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1 1. ( ) (phase diagram) 1) 10% 300 2) 210 3) (β ) 4) 5) ) β 1 2 7) Sn Zn o C 400 Temperature, T / o C Sn o C o C Concentration of Zinc, c / at.% Zn 1: Sn Zn [1]

2 I. 1 (Sn) (Zn) T melt 2: ( ) : Gibbs 2.2 3(A) ( )

3 (A) (B) A B 3: Seebeck (A) (B) ( ) Seebeck Seebeck Seebeck Seebeck 3(B) 2 A B E A ( ) E B ( ) 1K (thermocouple) ( 3(B) A B ) 1 R ( ) CO 1: + R Pt-13%Rh Pt K Ni, Cr Ni T Cu Cu, Ni

4 2: ( [2] ) mv K ( ) C 2 1 :? ( ) 2. 1

5 A ~ input 0.000mV AC100V 4: input :? 3. 2 ( ) (Tammann tube) 3 K 2 20 C mV(60 C ) 80

6 ( ) (A) 2 0 C 0 C 5(B) 20 C 100 C 1 0mV mV (A) V (B) V V o 0 C V 5: 4

7 2 0mV 0.798mV 0.798mV 0mV 100 C = 3.297mV 5(A) 5(B) 0 C = 0.798mV 6: 0 C 2 6 ( ) 400 T = T ( 2) Reference temperature, T/ o C ( Measured temperature, T / o C ) 7: T = (T +0.83) 7 ( A)

8 II. Sn Zn 1 Sn Zn [3] : No Zn (at.%) Sn (at.%) g g g g 79 mg /1.442 = g 25 g : ( ) 8(A) 8(B) 5 5

9 temperature l (A) (B) time time 8: 2 8(A) 1 l 1 : (T E ) (T L )? Gibbs T L T E l : Sn Zn x(at.%zn) T L ( C) T E ( C) l(min/g)

10 4 T L 4 T E Duration per weight, l/min g S A B C Concentration of Zn, c Zn /at.% D Z 9: 0 Zn(Sn) Sn(Zn) S Z 1g l ( 9 ) A B l = 0 S B C D l = 0 Z 3 S Z :?

11 III. 1 ( ) 2 3 ( ) ( 80 ) 4. ( ) ( ) , 400, 600, 800, 1000, ( ) ( ) Al 2 O 3 ( 0.3µm) : (96%) (4%)

12 7. ( ) 8. (TA) (a) (b) (c) (d) 9. 7 : :

11: 10 12 0.95 0.4 population, f 8000 7000 800 600 400 200 0 0.0 0.5 1.

13 11: population, f brightness, B (arbitrary unit) 200 1/ : % 8 (lever rule) ( ) Vegard ( ) Sn Zn Zn Sn 1%

14 IV (3 ) ) 2 2) 3) Q and A

15 10% 25% [1] H. Okamoto, Phase Diagrams for Binary Alloys, AMS International, Ohio, 2000 [2], (1996 ), [3],, 1991 [4],, 2004 [5],,, 1991

16 A 1 vs. 5 E = a T +b a b (a 0.0+b) 4.12 (a b) 9.34 (a b) (a b) ( ) a b S = { (a 0.0+b)} 2 +{4.12 (a b)} 2 (1) + {9.34 (a b)} 2 +{17.23 (a b)} 2 (2) a b S a S a = S b = 0 (3) { = 2 [ (a 0.0+b)] 0.0+[4.12 (a b)] } +[9.34 (a b)] [17.23 (a b)] ( ) = a b = 0 S b { = 2 [ (a 0.0+b)]+[4.12 (a b)] } +[9.34 (a b)]+[17.23 (a b)] ( ) = a 4b = 0 5: ( C) (mv)

17 a b a = b = N x = x 1,x 2,...x N y = y 1,y 2,...y N ( N = 4 x 1 = 0.0 x 2 = x 3 = x 4 = y 1 = y 2 = 4.12 y 3 = 9.34 y 4 = 17.23) N S = {y i (ax i +b)} 2 (4) i=1 S a N = 2x i {y i (ax i +b)} i=1 N N N = 2x i y i +2a x 2 i +2b x i = 0 i=1 i=1 i=1 S b N = 2{y i (ax i +b)} i=1 N N N = 2y i +2a x i +2b 1 = 0 i=1 i=1 i=1 a b N N a x 2 i +b x i = i=1 i=1 N N a x i +b 1 = i=1 i=1 N x i y i (5) i=1 N y i (6) i=1 6 : y = ax 2 +bx+c 6: x i x 2 i y i x i y i

18 B 10 ( ) ( Newton ) q = N(T T R ) (7) q T R N t T q t = mc( T) (8) m, C ( = ) dt dt T t = q mc = N(T T R) mc 1 dt T T R dt = N mc log e (T T R ) 11 h q (8) (9) ( q +h) t = mc T (10) 1 T T R dt dt = N mc 1 T T R h mc ( ) 10 t 1, t 2, t 3... T 1, T 2, T 3... t = (t 1 +t 2)/2 ( ) dt dt = T2 T1 t 2 t 1 11 (K) (9) (11)

19 Temperature, T / o C cooling curve log derivative Logarithmic derivative (min -1 ) Time, t/min 13: ( ) ( ) ( ) min ( 22 44min) 0.014min 1 ( ) (9) 45min 52min (7) (T F (m F C F )

20 C [4] I 30cm 1cm 1cm 10 1mm (JIS ) 21cm ( 14 ) 1mm 20.98cm 1mm 20.99cm 20.98cm cm 20.97cm 20.99cm ±0.02cm cm ( ) 1mm 21.00cm 21cm 10cm 20cm 22cm ( ) 5800K K cm = cm ? 29.61cm, 20.98cm cm, cm S true < S true < < S true < ±5 3 text :

21 cm 2 ( 20.98cm cm cm 2 ) 0.31cm? m n (m < n) m / / mm ( 1 ) 0.31cm=3.1mm = 4.69mm km mm (= km) = km 6378km km 3 ( km) ( km) = km 3 1? a, b δa, δb S δs S +δs S 1+ δs S = (a+δa)(b+δb) ab = ab ab + a δb + δa b ab ab = 1+ δa a + δb b (2 ) δs S = δa a + δb b ( ) 5% 2% 5%+2% = 7%

22 D A 15 A 5 12 Electromotive force, E / V (a) water (heating) Time, t / s Electromotive force, E / V (b) Tin (cooling) Time, t / s Electromotive force, E / V (c) Zinc (cooling) Time, t / s 15: (a) (b) (c) ( ) 15 15(b) 9.40mV 9.27mV E Sn = 9.34±0.07mV 7 7 4? 7: ( C) (mv) (mv)

23 Gauss [5] ( ) µ ( ) σ x x+δx P(x)dx = 1 ( ) exp (x µ)2 2πσ 2σ 2 ( ) E = at +b ( ) E = 232.0a+b 9.34mV ( ) 1 [9.34 (232.0a +b)]2 exp 2π ( 1 P = exp (E ice at ice b) 2 ) 2πσice 2σ 2 ice ( 1 exp (E water at water b) 2 ) 2πσwater 2σ 2 water ( 1 exp (E ) tin at tin b) 2 2πσtin 2σ 2 tin ( 1 exp (E ) zinc at zinc b) 2 2πσzinc 2σzinc 2 a b P = { ( 1 exp (E i (at i +b)) 2 )} i 2πσi 2σi 2 (12) { ( 1 = } exp ) (E i (at i +b)) 2 2πσi 2σ 2 (13) i i i S(a, b; T i, E i, σ i ) = i [E i (at i +b)] 2 σ 2 i A a b n E i T i σ 2 i i=1 n E i σ 2 i=1 i = a = a n T 2 i σ 2 i i=1 n T i σ 2 i=1 i n T i +b σ 2 i=1 i n 1 +b σ 2 i=1 i 7 a = b = ( 16)

24 20 Electromotive force, E / mv Temperature, T / o C 16: 4 ( σ i ) A

64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () m/s : : a) b) kg/m kg/m k

63 3 Section 3.1 g 3.1 3.1: : 64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () 3 9.8 m/s 2 3.2 3.2: : a) b) 5 15 4 1 1. 1 3 14. 1 3 kg/m 3 2 3.3 1 3 5.8 1 3 kg/m 3 3 2.65 1 3 kg/m 3 4 6 m 3.1. 65 5