## Q. 10.3

Solid-Solution Strengthening
From the atomic radii, show whether the size difference between copper atoms and alloying atoms accurately predicts the amount of strengthening found in Figure 10-6.

## Verified Solution

The atomic radii and percent size difference are shown below.
For atoms larger than copper—namely, zinc, tin, and aluminum—increasing the size difference generally increases the strengthening effect. Likewise for smaller atoms, increasing the size difference increases strengthening.

 Metal Atomic Radius (Å) $[ \frac{ r_{atom} \ – \ r_{Cu}} {r_{Cu}}]$  × 100% Cu 1.278 0 Zn 1.332 +4.2 Sn 1.405 +9.9 Al 1.432 +12.1 Ni 1.243 -2.7 Si 1.176 -8.0 Be 1.143 -10.6