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.

/pdf/efficient-stochastic-generation-of-special-quasirandom-svnfe83eez.pdf

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.

/pdf/experimental-and-thermodynamic-assessment-of-sn-ag-cu-solder-ohlm6kfv79.pdf

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

A combined thermodynamic/kinetic methodology was presented to give a rational approach to the metallization of n-GaAs when a reciprocal system of GaAs-MδGa-MδM’-MA’s exists. Fortunately, for many quaternary systems consisting of Ga-M-M’-As, such a reciprocal system does exist. This methodology may be used either for Schottky enhancement or ohmic contacts to n-GaAs. Two examples were used to illustrate the approach and preliminary results were given.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S1946427400469927

A Combined Thermodynamic and Kinetic Approach to the Metallization of GaAs

The solidification of hot-stage turbine blades made from Rene N4 nickel-base superalloy has been modeled to show the morphology of porosity and the local changes in solute concentration. The key task of the present study was the calculation of the solid-liquid phase equilibria of this 9-component nickel-base superalloy from the thermodynamic values of these phases. The Gibbs energies of the solid and liquid phases were obtained from those of the 36 binaries using the Muggianu and Kohler methods of extrapolation. The phase equilibrium data were then used to compute the change in fraction solid with temperature, initially using the complete mixing approximation (Scheil equation). The predicted freezing range was somewhat longer than measured. A modified Scheil equation was derived assuming incomplete mixing. Assuming 60 pct mixing of the solute, the calculated freezing range agreed with experiments. Fraction solid temperature allowed the detailed morphology of the“mushy”zone to be predicted. Using measured dendrite spacings and assuming the crystals to grow in a cubic array, the shape of the crystals and, consequently, the size of the liquid channels were predicted as a function of position. Hence, computation of the rate of fluid flow in the channels (from the known changes of temperature with time) allowed the pore morphology to be inferred.

Modeling solidification of turbine blades using theoretical phase relationships

A mathematical function, the relative stability, is defined which combines advantages of Darken's stability and excess stability function. The relative stability is finite over the entire composition range and approaches the value of one in terminal regions. A simple classification is given whether a solution phase is more stable than an ideal solution, less stable or even unstable in terms of values of the relative stability > 1,

Relative stability of alloys

The steady state growth equation for a paraboloid of revolution and a parabolic cylinder, taking the interfacial energy into account, is revisited. Although the consideration of the interfacial energy was necessary, the growth equation was much more complicated than the original equation with a zero interfacial energy, since both the thermodynamics and kinetics of the growth are considered in one equation. In the present work, we take advantage of the development in computational thermodynamics and consider the thermodynamics and kinetics of the process in separate equations, but solve them simultaneously. A consistent framework to describe the phenomena and compare it with previous treatment of the interfacial energy will be presented.

/pdf/on-the-applicability-of-the-ivantsov-growth-equation-528pbkbpal.pdf

Y. Austin Chang

Papers

A Combined Thermodynamic and Kinetic Approach to the Metallization of GaAs

Modeling solidification of turbine blades using theoretical phase relationships

Relative stability of alloys

On the applicability of the Ivantsov growth equation

A thermodynamic study of the Cu-Cr-O system by the EMF method