Equilibrium crystallization and distribution coefficients of alloy components in ternary systems with continuous solid and liquid solutions

Features of equilibrium crystallization of alloys in a ternary system consisting of solid and liquid solutions of components A, B, and C with melting points related as t _C < t _A < t _B are investigated in detail. It is demonstrated that, in alloys of any composition, the distribution coefficients of components B and C are k _B > 1 and k _C < 1, respectively. For the component A, this characteristic, depending on the alloy composition, can be either larger or smaller than unity, and at temperature t _A , k _A = 1.     

On the Nonequilibrium Interface Kinetics of Rapid Coupled Eutectic Growth

Nonequilibrium interface kinetics (NEIK) is expected to play an important role in coupled growth of eutectic alloys, when solidification velocity is high and intermetallic compound or topologically complex phases form in the crystallized product. In order to quantitatively evaluate the effect of NEIK on the rapid coupled eutectic growth, in this work, two nonequilibrium interface kinetic effects, i.e., atom attachment and solute trapping at the solid–liquid interface, were incorporated into the analyses of the coupled eutectic growth under the rapid solidification condition. First, a coupled growth model incorporating the preceding two nonequilibrium kinetic effects was derived. On this basis, an expression of kinetic undercooling (?T _k), which is used to characterize the NEIK, was defined. The calculations based on the as-derived couple growth model show good agreement with the reported experimental results achieved in rapidly solidified eutectic Al-Sm alloys consisting of a solid solution phase (α-Al) and an intermetallic compound phase (Al₁₁Sm₃). In terms of the definition of ?T _k defined in this work, the role of NEIK in the coupled growth of the Al-Sm eutectic system was analyzed. The results show that with increasing the coupled growth velocity, ?T _k increases continuously, and its ratio to the total undercooling reaches 0.32 at the maximum growth velocity for coupled eutectic growth. Parametric analyses on two key alloy parameters that influence ?T _k, i.e., interface kinetic parameter (μ _i ) and solute distribution coefficient (k _e ), indicate that both μ _i and k _e influence the NEIK significantly and the decrease of either these two parameters enhances the NEIK effect.     

Effect of heat treatment on the superplasticity of magnesium alloys

A necessary microstructural condition for the manifestation of the effect of superplasticity in alloys is a small grain size (d < 10 μm). The ingots of commercial magnesium alloys have a very coarse cast structure with d > 100 μm. We have studied the regimes of heat treatment of such materials in AZ91, AE42, QE22, and ZRE1 alloys with a purpose of obtaining a fine-grained structure. The optimum temperature of overaging of quenched magnesium alloys lies between 300 and 350°C. After hot pressing of heat-treated alloys, the average grain size is 6.4 (AZ91), 6.2 (AE42), 1.2 (ZRE1), and 0.7 (QE22) μm. The best characteristics of superplasticity are manifested by the ZRE1 and QE22 alloys with a relative elongation of 750% and strain-rate sensitivity m = 0.75 at T = 420°C and strain rate \(\dot \varepsilon \) = 3 × 10^?4 s^?1. Under these conditions, the AZ91 and AE42 alloys have δ ≤ 260% and m = 0.45.     

Effect of the severe plastic deformation temperature on the diffusion properties of the grain boundaries in ultrafine-grained metals

A model is proposed to explain the effect of the severe plastic deformation (SPD) temperature on the diffusion properties of the grain boundaries in ultrafine-grained (UFG) metals and alloys. It is shown that an increase in the SPD temperature in UFG metals leads to an increase in the activation energy of grainboundary diffusion from (3–5)k _B T _m, which corresponds to the diffusion parameters of nonequilibrium grain boundaries, to (8–10)k _B T _m, which corresponds to the diffusion parameters of equilibrium grain boundaries (k _B is the Boltzmann constant, T _m is the melting temperature). The dependence of the activation energy of grain-boundary diffusion on the SPD temperature is found to be determined by the kinetics of the competing processes of defect accumulation at grain boundaries and the diffusion accommodation of defects.     

Kinetics study on non-isothermal crystallization of Cu<Subscript>50</Subscript>Zr<Subscript>50</Subscript> metallic glass

In this paper, the crystallization kinetics of melt-spun Cu₅₀Zr₅₀ amorphous alloy ribbons has been investigated using differential scanning calorimetry. Moreover, the Kissinger, Ozawa and isoconversional approaches have been used to obtain the crystallization kinetic parameters. As shown in the results, the onset crystallization activation energy E _x is less than crystallization peak activation energy E _p. The local activation energy E _α increases at the crystallized volume fraction α < 0.2 and decreases at the rest, which suggests that crystallization process is increasingly hard (α < 0.2) at first, after which it become increasingly easy (α > 0.2). The nucleation activation energy E _nucleation is greater than grain growth activation energy E _growth, indicating that the nucleation is harder than growth. In terms of the local Avrami exponent n(α), it lies between 1.27 and 8, which means that crystallization mechanism in the non-isothermal crystallization is interface-controlled one- two- or three-dimensional growth with different nucleation rates.     

Microstructure and High Temperature Impression Creep Properties of Mg–3Ca–xZr (x = 0.3, 0.6, 0.9 wt%) Alloys

The current study has investigated the influence of zirconium (Zr) addition to Mg–3Ca–xZr (x = 0.3, 0.6, 0.9 wt%) alloys prepared using argon arc melting on the microstructure and impression properties at 448–498 K under constant stress of 380 MPa. Microstructural analysis of as-cast Mg–3Ca–xZr alloys showed grain refinement with Zr addition. The observed grain refinement was attributed to the growth restriction effect of Zr in hypoperitectic Mg–3Ca–0.3 wt% Zr alloys. Heterogeneous nucleation of α-Mg in properitectic Zr during solidification resulted in grain refinement of hyperperitectic Mg–3Ca–0.6 wt% Zr and Mg–3Ca–0.9 wt% Zr alloys. The hardness of Mg–3Ca–xZr alloys increased as the amount of Zr increased due to grain refinement and solid solution strengthening of α-Mg by Zr. Creep resistance of Mg–3Ca–xZr alloys increased with the addition of Zr due to solid solution strengthening of α-Mg by Zr. The calculated activation energy (Q_a) for Mg–3Ca samples (131.49 kJ/mol) was the highest among all alloy compositions. The Q_a values for 0.3, 0.6 and 0.9 wt% Zr containing Mg–3Ca alloys were 107.22, 118.18 and 115.24 kJ/mol, respectively.     

Microstructure of amorphous electrodeposited Co-Ni-W films

The phase composition of electrodeposited films of (Co_{100 ? x} -Ni _x )_{100 ? y} W _y alloys (x = 0–100 at % Ni, y = 0–30 at % W), the microstructures of amorphous films of this system on the submicrometer and nanometer scales, and the mechanism of their nucleation and growth are studied. X-ray diffraction analysis demonstrates that, as the tungsten concentration increases, the transition from a crystalline into an amorphous state in the films based on Co-W alloys occurs through a supersaturated hcp solid solution, whereas this transition in the films based on Ni-W alloys occurs through an fcc structure. Heterophase states consisting of a mixture of hcp and fcc structures are observed in the composition range x = 30–80 at % Ni, and, at concentrations higher than 12–14 at % W, an amorphous phase is also observed. A homogeneous amorphous phase forms at a refractory-metal content of 19–20 at % or more. Transmission and scanning electron microscopies show that the amorphous Co-W, Ni-W, and Co-Ni-W films have a network structure. The laws of the variation of the network microstructure with the chemical composition of the amorphous films are established and explained in the framework of the island model of thin film nucleation and growth.     

Structural Features of Al–Hf–Sc Master Alloys

Microstructural features of new master alloys of the Al–Hf–Sc system with metastable aluminides with a cubic lattice identical to the lattice of a matrix of aluminum alloys are investigated using optical microscopy, scanning electron microscopy, and electron probe microanalysis. Binary and ternary alloys are smelted in a coal resistance furnace in graphite crucibles in argon. Alloys Al–0.96 at % Hf (5.98 wt % Hf) and Al–0.59 at % Hf (3.77 wt % Hf) are prepared with overheating above the liquidus temperature of about 200 and 400 K, respectively. Alloys are poured into a bronze mold, the crystallization rate in which is ~10³ K/s. Metastable Al₃Hf aluminides with a cubic lattice are formed only in the alloy overheated above the liquidus temperature by 400 K. Overheating of ternary alloys, in which metastable aluminides Al _n (Hf_1–xSc _x ) formed, is 240, 270, and 370 K. Depending on the Hf-to-Sc ratio in the alloy, the fraction of hafnium in aluminides Al _n (Hf_1–xSc _x ) varies from 0.46 to 0.71. Master alloys (at %) Al–0.26Hf–0.29Sc and Al–0.11Hf–0.25Sc (wt %: Al–1.70Hf–0.47Sc and Al–0.75Hf–0.42Sc) have a fine grain structure and metastable aluminides of compositions Al _n (Hf_0.58Sc_0.42) and Al _n (Hf_0.46Sc_0.54), respectively. Sizes of aluminides do not exceed 12 and 7 μm. Their lattice mismatch with a matrix of aluminum alloys is smaller than that for Al₃Sc. This makes it possible to assume that experimental Al–Hf–Sc master alloys manifest a high modifying effect with their further use. In addition, the substitution of high-cost scandium with hafnium in master alloys can considerably reduce the consumption of the latter.     

Elasticity of Ni<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>W<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript> (<Emphasis Type="Italic">x</Emphasis> ≤ 0.1875) Alloys from First Principles Calculations

The elastic properties of Ni _x W_1?x alloys up to x = 0.1875 have been determined from first principles calculations. We have used stress–strain relationships to calculate the C _ij elastic coefficients and the Voigt–Reuss–Hill approximations to determine the bulk and shear moduli of polycrystals. The W alloying increases the compression modulus while the shear modulus remains almost constant. Furthermore, the W alloying has a minor effect on the elastic anisotropy and, therefore, on its contribution to the indentation modulus.     

The effect of the aging period on the martensitic transformation and kinetic characteristic of at % Cu<Subscript>68.09</Subscript>Al<Subscript>26.1</Subscript>Ni<Subscript>1.54</Subscript>Мn<Subscript>4.27</Subscript> shape memory alloy

In this work, the effect of aging period on the characteristic transformation temperatures, thermodynamic parameters and structural variations of CuAlNiMn shape memory alloys were investigated. Aging was performed at above the austenite finish temperature of the un-aged specimen (120°C) for six different retention times, namely 1h, 2h, 3h, 4h, 5h and 6h. The changes in the transformation temperatures were examined by differential scanning calorimetry at different heating/cooling rates. The aging period was found to have an effect on the characteristic austenite and martensite transformation temperatures and thermodynamic parameters such as the enthalpy and entropy of alloys. High-temperature order-disorder phase transitions were determined using a differential thermal analysis, which showed that all the un-aged and aged specimens had an A2 → B2, B2 → L2₁ and an L2₁ → 9R, 18R transition. The structural analysis of the un-aged and aged specimens was performed through X-ray diffraction measurements at room temperature. The intensities of the diffraction peaks varied according to the aging time.     

Quasi-steady-state characteristics of solidification of alloys made from VT3-1 alloy during vacuum arc remelting

Numerical calculations are presented of the depth of a liquid pool, time of local solidification, and temperature gradient in the axial region of an ingot during vacuum arc remelting (VAR) of VT3-1 titanium alloy (Ti-6.5Al-2.5Mo-1.5Cr-0.5Fe-0.3Si) corresponding to quasi-equilibrium conditions. Calculations were carried out for ingots of diameters D = 400, 800, and 1200 mm in the ranges of mass melting rates \(\dot M\) = 0.5–12.0, 0.5–35.0, and 1.5–30.0 kg/min, respectively. It is found that the depth of the liquid pool (H, mm) linearly increases with increasing \(\dot M\) and is virtually independent of D in the conditions under consideration and, therefore, can be presented as a unique dependence H = 66.63 \(\dot M\) + 71.91. A finite depth of the liquid pool at a zero mass melting rate is associated with that the state \(\dot M\) = 0 corresponds to a finite current of the arc, which holds a part of metal in the liquid state. It is shown that the time of local solidification depending on \(\dot M\) has a minimum associated with various physical processes, which determine the kinetics of the solidification front at small and large solidification rates. In relative units, which correspond to a minimum, these dependences are identical for all considered diameters of the ingot. In addition, based on autoradiographic investigations of solidification of VT3-1 alloy under the VAR conditions, critical values of the temperature gradient (G) and velocity of motion of the crystallization front (v) along the ingot axis, which determine the passage from the column structure to the equiaxial one, are determined. Starting from these results, the plots v(G) are constructed, which turn out to be very useful in the development of remelting modes, excluding the appearance of some type of liquation process. It is revealed that at the specified ingot diameter, the dependence v(G) is decreasing and, at the specified temperature gradient, the velocity of motion of the solidification front decreases as D increases, which indicates an increase in D for the smelting of the ingots of highly-doped alloys.     

Solidification Reaction Sequence of Co-Rich Nb-Al-Co Alloys

The freezing reaction sequence of Co-rich Nb-Al-Co ternary alloys with emphasis on the formation of Laves and Heusler phases has been examined. For Co-rich alloys, the solidification reaction sequence is observed as primary freezing of α-Co and CoAl phases, subsequent [Co + C36] and [CoAl + C36] eutectics, and the final ternary eutectic reaction [L → α-Co + C36 + CoAl]. The compositions of solidified α-Co and C36 phases agree with the corresponding vertices of the tie-triangle at the solidus temperatures. When the Nb concentration is over 20 at. pct in Co-rich alloys, the quasi-peritectic reaction [L + Co₂AlNb → C36 + CoAl] does not occur as equilibrium prediction. The formation of C36 and CoAl phases occurs through solid precipitation and must be distinguished from a solidification reaction.     

Evaluation of Solid-Solution Hardening in Several Binary Alloy Systems Using Diffusion Couples Combined with Nanoindentation

Analysis of solid-solution hardening (SSH) in alloys requires the synthesis of large composition libraries and the measurement of strength or hardness from these compositions. Conventional methods of synthesis and testing, however, are not efficient and high-throughput approaches have been developed in the past. In the present study, we use a high-throughput combinatorial approach to examine SSH at large concentrations in binary alloys of Fe-Ni, Fe-Co, Pt-Ni, Pt-Co, Ni-Co, Ni-Mo, and Co-Mo. The diffusion couple (DC) method is used to generate concentration (c) gradients and the nanoindentation (NI) technique to measure the hardness (H) along these gradients. The obtained H –c profiles are analyzed within the framework of the Labusch model of SSH, and the \( c^{2/3} \) dependence of H predicted by the model is found to be generally applicable. The SSH behavior obtained using the combinatorial method is found to be largely consistent with that observed in the literature using conventional and DC-NI methods. This study evaluates SSH in Fe-, Ni-, Co-, and Pt-based binary alloys and confirms the applicability of the DC-NI approach for rapidly screening various solute elements for their SSH ability.     

Enthalpy of mixing of liquid Cu-Ti-Zr alloys

The enthalpy of mixing of liquid Cu-Ti-Zr ternary alloys is studied by high-temperature isoperibolic calorimetry at 1873 K along three ray sections characterized by the ratios x _Zr: x _Cu = 3: 7, x _Ti: x _Cu = 3: 7, and x _Zr: x _Ti = 1 at x _Cu = 1?0.4. The isotherm of the integral enthalpy of mixing of these melts is described in terms of the Redlich-Kister-Muggianu model. Along with the substantial contributions of binary copper-titanium and copper-zirconium interactions, the contribution of a ternary interaction to the enthalpy of mixing of liquid Cu-Ti-Zr alloys also exists. The first partial enthalpies of mixing of Ni, Al, Si, Sn, and Y with the melts are studied to determine the character of the interaction between the ternary Cu-Ti-Zr melts and metal additions that facilitate amorphization upon melt quenching. The introduction of these metals into the ternary melts is shown to increase their thermodynamic stability.     

Elastic Properties,Thermal Expansion Coefficients,and Electronic Structures of Mg and Mg-Based Alloys

Ab-initio density functional theory (DFT) calculations were performed to study alloying effects on hcp Mg. The alloy solid solution strengthening represented by bond strength enhancement in alloys, elastic properties, thermal expansion coefficients, and electronic structures of Mg-based alloys was investigated. Results show that alloying additions with sp-metal Al and rare earth (RE) Y are capable of increasing the bond strength, with the addition of Y achieving a better effect. The bond strength enhancement due to an RE Y addition is associated with a hybridization between the d-orbital of Y and the p-orbital of the Mg atoms near the Fermi energy, and this was consistent with the electron localized function (ELF) evaluations showing that more localized and stronger covalent bonds are formed between Y and Mg atoms. It is also found that alloying additions of Al, Zn, and Y are not capable of increasing elastic coefficients and moduli, indicating that bond strength enhancement could play a major role in alloy solid solution strengthening in Mg-based alloys. Possible reasons for the elastic properties accompanying the alloying addition are given from the electronic point of view. Furthermore, from the calculated negative Cauchy pressure (C ₁₃ – C ₄₄ < 0), it is concluded that the chemical bonds between Y and Mg atoms show angular characteristics.     

The Friction Stress of the Hall–Petch Relationship of Pure Mg and Solid Solutions of Al,Zn, and Gd

Temperature and solute concentration effects on the friction stress, σ_o, of cast (texture-free) polycrystals of pure Mg, and of Mg-Al, -Zn and -Gd binary solid solutions are discussed using phenomenological arguments. The temperature effects on the pure metal suggest that σ_o relates to the ratio between the CRSS of prism and basal slip, against early suggestions that it should only relate to the CRSS for basal slip. Solid solution softening upon prism slip accounts for the minima in σ_o at ~ 0.5 at. pct in Mg-Zn and Mg-Gd alloys. In the concentrated alloys, solute-specific hardening effects upon slip and twinning lead to diverging behaviors: in Mg-Al and Mg-Zn, σ_o remains below that of pure Mg. Strong short-range order by Gd leads to a steep monotonic increase, and to a value larger in compression than in tension due to the activation of {10-11} twinning at high concentrations. The negative σ_o of the dilute Mg-Zn alloys is an artifact created by the tension/compression asymmetry stemming from the polar character of {10-12} twinning.     

Morphological Stability of <Emphasis Type="Italic">δ</Emphasis>-Ferrite/<Emphasis Type="Italic">γ</Emphasis> Interphase Boundary in Carbon Steel

The morphological changes of the δ-ferrite/γ interphase boundary have been observed in situ with a high-temperature confocal scanning laser microscope (HTCSLM) during δ/γ transformations (δ → γ and γ → δ) of Fe-0.06 wt pct C-0.6 wt pct Mn alloy, and a kinetic equation of morphological stability of δ-ferrite/γ interphase boundary has been established. Thereafter, the criterion expression for morphological stability of δ-ferrite/γ interphase boundary was established and discussed, and the critical migration speeds of δ-ferrite/γ interphase boundaries are calculated in Fe-C, Fe-Ni, and Fe-Cr alloys. The results indicate that the δ-ferrite/γ interphase boundary is very stable and nearly remains absolute planar all the time during γ → δ transformation in Fe-C alloy. The δ-ferrite/γ interphase boundary remains basically planar during δ → γ transformation when the migration speed is lower than 0.88 μm/s, and the interphase boundary will be unstable and exhibit a finger-like morphology when the migration speed is higher than 0.88 μm/s. The morphological stability of δ-ferrite/γ interphase boundary is primarily controlled by the interface energy and the solute concentration gradient at the front of the boundary. During the constant temperature phase transformation, an opposite temperature gradient on both sides of δ-ferrite/γ interphase boundary weakens the steady effect of the temperature gradient on the boundary. The theoretical analysis of the morphological stability of the δ-ferrite/γ interphase boundary is coincident with the observed experimental results utilizing the HTCSLM. There is a good agreement between the theoretical calculation of the critical moving velocities of δ-ferrite/γ interphase boundaries and the experimental results.     

Structural Changes of High-Temperature Nickel Alloy Containing Rhenium and Lanthanum on Heat Treatment

The properties of high-temperature nickel alloys for manufacturing depend on the thermal stability of the structure, the particle size, the shape, the quantity of strengthening γ' phase, and the strength of the γ solid solution. Such alloys are strengthened by the addition of rhenium and lanthanum. In the present work, the structure and phase composition of high-temperature nickel alloy with added rhenium (0.4 at %) and lanthanum (0.006 at %) are qualitatively and quantitatively investigated. The methods employed are transmission diffraction electron microscopy and scanning electron microscopy. The alloy structure is considered in three states: after directed crystallization (the initial state, sample 1); after directed crystallization, annealing at 1150°C for 1 h, and annealing at 1100°C for 480 h (sample 2); and after directed crystallization, annealing at 1150°C for 1 h, and annealing at 1100°C for 1430 h (sample 3). Primary and secondary phases are observed in the superalloy. The primary phases are γ' and γ. They form the structure of the alloy and are present in the form of γ' quasi-cuboids separated by γ layers. The secondary phases due to the presence of rhenium and lanthanum are β NiAl, AlRe, NiAl₂Re, σ, χ, and Ni₃La₂. The secondary phases seriously disrupt the structure of the γ + γ' quasi-cuboids. The rhenium and lanthanum do not uniformly fill the whole alloy volume, but only appear in local sections. Therefore, in all three states of the alloy, only some volume of γ + γ' quasicuboids is disrupted. Analysis of the secondary phases’ morphology shows that the σ particles are thin needles, whereas the Ni₃La₂ particles have internal structure with characteristic contrast and are relatively thick. Interestingly, the σ phase and Ni₃La₂ are deposited at the same locations. The introduction of rhenium and lanthanum changes the phase composition of the alloy, suppressing the formation of γ phase. The particles of secondary phase are localized in individual sections of the alloy with specific periodicity. The secondary phases are refractory: the melting point is about 1600°C for β phase, 2600°C for σ phase; and 2800° for χ phase. Thanks to the formation of refractory secondary phases and their periodic distribution in the structure, the strength of the superalloy with added rhenium and lanthanum is increased.     

Effect of Slag Composition on the Crystallization Kinetics of Synthetic CaO-SiO<Subscript>2</Subscript>-Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-MgO Slags

The crystallization kinetics of CaO-SiO₂-Al₂O₃-MgO (CSAM) slags was studied with the aid of single hot thermocouple technique (SHTT). Kinetic parameters such as the Avrami exponent (n), rate coefficient (K), and effective activation energy of crystallization (E _A ) were obtained by kinetic analysis of data obtained from in situ observation of glassy to crystalline transformation and image analysis. Also, the dependence of nucleation and growth rates of crystalline phases were quantified as a function of time, temperature, and slag basicity. Together with the observations of crystallization front, they facilitated establishing the dominant mechanisms of crystallization. In an attempt to predict crystallization rate under non-isothermal conditions, a mathematical model was developed that employs the rate data of isothermal transformation. The model was validated by reproducing an experimental continuous cooling transformation diagram purely from isothermal data.     

Kinetics and contact interaction mechanism of titanium carbonitride with the Ni–Mo melt

Kinetic features and the contact interaction mechanism of hot-pressed (residual porosity <3%) of titanium carbonitride samples of various compositions with the Ni–25% Mo melt (t = 1400–1500°C, τ = 0.1–25 h) are investigated by electron-probe microanalysis. It is established that the dissolution rate of the interstitial refractory phase (IRP) in the Ni–Mo melt lowers in a series TiC–TiC_0.7N_0.3–TiC_0.5N_0.5, while the degree of process incongruence rises. The composition of intermediate interaction products varies correspondingly. The peculiarities of formation of the most important phase component of the TiCN cermets—K-phase of the Ti_1–nMo_nC_x composition—are revealed. It is proven by the local mass spectrometry method that the K-phase has a carbide nature. It is also established that it is formed only if the initial titanium carbonitride TiC_1–xN_x is sufficiently enriched with carbon (x ≤ 0.5). It is stated that the K-phase is an actual basis of all cermets with the Ni–Mo binder. Its bulk concentration in alloys exceeds the content of the nominal alloy base by a factor of several times. The chemical substantiation of the selection of titanium carbonitride of the TiC_0.5N_0.5 composition as an optimal “precursor” of the K-phase, which is formed during liquid-phase sintering of TiCN cermets, is given originally.