结构与键合：密堆积与位错阻挡

Spheres, cells and slip

• The running case is engineering materials 工程材料 - the study of what to make the mount of. Metallic bonds give ductile conductors; the crystal structure 晶体结构 sets how easily that ductility flows: BCC iron packs $\pi\sqrt{3}/8 = \mathbf{0.6802}$, FCC aluminium $\pi/(3\sqrt{2}) = \mathbf{0.7405}$.
• The atomic packing factor 致密度 is geometry, not density - atomic mass still decides $ho$.

*Denser packing, finer grains: structure writes the property

Walls that strengthen

• A dislocation 位错 is the line defect whose glide IS plastic flow; a grain boundary 晶界 is a wall that blocks it.
• Grain refinement 细晶强化: $\sigma_y = \sigma_0 + k/\sqrt d$ - the bracket steel runs $120 + 0.45/\sqrt{50 imes 10^{-6}} = \mathbf{183.6}$ MPa at 50 µm and $\mathbf{262.3}$ at 10 µm, a gain of 78.7 MPa with no chemistry changed.

Three structure slips

Read the certificate the same way

• The mill certificate reports grain size alongside chemistry; the buyer multiplies by Hall-Petch before quoting a strength.
• "Fine-grain condition" on the certificate is the 183.6-vs-262.3 question answered in advance - check which number the supplier means.

Recap