Interactive physics models for Lecture 15: Laplacian curvature, Gaussian pulse, error function carburization, and Scheil coring.
Laplacian Curvature Intuition
Local accumulation rate is strictly proportional to geometric spatial curvature.
Instantaneous Planar Source (Gaussian)
Top: 1D Concentration Profile C(x,t) • Bottom: Physical 2D Diffusion Couple
Pinned Surface: Error Function & Part Carburization
Left: 1D Depth Profile • Right: Part Cross-Section with Case Depth xpen
Phase Diagram Tie-Line & Coring Gradient
Top: Phase Diagram & Tie-Line • Bottom: 1D Radial Concentration Profile • Right: 2D Grain Solidification
Cooling Rate & Coring: When cooling is slow (< 0.1 K/s), solid back-diffusion DS has ample time to homogenize the grain → Equilibrium Solidification (Lever Rule, uniform solid). As cooling accelerates (> 5 K/s), solid diffusion freezes (DS ≈ 0) → Scheil Coring (radial gradient from pure core kC₀ to solute-rich rim), shifting average solid C̄S leftward.