固体物理学课件：X射线

2 AB-CD=0
2dsinθ d n
2d sinθ = nλ
3 Ewald 1913 Ewald
P C
O
OC=2π/λ λ
A C
Ewald
B
C
2π/λmin 2π/λmax
X
f=
。 。
A
s0
s
r
O
C
D
O
φ
=
2π λ
(s
−
s0 ) ⋅ r
=
(k
−
k0) ⋅ r
=
2π
S ⋅r
X
X
1912
Friedrich and Knipping X
X X
X
。 X
——
、
1X
s0
s s0
=CO+OD
A
s
Rl
C
D
O
Rl ⋅ (s − s0 ) = µλ
k0
=
2π λ
s0
k
=
Biblioteka Baidu
2π λ
s
Rl ⋅ (k − k0 ) = 2πµ
Rl
k-k0
k − k0 = nKh
n
, (nh1 nh2 nh3)
(1/2,0,1/2) nh nk nl
(0,0,0) (1/2,1/2,0)
(0,1/2,1/2)
2π/a
n(h+k+l) 4π/a
1
2
K+
(0,0,0)
(
1 2
,
1 2
,0)
(0,
1 2
,
1 2
)
(
1 2
,0,
1 2
)
Cl-
(
1 2
,
1 2
,
1 2
)
(0,
1 2
,0)
(0,0,
1 2
)
(
1 2
k → k0
∫ f =
∞
U
(r
)
sin
βr
dr
0
βr
S →0
sin βr βr
→1
β
=
2π
S
λ
f = ∫∞U (r)dr = Z 0
Z
。
F
n rj
r1, r2,………rn
φ
=
2π λ
(s
− s0 ) ⋅ rj
=
(k
− k0 ) ⋅ rj
=
2π
S ⋅ rj
λ
∑ F =
f ei
2π λ
S
⋅rj
j
j
λ
∑Z
E = Ee eiφj
j =1
f=E Ee
ρ(r)
∫∫∫ f =
ρ
(r
i
)e
2π
S ⋅r λ
dτ
U(r)
U (r) = 4πr2ρ(r)
S
S ⋅ r = Sr cosϕ dτ = 2πr2 sinϕdϕdr
∫ ∫ f = 1
∞
π
U
i
(r)e
2π Sr cosϕ λ
2π
sin ϕ dϕ dr
4π 0 0
,0,0)
3 (a) 22° X
。
b)
111
c)
110
X
0.154nm,
55.8)
F = ∑ f e n i 2πn(hu j + kv j +lw j )
hkl
j
j =1
rj = u ja + vjb + wjc
k − k0 = n(ha* + kb * + lc*)
Ihkl ∝ Fhkl 2
, ---
Example
(0,0,0) (1/2,1/2,1/2) n(h+k+l)