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

Thermodynamic and phase diagram data in the Fe-Cu system are evaluated. For the liquid and fcc phases, the Margules-type of equations is used. For the bcc phase, the same type of equation is used to describe the non-magnetic contribution to the Gibbs energy. In addition, a magnetic term is included. Using the thermodynamic equations derived from equilibrium data, the stable and metastable equilibria of this system are calculated. Agreement between the calculated and experimental phase diagram is good except for temperatures higher than 1720 K. For these temperatures, the calculated liquidus tends to be higher. The possibility of supercooling which may account for some of the lower temperatures measured should not be excluded. The calculated metastable miscibility gap of the liquid phase also agrees with the experimental data.

Thermodynamic analysis of the iron-copper system I: The stable and metastable phase equilibria

The phase equilibria and thermodynamic properties of the ternary Al-Fe-Si system were analyzed and a complete thermodynamic description of the ternary system was obtained. The thermodynamic descriptions of the three binary systems were taken from the literature. Most of the binary intermetallic phases, except Al13Fe4(ϑ), FeSi2-L, and FeSi2-H, were assumed to have no ternary solubility. Based on the experimental data, seven stable ternary intermetallic phases were considered in the system. Two of them were treated as semistoichiometric compounds with homogeneity ranges for Al and Si, and the others were treated as stoichiometric compounds. Reasonable agreement was obtained between calculation results and experimental information in the ternary system.

Thermodynamic assessment of the Al-Fe-Si system

Phase diagram and thermodynamic data for twenty ternary copper‐silver‐X alloy systems—where X represents Al,Au,Cd,Fe,Ge,In,Mg,Mn,Ni,P,Pb,Pd,Re,S,Sb,Se,Sn,Te,Ti or Zn—were compiled and critically evaluated. Of the twenty ternary systems, thermodynamic data are available for only the seven systems containing Au,Pb,Pd,S,Sn,Te and Zn. The high‐temperature phase relationships in the iron‐rich region of the Cu‐Fe binary system were also evaluated and a recommended phase diagram is presented.

Phase Diagrams and Thermodynamic Properties of Ternary Copper-Sulfur-Metal Systems

A combined CALPHAD/first-principles remodeling of the thermodynamics of Al-Sr: unsuspected ground state energies by "rounding up the (un)usual suspects"

The intermetallic compound NiAl is highly ordered at stoichiometry, even at high temperatures. For instance, its point-defect concentration at 900 °C is on the order of 10−3 at this composition. Moreover, its enthalpy of formation is highly negative and exhibits a minimum at stoichiometry. All of these data suggest that the interdiffusion coefficient should exhibit a minimum at this composition. Yet, the literature data show that the minimum interdiffusion coefficient occurred between 48 and 49 at. pct Al. Accordingly, we have carried out diffusion-couple measurements employing single-phase NiAl wafers over the temperature interval from 700 °C to 1000 °C. The measured concentration profiles were analyzed in terms of the lattice mole fraction, yielding interdiffusion coefficients as a function of composition and temperature. For all the temperatures studied, the interdiffusion coefficients were found to exhibit a minimum at the stoichiometric composition, with a corresponding maximum in the activation energies obtained from the temperature dependence of the interdiffusion coefficients.

Y. Austin Chang

Papers

Thermodynamic analysis of the iron-copper system I: The stable and metastable phase equilibria

Thermodynamic assessment of the Al-Fe-Si system

Phase Diagrams and Thermodynamic Properties of Ternary Copper-Sulfur-Metal Systems

A combined CALPHAD/first-principles remodeling of the thermodynamics of Al-Sr: unsuspected ground state energies by "rounding up the (un)usual suspects"

An interdiffusion study of a NiAl alloy using single-phase diffusion couples