固体物理学习题解答-陈长乐 khdaw

导读:128,f,F(G)==8??j=1fjeiG·rj??πf1+eiπn(k+l)+eiπn(l+h)+eiπn(h+k)+ei2n(h+3k+3l)=??πf1+ei+eiπ2n(3h+3k+l)??课后答2????????案网w3×√2a??2ww=??3a,.khdaw.com§1.413,c/2,,c/a=(8/3)1/2=1.633.(2)a=ai

固体物理学习题解答-陈长乐 khdaw

128

,

f,

F(G)=

=

8??j=1

fjeiG·rj

??πf1+eiπn(k+l)+eiπn(l+h)+eiπn(h+k)+ei

2n(h+3k+3l)

=

??πf1+ei

+e

2n(3h+3k+l)

??

2

????????

w

3

×

√2

a

??2

ww

=??3a,

.k

hd

aw

.c

om

§1.4

13

,

c/2,

,c/a=

(8/3)1/2=1.633.

(2)

a=ai,b=

a3a

√2a2c.

2

Mg

i+

√2

j

??

·acj

Mg

,

ρ=

2

(3)

a2·

3

a

(bcc)

(hcp)

.c

,

Vbcc=a3bcc/2

Vhcp=

hd

aw

2,

ahcp=3.77×10?10m.

1.2

:.

(

)

ww

w

.k

,

,

,

,

.

1.3

a=3×10?10im,b=3×10?10jm,c=1.5×

10?10(i+j+k)m,

(1)(2)(3)

i,j,k

x,y,z

?

?

(

)

(1)

c′=3×10?10km,

c=

1

?

2

×27×10?30m3.

om

2

3a2c

??

Mg√=

????=??

a3

=4.3×1028m?3.

.

.

141.4

293K

47.75?,1273K

46.60?.

.

X

,

sinθ=nλ/2d,

cosθδθ=

?nλδd/2d2,

δd

=?cotθδθ.

).

,

δd/d=cot47?·1.15π/180=0.0187(

,

δθ

1

δT

??

=

0.0187

w

ww

h

22

2+k2+l2

??

a,b,c

.k

.

,

a.

cosβ=

uh+vk+wl

u2+v2+w2·

hd

(3)

[uvw]

??

(hkl)

aw

i,

u

22

2+v2+w2

;

j,k

,

a=ai,b=aj,c=ak.

(1)

Ghkl=

·

Ghkl

,Rhkl

Ghkl

,

(hkl)

.c

[hkl].

om

§1.4

15

(2)

[u1v1w1]

α,

[u2v2w2]

R1=u1a+

v1b+w1c=a(u1i+v1j+w1k)

R2=u2a+v2b+w2c=a(u2i+v2j+w2k).

cosα==

R1·R2u

??a

u1u2+v1v2+w1w2

??

2+w2·+v1211

u2

2+w2+v22

kj+lk)

.

[uvw]

(hkl)

β,

a

(hi+

=

a

ww

1h2

=

h1h2+k1k2+l1l2

??

222h1+k1+l1·

w

|Gh1k1l1|·|Gh2k2l2|

=

??

2+l2·+k11

.k

h2

2+l2+k22

2

2

(i+j?k)Rlmn=

a

(?i+j+k),a2=

(1.5)

,

hd

a2

(n1i+n2j+n3k),

(h1i+k1j+l1j)Gh2k2l2=

aw

uh+vk+wl

u2+v2+w2·

.c

u2+v2+w2·

h2+k2+l2

om

cosβ=

R·Ghkl

a2π

(hi+kj+lk)

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