Mechanical behavior of metallic glasses Mg–Cu–Y using nano-indentation

The mechanical properties of amorphous bulk metallic glassy (BMG) alloy, Mg₅₈Cu₃₁Y₁₁, are examined using nano-indentation scratching test. This study investigates the influences of different scratching conditions on the mechanical properties such as the friction force and the friction coefficient (μ) to understand the abrasive behavior of the BMG. The scratching conditions include applied normal load, depth of scratch, scratching velocity, and scratching temperature. The experimental results of the friction force, friction coefficient, hardness, and scratching morphology of BMG are characterized. The result shows that the friction force is nearly proportional to the normal load; and the friction force exhibits a slightly dependent on the scratching temperature. Then, regression analysis method is utilized to establish a formula to fit the scratching condition of BMGs. The regression analysis can be applied to model the mathematical relationship between the scratching parameters. The regression result shows a good agreement with experimental one.     

Assessment of the atomic mobility in fcc Al–Cu–Mg alloys

Various experimentally measured diffusivities of fcc Al–Mg, Cu–Mg and Al–Cu–Mg alloys available in the literature are critically reviewed in the present work. The first-principles calculations coupled with a semi-empirical correlation is employed to derive the temperature dependence of impurity diffusivity for Mg in fcc Cu. Atomic mobilities for the above fcc alloys are then evaluated as a function of temperature and composition by means of DICTRA (DIffusion Controlled TRAnsformation) software. Comprehensive comparisons between calculated and measured diffusivities show that most of the experimental data can be well reproduced by the presently obtained atomic mobilities. The concentration profiles and diffusion paths are predicted with the mobility parameters in a series of binary and ternary diffusion couples. A good agreement is obtained between experiment and simulation.     

First-principles study of binary special quasirandom structures for the Al–Cu,Al–Si,Cu–Si,and Mg–Si systems

Based on special quasirandom structures (SQS’s) and first-principles calculations, enthalpies of mixing have been predicted for four binary fcc solid solutions in the Al–Cu, Al–Si, Cu–Si, and Mg–Si systems at nine compositions (x=0.0625$x=0.0625$, 0.125, 0.1875, 0.25, 0.5, 0.75, 0.8125, 0.875, 0.9375, where x$x$ is the mole fraction of A atoms in the A–B binary system). The present results are compared with previous first-principles calculations and thermodynamic modeling results available in the literature. In order to provide insight into the understanding of mixing behavior for these solid solutions, the spatial charge density distributions in these binary solid solutions are also analyzed. The results obtained herein indicate that the SQS model can be used to estimate the thermodynamic properties of solid solutions, especially for metastable phases, the thermodynamic qualities of which are rarely measured.     

Thermodynamic assessment of the Si–Zn,Mn–Si,Mg–Si–Zn and Mg–Mn–Si systems

The binary Si–Zn and Mn–Si systems have been critically evaluated based upon available phase equilibrium and thermodynamic data, and optimized model parameters have been obtained giving the Gibbs energies of all phases as functions of temperature and composition. The liquid solution has been modeled with the Modified Quasichemical Model (MQM) to account for the short-range-ordering. The results have been combined with those of our previous optimizations of the Mg–Si, Mg–Zn and Mg–Mn systems to predict the phase diagrams of the Mg–Si–Zn and Mg–Mn–Si systems. The predictions have been compared with available data.     

Thermodynamic modeling of the Al–Bi,Al–Sb,Mg–Al–Bi and Mg–Al–Sb systems

All available thermodynamic and phase diagram data of the binary Al–Bi and Al–Sb systems and ternary Mg–Al–Bi and Mg–Al–Sb systems were critically evaluated, and all reliable data were used simultaneously to obtain the best set of the model parameters for each ternary system. The Modified Quasichemical Model used for the liquid solution shows a high predictive capacity for the ternary systems. The ternary liquid miscibility gaps in the Mg–Al–Bi and Mg–Al–Sb systems resulting from the ordering behaviour of the liquid solutions can be well reproduced with one additional ternary parameter. Using the optimized model parameters, the experimentally unexplored portions of the Mg–Al–Bi and Mg–Al–Sb ternary phase diagrams were more reasonably predicted. All calculations were performed using the FactSage thermochemical software package.     

Thermodynamic assessment of Sn–Cu–Ce system

Phase relations of Sn–Cu–Ce system are important in understanding metallurgical role of Ce in Sn–Cu based lead-free solder alloys. Thermodynamic assessment of Sn–Cu–Ce ternary system has been done based on experimental data about phase equilibria and thermodynamic properties by using the CALPHAD approach combined with first-principle calculations of formation enthalpy of key compounds. The solution phases (liquid, Fcc_A1, Bcc_A2 and Bct_A5) were treated as substitutional, of which the excess Gibbs energies were modeled by the Redlich–Kister polynomial. Considering its crystal structure and solid solubility range, intermetallic compound Ce₁₁Sn₁₀ was described with a three-sublattice model (Ce)_0.429(Sn)_0.429(Ce,Cu,Sn)_0.142. Other binary and ternary intermetallic compounds were described as stoichiometric phases because of their limited homogeneity ranges. During optimization, Ce–Sn binary system was first assessed; then phase relations in Sn–Cu–Ce ternary system were modeled by combining with the optimized Ce–Cu and Cu–Sn binary systems in literatures. A set of thermodynamic parameters for all known phases were obtained, which can reproduce most experimental data. The Scheil model was used to simulate the process of non-equilibrium solidification for a series of alloys.     

A thermodynamic description of the Gd–Mg–Sm system

The Mg–Sm, Gd–Sm and Gd–Mg–Sm systems were thermodynamically optimized using the CALPHAD technique. The solution phases, liquid, bcc, hcp and rhombohedral, were described by the substitutional solution model. The isostructural compounds, MgGd in the Gd–Mg system and MgSm in the Mg–Sm system with a B2 structure was assumed to form a continuous range of solid solutions in the Gd–Mg–Sm system. The order–disorder transition between the bcc solution with an A2 structure and compound Mg(Gd, Sm) with a B2 structure in the system has been taken into account and thermodynamically modeled. The other isostructural compounds Mg₅Gd and Mg₅Sm, Mg₃Gd and Mg₃Sm, Mg₂Gd and Mg₂Sm in the Gd–Mg–Sm system were described according to the formulae Mg₅(Gd,Sm), Mg₃(Gd,Sm), and Mg₂(Gd,Sm), respectively. The compound Mg₄₁Sm₅ with a homogeneity range was treated as a line compound Mg₄₁(Gd,Sm)₅ in the Gd–Mg–Sm system. Based on the experimental data in the Mg-rich corner of the Gd–Mg–Sm system, a set of thermodynamic parameters describing the Gibbs energies of individual phases of the Gd–Mg–Sm system as functions of composition and temperature was obtained. In addition, the complete ternary phase diagram of the Gd–Mg–Sm system were predicted.     

Thermodynamic assessment of the Al–Cu–Er system

The Cu–Er binary system had been thermodynamically assessed with the CALPHAD approach. The solution phases including Liquid, Fcc and Hcp were treated as substitutional solution phases, of which the excess Gibbs energies were formulated with the Redlich–Kister polynomial function. All the binary intermetallic compounds were treated as stoichiometric phases. Combining with the thermodynamic parameters of the Al–Cu and Al–Er binary systems cited from the literature, the Al–Cu–Er ternary system was thermodynamically assessed. The calculated phase equilibria were in good agreement with the experimental data.     

Thermodynamic modeling of the Mg–Bi and Mg–Sb binary systems and short-range-ordering behavior of the liquid solutions

In order to investigate the short range ordering behavior of liquid Mg–Bi and Mg–Sb solutions, thermodynamic modeling of the Mg–Bi and Mg-Sb binary systems has been performed. All available thermodynamic and phase diagram data of the Mg–Bi and Mg–Sb binary systems have been critically evaluated and all reliable data have been simultaneously optimized to obtain one set of model parameters for the Gibbs energies of the liquid and all solid phases as functions of composition and temperature. In particular, the Modified Quasichemical Model, which accounts for short-range-ordering of nearest-neighbor atoms in the liquid, was used for the liquid solutions. A comparative evaluation of both systems was helpful to resolve inconsistencies of the experimental data. The thermodynamic modeling shows the strong ordering behavior in the liquid Mg–Bi and Mg–Sb solutions at Mg₃Bi₂ and Mg₃Sb₂ compositions, respectively, and predicts the metastable liquid miscibility gaps at sub-solidus temperatures. All calculations were performed using the FactSage thermochemical software.     

Modeling short-range ordering in liquids: The Mg–Al–Sn system

A liquid solution of components A and B may often exhibit a tendency towards short-range ordering (SRO). This may be modeled by the Modified Quasichemical Model (MQM) which attributes the SRO to the preferential formation of nearest-neighbor A–B pairs or, alternatively, by an associate model which attributes the ordering to the formation of A_nB_m associates or molecules. Although both models can often provide similar and equally good fits to experimental thermodynamic and phase equilibrium data in a binary system, the MQM provides significantly better predictions of the thermodynamic properties of ordered ternary liquid phases A–B–C solely from the optimized model parameters of the A–B, B–C and C–A binary sub-systems. This is illustrated through coupled thermodynamic/phase diagram optimization of the Mg–Al–Sn system. A similar example for the Mg–Al–Sc system is also presented.