W. Craig Carter
= W. Craig Carter
{c}
{tag=Physics author}
{wiki}
= W. C. Carter
{c}
{synonym}
\b[W. Craig Carter] is a <materials scientist> at MIT whose research applies physical analysis and computation to the evolution of <microstructure>. His departmental profile identifies work on material properties, <phase transitions>, <fracture> and battery-electrode materials.<W. Craig Carter faculty profile at MIT>[Research section]{ref}
MIT's official course page identifies him as the instructor of its Fall2002 Thermodynamics of Materials course. The associated <Unstable Solutions: MIT 3.00 Lecture 32 by W. C. Carter> prints the byline W.C.Carter and develops the <regular solution model>, <common-tangent construction> and instability toward <phase separation>.<Unstable Solutions: MIT 3.00 Lecture 32 by W. C. Carter>[Official course instructor entry and Lecture32 resource; printed pp217–223, equations32-9 and32-15–32-17]{ref}
An original dimensionless version of the <regular solution model> makes one teaching point explicit. Let $x$ be <mole fraction> and
$$
g(x)=x\ln x+(1-x)\ln(1-x)+\chi x(1-x),\qquad 0<x<1.
$$
Its curvature is
$$
g''(x)=\frac1x+\frac1{1-x}-2\chi.
$$
At equal composition $x=1/2$, this becomes $4-2\chi$. For stipulated $\chi=3$, the value is $-2$. A small symmetric split of composition into $x\pm\delta$ changes the average free energy by $\tfrac12g''(x)\delta^2$ to leading order, which is negative here. The homogeneous state can therefore lower this model free energy through small composition fluctuations. This illustrates <spinodal decomposition>; it is a derivation in a chosen parameter convention, not a measurement of a named alloy.
The <common-tangent construction> separately determines equilibrium coexistence compositions. Carter's notes use these geometrical and thermodynamic conditions to distinguish stability questions from the eventual separated phases. His https://dmse.mit.edu/people/faculty/w-craig-carter/[MIT faculty profile] provides an institutional portrait.