X線-m.dvi

X Λ 1 X 1 O Y Z X Z ν X O r Y ' P I('; r) =I e 4 m c 4 1 r sin ' (1.1) I X 1sec 1cm e = 4:8 1 1 e.s.u. m = :1 1 8 g c =3: 1 1 cm/sec X sin '! 1 ß Z ß Z sin 'd! = 1 ß ß 1 sin χ cos! d! = 1+cos χ (1.) e 4 1 1 + cos χ I e = I (1.3) m c 4 r 1 χ (1+cos χ)= X e 4 =m c 4 = 7: 1 4 cm 1: X : X X Z X +Ze Z X (1.3) X 1 p I e Z Z p I e Z I e Λ 1

Z ρ eu(ρ) X 1.5νA X χ X Φ(s) = p I e Z 1 4ßρ sin sρ u(ρ) sρ dρ s = 4ß sin χ (.1) Z 1 f(s) = 4ßρ sin sρ u(ρ) dρ (.) sρ X (.1) I a = I e (s)f (s) (.3) 3 f(s) f(s) u(ρ) (atomic structure factor or Atomformfactor) p I e 1 f(s) 3: f(s) (atomic scttering factor ) s ( ) s = Z 1 f() = 4ßρ u(ρ)dρ = Z (.4) s 6= 3 f(s) <Z 3 X Bragg 3 (hk`) 1 spacing d 4 E,E 1,E,E 3 X p I e f X d X 4 E E 1 =N 1 O 1 +O 1 M 1 =N 1 O 1 =d sin (3.1) E p p

d sin = n n =; ±1; ±;::: (3.) χ = (3.3) Bragg X 1 X (3.) Bragg n Bragg Bragg X n 4: 4 X χ = (4.3) (ο; ; ) (x5 ) (4.1) (4.) i) ii) iii) a,b,c L,M,N I(ο; ; ) =I e jf (ο; ; )j G 1 (ο)g ( )G 3 ( ) s ß = sin = 1 d = s ο >= >; ψ a sin fi + b + c sin fi (4.1) I e = I e 4 m c 4 1 r 5: 1+cos χ! (4.) ο cos fi ( ) (4.3) ac sin fi G 1 (ο) = sin ßLο sin ßο ; G ( ) = sin ßM sin ß ; G 3( ) = sin ßL Laue( ) (4.4) sin ß jf (ο; ; )j = 8 < nx : j=1 f j cos ß(οx j + y j + z j ) = ; + 8 < nx : j=1 f j sin ß(οx j + y j + z j ) = ; (4.5) (x j ;y j ;z j ) 5 j R OP = X j = ax j ; PQ = Y j = by j ; QR = Z j = cz j (4.6) 3

! OR a; b; c (X j ;Y j ;Z j ) x17 Laue ο = h; = k; = `; G 1 (h)g (k)g 3 (`) =L M L (4.7) (4.7) Bragg (3.) X I e jf (h; k; `)j F (h; k; `) ( )(structure factor) 5 ο; ; ο; ; 3 a; b; c a (s s )=ο ; b (s s )= ; c (s s )= (5.1) s; s s s (5.) 6 a O P 1 s s (5.1) 1 a(cos ff 1 cos! 1 )=ON 1 P 1 M 1 = a = ο (5.3) (5.1) 3 ο a a ; b; c b; c 6: a ο = h( ); = k( ); = `( ) (5.4) a (s s )=h ; b (s s )=k ; c (s s )=` (5.5) 3 (5.5) s X (4.7) (3.) (5.5) Laue h; k; ` Laue 6 a s O OP 1 4

ff 1 b; c 3 X h; k; ` X 6 1 Slide 1 y P-1 P- 1 Slide z P-3 P-4 1 1 1 1 1 1 1 Slide 1 a >= >; >= >; (6.1) (6.) (4:4) M = N =1 G 1 (ο) = sin ßLο sin ßο G ( ) =1 G 3 ( ) =1 (6.3) (4:5) j =1 x 1 = y 1 = z 1 = jf (ο; ; )j = f (6.4) (4:)! I(ο; ; ) =I e f sin ßLο sin ßο! B sin ßLο sin ßο (6.5) (5:3)! a(cos ff 1 cos! 1 )=ο (6.6) (6.5) I e f X χ 3 Slide B (χ) =4 ρ J1 ff ((ß= )R" sin χ (6.7) (ß= )R" sin χ R " J 1 7: 7 3 7 R" sin χ =:61; 1:1; 1:6;::: B (χ) = (6.8) y P-1 3mm 1/3 P- P-1 z P-3.1mm, P-4 P-3 5

Slide (6.6)! 1 = a cos ff 1 = h h 6 h =; ±1; ±;::: 8 8: 1 8-() h = h 6= 8-(3) (6:6)! 1 = ff 1 = χ a" sin χ = h (6.) L h A h χ (6.) A h = L tan χ ο = Lχ ο = L h a" (6.1) (6.) (6.1) (6.6) 1 ( 1 (reciprocal lattice)) 7 1 1 (6.6) 1 cos ff 1 = 1 cos! 1 + h a (7.1) OP 1 O 6 OP 1 O h=a Q h OP 1 E a h O O 1= A A 1= A A E a h A AC h C h C h A A ff 1 6

AC h? E a h; OP 1? E a h; AC h k OP 1 ; 6 C h AO=6 P 1 OS =! 1 (7.) A =1= (7.3) S C h Q h : 1 cos ff 1 =AC h =AS cos! 1 =(AO+OS )cos! 1 1 = + OQ h! 1 = 1 cos! 1 cos cos! 1 + h (7.4) a ff 1 = ff 1 (7.5) " # O A ; (7.6) E a h a( a ) h A X X 6 4 (I) (II) (III) (IV) (V) a E a h X A E a h A A A O X X 3 7 5 (7.7) X 3 ( ) (I) E a h 1 a (II) A (Ewald's sphere of reflection) (IV) A O A X (III) E a h C h A A (Ausbreitungspunkt) 7

8 1 a b 1 a E a h b Eb h 1 a; b a b fl a 1 a ON 1 =1=a E a Ea 1 Ea ::: b b ON =1=b E b Eb 1 Eb ::: (5.5) Laue E a h E b k 1 O,P 1,P ;:::, Q,Q 1,Q ;:::, R,R 1,R ;::: OP 1 = ON 1 sin fl = 1 a sin fl ; OQ = ON sin fl = 1 b sin fl 6 P 1 OQ = ß fl (8.1) 1: a Λ =! OP 1 b Λ =! OQ (8.) 1 a Λ b Λ (8.1) ja Λ j jb Λ j = b a 6 d a Λ b Λ = ß fl (8.3) 6 4 11: 3 7 5 (8.4) 11 A ( ) O ( ) 11 8

" A # (8.5) E a h Eb k h; k Slide 3 x P-5 P-6 P-5 1.5 P-6 P-5 /3 Slide 3 P-7 P-6 P-6 P-7 P-6 Slide 3 3 1 ) (8.6) 3 6 4 3 a; b; c a b 3 c 1 6 3 3 7 5 (8.7) 3 a; b; c 3 E a h,eb k,ec` 3 H 1 H E a h Ea h ON 1! OH = h ON 1 = h=a a=a! ON 1 (h a=a) (h a) =h (.1) H E b k Ec` (h a) =h (h b) =k (h c) =` (.) (h k`) 1: 3 x P-5.1mm,.1mm P-6 P-5 P-5 1.5,P-7 P-6

h; k; ` (h k`) 13 E E a; b; c P,Q,R! OP = a h! OQ = b k! OR = c` (.3) O E ON ON= d! ON n n a n b n h = k = c` = d (.4) a n b n c n d d d = h; = k; = ` (.5) (:5) (:) h = n d (.6) 13: " O H(h k`) h hk` (hk`) # (.7) 6 4 (hk`) 7 5 (.8) 3 3 a; b; c R p = pa + qb + rc; p; q; r ; ±1; ±;::: (.) h h = ha Λ + kb Λ + `c Λ (.1) a Λ ; b Λ ; c Λ h a; b; c (.) (h a) =h = h(a a)+k(a b) +`(a c) (h b) =k = h(b a) +k(b b)+`(b c) (h c) =` = h(c a) +k(c b) +`(c c) h; k; ` a Λ >= >; (.11) (a a) =1; (a b) =(a c) = (.1) 1

a Λ? b; a Λ? c; a Λ = x[b c] (.13) (a [b c]) = v( ) xv =1 a Λ [b c] = b Λ [c a] = c Λ [a b] = (.14) v v v a; b; c a Λ ; b Λ ; c Λ 3 h a Λ ; b Λ ; c Λ (.1) 1 Bragg 3 11 14 O H 11! AH O! OS Laue (5.5) X 6 4 3 A 7 5 (1.1) 14: (5.5) (.) s s = h k k = h k = s ; k = s (1.) 14 k =! AH; k =! OA; h =! OH (1.3) 3 4OAH (.6) (.7) H (hk`) OH E 14 (hk`) E! OS! ) OS (1.4) E k BH; 6 B=χ= = 11

4OBH OB sin =OH; OB = ; OH = 1 d sin = (1.5) d Bragg (3.) Bragg n Laue h; k; ` 14 X AO (hk`) E! OS X (hk`) X! AH! OS X 6 4 (I) (II) (III) (IV) X X X X 3 7 5 (1.6) (7.7) 5 (7.7) (III),(IV) (1.6) (III) (Ewald's construction) 6 4 [ ] 14 OH Brillouin zone boundary (1:) k k = h k k A 5 (1.7) Brillouin zone boundary ο = h; = k; = ` ο; ; (5.5) Laue (5.1) X (4.) 6 4 (ο ) (4:) I(ο ) A X diffuse pattern 3 7 5 3 7 (1.8) 11 (Extinction Law) Laue (5.5) X (4.) Laue (4.4) ο = h; = k; = ` G 1 (h)g (k)g 3 (`) =L M N (11.1) 1

(hk`) χ Laue Laue X X (4.) I e r χ I e (4.5) jf (hk`)j = 8 < : nx j=1 f j cos ß(hx j + ky j + `z j ) = ; + 8 < nx : j=1 f j sin ß(hx j + ky j + `z j ) n Slide = ; (11.) Slide 4 P-8 P- ( 1 1 ) 1 P- P-8 1 (11.) jf (hk)j = f jf S (hk)j ; jf S (hk)j = f X j cos ß(hx j +ky j )g +f X j sin ß(hx j +ky j )g (11.3) Slide (6.5),(6.7) I e f! B(χ) P () 1 jf S (hk)j =1 (11.4) P- ( 1 1 ) jf S (hk)j = f1 +( 1) h+k g += ( 4 h + k h + k (11.5) P-8 P- h; k; ` Laue X X (1) () h + k P- (3) h + k + ` (4) h; k; ` (x j ;y j ;z j ) (x j + 1;y j + 1;z j + 1 ) f j f j [cos ß(hx j + ky j + `z j )+cosßfh(x j + 1 )+k(y j + 1 )+`(z j + 1 )g = f j cos ß(hx j + ky j + `z j )f1 +( 1) h+k+`g f j [sin ß(hx j + ky j + `z j )+sinßfh(x j + 1 )+k(y j + 1 )+`(z j + 1 )g = f j cos ß(hx j + ky j + `z j )f1 +( 1) h+k+`g P-8 P- >= >; (11.6) 13

(11.) f1 +( 1) h+k+`g X jf (hk`)j = f1+( 1) h+k+`g n= [f j=1 X n= cos ß(hx j +ky j +`z j )g +f j=1 sin ß(hx j +ky j +`z j )g ] (11.7) h + k + ` f1 +( 1) h+k+`g (International Table ) Slite 5 k P-1 () 1 jf S (hk)j =1 P-11 () ( 1; 1 ) 3 jf S (hk)j = f1+( 1) k cos h1 g +f+( 1) k sin h1 g =f1+( 1) k cos h1 g P-1 () ( 1; 1 ) ( ; 1 ) 3 3 3 jf S (hk)j = f1 +( 1) k [cos h1 +cos h4 ]g + fsin h1 +sin h4 g (11.8) = f1 +( 1) k cos h1 g (11.) (11.8) (11.) 1 15 P-1 P-11 P1 1 (11.8) (11.) k n h 3n 3n ± 1 k n h 3n 3n ± 1 4 1 3 1 4 15: (1) (11.8) () (11.) 4 (11.1) 1 X X i) ii) iii) (1.1) >= >; k P-1 P-11 P-1 3 14

13 Debye-Scherrer (1.1) ii) X 16 (hk`) O 1=d A N 1 N (hk`) X N 1 N A χ = 16: Debyr-Scherrer A O O L O O' r r = L tan (13.1) Debye-Scherrer Bragg d sin = ((3:) n d=n d ) (13.) d (h; k; ` n (hk`) d Bragg (13.1) r O' 14 (1.1) ii) X Debye Debye 17 1=d Y b Y ' ρ vcb B B b 15

(hk`) Y X 18 N 1 N N1 dn X P1 dp 8 >< >: cos(' ρ) cos ffi 1 = cos cos ffi = cos(' + ρ) cos (14.1) 17: 18: ( h; μ k; μ μ` 4 15 b b Y ' ' Y ' = Y b b X (hk`) Y X (1.1) i) Debye (14.1) ' = cos ffi 1 =cosffi = cos ρ (15.1) cos 1: 4 1 b E b k a Ea h Q R,Q 1 R 1,Q R ( 11 ) c Ec` E b k 16

N! AN! OP X X b E b k A 7 (5.3) (5.5) b! = o b cos ff = b sin fi k = k (15.) P A A O O 1 P (x; y) cos ffi = sin fi k = y p x + y ; sin = p x + y y p =sin cos ffi L + x + y p L + x + y ; cos ψ = L p L + x >= >; (15.3) E b k (Layer line) k = O' (equator) k 6= k = ±1; ±; ::: k b [p; q; r] I I (5.5) I = I cos ff = I sin fi = m (15.4) I = I s = I (s s )=(pa + qb + rc) (s s )=(ph + qk + r`) (15.5) (15.4) Polanyi I (15.) ph + qk + r` = m (15.6) p =; q =1; r = m = k (15.7) Slide 6 ΛΛ P-13 P-14 ±15 P-15 P-13 P-14 ±15 P-16 5 (15.8) 16 X 1»» X ΛΛ P-13 P-14 P-15 17

1= 1 1= A 1,A (1.1) iii) H O A AH=AO X : 17 (4.4) G 1 (ο) = sin ßLο= sin ßο L 1 (L ) L Slide 7 P-16 P-1 L = 1; ; 4; 8 1: 6 yy (17.1) 18 (1) a a 1=a E a h () (a; b) a E a h b Eb k (3) a; b; c E a h,eb k,ec` 1 H(hk`) h (hk`) d yy Slide 7 1 1,,4 4,8 8 18

(4) (5) (6) (7) (8) A (1.1) X Y E e ßiνt ff Y mff = ee e ßiνt ff(t) = (e=m)e e ßiνt (A.1) 1 O ff(t) ( ) O r,y ' P r=c! OP Y! OP E E(t + r c )= e c r ff(t) sin ' = E e 1 sin mc 'eßiνt (A.) r retarded potential (c=4ß)jej I('; r; t + r c )= c 4ß je(t + r c )j =( c 4ß E ) e4 1 m c 4 e 4 1 r sin ' = I m c 4 r sin ' (1:1) (1.) 3 ABC AB AC d BC; d CA; d AB ff; fi; fl cos = cos ff cos fi cos fl ; = cos ff =cosficos fl (A.3) sin fi sin fl = ; ff = '; fi = χ; fl =! cos ' =sinχ cos! (A.4) : Z 1 ß Z sin 'd! = 1 ß ß ß (1 sin χ cos!)d! = 1 ß (ß sin χ ß )=1+cos χ 1

(.1) 6 a s s( ) O P 1 s =ON 1 M 1 P 1 = a s a s = a (s s ) (A.5) s s 3 s s s s y O s A OA=OB=1 OACB js s j = OC = OM =sin(χ=) OC? y (A.6) ) 3: 4:! OC z y z x 4 O! OP = ρ u(ρ) ρ (ρ; ; ') p Z 1 Z ß Z ß Ψ(s s ) = I e u(ρ ') expfßi (ρ s s ) gρ sin d'd dρ p Z 1 Z ß Z ß = I e u(ρ ') expf ßi (ρ sin χ cos )gρ sin d'd dρ p Z 1 Z ß Z ß = I e u(ρ ') exp(iρs cos )ρ sin d'd dρ u(ρ ') u ρ u(ρ) ' p Z 1 Z ß Ψ(s s ) = I e ρ u(ρ) ß sin exp(iρs cos )d dρ p Z 1 " # e iρs cos ß p Z 1 = I e ßρ u(ρ) dρ = I e 4ßρ sin sρ u(ρ) dρ (:1) iρs sρ (4.),(4.4),(4.5),(5.1) (pqr) j R p = pa + qb + rc; r j = x j a + y j b + z j c p I e f j expfßi(r p + r j ) (s s )= g (A.7) (A.8)

Ψ n (A.8) p L 1 X Ψ(s) = I e p= M 1 X q= N 1 X nx r= j=1 ρ f j exp ßi (R p + r j ) (s s ) (.14) a Λ ; b Λ ; c Λ (.1) ff (A.) (a a Λ )=(b b Λ )=(c c Λ )=1 (A.1) (b a Λ )=(c a Λ )=(c b Λ )=(a b Λ )=(a c Λ )=(b c Λ )= (A.11) (s s )= (s s )= = οa Λ + b Λ + c Λ (A.1) a; b; c (A.1),(A.11) a (s s )=ο ; b (s s )= ; c (s s )= (5:1) (A.7) (A.1) (A.1),(A.11) (R p + r j ) (s s ) = (pa + qb + ec + x j a + y j b + z j c) (οa Λ + b Λ + c Λ ) = pο + q + r + x j ο + y j + z j (A.13) (A.) p L 1 X Ψ(ο ) = I e p= M 1 X e ßipο q= p L 1 X p= N 1 X e ßiqο r= e ßirο nx j=1 e ßipο = 1 eßilο 1 e ßiο = eßilο (e ßiLο e ßiLο ) e ßiο (e ßiο e ßiο ) = sin ßLο sin ßο eßi(l 1)ο = f j e ßi(οx j + y j + z j ) q G 1 (ο)e ßi(L 1)ο! (4:4) (A.14) (A.15) j F (ο ) = = nx j=1 nx f j e ßi(οx j + y j + z j ) f j cos ß(οx j + y j + z j )+i nx j=1 j=1 f j sin ß(οx j + y j + z j )(A.16) (4.5) (A.15),(A.16) (A.14) Ψ(ο ) = p I e qg 1 (ο)g ( )G 3 ( )e ßif(L 1)ο+(M 1) +(N 1) g (A.17) 1

(4.3) (.6) (.1) 1 d = h =(ha Λ + kb Λ + `c Λ ) = h a Λ + k b Λ + `c Λ +hk(a Λ b Λ )+k`(b Λ c Λ )+`h(c Λ a Λ ) (A.18) b a c (.14) v = abc sin fi; (A.18) ja Λ jb cj j = abc sin fi = 1 a sin fi jb Λ jc aj j = abc sin fi = 1 b jc Λ ja bj j = abc sin fi = 1 c sin fi b Λ? a Λ b Λ? c Λ 6 >= >; d a Λ c Λ = ß fi (a Λ b Λ )=(b Λ c Λ )= (c Λ a Λ cos fi )= ac sin fi (A.1) (A.) 1 d = h a sin fi + k b + ` c sin fi h` cos fi ac sin fi (A.1) (4.3) (A.1) Bragg h; k; ` ο; ; Bragg (11.6),(11.7) F (hk`) (A.16) e ßi(hx j +ky j +`z j ) + e ßifh(x j + 1 )+k(y j + 1 )+`(z j + 1 )g i = e ßi(hx j +ky j +`z j ) h1+e ßi(h+k+`) F (hk`) =f1 +( 1) h+k+`g n= = f1 +( 1) h+k+`ge ßi(hx j +ky j +`z j ) X j=1 f j e ßi(hx j +ky j +`z j ) (A.) (A.3) (14.1) 18 (A.3)