Teaching Conditional Comparison in Computational Materials Science through Stacking-Fault Energies

Comparing material properties requires attention to the conditions that define each quantity, yet correct arithmetic can conceal an invalid comparison. This study develops a specialized course in computational materials science using paired stacking-fault energies for cubic borides, carbides, and nitrides. Eighteen complete fixed-cell and relaxed-cell comparisons are examined through signed differences, ordering reversals, diamond-relative selection rules, material-deletion checks, and elastic-energy curvature. The two energy rankings have a Spearman coefficient of 0.9690, although eight material pairs reverse order. Restricting the comparison to the twelve materials with positive energies under both conditions retains five reversals and reduces the coefficient to 0.9371. Three of seventeen non-reference materials change membership under a positive-energy rule referenced to diamond. Exact threshold intervals show that the maximum of four disagreements occupies a narrow multiplier range rather than a broad decision region. VN crosses zero, HfN has a positive condition difference, and the cubic PtN stiffness coefficients identify a descending tetragonal strain direction. These distinct cases support a thirty-hour course combining individual calculations, guided comparison, evidence requests, and technical argument. The instructional sequence, assessment criteria, worked answers, and transfer tasks are specified without claiming measured learning gains. The contribution connects mathematically checkable discrepancies with the disciplinary judgments required to interpret atomistic calculations and communicate their limits.