往届学习供参考远固体物理noteschapter

Chapter1,Crystal a3EarlyResearchonCrystal20世纪初（晶体X射线衍射 飞跃式的认CrystalStructuredeterminesthephysicalpropertiesofWhenacrystalgrowsinaconstantenvironment,theformdevelopsasif:IdenticalbuildingblockswereaddedAcrystalisathree-dimensionalperiodicarrayofSTMimageofa tinumsurface(regularrowsofPtatoms)

STMimageofagraphitesurface(graphiteringswith6-atoms,triangulargeometryofeachCatom)Arrangementofperiodicarrayof carbonnano-Similarity:containonlyonekindofatom–Difference:howthoseatomsare§1-1.PeriodicityofcrystalsandPeriodiclattice(anidealperiodicperiodicarrayofpointsinoneatomorgroupofattachedtothelatticelattice+basiscrystal crystalLatticepoints&+(LatticepointsdonotlieatthecentreofLatticepoints&Mathematical可以通过一个平移操作，从一个格点平移到另一格点

Tuu 2

ru1a1u2a2u3a1,a2,a3:translation r如果对于任意如果对于任意结 rr，都能找到合u1u2u3，则Oa1,a2, a1,a2,

称为primitivetranslationvectors（初基平 组成的体积单元为最小，称primitivecell（初基晶胞或原Translation Tu1a1

Tuu

a3对于一个格子来讲，它是无限的列阵。无论从列阵的哪点来观察，周围点的分布和排列方式都是完全相同UnitCellandPrimitiveUnitcell:thesimplestofthelatticesystem.ItpossessmorethanonelatticePrimitivecell:minimumvolumeunitcelltofillallcrystalspacethroughpropertranslationoperation.Itpossesesonlyonelatticepoint.物理学原胞：最小重复单结晶学原胞(conventionalcell)：与结构对称性相---是重复单元，但必须覆盖整个MauritsC.(1898-theDutch forhisprintsshowingrealisticillusionsandpuzzlesin初基平 对于初基平

Tu1a1u2a2（一种初基平

（非初基平 某一阵点与相邻点连线的中（或中垂线）所围成的最小 （2D:5种；3D:14种）Bravaislattice：晶体由完全相同的一种原子组成。Complexlattice:多个Bravais格子的套构。基元中包含两种或两种以上的原则：同种原子构成Bravais不同网格有相对的位移，即complexlattice crystal2Dexample–rocksaltstructures ThisisaunitcellItdoesn’tmatterifyoustartfromNaor -orifyoudon’tstartfroman ThisisNOTaunitcelleventhoughtheyareallthe--emptyspaceisnot Whatistheprimitive§1-2.Symmetryofcrystalsandsymmetry晶体存在一不变操作A，则也存在其逆不变操作A-1A和B都为晶体的对称操作，则AB也是一个对称操1-,23-,4-,6-foldSymmetryOperation(asymmetric

(symmetricSymmetryOperationSymmentry1)rotation,2)mirrorreflection,3)central4)rotation-reflection,5)rotation-§1-3.Types,

2D-Bravaislattices(5(<30,mirror)

③六角③

(30<<45,

正方 (=90,

(60<<90,

六角

(45<<60,mirror)3D-Bravaislattices(14Cubic-Bravaislattices–simplecubic,a

a2a3

,a(1atomper

Cubic-Bravaislattices–body-centeredcubic,结晶原胞

a112 2a3体积a3,原子数

物理原胞

a12(ijk a

(2atomsper

a22(ijk a a32(ijka32,原子数2example:bcc-

Or:twoscBravaisHand-footandmouth bccCubic-Bravaislattices–face-centeredcubic,(4结晶原(4

a112 2a3a3,原子数：81/8物理原胞

a12(jk a22(kiper

a a32(ija34,原子数2最近邻原子数12，最近邻距离a2example:fcc-

Or:fourscBravaisNaturalPhasesof 1534C(melting

b(-b(-2.2structuresof

Structurephasestructure- magnetization-

Cu(001) 11Cu(001)

FeCubic-Bravaislattices--sc,bcc, (the Numberoflatticepointsper(3atomper

cc物理原胞

3a aa1

i j

a2cClosed-packedstructures(hcp&Closed-packedstructures(hcp& Basis:(000),example:hcp-Closed-packedstructures(hcp&§1-4.CrystalstructuresincubicNaCl&CsCl(MgO,MnO,PbS,KCl, (AlNi,CuZn-,CuPd,NH4Cl, (8atomsper两个fcc套构（在边线1/2处Or:fccwith

两个sc套构（在体心处Or:scwithNa+(000),Cl-(½½½)orCl- Cs+(000),Cl-Diamond&ZnS(Ge, (8atomsper((两个fcc在对角线1/4处套构(twofccstructures ced¼Or:fccstructurewithbasis:(000),Diamond&ZnS (两个fcc在对角线1/4处套构(SiC,CuCl,ZnSe,GaAs,(8atomsperOr:fccstructurewithbasis:S(000),Perovskite(CaTiO3,BaTiO3,PbZrO3,LiNbO3,五个sc套构（BaTiOIOII配位数为12：hcp,

配位数为4：正四面体中§1-5.Millerindex（discribingthe (通常)记为来量以点阵常来量以点阵常数2neintercepts:3