The k(T) curve: boundary rise, peak, umklapp fall

A schematic crystalline conductivity curve with the amorphous comparison that never shows a comparable peak. Raise defect scattering and watch the peak drop and broaden — exactly what point-defect scattering does, and what boundary scattering in small specimens does too. The axis rescales to the data so the whole rise-peak-fall shape stays visible, and the marker reports which regime your measurement temperature sits in.

crystalline k(T)amorphous comparisonyour measurement temperature

Schematic curve blending a boundary/defect-limited rise with an umklapp decline; not a fitted Callaway model and carrying no material-specific parameters. Real curves add isotope, electronic and radiative contributions.