There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We present a new algorithm to generate Special Quasirandom Structures (SQS), i.e., best periodic supercell approximations to the true disordered state for a given number of atoms per supercell. The method is based on a Monte Carlo simulated annealing loop with an objective function that seeks to perfectly match the maximum number of correlation functions (as opposed to merely minimizing the distance between the SQS correlation and the disordered state correlations for a pre-specified set of correlations). The proposed method optimizes the shape of the supercell jointly with the occupation of the atomic sites, thus ensuring that the configurational space searched is exhaustive and not biased by a pre-specified supercell shape. The method has been implemented in the “mcsqs” code of the Alloy Theoretic Automated Toolkit (ATAT) in the most general framework of multicomponent multisublattice systems and in a way that minimizes the amount of input information the user needs to specify and that allows for efficient parallelization.

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Efficient stochastic generation of special quasirandom structures

The relative effects of pressure, temperature and oxygen fugacity on the solubility of sulfide in mafic magmas

Solidification microstructures: recent developments, future directions

Sn-rich alloys in the Sn-Ag-Cu system are being studied for their potential as Pb-free solders. Thus, the location of the ternary eutectic involving L, (Sn), Ag3Sn and Cu6Sn5 phases is of critical interest. Phase diagram data in the Sn-rich corner of the Sn-Ag-Cu system are measured. The ternary eutectic is confirmed to be at a composition of 3.5 wt.% Ag, 0.9 wt.% Cu at a temperature of 217.2±0.2°C (2σ). A thermodynamic calculation of the Sn-rich part of the diagram from the three constituent binary systems and the available ternary data using the CALPHAD method is conducted. The best fit to the experimental data is 3.66 wt.% Ag and 0.91 wt.% Cu at a temperature of 216.3°C. Using the thermodynamic description to obtain the enthalpy- temperature relation, the DTA signal is simulated and used to explain the difficulty of liquidus measurements in these alloys.

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Experimental and thermodynamic assessment of Sn-Ag-Cu solder alloys

Phase diagrams of Fe-Ni-Cr are calculated as a function of temperature from the liquid phase down to 500 K using thermodynamic values of the pertinent phases. These phases are the liquid, fcc, bcc, sigma, and γ′-FeNi3 phases. Not only the thermodynamic values calculated from the models for the various phases are in agreement with experimental data available in the literature, the calculated phase diagrams are also in agreement with experimental data over a wide range of temperature. Below 1123 K, no conventional phase diagram data are available in the literature due to kinetic difficulties. However, the calculated diagram is able to explain the results obtained when the alloys are subjected to electron irradiation.

A thermodynamic analysis and calculation of the Fe-Ni-Cr phase diagram

The solid + liquid phase equilibria between α-Al and β-AlLi were determined using differential thermal analysis (DTA), metallography, and chemical analysis. Boron nitride (BN), which was found to be inert to these alloys, was used as the container. These measurements were carried out in order to resolve the discrepancies reported in the literature. The α-Al+β-AlLi eutectic temperature and composition were determined to be 600 °C±1 °C and 25.8±0.5 at. pct Li. Using these data and data reported in the literature concerning the phase equilibria and thermodynamic properties, thermodynamic models for all the phases were obtained by optimization. The thermodynamic values obtained for the β-AlLi phase describe not only the phase equilibria, but also yield structural defect data in agreement with measured values. The assessed enthalpies of formation, excess entropies of formation, and entropies of melting for all the intermetallic phases obtained are compared with empirical correlations when experimental data are not available. In addition to the stable diagram, a metastable diagram involving the δ′-Al3Li is also calculated from the thermodynamic models. The calculated diagram is in good agreement with the experimental data.

Phase equilibria of the Al-Li binary system

Computational thermodynamics to identify Zr–Ti–Ni–Cu–Al alloys with high glass-forming ability

The phase equilibria and thermodynamic properties of the binary Co-Ta system were analyzed and a complete thermodynamic description of the binary system was obtained with the CALPHAD technique using a computerized optimization procedure. The thermodynamic descriptions of pure Co and Ta elements were taken from the SGTE database. Based on the experimental data, six binary intermetallic compounds were considered. They are three Laves phases, μ phase, θ phase and Co 7 Ta 2 phase. The last two compounds are treated as stoichiometric compounds. Good agreement was obtained between calculated results and experimental data in the binary system.

Thermodynamic assessment of the Co-Ta system

Sputter-deposited, equiatomic Ni-Mn thin films were observed to possess a metastable, nanocrystalline, chemically disordered, fcc (A1) structure. Grain growth and a phase change to a chemically ordered, antiferromagnetic L10 structure were identified by x-ray diffraction (XRD) and transmission electron microscopy (TEM). Differential scanning calorimetry (DSC) experiments revealed exothermic signals that correspond to the grain growth and phase transformation reactions. The enthalpy of transformation for the A1 to L10 phase change was calculated as −3.5 kJ/mol, which agress with thermodynamic modeling. An activation energy of 139 kJ/mol was calculated for the phase transformation by the Kissinger method.

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Y. Austin Chang

Papers

A thermodynamic analysis and calculation of the Fe-Ni-Cr phase diagram

Phase equilibria of the Al-Li binary system

Computational thermodynamics to identify Zr–Ti–Ni–Cu–Al alloys with high glass-forming ability

Thermodynamic assessment of the Co-Ta system

Paramagnetic to antiferromagnetic phase transformation in sputter deposited Pt–Mn thin films