Structure of perfect crystals

Crystals Amorphous and Glassy Perfect crystals Defect crystals,,

1 2.1 2.1.1

FEVFVE2F 4 8 6 1 0 12V 6 12 12 15 18 E 4 6 8 7 8

2

3 TmTg

4

: 2.1.24

CO2Na+ClCa 2+F 1

24

Latticelattice point

== +

Unit Cell

A BDABDECABA

2

3 1 21.

, === +

6O3abc3xyzaxb yc zbccaabNaCl2.22.2 NaCl(a)(b)

714PIF

a=b=c===90P I F124

PPI

a=bc===90P I12

PPIF

abc===90PI F C1242

HRP

a=bc== 90=120H13a=b=c==90R 1

abc==9090P C12abcP1

3abcaoxb oyc ozabc3xyz2.3Popop=xa+yb+czxyzabcxyz1xyz 2.1.31.2.3

2.2NaCl Cl0,0,01/2,1/2,01/2,0,1/2 0,1/2,1/2 Na+1/2,0,00,1/2,0 0,0,1/2 1/2,1/2,1/2 1- Cl 1/2,1/2,1/20,0,1/2 0,1/2,0 1/2,0,0 Na+ 0,1/2,1/2 1/2,0,1/21/2,1/2,00,0,0

2. Miller ------ 1 2 3 4

.

Miller Miller hkl

0 - {hkl}Miller

{100}[100][010][001][00][00][00]6{110}{111}

[100][010][001] 110111 d

[hkil]h+k+i=01203a1a2a34c 1 [0001]1-1 [100]1-1 [100]-11 [010]Miller

2.2 80%Structure PapersA1A2A32.2.1 1 A2 BCCBody Centered Cublic gratingAB AB AB AB AB

BCCa=b=c ===90, : n=1/88+1=2[110]ra -FeB.C.C,a=286.4pm,r=124.1pm.

Coordination Number BBC8d

,6aa=1.15dBCC148d61.15d KK=nV/V K=2(4/3)r3/a3 (8/3)( /4 a)3 a30.6801

2. F.C.C(Face-Centered Cublic grating) H.C.P(Hexagonal Close Grating):6A2CB

ABCAFCC

ABABABHCP

n=1/8 81/2 6=4ar [100] 4r)2=a2+ a2=2a2 4r= a r=( /4)a K=44/3 ( a/4) 3 / a3 =0.7405C.N.=12 F.C.C

H.C.P acn =1/6 121/2 23 =6 r=1/2a d=a c=2 /3a, c/a = 1.633K=64/3 r3 /3a3 =0.7405

1.633c/a 1.633da c/a1.633da

4. 1r=1/2 a k=4/3 1/2 a3 /a3 =05239C.N.=6; , C.N.=4,r=3/8 a k=84/3 3/8 a 3 /(8/3)a3 =0.3401 2.10

5.

akA1F.C.C.40.7405A2B.C.C.20.6801A3H.C.P. 60.7405A480.3401

dfA1SrCaAlPbFeCoRhIrNiPdPtCuAgAuCePrYbThA2LiNaKRbCsBaTiVNbTaCrMoWFeA3BeMgTlScYLaTiZrHfFeRuOsCoNiCuCdCeEuHoPuGdDrNdTbErTm LuA4SiGeSnPb

2030, L.C.Pauling 5 1.2.3 2.3.1 Pauling

4

33 rR2.12 AF=Rr AD=R RtAEDFAD=30 2.12 AD/AF=R/(R+r) =cos30=3/2 r/R=(2/3)1=0.1551.

4T2 T+ T a2a2R=2aa=2 R3 a=6 RR+r=6 R/2 r=6 /2 1R=0.225Rr/R=0.225T+2.13

6O2.14. 6R+r=2 Rr=21R=0.414 Rr/R=0.4142.14

8BC=2(R+r) (BD)2=(CD)2+(BC)2 [2(R+r)]2=(22R )2+(2R )2, 4(R+r)2=12 R2 r=(3-1) R=0.732R 6r=0.528R 2.15

r/R0.1550.2250.4140.5280.732C.N.34668

O:6T :,21/43/412nOT = 2612 = 1342

O4T84T+4T-nOT=448=112

1/32.1643C-C1/43/46A-A7B-B33/85/812

nOTnOT26121364481126612112

2.Pauling Pauling Mm+ (r)Xn- (r)Pauling Pauling

SIiSI SIm/n, mn e.g.NaClNa+6Cl-Na+1/6611Cl-21 Pauling

1 Si+4,SSi4/41 O2--22O2-Si+421O2-2 MgAl2O4 Mg2+[MgO4] Al3+[AlO6] Mg2+, SMg2/41/2Al3+, SAl3/61/2(Mg2+ +3Al3+) (1/2+1/23)=2 Al3+Mg2+

2A2X7Cl2O7A2X11Nb2F11-(AX3)nP4O124-A4X20Mo4F20(A2X5)nP4O10AX5()VF5CrF5(AX2)nSiO2AX4K2NiF43(AX2)nAlOCl2AX3(3D)FeF3,ReO34AX)nZnSA2X10Nb2Cl10A2X6Al2Cl6AX4()TcCl4(AX2)nBeCl2AX3YCl3(A2X3)nCs(Cu2Cl3A2X9W2Cl93AX)nPbOAX3()CsNiCl3

3.Pauling 33 1

110.580.710.330.58

4.Pauling

2.3.2 Born r M2X 2- FF rr0 FFr

B/rn Bn Born512LiF 5.9 LiCl 8.0 LiBr 8.7 NaCl 9.1 NaBr 9.5 rr0

53 NaClMXMr0X6 M8 X82 r0M6 X241mol U

2. A2. r/R r0/R0r/R> r0/R0

AA6:61.747568:45.038788:81.762676:34.8284:41.638066:425.03124:41/64132

3. r0 r0 r r Pauling rNa95pm rF136pmPauling Goldachmidt 80

Shannon Prewitt r02-140pm rF133pm Pauling

1/2 0 0 0 1/2 0 0 0 1/2 1/2 1/2 1/2 T+: 1/4 1/4 1/4 3/4 3/4 1/4 1/4 3/4 3/4 3/4 1/4 3/4 T-: 1/4 3/4 1/4 3/4 1/4 1/4 1/4 1/4 3/4 3/4 3/4 3/4.2.3.21.(NaCl) (ZnS) Na2OFCC484T+4T-

(NaCl)(ZnS)Na2Ol-S2-O2-Na+Zn2+Na+O400044T048440Na++4l-Zn2++4 S2-Na++4 O2-C.N.6:6 4:4 4:8

Ca2FCCF-Na2OO2FCCNaONa8ONa8NaO4

HCPOC-C1/43/4 0,0,1/4; 1/3,2/3,3/4;TA-A3/85/8 T-: 1/3,2/3,3/8; 0,0,5/8; B-B3/85/8 T+: 2/3,1/3,3/8; 0,0,5/82. ZnS(iAs)

ZnS(iAs) ZnS (iAs) T+ T-2 O OT- T+ T-4 T+ T- 3.CsCl Cl-:0,0,0; Cs+:1/2,1/2,1/2. C.N.=8:8

4.TiO2 TiO2O2 TiO6C

Ti4+ O2-O2-,1/41/88+1=2Ti4+1/222+12=4O2-,1:26.a=b=458pm,c=295pm Paulingr+/r-=0.480.414, Ti4+C.N.=6,PaulingTi4+O2-Si=4/6=2/333

5. CdCl2 CdCl2Cl-OCdCl2

ABO3 BaTiO3Pb(Zr,Ti)O3(PZT)KTaO3KNbO3 ABO3 CaTiO33 O2- Ca2+ Ti4+ ABA 2 BA 1B5 BaTiO3KNbO32.3.4 ABO3

O2-ACa2+Ba2+BO2-C.N.=6BO68BO6C.N.=12Pauling O2-C.N.( O2-)C.N.()1C.N.()1/3={61121}/3=6

n(Ca2+)=81/8=1n(Ti4+)1 n(O2-)61/2=3CaCa2+: 0,0,0; Ti4+: 1/2,1/2,1/2 O2-: 1/2,1/2,0; 1/2,0,1/2; 1/2,1/2,0Ti4+Ca2+:1/2,1/2,1/2 Ti4+:0,0,0; O2-:0,0,1/2; 0,1/2,0; 1/2,0,0 Ti4+C.N.=6Ca2+C.N.=12 O2C.N.=Pauling Ti4+O2Ca2+O24/622/124=2

t 0.77~1.1 t AB6ABO2-rA rB roABO2-AO2-Bt

BaTiO3 BaZrO3 BaSnO3 SrTiO3 SrZrO3 SrSnO3BaTiO3 PbTiO3 PbZrO3 CaTiO3 CaSnO3 CaZrO3 BaTiO3BaTiO3 BaTiO3 CaTiO3 MgTiO3 a=b=c ==90 c a=bc ===90 cababc ===90

t 0.77Fe2+ABO3rA85pmABFeTiO3FeO6[TiO6]O2-Fe2+Ti2/31/3FeTiO3

t1.1ABB

[] NaClCa2Na+CO32-Cl-9010155Ca2+[] 111[][]

ABO3 AB B A 1.1 0.77~1.10.77t

Cr3+ Fe 3+,Fe2+ Fe 3+8-Al2O3a=808pm8MgAl2O4,8Mg2+16Al3+32O2-32O2-643232O2- 64 3216Al3+ 1/28Mg2+ 1/81 MgAl2O42AB2O4

NM Mg2+448MMg2+NAl3+ Mg2+FCC448Al3 M416 Mg2+O2-4Al3 O2-6 3O2-3M 100AB2,3 MgAl2O4; 2,4 Mg2TiO4; 1,3,4 LiAlTi2O41,3 Li0.5Al2.5O4; 1,2,5 LiNiVO4; 1,6 Na2WO4

[] A[AO4] At,B[BO6] BO At B2OO4 32O2- 64 32 16A3+ A3+ 8A3+ 8B2+ 8B2+[BO4] [BO6] [AO4] Bt (A,B)OO4NiZnMnYBaSrFe3O4Fe2+Fe3+2O4(Fe2+8Fe3+16O32) [Fe3+]T [Fe2+ ,Fe3+]O O4

AB2O4 1. 2. BABt(AB)OX4

3 1. 2. UL ULzz/r+-(2+,3+)MgTi2O4

3. d 3d Cr3d-dd3

t2g eg0 t2ett4/90 t2gegd- d3Cr3+at2gCFSE d-t2g(dxy,dyzdxz)eg(dx2y2,dz2)

0CFSE32/50=6/50 Cr3+be2t1CFSE23/5t2/5t =4/5t1/30 CFSECr3+MgCr2O4CFSEMgtCr2oO4

CFSE2+3+(kJ mol1) Cr3+158 kJ mol1CFSE6/504/5t,3+

Fe3O4CFSEFe3O4 Fe2Fe23O4Fe3CFSE0d51CFSEd6Fe2CFSE17 kJ mol1Fe2Fe3O4,Fe2CFSE,Fe2(Fe3+)t(Fe2+,Fe3+)oO4Fe2Fe3+,,Fe3O4Fe3O4CFSE,

Fe3+CFSE2+2+3+CFSENi2CFSE86 kJ mol1NiAl2O4Ni2Alt(NiAl)oO4