《固体物理学》课程教学课件（讲稿，Solid State Phyics）Chapter 4 Real Crystals

1.3 Real Crystal Structures一.堆积二.晶体结构的表达方法三.典型晶体结构四.多晶型现象和结构相变五：晶体表面结构

1 3. Real Crystal Crystal Structures Structures

What structure do the solids have?Can wepredict it?让我们来试着预测固体的结构Consider inert elements (spheres). This could be anything withno directional bonding (noblegases, simple andnoble metals)考虑没有直接成键的元素，例如情性气体、贵金属等Just put the spheres together in ordertofill all space.Thisshouldhavethelowestenergy.将它们尽量密集地堆放在-起，这样它们将具有更低的能量（原因我们下一章阐述）Asimplecubicstructure?简立方？

What structure do the solids have? Can we predict it? 让我们来 着 结构 试 预测固体的结构 Consider inert elements (p ) s heres). This could be any g thin with no directional bonding (noble gases, simple and noble metals) 考虑没有直接成键的元素，例如惰性气体、贵金属等 Just put the spheres together in order to fill all space. This should have the lowest energy. 将它们尽量密集地堆放在一 起，这样它们将具有更低的能量 （原因我们下一章阐述） A simple cubic structure? 简立方？

Simple cubic 简立方The simplecubic structureis a Bravais lattice.TheWigner-SeitzcellisacubeThe basis is one atom. So there is one atom per unit cell.Rmno = mai + na2 + oa3a2a1a3

Simple cubic 简立方 • The simple cubic structure is a Bravais lattice. • The Wigner‐Seitz cell is a cube • The basis is one atom. So there is one atom per unit cell

Simple cubic.We canalsosimplycount theatoms weseeinoneunit cell计算每个晶胞中的原子数目n=1·Butwehavetokeeptrackofhowmanyunitcellssharetheseatoms.要注意同一个原子有多少个晶胞分享1/8 atom1/8 atom1/8 atom1/8 atom1/8 atorh1/8 atom1/8 atom1/8 atom

Simple cubic • We can also simply count the atoms we see in one unit cell. 计算每个晶胞中的原子数目 n=1 • But we have to keep track of how many unit cells share these atoms.要注意同一个原子有多少个晶胞分享

Asimple cubic structure isnot a good ideafor packing spheres (theyoccupyonly52%ofthetotalvolume)Onlytwoelementscrystalliseinthesimplecubicstructure(Fando)S.C.,52%full

A simple cubic structure is not a good idea for packing spheres (they occupy only 52% of the total volume). Only two elements crystallise in the simple cubic structure (F and O)

Betterpackingbcc:Inthe body-centred cubic (bcc) structure 68%of the totalvolumeisoccupied.惯用晶胞中的原子数n=?

惯用晶胞中的原子数n=?

具有体心立方点阵排列的元素晶体有：Li,Na,K,Rb,Cs,Ba,Cr,Nb,Ta,W 等,它们原子的空间排列方式都相同，只是原子间距有所不同。例如：Li:a=3.49,Baa=5.02,Fea=2.87,Va=3.03,Cra=2.88,Taa=3.30,Wa=3.16,(单位10-10m)

Close-packed structures 紧密堆结构

Close‐packed structures 紧密堆结构

Close-packed structures 紧密堆结构fccandhcp面心立方与密堆六方fcchcpABABAB...ABCABCABC

Close‐packed structures 紧密堆结构 fcc and hcp 面心立方与密堆六方 面心立方与密堆六方

fcchcpABABAB...ABCABCABC