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# 5555．．．．X線回折 - nda.ac.jp

X . 1.. 2.. X X X . EXCEL .. X X .. 34. 3.. Check 1. X . Point 2.. X . [ ] [ ].. 1 150 mSv / . 2 500 mSv / . 3 13 mSv / . 4 10 mSv / . ( 2 mSv / ) . ( Bq ) .. ( Sv ) . X . X.. 4.. X . Check 1. X X . Point 2. X X . X X . X t ( cm ) I0 I . (1 / cm ) . I = I 0 e t (1). 35. X ( g / cm3 ) . / . ( cm2 / g ). 1 .. Check 1. X . Point 1 X .. (2).. d . X .. Check 1.. Point 2.. 2 X .. 2 . 36.. ( unit cell ).. 3 . a, b, c , lattice constants .. , , . a 3 .. ( Miller indices ) h k . a b b / k . a / h c / . h k 4 . 100). 100 ). 100). 100 ). 200). 200 ) 200). 200 ). 110). 110 ) 200). 200 ).. a a 111). 111). 110). 110) 111). 111). a a 4 .. ( cubic ) = = = 90 . a = b = c .. 2 .. 37. (2) (3) cubic X X a .. Check 1. X . Point 2.. f F . 3 .. N. F = f n e 2 i (hxn +kyn +lzn ) (5). n =1. 5 .. ( body-centered cubic, bcc ) . 2 N = 2 5 . r r r r rn = x n a + y n b + z n c 1 a . (x1, y1, z1) = (0, 0, 0) (x2, y2, z2) = (1/2, 1/2, 1/2) 2 . 5 .. {. F = f 1 + e i ( h+ k +l ) }. 3 . h + k + F = 0. h + k + F = 2f 6.

34 5555．．．．x線回折 1. はじめにはじめに 2. 目的目的 x線の性質（x線の吸収）を調べる。粉末x線回折実験を行い、未知試料の結晶構造を

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### Transcription of 5555．．．．X線回折 - nda.ac.jp

1 X . 1.. 2.. X X X . EXCEL .. X X .. 34. 3.. Check 1. X . Point 2.. X . [ ] [ ].. 1 150 mSv / . 2 500 mSv / . 3 13 mSv / . 4 10 mSv / . ( 2 mSv / ) . ( Bq ) .. ( Sv ) . X . X.. 4.. X . Check 1. X X . Point 2. X X . X X . X t ( cm ) I0 I . (1 / cm ) . I = I 0 e t (1). 35. X ( g / cm3 ) . / . ( cm2 / g ). 1 .. Check 1. X . Point 1 X .. (2).. d . X .. Check 1.. Point 2.. 2 X .. 2 . 36.. ( unit cell ).. 3 . a, b, c , lattice constants .. , , . a 3 .. ( Miller indices ) h k . a b b / k . a / h c / . h k 4 . 100). 100 ). 100). 100 ). 200). 200 ) 200). 200 ). 110). 110 ) 200). 200 ).. a a 111). 111). 110). 110) 111). 111). a a 4 .. ( cubic ) = = = 90 . a = b = c .. 2 .. 37. (2) (3) cubic X X a .. Check 1. X . Point 2.. f F . 3 .. N. F = f n e 2 i (hxn +kyn +lzn ) (5). n =1. 5 .. ( body-centered cubic, bcc ) . 2 N = 2 5 . r r r r rn = x n a + y n b + z n c 1 a . (x1, y1, z1) = (0, 0, 0) (x2, y2, z2) = (1/2, 1/2, 1/2) 2 . 5 .. {. F = f 1 + e i ( h+ k +l ) }. 3 . h + k + F = 0. h + k + F = 2f 6.

2 38.. a (0,0,0) (1/2,1/2,1/2). 5 bcc . ( face-centered cubic, fcc ) . fcc N = 4 6 . (x1, y1, z1) = (0, 0, 0) (x2, y2, z2) = (1/2, 1/2, 0) (x3, y3, z3) = (1/2, 0, 1/2) (x4, y4, z4) = (0, 1/2, 1/2) 4 . 5 . {. F = f 1 + e i( h+ k ) + e i( k +l ) + e i( l + h ) }.. h, k, (h, k, : mixed) F=0. h, k, (all odd) (all even) F = 4f 7 .. (0,1/2,1/2). (1/2,0,1/2). (0,0,0) (1/2,1/2,0). a 6 fcc . 39.. ( diamond structure ). N = 8 7 . 8 . (x1, y1, z1) = (0, 0, 0). (x2, y2, z2) = (1/2, 1/2, 0) (x3, y3, z3) = (1/2, 0, 1/2) (x4, y4, z4) = (0, 1/2, 1/2) . (x5, y5, z5) = (1/4, 1/4, 1/4) . (x6, y6, z6) = (1/4, 3/4, 3/4) (x7, y7, z7) = (3/4, 1/4, 3/4) (x8, y8, z8) = (3/4, 3/4, 1/4). 5 .. i( h + k + l ) . {. F = f 1+ e i( h + k ). +e i( k + l ). +e i( l + h ). }. 1 + e 2 .. i( h + k ). fcc Ffcc = 1 + e + e i( k +l ) + e i( l + h ) .. i( h + k + l ) . F = f Ffcc 1 + e 2 .. fcc . all odd all even Ffcc = 4.. i( h + k + l ) . F = 4 f 1 + e 2 7 .. h + k + = 4m F = 8f h + k + = 4m 1 F = 4 (1 i) f h + k + = 4m 2 F= 0.

3 8 . F = 0 . ( extinction rule ) . 40. 5.. 2 . 1 2. X .. X .. X . Check 1. X . Point 2.. 40,000 cps X .. E R. R = [J /mol /K] . E . = A exp (9). RT . ( ) (kg/m/s). 20 25 30 35 40 45 50 1 . 41.. mm 1 10. X .. X X 6000 .. t ( cm ) . X (1) / . ( cm2 / g ) EXCEL . ( g / cm3 ) 4 .. ( Si ) . Check 1.. Point 2.. K . 2 .. 2 8 . h, k, . 4 . 2 a 2 a . a / a .. Check 1. X . Point . NaCl ( sodium chloride structure 8 ) CsCl cesium chloride structure, . 9 Na, Cs, Cl . fNa, fCs, fCl . 42. 8 NaCl 9 CsCl .. NaCl CsCl . Na 0, 0, 0 1/2, 1/2, 0 1/2, 0, 1/2 0, 1/2, 1/2 Cs 0, 0, 0. Cl 1/2, 0, 0 0, 1/2, 0 0, 0, 1/2 1/2, 1/2, 1/2 Cl 1/2, 1/2, 1/2. ( NaCl ) ( CsCl ) . NaCl a = CsCl a = . KCl a = CsBr a = . CsI a = 10 . h, k, . 4 5 2 Cubic . 100 010 001 2 h, k, 2. 440 . h k l NaCl KCl CsCl CsBr CsI. 1 0 0. 1 1 0. 1 1 1. 2 0 0. 2 1 0. 2 1 1. 2 2 0. 2 2 1. 2 2 2. 3 0 0. 2 h, k, 2 . 43.. 5 A, B, C, D, E .. 2 . K 2 2 . NaCl, KCl, CsCl, CsBr, CsI .. 6.. a 2 .. X . 7.. X . X . a / a . NaCl CsCl .. 1. X 1988 . 2. X 1994.

4 3. X 1982 . 44. 1 X . I. X x . I. dI. = dx . I. dI. I. = dx ln I = - x + C. I = e x e C. x = 0 I = I0 . I = I 0 e x 11 . 2 .. r n = ( p q r ) = ( p q r ). r r = ( x y z ). r r r n ( r r0 ) . r-r0. 10 . r r r n (r r0 ) = 0. p(x - x0) + q(y - y0) + r(z - z0) = 0.. px + qy + rz = px0 + qy0 + rz0 = s 0. px + qy + rz = s . r t n = ( tp tq tr ) 10 . p(tp) + q(tq)+r(tr) = s t ( p2 + q2 + r2)=s s t=. p + q2 + r 2. 2. ( px + qy + rz = s ) d . r s s d =tn = p2 + q2 + r 2 = 12 . p +q +r 2 2 2. p2 + q2 + r 2. 45. 3 .. 1 2 .. unit cell 2 . 11 .. A x = 0. B x = 1/2. (x= 1) .. X .. X . 11 . 11 . x t (x, t) c . x x ct (x, t) = f(x - ct) f(x) . 2 ( x, t ). x 2 = f" (x ct ) t 2 . x 2. 2 ( x, t ). = c 2 f" (x ct ) . t 2. 1 2 2 . = 2 13 . c 2 t 2 x 2 . G = = 2 c = c = . G. 1 2 1 2 . = 14 . 2 t 2 G 2 x 2. r r A cos ( G x - t) = A cos G(x /G t) = A cos G(x ct) . r r r r B sin (Gx - t) = A cos ( G x - t) + B sin ( G x - t) . B = iA ei = cos + i sin . r r = Aei( G x t ) . 46.. z e . z2 z3 z4. e = 1+ z +. z + + +L.

5 2! 3! 4! 2 3 4 5. e i = 1 + i i + +i L. 2! 3! 4! 5! 2 4 3 5 . e i = 1 + + L + i + L . 2! 4! 3! 5! . e i = cos + i sin 15 .. z = x + i y (x, y) 1 . 12 . i . e = 1.. i i e 2. =i sin .. -1 cos 1.. -i 12 . 2. X ( = 0) e i t = 1 . r r = Ae i( G x t ) 1 . N rr F = fne iG xn G=ha +kb +lc * * *. r r s r . n =1. r r r r rn = x n a + y n b + z n c . 47. r r r r r r a* a = b* b = c* c = 2 . r r r r r r a* b = b* c = c* a = =0 16 . r r r r r r 1 G = ha * rn = x n a G rn = 2 hxn . A ( x1 = 0, f1 = 3 ) B ( x2 = 1 / 2, f2 = 1 ) N = 2 . N. F = f n e 2 ihxn = f1e 2 ihx 1 + f 2 e 2 ihx2 = f1 + f 2 e i h n =1. h = 2m F = f1 + f2 = 4 I F * F = 16. h = 2m 1 F = f 1 + f 2 e i = f 1 f 2 = 2 I F *F = 4 17 . 48. 4 .. (precision).. (accuracy).. 3 .. 0 . 0 . 0 .. 4 5 . 15670 .. 49.. A B C 1 .. +) . 4 . 2 .. +) 1 .. x . m 2 (x ) = (x i ) f ( x i ) = x 2 2. 2 2. i =1 19 . (x) . 50.. (x) . 1 (x )2 = f (x) = exp . 2 2 . 2. f(x). 20 . 13 .. =1. <x> .. =2. x = x f (x )dx . 0 5 10 15 20. X. 1.. (x )2 . = x exp 2 2 dx 2.

6 13 . x = 21 .. <(x- )2> (x ) . (x ) f (x )dx 2. =. 2.. (x )2 = 2 22 . 13 .. 2 . x1, x2, x3, xn . n . 1 n x = xi n i =1 23 . 1 n 2 n 1. s 2 = ( x i x ) 2 s = 2. 2. n i =1 n 2 24 . 1 n s2 = . n 1 i =1. (x i x)2. 24 . 2.. 51. 25 . s2 = 2.. 24 .. x .. 2 s2. (x ) 2. = = 26 . n n x s2 . s =. n 27 .. x .. , . f ( x , y) f ( x , y). z = x + y x y 28 . z = x z = x y ( x, y) . y z x y z 0 .. f(x, y) x, y .. z = f ( x , y) x, y 29 . z zi z = (x i x ) + z (yi y ). x y 29 . n 1 . (z i z ) 2. 2. sz =. n 1 i =1. 2 2. z 2 z 2. = s x + s y 2. sz 30 . x y .. 52.