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X = n1a1, Y = n2a2, Z = n3a [n1n2n3] ai i = 1, 2, 3 ni [n1n2n3] ni [n1n2n3] I = a n2 + n2 + n2 1 2 a (hkl) q = 0, 1, 2,... {(hkl), q} (hkl) (hkl) [n1n2n3] n1h + n2k + n3l = q q = 0 (110) z (100) yz d q q d =, b = h + k + l 0 1 2 i = 1, 2, 3 i [, ] [, ] [, ] 2 3 3 1 1 =, =, =, 1 2 V0 V0 VV0 d q = 0 (hkl) d =. h2b2 + k2b2 + l2b1 2 a1q a2q a3q xq =, yq =, zq =, h k l q/h q/k q/l V =. V0 = a3, a N ra 1/2 f 0.393 a d a = d 2.

a = 0.393 10-9 2 = 5.56 10-10.

z 40 10-3 = = = 1.55 103 /.

NA a3 6.02 1023 (5.56 10-10) = 4010-3 z = 4 a = 5.56 10-10 = 1.55 103 I [231] NaCl = 2.17 NaCl 1/z a =.

NA z = 4 Ar(Na) = 23 Ar(Cl) = 35 Mr(NaCl) = Ar(Na) + Ar(Cl) = 58 (NaCl) = 58 10-3 a = 5.62 10- [231] I = a n2 + n2 + n2 = 5.62 10-10 4 + 9 + 1 = 13.3 10-10.

1 2 I = 1.33 [010] [122] [132] [n1n2n3] (hkl) n1h + n2k + n3l = q, h, k, l, q k = q, h + 2k - 2l = q, h + 3k + 2l = q.

h = -6 k = 4 l = -1 q = 4 {(641); 4} x0 = a1q/h = - a1, y0 = a2q/k = a2, z0 = a3q/l = -4a3.

ai i = 1, 2, {(641); 4} {-2/3a1, a2, -4a3} 8.96 103 3 1.932 104 910 a = 2.86 10-10 910 a = 3.56 10-10 A = a B = 0.5a C = 1.5a a (123) [001] [100] [110] a 0.5a 1/3a d (hkl) a a d =.

h2 + k2 + l d100 d110 d111 1.537 10- (111) 1920 2700 0. qU(r) = - +. 40r rn q r n const U(r) = -. r 2/9e2 3 2 U(rs) = - +. 400rs 10mrs m rs qU(r) = - + C exp (-r), 40r C 10-10 qU(r) = NUi = -N -. 40r rn dU(r) = 0, dr r=r n-q2r = 40n n-q2 1 rU(r) = -N 1 -. 40r n r q - N 40r n-q2 1 r U(r) = -N 1 - 40r n r e r =, r0 j,j=i rj rj j 1 1 1 = 2 - + - +..., r0 r0 2r0 3r0 4r 1 1 = 2 1 - + - +.... 2 3 rj x2 x3 xln(1 + x) = x - + - +.... 2 3 2 ln = 2 ln 2N e 1/rn n a NaCl NaCl r = r0 e2 E = NA 1 -, 40r0 n NA a n NaCl KCl r0 = a/ r0 NaCl eU(r) = - + A exp (-r/), 40r A Ec 4r0/3 = a3/ D C = 3R, R = 8.31 C = 3nR, n C c = 3nR c = i p h =, p =. D = (62n)1/3. n = N/V = NA/ D D =. kB T D 12 T C = 4R. 5 D 1 4 D/T 9 T x3dx = RD 1 + 8. 8 D 0 ex - C AlBr3 V = 200 = 3.01 T > D AlBr3 n = 4 C = 3nR, C CV 12RV C = = =, Ar(Al) + 3Ar(Br) 10- C = 225 = 0.1 D = 11. = 207 D = (62n)1/3, n n = NA/.

F = 2/, = E/p = F = 20/D.

F =.

(62NA/)1/ F = 5 m = 15 T1 = 5 T2 = 10 Q = 6.8 10-2 T D T D 12 T C = 4R. 5 D C Cm C = T1 T2 34mR 4 Q = T2 - T1. 5D 1/ 34mR 4 D = T2 - T1. 5Q D = 210 c KCl CaF Ar(K) = 39.0 Ar(Cl) = 35.Ar(Ca) = 40.0 Ar(F ) = 19. NaCl 3 V = 100 = 2.2 Al2O3 T1 = 30 T2 = 150 m = 30 Ar(Al) = 27.0 Ar(O) = 16.0 T > D 50 T1 = T2 = 15 300 T D Ar(Cu) = 64. T = 12 308 Ar(Zn) = 65. M y a m1 m2 (k) l t [, +d] N N [, + d] D/4 D = 160 = 0.97 374 0.02698 N T D T D N S [, +d] 1014 106 1860 a = 1.54 10- T D T D f() =, - F exp + kBT 2 kBT F (T ) = F (0) 1 - 12 F (0) 2/p2 2 N F F = F (T = 0) = = 32n, n =. 2m 2m V m pF p T = 0 = F = const T = 0 3F =. F TF =, Td = TF. kB (9)1/ 8.9 64 2/ F = 32n. 2m n = NA/. 2/ F = 32NA/ = 6.93. 2me C = 6.93 T = 0 F = 3.12 3/1 2mF n =. 32 nat = NA/. 3/n 2mF N = = = 0.9952 1. nat 32NA N = T = 0.081 p = nkBT 2/ 2 p F = 32 = 8 10-25. 2me kBT 4 F Td = = 7.9 10-2. (9)1/3 kB n = /mHe = -1.62 1026 2/ F = 32n = 6 10-23, 2me 4 F Td = = 5.25. (9)1/3 kB F = 810-25 Td = 7.910-2 F = 6 10-23 Td = 5. F = 3.5 T = Td = 3.6 104 T = ne = 2.5 - T = 0 Td = 860 - Nd = 1023 T = 300 - Nc = 2.5 1025 = 2k2/2m m g() V = 1 m = m 10.5 Ar(Ag) = 107.87 m m n max m = 1.2m 1 T = 0 g() 1/2 m = m [, + d] 3 m 1 mdn() = 2 exp - + A 3d, h kBT A A kBT A T 5 2 T = 2000 T1 = 1500 T2 = 2000 5000 F = 3. -1 - = 2.3 107 m = m F = 2.1 -1 -T = 0 = 1.6 107 m = m S = 0.01 I = 20 T = m = m T = 300 -1 -2.17 107 m = 1.2m T = 100 1 110 60 4 0.52 0.68 0.3 - 4.71 10-29 1.28 10-10 8.49 4.08 10-10 1.44 10-10 5.91 3.15 10-10 1.038 (362) [111] [111] [111] [111] a 0.5a 1/3a d100 = a d110 = a/ 2 d111 = a/ d100 = a/2 d110 = a/ 2 d111 = a/2 d100 = a/2 d110 = a/2 2 d111 = a/ e2 U(a0) = -NA 1 -.

40a0 n 1. 1. e2 E = NA 1 - 40r0 n 41/(n-1) 4n/(n-1) e2 40r0Eb Eb = N0 1 -, = r0 1 -.

40r0 r0 N0e 2.64 10-10 673.8 958.8 187.5 4.40 23.65 1013 0.571 0.141 d2Un M = - 2Un - Un-1 - Un+dt max sin ka = = amax cos(ka/2)/ 1/ V 2d 1 2 182N + = 22 3 3 kB t l V 1/3 + 2/t l 2d 9N p = 1.6kBT p = 0.4kB kB exp /kBT - T = 0. n T n T Sd 2 (N/S)1/ 2 kB 34 T U0 + 3NkBT U0 + NkBT U0 = NkB 5 - 3 1028 1.5 1.2 106 2.45 1.04 106 4.71 Td = 3.12 (F - Ec) = -0.143 4 3/ g()d = 2m d h2/8ma 6.2 10-23 -1 - 1.2 1010 4.5 1020 1.49 106 3.2 4.7 4.6 2.6 104 25000 j = BT exp - A/kBT B = 4ek2m/h 0.02 4.1 3.16 10-14 3.54 10-8 1.5 10-3 vF /vd = 2.7 10-8 0.44 0.004











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