課件參考晶體學(xué)

a a

布拉菲點(diǎn)陣

下面表示正

？

（3）ca3=-(a1+c==90o,aba3abaa3=-

截距

a1,a2,a3,

AC=OC-OA=a3 C a=-(a+a

(1 a a1

CB=OB-OC1 1 1a(11

( 1):11:( h+i

i=h+k 令：TR=ua1+va2+R=Ua1+Va2+Ta3+=Ua1+Va2+[-(U+V)][-a1-a2]+=(2U+V)a1+(U+2V)a2+Wu=2U+Vv=U+w=

U=(2u-v)?3V=(2v-u)?3T=-(U+V)W=u=2U+Vv=U+w=U=(2u-v)?3V=(2v-u)?3T=-(U+V)W=

正點(diǎn)陣1。倒易a*

bcabcb*abac*

ab

bcbcnb.c =na.bca.n = a*=bc Vb*.c*b*c*cosb*.c (ca).(acos b*c*V(c.a)(a.b)(c.b)(a=b*c*V=a2bccoscosa2bccoscasinabsin coscossinsina*bcsinVb*casinVc*abVcos*coscoscossinsincos*cos cossinsincos* sinsinVabc(1cos

cos2cos22

coscos)1/2。倒易點(diǎn)陣與正點(diǎn)陣的關(guān)aa*a(bc)abab*a(ca)aba·a*=1,a·b*=0,a·c*=b·a*=0,b·b*=1,b·c*=c·a*=0,c·b*=0,c·c*=a*bab

= = =A*BAB

(a*)*

b*ca*b*ca*·(a*)*= （a*)*=因此，正空間基矢也可用倒易空間基矢來(lái)表示a b*ca*b*cb c*aa*b*ca*bca*b*c(010)

立ab

六ab

四ab

三ab

正ab

單ab單胞參 90 倒易點(diǎn)

a3 3 a a31-3cos22cos3 abcsin2 2a a cos-1( cos-1( 180-*

a a

a1-3cos22cos3 a1-3cos22cos3 a1-3cos22cos3 11

b11 cos-1( 1特 a*b* a*b* a*b* a*b* a*b* a*b***

***

**

**

**

**900=== b*//b b*=1/b;

D

=(ha*+kb*+lc*)(b/k-a/h)=同理，r*hkl·ACOn=

/

a/h

a

=OD=a/h·n=1/

r*r*hklha*kb* ⊥（hkl）r*hkl=1/dhklcCAB=OB- =b/k-正點(diǎn)陣晶胞體積Va·bXV*a*·b*Xc*VV*(a·bXca*·b*Xc*)aaabac100VV*babbbc=010ca cb cc (4)點(diǎn)陣平面與晶帶軸的對(duì)應(yīng)關(guān)系 [uvw]晶帶軸：R=ua+vｂ＋如果晶面(hikili(hikili)面的法線都垂直于 li)面的倒易點(diǎn)在同一平面PG*ihia*kib*lic*hikiliG*ｉ所代表的倒易點(diǎn)構(gòu)成了一個(gè)倒易點(diǎn)陣平這個(gè)倒易點(diǎn)陣平面的指數(shù)為(uvw)*，它的法線方向?yàn)閇uvw]。[uvw]平行于(uvw)*倒易面的§2-3帶定1。晶帶定律的定晶體中若干晶面平行于同一晶向[uvw]時(shí)，這些晶面便組成了一個(gè)晶帶，這些晶面所平行的晶向叫做,[[uvw]的方向 ruvw=ua+vb+w（hkl）面的法線方向:r*hklha*kb*lc*(ha*+kb*+lc*)·（ua+vb+wc)=hu+kv+lw=晶帶h1u+k1v+l1w=0h2u+k2v+l2w=

h1u+k1v=-h2u+k2v=-

w ul2w

v

l2w

w

u:v:w

l1:

h1

k l2 l k

uvu1h+v1k+w1l=0u2h+v2k+w2l=→h:k:l

w1

u1

例:（h1k1l1）和(h2k2l2)同屬于[uvw(h1u+k1v+l1w)·p=0;(h2u+k2v+l2w)·q=0(ph1+qh2)u+(pk1+qh2)v+(pl1+ql2)w=即(ph1+ pl1+ql2)也屬[uvw]晶帶軸cBA aOB:

20120112212234

OAB面:(234)

A

ED

AB,FE:(101)AF,CD:(011) 面心點(diǎn)陣的初基胞基矢（abc'）與非初基胞基矢（abc）的關(guān)系式為： 1/ 1/2b'1/ 1/2

a

1/

01

c

體心點(diǎn)陣c

a' 1/

1/ 1/2ab'1/

1/ 1/2

1/ 1/

0 a 0

1a'

1/ 1/

0a b'1/

1/

0

a

0 b

0

A

ar hO OhA

ah=ar-

ah

0arbh=

-

b

1bh h

ch=ar+br+ar=(2ah+bh+

2/

r 1/ 1/3r br=(-ah+bhc=(-a-2b

++c

br1/

1/2/

1/3bh 面指數(shù)hh=hr-kh=kr-lh=hr+kr+

hr=(2hh+kh+lh)/3kr=(-hh+kh+lh)/3 -hh-2kh uh=(2ur-vr-wr)/3vh=(ur+vr-2wr)/3wh=(ur+vr+wr)/3ah·ah=(ar-

ur=uhvr=-uh+vh+whwr=-vh+wh·ar-a2=a2+b2-2ab

2(1cos)3(12cos三斜g21[h2b2c2sin2k2a2c2sin2 cosV

V2

r2a2u2b2v2 cosl2a2b2

Ahhb2c2

kka2c2

lla2b2

2bcvw

Ba2uub2vvc2w1 1 1 1 1 1-cos)2klbc(coscoscos2hlac(coscoscosV2a2b2c2(1cos2cos2cos22coscoscos

abc2(coscoscos)(khhk1 11 1ab2c(coscoscos)(h1 11 11 1a2bc(coscoscos)(lk1 1

2cawucos2abuv

bc(v1w2w1v2)ca(w1u2u1w2)cosab(u1v2v1u2) k l

h k l

2 2 2

單斜g

cos 1 12 1

raubvc

cos ,Cauubva2sin2

c2sin2

a2sin2

b2c2sin2

1 1-2hlcos

-(l1h2h1l2)cos]/g

c2wwac(wuuw)cosacsin2 4(h2hkk2 l

acsin 1

1 1 1 六角g

cos{3a2[h1h2k1k22(h1k2k1h2l

r2a2(u2uvv22

cos ,Da(u1u2v1v2 k l

12}/g1g2hh/a2kk/b2ll/

c 2 2 2

-2(u1v2v1u2)ca2uub2vvc2w正交ga2b2

cos1 1 1

raubvc

cos 1 1 1四方g2

h2k

l

(