Computational materials science
Which statement about the phase-field method is correct?
- AIt uses a diffuse interface across which an order parameter changes smoothly and evolves the order parameter so as to lower the free energy, computing microstructural change without tracking the interface directly
- BIt treats the interface as a sharp boundary of zero thickness, so each point on the interface must be tracked one by one and moved at every time step according to a separate equation for the local interface velocity
- CIt takes the positions and velocities of individual atoms as variables and solves Newton's equations of motion with forces from interatomic potentials to follow microstructural change
Show answer and explanation
Answer: A. It uses a diffuse interface across which an order parameter changes smoothly and evolves the order parameter so as to lower the free energy, computing microstructural change without tracking the interface directly
In the phase-field method, an order parameter that takes, for example, 1 in the solid and 0 in the liquid is assigned to each point in space, and at the interface its value changes smoothly over a finite width. The total free energy is written as the sum of the chemical free energy at each point and an interfacial energy proportional to the gradient of the order parameter, and the system evolves in time in the direction that lowers it. Non-conserved quantities such as crystal orientation are handled by the Allen–Cahn equation, and conserved quantities such as concentration by the Cahn–Hilliard equation. Because the interface need not be tracked explicitly, microstructures with complex changes of shape, such as dendrite growth, grain growth and precipitate coarsening, can be calculated. Tracking interface points belongs to sharp-interface methods, and solving atomic equations of motion is molecular dynamics.