熊本大学学術リポジトリ Kumamoto University Repositor Title 固体物性学講義ノート Author(s) 黒田, 規敬 Citation Issue date 2008 Type URL Learning Material

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1 熊本大学学術リポジトリ Kumamoto Univrsity Rpositor Titl 固体物性学講義ノート Author(s 黒田, 規敬 Citation Issu dat 8 Typ URL Larning Matrial Right

2

3 . (

4 c (unit cll a β γ α b a, b, c : (lattic constants. 4 Triclinic Monoclinic Orthorhombic (P (P (C (P (C ( (I a b c α β γ a b c α γ 9 β a b c α β γ 9 Ttragonal (P (I (P Cubic ( (I (P Rhombohdral Trigonal a b c α β γ 9 a b c α β γ 9 a b c α β γ < 9 Hxagonal (P a b c α β 9 γ

5 . NaCl CsCl (primitiv unit cll 4

6 .4 a, b, c a, b, c (fcc Al, Cu, Ag, Au, Ni, N, Ar, Kr, X tc. (bcc, W tc. (hcp, Mg, Co tc. NaCl, Kr, PbS, Agr, MgO tc. CsCl, TlCl, Tlr, AgMg, AlNi tc. C G, Si (zincblnd ZnS, InSb, CuCl tc. C N, TaS, TaS, TiS, NbS, GaS, GaS tc. 5

7 abc n n n T n a n b n c n n n (Millr indics T n n n n n n abc m m m / m /m m hkl hkl (h + k i hk il a, b, c a, b, c // 6 (6 (6 ( ( ( (.5 6

8 (h k l m c abc a/hb/kc/l ξ c/l Millr O : : h : k : l : : m m m h k l a/h η a m a, m b, m c c b/k b P m b N (h k l m a.6 (h k l abc a/h, b/k, c/l ( a/h ( b/k (ab b (h k l b O (h k l b/ a a O a/ a, b, c a/h b/kc/l (h k l (h k l abc a/h, b/k, c/l.7 ( 7

9 (rciprocal lattic abc b c c a a b A π, π, C π a ( b c a ( b c a ( b c AC G ha + k + lc (- hkl G (h k l (h k l π π d( hkl G G (h k l G d(h k l A a b C c π b A c, a c, C a C b A (-5 (h k l G a a/h c c/l ξ a a/h b b/k η ξ c a b a, η (-6 l h k h G h A + k + lc πl πh πk πh ξ G, η G (-7 l h k h G ξ η G (h k l 8

10 (h k l ahbk cl G G G G a G a G a G π d ( h k l ( ( (-8 h G h G G G π ( hi + kj + lk G π h + k + l a a d( h k l (-9 h a + k + l (st rillouin zon A O.8.9 9

11 . Γ (4 λ x d dsinθ mλ, m,,, (- x λ θ θ θ θ

12 π k λ G // π sinθ π cosθ k k k λ λ // + // + // // // k x d sinθ λ m,, m k // k // k // λ λ 4π sinθ mπ k k// // // λ d mg (-4 G G k ± mg ik x λ Β m π π k + k k mg k k' (-6 d d k i k Β k k x d k k (-7 k G ± π ± d

13 k ( ( k. π π k a a f f f f u l- u l u l+ m m m a a ω ω x l- x l x l+ - π/a π a k ~ π a π/a h k l a a b ca b c A O

14 . L x L y L z N N x N y N z a k π x, y, z ± a π k x,y,z x, y, z L x, y, z π k x, y, z n x, y, z Lx, y, z π π N x, y, z N x, y, z k x, y, z n a a x, y, z k N x N y N z N k k y n x N x 4π L y π L y π π π nx n a L N a n x x N x x x π a π L x 4π L x k x π a. k k k k (stat k k kx, y, z a a π π

15 k k k k (x, y, z k a du ( T C dt U(T T k U T n k ( T hω ( k (- k n k (T k T k n k (T nk ( T hωk ( p.5 (- k / NA/ 6 n k ( T hωk k T (- k dk k V V dn( k ( 4πk dk k dk (-4 8π π VL x L y L z k 4

16 U k V ( T ( π k hω k k hωk k T dk (-5 (instin modl (-4 ka h ωk hω sin (-6 hωk hω h ω h k ω (-(- V π U ( T ( ( 8π a ( hω V hω ( hω hω a kt kt V C ( a k hω ( k T ( hω k T V N A a R hω C R( k T ( hω k T (-7 hω (-7 5

17 (Dby modl.(a (a k y (b π a k D ω ωd ω π a π a π a k x - π/a k π D a k π/a π a k D. (a (b k D 4π k D π a ( k D π π.47( (-8 4π a a.(b ω ka ω (-9 (Dby modl k π D a D ω ω (- ω 4 6

18 7 (-5 dk k V T U D k k T k k ( ( ω ω π h h (-9 kω D D T k D T k d a V d a V T U ω ω ω ω ω ω ω ω ω ω π 9 ( h h h h D k T D d a V ω ω ω ω ω h h h h h ( ( ( 9 D x x x D dx x T k a Vk dt du 4 ( ( 9 hω T k x T k x D D hω hω, (- D D Θ k hω (- (- T Θ x x D D dx x Θ T a Vk dt du / 4 ( ( 9 T Θ x x D D dx x Θ T R C / 4 ( ( 9 (- T Θ D ( 4 4 π x x dx x } ( { π + x x x dx x x dx x dx d Q

19 T << Θ D T C 4( R (-4 Θ D T. T.4.5 T T 6 k k a l u i( k x t l x l ω π u u k x ± a ω θ θ << i π + iθ k x << ω a k x ω 8

20 Θ. D Θ C v /R T/Θ D T Θ R 4.94 J/mol.K 4.94/4.8 cal/mol.k 5.97 cal/mol.k.4.5 C/T T 9

21 . Natur abhors a mtal. k u k (x ikx ψ ( x u k ( x (- ( (loch thorm (n, l, m (. k ( x, y, z k k k k ( (n, l, m (hybridization (hybridizd orbit (rmi

22 }. ( II ~. C s p

23 . Si (GaAs ( 4

24 b a X, ax b, X a X a b X a H Cu ( ( H H Li 4 5 C 6 N 7 O 8 9 N Na Mg Al Si 4 P 5 S 6 Cl 7 Ar 8 K 9 Ca Sc Ti V Cr 4 Mn 5 6 Co 7 Ni 8 Cu 9 n K s n L s p n M s p d n4 N 4s 4p 4d 4f

25 Ψ nlm (r (x, y, z dv (n, l, m dv Ψnlm ( r dv Ψnlm (r n, l, m n n (K, (L, (M, 4 (N, 5 (O, 6 (P, 7 (Q ( Q l l (, (, (, ( n- m m -l, -l+,,,, l-, l l + (n, l, m s- Ψ n ( r Rn ( r s (- ( x / r p- Ψnm ( r Rn ( r ( y / r 4π ( z / r px p y pz (- d- Ψnm( r 5 4π R n ( r ( x (z y r yz / r zx / r xy / r /( /(r r d d d yz zx xy d x d y z r (-4 n l n ( W 6s 5d 4 K N n 5d 4 n 6s 4

26 n K n L n M n 4 N n 5 O n 6 P n 7 Q s s p s p d s p d f s p d f s p d f s p d f s p dxy.5 +, 5

27 4. Gibbs G U + PV TS PV TS U A Φ + r r ( r (4- m n r A Φ ( r + r r (4-6.4 r Φ.5. r r r ( 6 (4- -. A Φ(r A Φ( r V ( r -6 r 4. A 6-- ( rr / a [ ] Φ( r Φ Φ, Φ const. (4-5 r r Φ(r Φ(r V -Φ a 6

28 6- - ( 6 r (4- A r 6 r Φ ( r [ ( + ( ] (4-6 r r r N fcc N N r 6 r U Φij ( r [ ( + ( ] (4-7 r j pij r pij r p ij i j fcc 4.454, 6 j pij j pij. N r U du dr 6 N r 6 r [4.454(.( ] r r r r (4-8 r ( 6 r..97 (4-9 U(r ( dp d dw d W d U b V V ( V V (4- dv dv dv dv dv W P a fcc a /4 Nr Nr r r a / N V ( r V U β β + U (4-4 V V N.N β, β 6 r 8 5/ β b (4- β / b N A 7

29 (Van dr Waals (a ( cation A +Z ( anion -Z A +Z -Z A +Z -Z (< V N Z r i ij j ( Z α (4- r α r A- α CsCl NaCl (zincblnd α ( ( Z (b H H s H ( H N s p 6, Ar s p 6, Kr 4s d 4p 6, X 5s 4d 5p 6 n s, p 8 s-p ( 8

30 C s p (sp 4 (sp 4. ( 4. 4 sp s p : p σ σ p π π 4 s p : 4 σ ( 8 A 4 A 4. Hitlr London (98 (c IA (Li, Na, K, Rb, Cs bcc hcp s s s M + ( 9

31 IA p, d ( (d OH NH XY X H + Y O H + O ON Cl X Y H + Y X H + ( / ( X H + Y ( H + X Y O H + O.8 nm 44 DNA O H + N N H + N H + ( Y H + 44 DNA (

32 ( (Van dr Waals (b C 4 sp σ p z C p z π p z π GaS III-VI 45 GaS 9 sp 7 S p z p z TaS,. 4.5GaS III-VI III µ S gµ S (4-4 S gµ g S

33 d ( d d m µ L γ mjm -, -,,, (4-5 j γ m d m (Hund rul ( d d ( d ( s s-d s p (supr-xchang ( Z σ π π

34 5. k ψ k ( x ikx u k ( x u k (x k u k (x u k (xk 4 5. Pt ζ 5. n X 5. d p Pt d-p- ζ k

35 (a Pt + Pt 4+ Pt + Pt 4+ Cl - Cl - Cl - Cl - (b 5d z 5d z (c 5d z 5d z (a (b(c 5d z Pt + 5dz 5.(a Pt + Pt 4+ Pt + Pt 4+ 5dz Pt + 5dz Cl Pt 4+ Pt + 5dz 5.(b Pt 4+ 5dz Pt + 5dz (d rogli h h p hk h π (5- k p k h ( k ( k k m * + (5- m 4

36 p (5-4 m m* (m 9. kg m* (ffctiv mass (k m*> m*< m*< m h * m*< m h * m* > k k x y k ( k h ( + + m * m * m x y z z * (k k k m x x k y k z + + * m * m * h y z 5

37 <> X <> L 5.4 fcc 4 Γ L 55 L k V q π ( (5-7 L k k dk 4πk dk k dn dn ( 4πk dk (5-8 V q h k (5-9 m * k k m dk * ( d h (5- π L 4π π L L ( 5.5 k 6

38 4π m * dn ( V h q L π m * ( h L D( d d d (5- k +d D( D dn m * ( ( (5- L d π h D( dn( D( n (5- d D( (dnsity of stats m* D( (5-5 n (5- D( d n (5-4 V 5 V 5 V V ( p.75, (6.5. S 7

39 T K G U + PV TS T U TS S f ( (5-5 kt + T K f, f, < > ( n n d n f ( D( ( f (D( f Df D k T/ k T/ k T/ D( k T f (D( / / k T. 8

40 T K k T << n (5- D( n( dd n π ( D( f ( d n( n( + ( kt 6 d (5-7 (. J. latt, Physics of lctronic Conduction in Solids, (McGraw-Hill, Nw York, 968 / ( m* / π kt n [ ( ] + (5-8 π h 8 D( n n( T K T K π ( kt dd( D( d 6 (5-9 (5-7 D( π kt [ ( ] (5- π h n ( (5- m * π 9

41 f( k / 9 ~ N M N M W N! M!( N M! W W ( N CM ( (5- N N-M N S k lnw k[ln N! ln M! ln( N M!] (5- k [ N ln N M ln M ( N M ln( N M ] k U U + U M ( (5-4 ds ds ds T dq du ( (5-5 dm S M M N f ( k T + (5-6 ( ( 6.7 p.4 M N n ( k T 4

42 (5-7 (5-8 (5-7 (5-9 f kt << ( f d f d 4

43 6. T, T (T > T (5-8 T T T T T T T T T T (+T (- Sbck ffct T + T T (6- T T << T V ( T T S( (6- T S T T, V (6- (6- - (T - (T 5. S(T (5- (6-(6- π S( T kt ( V (6-4 T T K S -6 V/K 6 S Cu( 7. V Ag( 5.5 V Au( 5.5 V (6-4 S K S V/K - ( S A 4-5 V/K ( I S Ni 45 Cu 55 d D( (5-9 S 6. Pt Pd S < -6 V/K 4

44 6. T T T T T T T S A, 6 ( + ( V ( T T ( S A S (6-5 S A S S A S A > V > S A S A S A < V < 6 A v / m * 4

45 A A, Q, T,, ( T k T k T k T k TD( / T U ( T U ( + k T D( (6-7 C v U ( T ktd( (6-8 T C v f ( Cv D f d D d T ( ( ( ( ( T k T << f ( π Cv D( ( d k TD( (6-9 T ( ( f f ( ( d ( π d ( k T π / 44

46 n n D( n D( (6- D( n n D( (6- kt T / k D( (6-9 C v π k T n (6- T Cv T π k n T (6- C v nk n πt/t ~ / 9 5 Ag C v / T k y x m * v p hk k k x dkx x kx k dt h τ k x τ x h τ x k x k + h 6. 45

47 6 k < k > x < k τ x > h J x nvx hn < kx m * > n τ x m * ( τ v x x µ x m * (6-8 v x x (6-7 µ [m /Vs] µ τ τ J σ x nµ [S/m] (6-9 x ρ σ [Ωm] (6- τ σ, ρ n σ, ρ τ τ ( τ Θ T x T D / 5 5 x dx ρ ( T C( Θ (6- x D ( (lochgrünisn formula C Θ D 46

48 5 T ρ ρ T (6-64 ρ ρ γ ρ + at γ > (6- ρ (rsidual rsistivity Θ 64 J ardnjapplphysvol pp88- (94 (6- ρρθ ardn T/Θ D >. ardn Θ q - κ T(r C v l κ v l v τ v m * 47

49 (Widmann-ranz law κ LT, σ π k L 8.45 WΩK π S kt 6 7. V S ****************************************** ********************************************* ( (KittlIntroduction to Solid Stat Physics (latt Physics of lctronic Conduction in Solids Mathmatica (6- ρ(t/ρ(θ D T/Θ D (- x 5 x 4 T/Θ D.6 T/Θ D.6 9 Th Thory of Mtals 6. T/Θ D 6.5 (Au Θ D 75 K ρ(75/ρ(7 ρ(7/ρ( ρ(t/ρ(θ D 48

50 6.4 Θ D 5~7 K 6. (Θ D 75 K (A. H. Wilson, Th Thory of Mtals (Cambridg Univrsity Prss, Nw York, 965 T (K ρ/ρ( Θ Θ ρρθ ρ/ρθ CS ****************************************************************************************** 49

51 p - n k GaAs, GaN, CdS tc. k Si, G, GaP tc (a (b Si Si Si Si Si Si Si Si Si Si - Si Si Si Si Si Si Si + Si Si Si Si P + Si Si Ga - Si Si Si Si Si Si Si P + Ga - 7. Si (a (b (a (b ( carrir ( Smi conductor n p n p tc. 5

52 n- ζ β k T 5, 6 f ( n, p fn ( ( ς β n + f p f n f p ( (ς β + D n f n D n ( c ζ f p ( f n ( v D p ( D p f p D(f(, D(f( 7. D n(p f n(p 5

53 k T T K 6 mv G V G >> k T 7. f n (<< f p (<< ( ς β f n ( (7- (ς β f p ( (7- n p ( ς β n D ( ( c n fn d Nc (7- c v (ς β p ( ( v D p f p d Nv (7-4 c, v N N mnkt ( c (7-5 πh m pkt ( v (7-6 πh m n m p N c N v c v n p n p Nc Nv ( c v β Nc Nv G kt (7-7 + k T m c v p ς + log (7-8 4 mn ζ G / 5

54 ( N D D c D d (7-9 << d, kt G (7- n c D n ( D n f n d ζ D N D f D N D f n ( D n f n D n f n, N D 7.n n D n D N D f D ( D (7- n + n D N D (7-5

55 f D ( D ( ς β + D ( ς β D f D ( D (7- ( ς β + D ( k T << d (ς β f ( D D D (7-4 ( ς β n N c c ( c D n Nc N D ( c D β Nc N D d kt (7-6 c + D kt Nc ς log (7-7 N D ( N A < N D n ( (compnsation N A ζ n an c ( c ς β an c d kt, a ( N N D A (7-8 N A < N D n 54

56 ( n n d kt (7-9 N A ( c D n d kt (7- G k T n N D N A (7- ( n G kt p Nc Nv (7- (i (iv /T log n 74 n-g 75 55

57 τ 6 logn (iv (iii (ii (i G / d / d /T (K - 7.4n- 7.5n-G ( 56

58 Si ~ V ~ mv p- n- p- n- p- n- p- 7.6(a φ p- n- p-n ( : dpltion layr w φ (7- w p-n 6 p-n p- n n- p 7.6 p n + Dn( p I g ( vnn p + v p pn v n( p (7-4 L n( p v n(p n p p n D n(p L n(p ( ( ( ( : minority carrir injction V I s c V φ k T Is k V T φ k T I s c (7-5 57

59 (a I s +I g φ p n I s I g φ (b V > I s +I g φ V p n V I s I g φ V (c I s +I V< g p n I s I g φ V φ V V 7.6 p-n ( ( (a (b (c V< 76(c p n p-n V I I g + I s I g kt + I s (7-6 58

60 V I I g + I s (7-7 (7-6 V k T s I I ( (7-8 V > V V < V I I s I g I s (7-8 p-n I-V 7.7 I V 7.7 (7-8 p-n I-V 59

61 [7-] d n- k T d [7-](a 7.5 n-g (b [7-] [7-4] 7.7 p-n 6

62 9 (M. Planck ν hν 95 (A. instin hν ( : Photon 8. ( n ( m hν mn m - n (8- (N. ohr n hν mn 578 K m H, H, O, C, 8. (. rmi (rmi s goldn rul hν nm 6

63 m ω u d u du + ω u + ϖ dt dt m (8- ϖ ω i ω t (8- i t u u ω u ω ω iϖω m (8-4 (8- ω N n N P χn + Nu ( χn + (8-5 m ω ω iϖω ε(ω ε + P ε ( ω ε (8-6 ε /m ω p ε ( ω ε n[ + ] (8-7 ω ω iϖω ε χ n n + (8-8 ε ω N p ε nε m (8-9 ω p ε nω p S (8- ω 6

64 ε ε ε ε + iε ( n iκ (8- ε + ε n κ ε nκ (8- n κ ε ω ε ε n κ ω ( c ω k ( n + iκ ( (8- c ω ω(k i( n+ ik k x iω t i( nkx t kx ω κ (8-4 k λ k π λ (8-5 λ ε ( n + κ R (8-6 + ε ( + n + κ κk x αx (8-7 α α 4πκ (8-8 λ ω ( 6

65 k k 8. A + A - A + ω N 8. A 8. ω Im[ε] ε Im[/ε] (8-7 ω ω L ϖ /ω << L ε ( (8-9 ε n ω ω (8-7 - (Lyddayn-Sachs-Tllr ε ε ε ε 8. ε n.s.5 ϖ /ω. ε ε Im[/ε] ε ωω ε 64

66 ε n.s.5 ϖ /ω. ε ε Im[/ε] 8. (8-9 ω L.5 ω 8.4 ω ω ω L % ε n S ϖω 8.4 ωω ω (8-7(8-8 (8-9 N ε ( ω ε n [ + ( ] (8- ε nεm ω ω iϖω ω ε nεmω << (8- κ ( ϖω ε nεm ( ω - ω + ϖ ω 65 (8-

67 κ ω ω ω ϖ / ω ω ω ω +dω D(ω dω ω 4π D( ω ϖ α( ω D( ω (8- λ ε ε m ϖω ε ε mc n n D(ω 8.5 G G L k Si Si X k //<> L Γ 8.5 G m c m v G h h ω G k +, + (8-4 µ µ mc mv µ D( ω ( hω G (8-5 π h µ D ( (8- α( ω C hω G, C (8-6 66

68 α (arb. units h ω α - 4 cm - G L X q ( h ω G q ( hω G + q n q n q n q + 67

69 8.5 α( ω C [ n ( h ω + + ( n + ( hω ] (8-7 q q G q q G C n q 8.7 α hω 8.7 G α 5 cm α hω G G.8 V.7 V G 68

70 ω ω p ε ( ω ε n [ ] (8-8 ω + iϖω (8-8 ϖω R[ε] 8.8(a % (a µ 8.8 (a (b (b ε n ϖω P 69

71 8.8(b (b (8- ω du v (8-9 dt v ( m iω +ϖ (8- (mobility µ ( m iω + ϖ (8- σ N (8- N µ ( m ε ε nω p iω + ϖ iω + ϖ σ σ p iσ p ε ε n + (8- ε ω τ τ ϖ (8-4 σ (8-5 σ σ ( N τ ε ε nω p ε ε nω pτ m ϖ ε n ω p ϖ σ 7

72 7 G Si GSi p-al x Ga -x As.5 µm (a GaAs n-al x Ga -x As 8.9 (b (a + - (Light mitting Diod : 97 (Lasr Diod 8.9(a 8.9(b p-al x Ga -x As n-al x Ga -x As p-al x Ga -x As n-al x Ga -x As GaAs GaAs N N h W W N N h (8-6 7

73 (Molcular am pitaxy (Chmical Vapor Dposition (Supr Lattic - Al x Ga -x As GaAs 8.(a 8.(b 8.(c (a (b (c InGaN I np InGaN (Multipl Quantum Wll MQW p n -4 µm 8. InGaN LD 7

74 [8.] [8.] - (a GaAs (b GaAs [8.] (a ε n 5 (b m N (c hϖ 5 % % [8.4]Drud (a ω (b Im[ ] ω ε 7

75 V K J cal V K k K J cal ε /m c m/s h Js h h π Js ( m kg m p kg k.8658 J/K C 74

76 [.] a, b A, aa b π a ba A, b, a a, b π a, b A, [ ] [.] fcc bcc bcc fcc [ ] π d( hkl Ghkl fcc d( hkl a a ( h + k + l + ( h k + l + ( h + k l h + k + l + ( h k + ( k l + ( l h bcc d( hkl h + k + ( k + l + ( l + a ( h [.] a a b + c b b c + a c c a + b [.4] bcc fcc 4 fcc x, y, z 4 6 bcc [.5] 75

77 76 [.6] [.7] ( ( l l l l l l l l u u u f u u u u f dt u d m i( t kx j j u u ω (cos ( (i i i + ka fu fu u m l ka ka l l ω cos ( ka f m ω sin 4 ka f m ω sin ka m f ω a k a π π a nπ ± -C-(A+ +A A O + A C -C

78 [.] (a (b (. [.] f k a (a sin x π f ω k x ± ω m a m i( kx j ω t u j u -i x u t x u ω i( ± π ω t iω t x ±a ux ± a u u ( ( f a f (b ω kx a kx m m ( ( (c k x k x ω [.] 4 (- n k U ( (- du dw + dq dw U du > dq > [.] (a Pd 46 (s + (s + 6(p + (s + 6(p + (4s + (d + 6(4p + (4d Kr 6 + (4d (b Nd 6 X 54 + (6s + 4(4f (c Pb 8 X 54 + (6s + 4(4f + (5d + (6p ( ( [4.] 77

79 R R ρ ε z q U N( α R R ρ + zε α ε ρ U du dr q N( α R zε ρ R ρ zε R ρ ρ q α R U q ρ U Nα ( R R z - /R CsCl.44 NaCl I( 6 [4.] C6H6 C6H6 78

80 79 [5.] * (, ( ( h m a a D d dn π ( ( a d a d D n ( 6 ( ( ( 6 ( ( ( a T k a a T k n d dd T k n n n π π π π [4.] p z π σ π H C

81 8 ] 8 ( [ T k a π + [5.] ( ( ( 6 ( ( ( n n d dd T k n n n + π d dd T k n n ( 6 ( ( ( π n( ( ( ( ( ( ( ( D n d dn n n + + ( ( 6 ( ( ( 6 ( d dd D T k d dd D T k π π [5.] ] ln( ( ln ln [!] ln(! ln! [ln ln M N M N M M N N k M N M N k W k S ln( ln( ] ln( ln [ + + M N k M M N k M N M k dm ds ln( ( ln( ( ( M N k M N k dm ds T k T M N

82 M N f ( k T + [5.4] (x x x (x - x f ( f ( k T + k T k T + k T f( - f( >> k T + > f( [ f ( ] d f ( d f ( d - f( [6.] V ( T ( T kπ ( T T k π ( T + T ( T T S( T T S kπ k T T π ( + T 6 [6.] 7. [V] [J]k.8 - [J/K] T + T 6 K S 4 (.8 π ( [V/K] [6.] Ag n 6. 8

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