetic shape memory alloys

The effect of Co addition on the phase transformation temperatures (martensitic and Curie point) and crystal structure of Ni–Mn–Ga–Co shape memory alloys has been investigated on (Ni_50.26Mn_27.30Ga_22.44)_100−xCo_x (x = 0, 2, 4, 6) alloys as well as on alloys having different Ni/Mn/Ga ratios and a fixed amount of Co. Alloying by Co affects the martensitic transformation temperature and the transformation enthalpy change mainly through the change on the valence electron concentration (e/a), but the transformation entropy is almost unaffected. On the other hand, the composition (analyzed through the e/a ratio) shows a different influence on the Curie temperature depending on the crystallographic phase (austenite or martensite) in which the magnetic ordering takes place. It is also reported that in Ni–Mn–Ga–Co alloys the Curie temperature of the martensitic phase is lower than that of the austenitic phase, opposite to what occurs in ternary Ni–Mn–Ga alloys.     

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.     

Effect of magnetron sputtering conditions and subsequent annealing on the structure and magnetic properties of Fe97−x Zr3N x films

X-ray diffraction analysis was used to study the structure of Fe_97?x Zr₃N _x thin films produced under different conditions of rf magnetron sputtering (on rotary and stationary substrates) and subsequent annealing. Either a single-phase structure, namely, a supersaturated bcc α-(FeN) solid solution, or a mixed structure that consists of two crystalline phases, such as a supersaturated bcc α-Fe(N) solid solution and an fcc Fe₄N nitride, and a Fe-based amorphous phase were shown to be formed in films deposited on either stationary or rotating substrate, respectively. As the annealing temperature increases, the content of nitrogen in the bcc phase decreases; the grain size of the bcc phase in the films deposited on rotating and stationary substrates increases from 8 to 14 nm and from 10 to 30 nm, respectively; the amount of the Fe₄N phase increases. The results of the study of the magnetic properties of the films are reported. The maximum saturation induction B _s reached is 1.8–1.9 T; the minimum coercive force H _c is 1 Oe. The optimum combination of the magnetic properties (B _s = 1.8–1.9 T and H _c = 1.5–1.8 Oe) is observed for the films deposited on the rotating substrate and subsequently annealed at 400°C.     

Microstructural evolution and formation of nanocrystalline intermetallic compound during surface mechanical attrition treatment of cobalt

Nanocrystalline intermetallic Co₃Fe₇ was produced on the surface of cobalt via surface mechanical attrition (SMA). Deformation-induced diffusion entailed the formation of a series of solid solutions. Phase transitions occurred depending on the atomic fraction of Fe in the surface solid solutions: from hexagonal close-packed (<4% Fe) to face-centered cubic (fcc) (4–11% Fe), and from fcc to body-centered cubic (>11% Fe). Nanoscale compositional probing suggested significantly higher Fe contents at grain boundaries and triple junctions than grain interiors. Short-circuit diffusion along grain boundaries and triple junctions dominate in the nanocrystalline intermetallic compound. Stacking faults contribute significantly to diffusion. Diffusion enhancement due to high-rate deformation in SMA was analyzed by regarding dislocations as solute-pumping channels, and the creation of excess vacancies. Non-equilibrium, atomic level alloying can then be ascribed to deformation-induced intermixing of constituent species. The formation mechanism of nanocrystalline intermetallic grains on the SMA surface can be thought of as a consequence of numerous nucleation events and limited growth.