29 1 6 1

1 1.1 1.1 1.1( ) 1.1( ) 1.1: 2

1.2 1.2( ) 4 4 1 2,3,4 1 2 1 2 1.2: 1,2,3,4 a 1 2a 6 2 2,3,4 1,2,3,4 1.2( ) 4 1.2( ) 3

1.2( ) 1.3 1.3 1.3: 4

1.4 1.4 1.4: 1.5 1.5 1 2 1 a a R = l a l 5

R = l a + const. a 1.5: a, b 1.2 6

1.6 7 14 R = l a+m b+n c l, m, n a, b, c α, β, γ 7 14 1.6 1.9 2.1 1.6: 7 14 1/4 7

1.7: 7 14 2/4 1.8: 7 14 3/4 8

1.9: 7 14 4/4 2 2.1 7 14 a, b, c α, β, γ 1.2 a 360 90 180 n n = 1, 2, 4 2.1 32 9

2.1: 5 a 7 2.2 1.4 7 14 32 14 230 230 10

International Tables for Crystallography vol. A 2.2: 2.2 P 2 1 /c 2.3 2.3 a, b, c [u, v, w] R = u a + v b + w c [uvw] [111] [222] [ 1 1 1 2 2 ] 2 [111] a, b, c [111] [111] < 111 > 11

2.3: a, b, c a, b, c (hkl) h k l i 2.4 2.4 2.5 ABCABC ABAB < 111 > < 001 > 2.5 (hkl) (h k l ) [uvw] [uvw] 2.6 [uvw] 12

2.4: 2.5: 13

(hkl) [uvw] hu + kw + lv = 0 2.6: 2.6 2.7 14

2.7: 2.8 2.7 2.9 (001) 2.9 001 2.9 100 111 011 111 100 [011] (2.5 ) (hkl) (h k l ) (phqh pkqk plql ) p, q 15

2.8: 2.9: 001 16

3 Ewald 3.1 3.1 (010) 010 (hkl) g hkl 3.1: 17

3.2 3.2 3.2: 3.3 3.4 3.2 3.5 1.2 3.6 18

3.3: 3.4: (1/2) 19

3.5: (2/2) 3.6: 20

3.3 3.7 A, B k 0 k k 0 k λ k 0 = k = 1 λ R Ψ A Ψ B 3.7: Ψ A Ψ B 3.8 l λ l A B λ r r k k 0 k k 0 k 0 k r q = 3.9 e iθ = cosθ + isinθ n 21

3.8: 3.4 r n q 3.10 R pqr = p a + q b + r c r n = R pqr g hkl R pqr = q = g hkl q = g hkl 2sinθ = 1 λ d hkl λ = 2dsinθ 3.5 Ewald Ewald 3.11 22

3.9: 3.10: 23

λ 1 λ k 0 0 Ewald 0 k 0 = k = 1 λ k 0 k q k k 0 k 0 k g hkl q 3.11: Ewald Ewald 24

4 4.1 t T 0 x(t) x(t) = a 0 2 + {a n cos(nω 0 t) + b n sin(nω 0 t)} (4.1) n=1 ω 0 T 0 f 0 ω 0 = 2πf 0 = 2π T 0 (4.2) (4.1) ω 0 nω 0 a n b n a n b n a n = 2 T 0 T0 2 b n = 2 T 0 T0 2 T 0 2 x(t)cos(nω 0 t)dt (4.3) T 0 2 x(t)sin(nω 0 t)dt (4.4) 4.2 (e iθ = cosθ + jsinθ) x(t) = n= c n e jnω 0t where, c n = 1 T 0 T0 2 T 0 2 x(t)e jnω 0t dt (4.5) nω 0 ω 0, 2ω 0, 3ω 0 ω 0 0 ω X(ω) = c n T 0 X(ω) = 25 x(t)e jwt dt (4.6)

(4.6) x(t) t s ω s 1 4.1 4.2 4.1 f(t)=sin(t) g(t)=sint(2t)+ 1sin( t 2 2 ) f(t) t(s) sin g(t) sin(t) ( ) 4.2 f sin(t) 2,000(s)(0.5 mhz) sin(t)( ) 0.5 mhz 2t t 0.25 mhz 2 1.0 mhz 1.0 0.5 sin(t) 0.0-0.5-1.0 0 2000 4000 t / s 6000 8000 4.1: f(t) g(t) 4.3 x(t) x( ) 26

Power 0.0 0.2 0.4 0.6 0.8 1.0 f / Hz 1.2 1.4 1.6 1.8 2.0x10-3 4.2: f(t) g(t) 4.3 4.4 4.5 4.6 4.3 4.4 27

4.3: 2 4.4: 2 28

4.5: 2 4.6: 2 29

5 5.1 5.1 X 5.2 Mo 5.1 5.1: 30

5.2: l l = ±1 31

5.3 5.3 K α1, K α2 α1,α2 K α1 K α2 K α1 K α2 K α1 K α2 K α1 K α2 K α 5.3: K α X K β K α K α X K α K β 5.4 5.5 32

5.4: X 5.2 5.6 ω θ θ 0 o ω θ θ θ 33

5.5: 5.6: 34

( 1 + cos I = F 2 2 ) 2θ 1 2µt p (1 e 2sin 2 sinθ )e 2M θcosθ 2µ (5.1) F 2 p 1 2µt (1 e sinθ ) 2µ - e 2M (5.1) 1. hkl N F hkl = f j e 2πi(hu j+kv j +lw j ) j=1 f j j u j, v j, w j j N 2. 3. {100} (100), (010), (001), (100), (010), (001) 4. 5.7 2θ 35

2θ 5.7: 5. 5.8 γ = β = θ 1 2µt (1 e sinθ ) 2µ t 1 2µ 6. - u 2 2 M = 8π 2 u 2 ( sinθ 2 λ ) = B( sinθ λ 2 ) (5.2) 36

5.8: 5.3 5.9 (5.1) 4sin 2 θ λ 2 = 1 d 2 = h2 + k 2 + l 2 a 2 (5.3) θ 5.2 h 2 + k 2 + l 2 a (5.3) 5.2 2 1 0.1828 0.1828 1 2, 1 3 0.1828 1 3 37

5.9: JCPDS(Joint Committee on Powder Diffraction Standards) 38

6 6.1 6.1 6.2 6.2 6.1: 6.2 39

6.2: 6.2.1 1. a, b, c a = b c a (b c), b = c a b (c a), c = a b c (a b) (6.1) a, b, c bc ca ab a, b, c a, b, c a, b, c a = 1 a, b = 1 b, c = 1 c (6.2) 40

2. 1. (hkl) F (hkl) F (hkl) 2 F (hkl) = n f n e 2πi(hxn+kyn+lzn) (6.3) f n n (x n, y n, z n ) n (6.3) n 6.3 6.3: 41

6.3 1. R d Rd = Lλ (6.4) 6.4 6.4: 2. 42

100kV 1 100 6.5 6.5: [double reflection] 6.6 Nd 2 Fe 1 4B 6.6(b) h + l = 43

2n + 1(n ) h + l = 2n + 1 6.6(a),(c) h + l = 2n + 1 300, 003 6.6(b) (a),(c) (b) h + l = 2n + 1 (a),(c) 6.6: [systematic reflections] h00 h = 0, +1, +2... 6.4 1. h, k, l h + k + l 44

1 1 1 4 4 4 [110] [110] 2. 6.7 Cu 3 Au CsCl ZnS 6.7: 45

3. Incommensurate Structure [Incommensurate Structure] 6.8(a) Cu 3 Pd M 6.8 6.8(b) Tl- a 5.9 (a) (b) 6.8: 46

4. SiC 6.9(a) 6.9: 6.9(b) c 47

7 7.1 7.1 d λ n 7.1: d = 0.61λ (7.1) n sinα α n sinα 1.5 λ 0.5 µm 0.2 µm (7.1) 48

d e CS λ e d e = 0.65C 1 4 s λ 3 4 e (7.2) 300kV 0.00197 nm 0.60 mm (7.2) 0.17 nm 7.2 7.2 kev 0.8 7.1 A-B 7.3 θ 49

7.2: 0.1µmϕ nmϕ 7.3 7.4(a) 7.4(b) 50

7.3: 7.5(a) (b) 7.5(b) g 7.6(a) 7.6(b) (c) 7.6(b) g 3g g 51

7.4: 7.5: 52

7.6: 7.6(c) g 7.6(b) g g-3g 3g 7.7 g = 220 g 3g nm 7.4(c) (7.2) 7.8 53

7.7: 54

7.8: 55