34

X

1.

2.

XXX

EXCEL

XX

35

3.

X

[ ] [ ]

1 150 mSv /

2 500 mSv /

3 13 mSv /

4 10 mSv /

( 2 mSv / )

( Bq )

( Sv )

XX

4.

4.1 X

XX

X t ( cm ) I0 I

(1 / cm )

tII = e0 (1)

Check 1. X

Point 2.

Check 1. XX

Point 2. XX

36

X ( g / cm3 ) / ( cm2 / g )

1

4.2

1X

(2)

d

X

4.3

2X

2

Check 1. X

Point

Check 1.

Point 2.

37

( unit cell )

3

a, b, c

, lattice constants

, ,

3

( Miller indices ) h k

ab a / hb / kc /

h k 4

4

( cubic ) a = b = c = = = 90

2

aaaa

aaaa

100100100100))))200200200200)))) 200200200200))))

100100100100))))

200200200200))))

aaaa

110110110110))))

aaaa

111111111111))))

111111111111))))

aaaa

110110110110))))

38

(2)(3)cubic X X a

4.4

f F

3

( )

=

++=N

1n

i2

nnnnezkyhx

fFl

(5)

5

( body-centered cubic, bcc )

2 N = 2 5

czbyaxrrrrrnnnn ++= 1 a

(x1, y1, z1) = (0, 0, 0) (x2, y2, z2) = (1/2, 1/2, 1/2) 25

{ })(ie1 l+++= khfF 3

h + k + F = 0

h + k + F = 2f 6

Check 1. X

Point 2.

39

5 bcc

( face-centered cubic, fcc )

fccN = 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) 45

{ })i()i()i( eee1 hkkhfF +++ +++= ll

h, k, (h, k, : mixed) F = 0

h, k, (all odd) (all even) F = 4f 7

6 fcc

(0,0,0)(0,0,0)(0,0,0)(0,0,0) (1/2,1/2,1/2)(1/2,1/2,1/2)(1/2,1/2,1/2)(1/2,1/2,1/2)

aaaa

(0,0,0)(0,0,0)(0,0,0)(0,0,0) (1/2,1/2,0)(1/2,1/2,0)(1/2,1/2,0)(1/2,1/2,0)

(1/2,0,1/2)(1/2,0,1/2)(1/2,0,1/2)(1/2,0,1/2)

(0,1/2,1/2)(0,1/2,1/2)(0,1/2,1/2)(0,1/2,1/2)

aaaa

40

h + k + = 4m F = 8f

h + k + = 4m1 F = 4 (1i) f

h + k + = 4m2 F = 0

( 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(

2

)i()i()i( e1eee1l

llkh

hkkhfF

fcc)i()i()i(

fcc eee1hkkh

F+++ +++= ll

+=++ )i(

2

fcc e1lkh

FfF

fcc

all odd all even Ffcc = 4

+=++ )i(

2

e14lkh

fF 7

8

F = 0

( extinction rule )

41

5.

2

1 2

X

X

5.1 X

E R

R = 8.31441 [J /mol /K]

=RT

EexpA (9)

() (kg/m/s)

20 0.000971

25 0.000906

30 0.000787

35 0.000733

40 0.000659

45 0.000598

50 0.000541

1

Check 1. X

Point 2.

40,000 cps X

42

0.2 mm 1 10

X

XX 6000

t ( cm )

X (1) /

( cm2 / g ) EXCEL

2.71 ( g / cm3 ) 4

5.2 ( Si )

K2

28

h, k, 4

2 a 2 a

1.5406 a / a

5.3

NaCl ( sodium chloride structure8 ) CsCl cesium chloride structure,

9 Na, Cs, Cl

fNa, fCs, fCl

Check 1.

Point 2.

Check 1. X

Point

43

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 = 5.6402 CsCl a = 4.123

KCl a = 6.2917 CsBr a = 4.296

CsI a = 4.5679 10

h, k,

45 2Cubic

100 010 001 2 h, k, 2

440 1.5406

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

44

5A, B, C, D, E

K2 2 2

NaCl, KCl, CsCl, CsBr, CsI

6.

a 2

X

7.

X

X

a / a

NaClCsCl

1.X 1988

2.X 1994

3.X 1982

45

1 X

X xI

I

xI

Id

d=

= xII

dd

ln I = - x + C

C ee = xI

x = 0 I = I0

xII 0 e= 11

2

nr = ( p q r )

rr = ( x y z )

nr ( 0rr

rr )

10

( ) 00 = rrrrr

n

p(x - x0) + q(y - y0) + r(z - z0) = 0

px + qy + rz = px0 + qy0 + rz0 = s

px + qy + rz = s

ntr= ( tp tq tr ) 10

p(tp) + q(tq)+r(tr) = s

t ( p2 + q

2 + r

2)=s

222 rqp

st

++=

( px + qy + rz = s ) d

222

222

222rqp

srqp

rqp

sntd

++=++

++==

r 12

= ( = ( = ( = ( p q r p q r p q r p q r ))))

r-rr-rr-rr-r0000

0000

46

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)

x 2 )(f"),(

2

2

ctx =

x

txt 2

)(f"),( 2

2

2

ctx =

c

t

tx

2

2

2

2

2

1

xtc

=

13

=2

G = 2c = G

c

=

2

2

22

2

2

1

1

xGt

=

14

A cos ( xGrr

- t) = A cos G(x /Gt) = A cos G(x ct)

B sin (Gx - t) = A cos ( xGrr

- t) + B sin ( xGrr

- t)

B = iA ei = cos + i sin

= )i(Ae txG rr

47

ez

L+++++=!4

z

!3

z

!2

zz1e

432z

L!5

i!4!3

i!2

i1e5432

i +

+

+=

+

++

+

= LL

!5!3i

!4!21e

5342i

+= sinicose i 15

z = x + i y (x, y) 1

12

1e i =

ie 2i

=

12

X ( = 0) 1e2

i =t

= )i(Ae txG rr

1

=

=N

1n

i

nnexG

fFrr

*** cbkahGrl

srr++=

crrrr

nnnn zbyaxr ++=

1111-1-1-1-1

iiii

-i-i-i-i

coscoscoscos

sinsinsinsin

48

aa*rr

= bb *rr

= cc*rr

= 2

ba*rr

= cb *rr

= ac*rr

= = 0 16

1 *ahGrr

= axrrrnn = nrG

rr = 2hxn

A ( x1 = 0, f1 = 3 )B ( x2 = 1 / 2, f2 = 1 )N = 2

hhxhx fffffF

=

+=+== i21i22i21N

1n

i2

n eeee21n hx

h = 2m F = f1 + f2 = 4 16* = FFI

h = 2m1 2e 21i

21 ==+= ffffF 4* = FFI 17

49

4

69.5 3

4 5

15670 25.160

(precisionprecisionprecisionprecision)

(accuracyaccuracyaccuracyaccuracy)

0

0

0

50

1.583

+) 319.2

320.783 320.8

4

2

5.2976348

+) 5.2976347

0.0000001 1

x

19

(x)

ABC 1

( ) ( ) 22m

1i

i

2

i

22 x)x(fxx == =

51

(x)

20

13

13

21

22

13

2

x1, x2, x3, xn

n

23

2

2 24

24

2

( )

=2

2

2

xexp

2

1)x(f

0 5 10 15 200.0

0.5

1.0

= 2

= 1

= 0.5

f(x)

f(x)

f(x)

f(x)

XXXX( )

= dx2

xexpx

2

12

2

=x

dx)x(fxx

=

( ) ( ) dx)x(fxx 22

=

( ) 22x =

=

=n

1i

ixn

1x

=

=n

1i

2

i

2 )xx(n

1s

22

n

1ns

=

=

=n

1i

2

i

2 )xx(1n

1s

52

25

24

26

s2

27

,

28

(x, y)

z 0

f(x, y) x, y x, y

29

29

30

22s =

x

( )n

s

nx

222 =

=

x

n

s=

x

yy

)y,x(fx

x

)y,x(fz

+

=

y

xz =

y

y

x

x

z

z

=

)y,x(fz =

( ) ( )yyy

zxx

x

zzz iii

+

=

=

=n

1i

2

i

2

z )zz(1n

1s

2

y

2

2

x

2

2

z sy

zs

x

zs

+

=