Effect of alloying elements on the elastic properties of Mg from first-principles calculations

The influence of different alloying elements on the lattice parameters and elastic properties of Mg solid solution has been studied using first-principles calculations within the generalized gradient approximation. The solute atoms employed herein are Al, Ba, Ca, Cu, Ge, K, Li, Ni, Pb, Si, Y and Zn. A supercell consisting of 35 atoms of Mg and one solute atom is used in the current calculations. A good agreement between calculated and available experimental data is obtained. Lattice parameters of Mg–X alloys are found to be dependent on the atomic radii of the solute atoms. A correlation between the bulk modulus of Mg–X alloys and the nearest-neighbor distance between Mg and X is shown. Addition of solute atoms belonging to the s-block and p-block of the periodic table results in a lower bulk moduli than d-block elements. A strong dependence of the elastic modulus of Mg–X alloys on the elastic properties of the solute atoms is also observed. Using the bulk modulus/shear modulus ratio (B/G), the change in the ductility of Mg due to the addition of the solute atom is briefly described. Linear regression coefficients for the elastic constants of each of the alloys are obtained as a tool for predicting the trend in the elastic properties of Mg as a function of concentration of the solute atoms.     

Recovery,recrystallization, grain growth and phase stability of a family of FCC-structured multi-component equiatomic solid solution alloys

The equiatomic high-entropy alloy FeNiCoCrMn is known to crystallize as a single phase with the face-centered cubic (FCC) crystal structure. To better understand this quinary solid solution alloy, we investigate various binary, ternary and quaternary alloys made from its constituent elements. Our goals are twofold: (i) to investigate which of these lower order systems also form solid solution alloys consisting of a single FCC phase, and (ii) to characterize their phase stability and recovery, recrystallization, and grain growth behaviors. X-ray diffraction (XRD) and scanning electron microscopy with backscattered electron images showed that three of the five possible quaternaries (FeNiCoCr, FeNiCoMn and NiCoCrMn), five of the ten possible ternaries (FeNiCo, FeNiCr, FeNiMn, NiCoCr, and NiCoMn), and two of the ten possible binaries (FeNi and NiCo) were single-phase FCC solid solutions in the cast and homogenized condition, whereas the others either had different crystal structures or were multi-phase. The single-phase FCC quaternary, FeNiCoCr, along with its equiatomic ternary and binary subsidiaries, were selected for further investigations of phase stability and the thermomechanical processing needed to obtain equiaxed grain structures. Only four of these subsidiary alloys—two binaries (FeNi and NiCo) and two ternaries (FeNiCo and NiCoCr)—were found to be single-phase FCC after rolling at room temperature followed by annealing for 1 h at temperatures of 300–1100 °C. Pure Ni, which is FCC and one of the constituents of the quinary high-entropy alloy (FeNiCoCrMn), was also investigated for comparison with the higher order alloys. Among the materials investigated after thermomechanical processing (FeNiCoCr, FeNiCo, NiCoCr, FeNi, NiCo, and Ni), FeNiCo and Ni showed abnormal grain growth at relatively low annealing temperatures, while the other four showed normal grain growth behavior. The grain growth exponents for all five of the equiatomic alloys were found to be ∼0.25 (compared to ∼0.5 for unalloyed Ni), suggesting that solute drag may control grain growth in the alloys. For all five alloys, as well as for pure Ni, microhardness increases as the grain size decreases in a Hall-Petch type way. The ternary alloy NiCoCr was the hardest of the alloys investigated in this study, even when compared to the quaternary FeNiCoCr alloy. This suggests that solute hardening in equiatomic alloys depends not just on the number of alloying elements but also their type.     

Impacts of Microalloying Elements on the Hardening β"-Phase in Automotive AlMgSi Alloys

Microalloying elements play a crucial role in mechanical properties and phase stability of metallic alloys. In this work, we employ first-principles calculations and atomic-scale high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) to find promising microalloying elements that will improve the stability and properties of β"/Al interface and β" phase in Al-Mg-Si alloys. First, we define a substitution energy for evaluating the stability of β" phase and β"/Al interface with microalloying elements doped. Then, experiments of HAADF-STEM imaging are carried out to verify the calculational results. Next, using the most stable structures doped with microalloying elements, the mechanical properties of the β" bulk and the β"/Al interface were calculated and analyzed. At last, we have figured out the effects of all considered microalloying elements and obtained a rule that the stable occupancy of solute atoms is related to their own radius and the radius of Mg, Si, and Al. These findings will provide some theoretical basis for future microalloying strategies of Al-Mg-Si alloys.     

Theoretical design and distribution control of precipitates and solute elements in Al−Zn−Mg−Cu alloys with heterostructure

In order to simultaneously improve strength and formability, an analytical model for the concentration distribution of precipitates and solute elements is established and used to theoretically design and control the heterogeneous microstructure of Al−Zn−Mg−Cu alloys. The results show that the dissolution of precipitates is mainly affected by particle size and heat treatment temperature, the heterogeneous distribution level of solute elements diffused in the alloy matrix mainly depends on the grain size, while the heat treatment temperature only has an obvious effect on the concentration distribution in the larger grains, and the experimental results of Al−Zn−Mg−Cu alloy are in good agreement with the theoretical model predictions of precipitates and solute element concentration distribution. Controlling the concentration distribution of precipitates and solute elements in Al−Zn−Mg−Cu alloys is the premise of accurately constructing heterogeneous microstructure in micro-domains, which can be used to significantly improve the formability of Al−Zn−Mg−Cu alloys with a heterostructure.     

Formation and growth mechanism of TiC crystal in TiC_p/Ti composites

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Solid solution strengthening and damping capacity of Mg−Ga binary alloys

The mechanical behaviors and damping capacities of the binary Mg?Ga alloys with the Ga content ranging from 1 to 5 wt.% were investigated by means of optical microscope (OM), scanning electron microscope (SEM), X-ray diffraction (XRD), hardness test, tensile test and dynamic mechanical analyzer (DMA). The hardness (HV_0.5) increases with the increase of Ga content, which can be described as HV_0.5=41.61+10.35c, and the solid solution strengthening effect Δσ_s of the alloy has a linear relationship with cⁿ, where c is the molar fraction of solute atoms and n=1/2 or 2/3. Ga exhibits a stronger solid solution strengthening effect than Al, Zn or Sn due to the large atomic radius difference and the modulus mismatch between Ga and Mg atoms. The addition of Ga makes the Mg?Ga alloys have better damping capacity, and this phenomenon can be explained by the Granato?Lücke dislocation model. The lattice distortion and the modulus mismatch generated because of the addition of Ga increase the resistance to motion of the dislocation in the process of swinging or moving, and thus the better damping capacity is acquired.     

Classification of the role of microalloying elements in phase decomposition of Al based alloys

The fundamental role of microalloying elements in several aluminium alloys such as Al–Cu, Al–Li–Cu and Al–Cu–Mg has been investigated using a Monte Carlo computer simulation. All the utilized simulation parameters, e.g. pair interactions between same atoms species, between different atom species and between an atom and a vacancy, were derived from known thermodynamic or kinetic quantities. A small addition of Mg to Al–Cu alloys exhibits a strong tendency to form Mg/Cu/Vacancy complexes in the atom configurations, which is more remarkably revealed in Al–Li–Cu alloys. The combined addition of Ag or Si with Mg significantly increases the number of Mg/Cu/Vacancy complexes in Al–Cu–Mg alloys. From the comparison with experimentally reported results, these complexes are reasonably regarded as an effective heterogeneous nucleation site for GP zones, GPB zones and/or the Ω phase. The utilized simulation model, furthermore, permits the role of microalloying elements to be well classified in terms of the characteristic features of each element.     

Study on Influence of Solute Atoms on Grain Boundary Character Distribution with Internal Friction Method

Based on the relationship between parameters of grain boundary internal friction peak(GBP)andgrain boundary character distribution(GBCD),and the internal friction results of Al-Mg,Al-Ga,Al-Cu andAl-Zn alloys,the addition of different kinds of solute atoms has different effects on GBCD.Among them,Mg atoms are able to concentrate and stabilize GBCD in AI-Mg alloys.The origin of these effects of soluteatoms on GBCD is also discussed.     

First-principles prediction of yield stress for basal slip in Mg–Al alloys

The finite-temperature yield stress of Mg–Al alloys undergoing basal slip is investigated using a recently developed parameter-free solute strengthening model. The model takes input from first-principles calculations of the dislocation/solute interaction energy and evaluates the solute strengthening due to fluctuations in solute concentration, taking into account the correlation of these fluctuations as a function of dislocation roughening. Due to the wide partial separation of the Mg basal edge dislocation, a smaller roughening is required to decorrelate the solute fluctuations in the partials compared to that required to decorrelate the fluctuations in the “far field”. As a consequence, the dislocation has two stable configurations in the random field of solutes, corresponding to “short-range” and “long-range” solute interactions. The configuration of the “short-range” interactions control the strength at low temperatures or high stress, whereas the “long-range” interactions control the strength at higher temperatures or lower stresses. Predictions of the model are in very good agreement with experiments over a wide range of solute concentrations and temperature. In particular, the model naturally predicts the “plateau stress” observed at high temperatures, which is attributable to the “long-range” solute interactions.     

Bi掺杂Mg2Si的稳定性,弹性性能和电子结构的第一性原理计算

从动力学角度研究合金元素Bi对Mg_2Si的掺杂情况,采用CASTEP中基于密度泛函理论的第一性原理方法分析了合金元素Bi掺杂Mg_2Si的占位情况、结构稳定性、弹性性能和电子结构。计算结果表明:Mg_2Si、Mg-7Si_4Bi、Mg_8Si_3Bi均可稳定存在于体系中,Bi原子优先占据Mg_2Si晶体中Si原子位置,Mg_8Si_4Bi间隙固溶体不稳定存在体系中;Mg_Si、Mg_7Si_4Bi、Mg_8Si_3Bi均为脆性相,掺杂合金元素Bi后可以提高Mg_Si的韧性、合金化能力和导电性;Mg_2Si的成键本质是金属键、共价键和离子键的结合,Bi原子掺杂Mg2Si后产生Bi-Si和Bi-Mg键合作用,有利于提高体系的稳定性。     

Solute–vacancy binding in aluminum

Previous efforts to understand solute–vacancy binding in aluminum alloys have been hampered by a scarcity of reliable, quantitative experimental measurements. Here, we report a large database of solute–vacancy binding energies determined from first-principles density functional calculations. The calculated binding energies agree well with accurate measurements where available, and provide an accurate predictor of solute–vacancy binding in other systems. We find: (i) some common solutes in commercial Al alloys (e.g., Cu and Mg) possess either very weak (Cu), or even repulsive (Mg), binding energies. Hence, we assert that some previously reported large binding energies for these solutes are erroneous. (ii) Large binding energies are found for Sn, Cd and In, confirming the proposed mechanism for the reduced natural aging in Al–Cu alloys containing microalloying additions of these solutes. (iii) In addition, we predict that similar reduction in natural aging should occur with additions of Si, Ge and Au. (iv) Even larger binding energies are found for other solutes (e.g., Pb, Bi, Sr, Ba), but these solutes possess essentially no solubility in Al. (v) We have explored the physical effects controlling solute–vacancy binding in Al. We find that there is a strong correlation between binding energy and solute size, with larger solute atoms possessing a stronger binding with vacancies. (vi) Most transition-metal 3d solutes do not bind strongly with vacancies, and some are even energetically strongly repelled from vacancies, particularly for the early 3d solutes, Ti and V.     

First-principles data for solid-solution strengthening of magnesium: From geometry and chemistry to properties

Solid-solution strengthening results from solutes impeding the glide of dislocations. Existing theories of strength rely on solute/dislocation interactions, but do not consider dislocation core structures, which need an accurate treatment of chemical bonding. Here, we focus on strengthening of Mg, the lightest of all structural metals and a promising replacement for heavier steel and aluminum alloys. Elasticity theory, which is commonly used to predict the requisite solute/dislocation interaction energetics, is replaced with quantum-mechanical first-principles calculations to construct a predictive mesoscale model for solute strengthening of Mg. Results for 29 different solutes are displayed in a “strengthening design map” as a function of solute misfits that quantify volumetric strain and slip effects. Our strengthening model is validated with available experimental data for several solutes, including Al and Zn, the two most common solutes in Mg. These new results highlight the ability of quantum-mechanical first-principles calculations to predict complex material properties such as strength.     

A three-dimensional cellular automaton model for dendritic growth in multi-component alloys

A three-dimensional (3-D) cellular automaton model for dendritic growth in multi-component alloys is developed. The velocity of advance of the solid/liquid (S/L) interface is calculated using the solute conservation relationship at the S/L interface. The effect of interactions between the alloying elements on the diffusion coefficient of solutes in the solid and liquid phases are considered. The model is first validated by comparing with the theoretical predictions for binary and ternary alloys, and then applied to simulate the solidification process of Al-Cu-Mg alloys by a coupling of thermodynamic and kinetic calculations. The numerical results obtained show both the free dendrite growth process as well as the directional solidification process. The calculated secondary dendrite arm spacing in the directionally solidified Al-Cu-Mg alloy is in good agreement with the experimental results. The effect of interactions between the various alloying elements on dendritic growth is discussed.     

合金元素掺杂对TiV_(2.1)Ni_(0.4)合金相结构及电化学性能的影响

研究了合金元素掺杂对TiV2.1Ni0.4系列合金的相结构及电化学性能的影响。XRD分析表明,该合金由V基固溶体主相和以网状分布于主相晶界的Ti2Ni第二相和C15型Laves第三相组成。BEI、EDS和电化学测试表明,Zr、Cu合金元素进入第二相晶格而使合金的电化学容量略降,但提高了合金的循环性能;Cr元素由于大部分进入到主相晶格而使合金的电化学循环性能大幅度提高,经40次循环后容量保持率仍达88.4%,但最大放电容量有所降低。     

Possible role of two iron sites in the metamagnetic transition observed in LaFe12 B6

Fixed spin moment calculations within TB-LMTO-ASA method using LSDA were performed for the compound LaFe₁₂ B₆ and for lattice constants taken from experimental data. Minima corresponding to the observed low moment and high moment states were found. However, their relative stability is not in agreement with experimental data. Fixed spin moment calculations on model compounds where Fe atoms at either crystallographic sites were replaced by Cu atoms were also performed. It was found that the stability of magnetic moment of Fe atoms at 18(h) site is much more dependent on environment than the stability of magnetic moment of Fe atoms at the 18(g) site.     

Magnetism-induced solid solution effects in intermetallic Ni60Al40

In this study, experimental work on solute effects in an intermetallic alloy, NiAl, has been complemented by first-principles quantum mechanical calculations to investigate the effect of iron and cobalt solutes on lattice parameter and hardening. Ternary additions of iron and cobalt with similar atomic sizes were added to replace nickel in NiAl containing 40% Al. Cobalt solutes did not affect the lattice parameter or the hardening behavior of NiAl alloys. Iron solutes, on the other hand, substantially expanded the lattice, resulting in unusual solid solution softening. These results could not be explained from a consideration of the size mismatch based on the Goldschmidt radii for iron and cobalt atoms. From the contrasting behavior of the iron and cobalt solutes, magnetic interactions induced by iron atoms located on the aluminum sublattice have been identified as a new factor responsible for the unusual large lattice dilation and resultant solid solution softening in these intermetallic alloys.     

The structure and the properties of S-phase in AlCuMg alloys

The S-phase is one of the key strengthening precipitate phases in high-strength 2xxx (AlCuMg) aluminum alloys. Nonetheless, the crystal structure of the S-phase remains controversial, and therefore its physical properties are almost unknown. Using atomic-resolution imaging in electron microscopy and first-principles energy calculations, it was confirmed at last that the structure model proposed by Perlitz and Westgren in 1943 is the only right model for well-developed S-phase precipitates. The structure model proposed by Perlitz and Westgren in 1943 is the only right model. Detailed calculations analysis of the S-phase structure reveals that the characteristics of Cu–Mg bonding and Cu–Al bonding in the structure are basically metallic, but with an ionic character due to electron charge transfer between atoms, leading to a large elastic modulus for the S-phase precipitates to strengthen AlCuMg alloys.     

A phase-field model coupled with a thermodynamic database

A phase-field model for the solidification of multi-component alloys, capable of being integrated with thermodynamic databases, has been developed. The solid–liquid interface is modelled as a mixture of solid and liquid phases. The solute concentration of the solid phase depends only on the local temperature while the solute concentration of the liquid phase is affected by solute rejection (or absorption) from the solid being formed together with the extent of any chemical diffusion in the liquid. The governing equations for the phase-field model have been derived in a thermodynamically consistent way such that the parameters in these equations are fully determined. By linking directly with the thermodynamic database MTDATA, the model is capable of simulating the microstructural evolution of real alloys. Numerical calculations for aluminium–silicon alloys show that the phase-field driving force changes in a similar manner to the thermodynamic driving force, although the phase-field driving force changes more quickly than the thermodynamic driving force when the system approaches equilibrium. The phase-field mobility is shown not to be a trivial function of constitutional undercooling. With the new phase-field model, the width of the liquid–solid interface region is allowed a much large value with the continuity of all parameters in the phase-field model and properties of interface maintained, and hence the model is suitable for simulating large-scale systems.     

Microstructure and thermophysical properties of Mg−2Zn−xCu alloys

The microstructure and thermophysical properties of Mg−2Zn−xCu alloys (x=0.5, 1.0 and 1.5, at.%) were investigated through microstructural and thermophysical characterization, heat treatment, and first-principles calculations. It was found that the addition of Cu had influence on the microstructure and thermophysical properties of the alloy. As the Cu content increased, the content of the MgCuZn phase increased in the as-cast alloys along with the electrical and thermal conductivities. After solution treatment, the eutectic structure partially decomposed and Zn atoms dissolved into the matrix, leading to the decrease in both the electrical and thermal conductivities of the alloy. During the early stages of the aging treatment, solute atoms precipitated from the matrix, thus increasing the electrical conductivity of the alloy. After aging for 24 h, the thermal conductivity of Mg−2Zn−1.5Cu alloy reached the maximum of 147.1 W/(m·K). The thermostable MgCuZn phases were responsible for increasing the electrical and thermal conductivities. Smaller amounts of Zn atoms dissolved in the matrix resulted in smaller lattice distortion and higher conductivities. The first-principles calculations findings also proved that the MgCuZn phases had very high conductance.