APPENDIX A

Physical Parameters and Data

A.I Physical Constants and Relations

TABLE A.I. Physical constants. Velocity of light e = 2.99792· IO lOemjs Planck constant h = 6.62608 . 10 -27 erg· s

Fz = 1.05457· 10 -27 erg· s Electron charge e = 4.8032 . 10 -lOeGSE

e2 = 2.3071· 10 -1gerg . em Electron mass me = 9.1094· 1O-2~g Proton mass mp = 1.6726·1O-24g

Atomic unit of mass 1.6605 . 10 -24 g

Avogadro number 6.0222. 1023 mol -I Stefan-Boltzmann constant (J' = 5.670· 10 -12 W j(em2 K4)

TA

BL

E A

.2.

Con

vers

ion

fact

ors

for

ener

gy u

nits

.

J er

g eV

ca

l/m

ol

em

J 1

10

6.2

42

.10

1 " 1.

4384

. lO~j

5.03

46 .

10"

erg

10 ·7

1

6.2

42

·10

1.

4384

. 10

10

5.

0346

. 10

1 >

eV

1.60

2· 1

0 I~

1.60

2· 1

0 ·I

~ 1

2.30

45·

10'

8.06

60·

10j

cal/

mol

6.

952

. 10

-'"

6.9

52

·10

4.

3393

. 1

0->

1 0.

3497

3 em

1.

986

. 10

-"

1.98

6. 1

0 ·1

0

1.23

98 .

10-4

2.

8573

1

K

1.38

06 .

10 -~j

1.38

06 .

10 -1

6

8.6

17

.10

-5

1.98

59

0.69

504

kJ/m

ol

1.66

06.1

0 -~

v 1.

6606

.10-

14

0.01

036

238.

85

83.6

1 ---------

K

7.24

3. I

OU

7

.24

3.1

01 >

1.

1605

· 10

" 0.

5031

9 1.

4386

1

120.

28

-----------

kJ/m

ol

6.02

2·10

'u

6.02

2·10

u

96.4

8 4.

187·

10 -j

0.

0119

6 8.

314.

10 -3

1 -------

~ ? [ ("

) I 8- ~ I· IV

Vl ....

TA

BL

E A

.3.

Som

e re

lati

ons

of p

lasm

a ph

ysic

s ex

pres

sed

in c

onve

nien

t uni

ts.

Rel

atio

nshi

p F

orm

ula

Fac

tor

C

Uni

ts

1 v

= .j

2s/

m,

v =

C.j

s/m

5.

931·

10 c

m/s

si

n e

V, m

in

emu'

) v-

velo

city

, s-e

nerg

y, m

-mas

s 1.

389·

1O°c

m/s

si

n e

V, m

in a

mu'

) 5.

506·

10'

cm/s

si

n K

, m i

n em

u')

1.28

9· lO~cm/s

sin

K, m

in a

mu'

)

2 -

J:8T

v=

- "m

v=CJ~

6.69

2.10

7 cm

/s

Tin

eV

, m i

n em

u·>

6.21

2· 1

05cm

/s

Tin

K, m

in

emu'

) 1.

455·

104

cm/ s

T

in K

, min

am

u')

3 rw

= (1;

,;) Il

j -th

e W

igne

r-Se

its

radi

us

rw =

C (~r

j 0.

7346

A

m i

n am

u'>,

p i

n g

/cm

3

4 ko

= v

. nr

?v -

rate

con

stan

t ko

=

T1 1

2m1 /

6p

-2/3

2.44

6 . 1

0 .1

2 cm

3 / s

Tin

K, m

in a

mu'

),

pin

g/c

m3

5 w

= s

/n, s

-ph

oto

n e

nerg

y, w

-fr

eque

ncy

W=

CS

1.52

0 . IOI~ s

-I

sin

eV

w =

2nc

/A, A

-wav

elen

gth

W=

C/A

1.

885

. 10

" s -

I A

incm

6 w

p =

J 4

n N

ee2 /

me,

wp

-pla

sma

freq

uenc

y w

p =

c..[

fii;

5.64

2. I

04s

1 N

einc

m

3

7 rD

= J

T /(

8n

Nee

2 )-D

ebye

-Hii

ckel

rad

ius

rD =

../

T/N

e 52

5.6c

m

Nei

ncm

3

, T

ineV

4.

879c

m

Nei

n cm

-j, T

in K

8

N =

p/T

N

= C

p/T

7.

340.

I02

1cm

-3

p

ina

tm,

Tin

K

p -

pres

sure

, N

-num

ber

dens

ity

9.65

8 . 1

01s c

m -3

p

in T

orr,

T i

n K

9

D =

3A

.j'i

nT

/J.L

/(\6

Na

)-D

= C

../T

/J.L

/(N

a)

4.27

8. I

Ol9

cm2/s

T

in K

, J.L

in am

u,*>

di

ffus

ion

coef

fici

ent

N i

n cm

-j,

a i

n A

2 J.

L-r

educ

ed m

ass,

a-m

ean

cro

ss s

ecti

on

1.59

5cm

'/s

the

sam

e T,

J.L,

a,

N =

2.6

89·

10lY

cm-j

10

Fac

tor

of S

aba

form

ula

f =

CT

3 /2

7.63

5. 1

01

9cm

-3

Tin

IO'K

,min

emu

f

= lm

T/(

2n/i

l)3

/2J

3.01

8. l

Oz1

cm -

3

T in

eV

, m i

n em

u 1.

879.

lO

zocm

-3

T in

K, m

in

amu

. emu-

elec

tron

mas

s un

it (m

e =

9.10

94·

1O

-Z8g

),am

u-at

omic

mas

s un

its

(ma

= 1.

6605

· 1O

-Z48)

.

i I ! I

N

V>

.j:

>.

?> I [ '1:1 I 8- o ~

TA

BL

E A

.4.

Ioni

zati

on p

oten

tial

(J)

of a

tom

s in

the

gro

und

stat

es.

Ato

m

J,eV

A

tom

J,

eV

Ato

m

J,eV

A

tom

H(~SI/2)

13.5

98

Ke

S l/2

) 4.

341

Rb(

'SI/

2)

4.17

7 CS(~SI/2)

He(

So)

24

.586

C

a( S

o)

6.11

3 Sr

(' S

o)

5.69

5 B

a( S

o)

Li("

SI/2

) 5.

392

SCe

D3/

2)

6.56

2 Y

(' D

3/2)

6.

217

La('

-D3/

2)

Be(

So)

9.

323

TW

F2)

6.

82

ZrC

F2)

6.

837

Ce(

G4

)

Be

Pl/2

) 8.

298

Ve F

3/2)

6.

74

Nb(

bD1/

2)

6.88

Ta

(4 F

3/2)

C

ep o

) 11

.260

C

rCS 3

) 6.

766

MO

CS 3

) 7.

099

WC

SDo)

N

(4 S

3/2)

14

.534

M

n(b

SS/2

) 7.

434

TC(b

SS/

2)

7.28

Re

(b S

S/2)

O

ep 2

) 13

.618

F

eeD

4)

7.90

2 R

uCF

s)

7.36

6 O

sCD

4)

Fe

p 3/2

) 17

.423

C

oe

F 9/ 2

) 7.

86

Rh

e F 9

/ 2)

7.46

Ir

e F

9/2)

N

e( S

o)

21.5

65

Ni(

3F 4

) 7.

637

Pd(

So)

8.

336

PtC

-D3)

N

a("S

I/2)

5.

139

CU(~SI/2)

7.72

6 A

g('S

I/2)

7.

576

AU

("SI

/2)

Mg(

So)

7.

646

Zn(

So)

9.

394

CdC

So)

8.99

4 H

g( S

o)

AW

P1/

2)

5.98

6 G

a('-

P 1/ 2

) 5.

999

In('

-P1/

2)

5.78

6 T

WP

1/2)

Si

C Po

) 8.

152

Gee

Po)

7.

900

SnC

P o)

7.34

4 P

h(' P

o)

P(Q

S3/2

) 10

.487

A

Se

S 3/2

) 9.

789

Sb

eS 3

/2)

8.60

9 B

ieS3

/2)

Sep

2)

10.3

60

Seep 2

) 9.

752

Teep 2

) 9.

010

Rn(

'So)

C

WP

3/2)

12

.968

B

rep 3

/ 2)

11.8

14

Ie P

3/2)

10

.451

R

a(' S

o)

Ar(

'So)

15

.760

K

r('S

o)

14.0

00

Xe(

'So)

12

.130

U

CL

6)

--

J,eV

3.

894

5.21

2 5.

577

5.53

9 7.

89

7.98

7.

88

8.73

9.

05

8.96

9.

226

: 10

.438

6.

108

7.41

7 :

7.28

6 10

.75

I

5.27

8 !

~.194 -

>

tv

~ S

.....

(") "'"0 ~ ~

)­ N f. i N

V

I V

I

TA

BL

E A

. 5.

Ele

ctro

n af

fini

ties

(E

A)

of a

tom

s. E

A i

s th

e el

ectr

on b

indi

ng e

nerg

y in

the

neg

ativ

e io

n w

hose

el

ectr

on s

tate

is i

ndic

ated

; "n

ot"

mea

ns th

at t

he e

lect

ron

affi

nity

of t

he a

tom

is

not

a po

siti

ve v

alue

. Io

n E

A,e

V

Ion

EA

,eV

Io

n E

A,e

V

Ion

EA

,eV

H

C

S)

0.75

416

S ep

) 2.

0771

Se

ep

) 2.

0207

I

CS

) 3.

0590

H

e no

t C

l C

S)

3.61

27

Br

CS)

3.

3636

X

e no

t L

i (

S)

0.61

8 A

r no

t K

r no

t C

S C

S)

0.47

16

Be

not

K

CS)

0.

5015

R

b eS

) 0.

4859

B

a no

t B

ep

) 0.

2797

C

a ("

P)

0.02

45

Sr

("P

) 0.

048

La

CF

) 0.

5 C

(4

S)

1.26

29

SC

CD

) 0.

19

Zr

CF

) 0.

43

HI

not

CeD

) 0.

035

Ti

CF

) 0.

08

Nb

C'D

) 0.

89

Ta

C'D

) 0.

32

N

not

V

C'D

) 0.

53

Mo

(~S)

0.

75

W (~S)

0.81

6 o

("P

) 1.

4611

C

r (O

S)

0.67

T

c ('

D)

0.6

Re

C'D

) 0.

15

F

eS

) 3.

4012

M

n no

t R

u (,

F)

1.0

Os

("F

) 1.

1

Ne

not

Fe

('F

) 0.

151

Rh

('F

) 1.

14

Ir

eF

) 1.

5638

N

a eS

) 0.

5479

C

o ('

F)

0.66

2 P

d ("

D)

0.56

P

t ("

D)

2.12

8 M

g no

t N

i ("

D)

1.l

5

Ag

( S)

1.

302

Au

( S)

2.

3086

A

l ('

P)

0.44

1 C

u (

S)

1.23

5 C

d

not

Hg

not

Si

('S

) 1.

385

Zn

not

In ep

) 0.

3 T

l ep

) 0.

2 Si

("

D)

0.52

3 G

a ep

) 0.

5 Sn

(4

S)

1.l1

2 P

b (4

S)

0.36

4 Si

("

P)

0.02

9 G

e (4

S)

1.23

3 Sb

ep

) 1.

05

Bi

ep

) 0.

95

P

(,P

) 0.

7465

A

s ep

) 0.

80

Te

ep

) _

1.97

08_

Po

ep

) 1.

9 -

tv

Vl

0\ ?> 1 <J

> [ '" el i 8- a !=l. '"

A.3 Gaseous Values 257

A.3 Gaseous Values

TABLE A.6. Coefficients of self-diffusion.The diffusion coefficients of atoms or molecules in the parent gas are reduced to the number density N = 2.689· 1019cm-3corresponding to normal conditions (T = 273K, p = 1 arm).

Gas D,cm~/s Gas D,cm"/s Gas D,cm"/s He 1.6 H2 1.3 H2O 0.28 Ne 0.45 N2 0.18 CO2 0.096 Ar 0.16 O2 0.18 NH3 0.25 Kr 0.084 CO 0.18 CH4 0.20 Xe 0.048

TABLE A. 7. Thermal conductivity coefficients of gases. Values correspond to pressure I arm and are expressed in 1O-4 W /(cm . K).

T,K 100 200 300 400 600 800 1000 H2 6.7 13.1 18.3 22.6 30.5 37.8 44.8 He 7.2 1l.5 15.1 18.4 25.0 30.4 35.4

CH4 - 2.17 3.41 4.88 8.22 - -NH3 - 1.53 2.47 6.70 6.70 - -H2O - - - 2.63 4.59 7.03 9.74 Ne 2.23 3.67 4.89 6.01 7.97 9.71 11.3 CO 0.84 1.72 2.49 3.16 4.40 5.54 6.61 N2 0.96 1.83 2.59 3.27 4.46 5.48 6.47 Air 0.95 1.83 2.62 3.28 4.69 5.73 6.67 O2 0.92 1.83 2.66 3.30 4.73 5.89 7.10 Ar 0.66 1.26 1.77 2.22 3.07 3.74 4.36

CO2 - 0.94 1.66 2.43 4.07 5.51 6.82 Kr - 0.65 1.00 1.26 1.75 2.21 2.62 Xe - 0.39 0.58 0.74 1.05 1.35 1.64

258 A. Physical Parameters and Data

TABLE A.8. Viscosity coefficients of gases. Values of viscosity coefficients correspond to the pressure 1 atm and are expressed in units of 10-5 g j(cm . s).

T,K 100 200 300 400 600 800 1000

H2 4.21 6.81 8.96 10.8 14.2 17.3 20.1 He 9.77 15.4 19.6 23.8 31.4 38.2 44.5

CH4 - 7.75 Il.l 14.1 19.3 - -H2O - - - 13.2 21.4 29.5 37.6 Ne 14.8 24.1 31.8 38.8 50.6 60.8 70.2 CO - 12.7 17.7 21.8 28.6 34.3 39.2

N2 6.88 12.9 17.8 no 29.1 34.9 40.0 Air 7.11 13.2 18.5 23.0 30.6 37.0 42.4 O2 7.64 14.8 20.7 25.8 34.4 41.5 47.7 Ar 8.30 16.0 22.7 28.9 38.9 47.4 55.1

CO2 - 9.4 14.9 19.4 27.3 33.8 39.5 Kr - - 25.6 33.1 45.7 54.7 64.6 Xe - - 23.3 30.8 43.6 54.7 64.6

AA Parameters of Condensed Systems

Below we treat some infonnation for bulk liquids at the melting point and give parameters corresponding to liquid large clusters. Data for parameters of liquids are taken from some reference books, mainly from "Handbook of Chemistry and Physics", 79 Edition (ed. D.R.Lide) (London, CRC Press, 1998-1999). In the following Tables Tm is the melting point of a metal, Tb is its boiling point, and we use fonnula (3-15) for the binding energy of atoms in a large liquid cluster consisting of n atoms, which has the fonn

(A4-I)

where the parameter Co is the cohesive energy of bulk per atom, and the parameter A follows from fonnula (3-28), which connects the surface energy with the surface tension and corresponds to the bulk liquid state at the melting point. Here we define Co as the evaporation energy per atom for a bulk liquid in the vicinity of the melting point. Analogously, the equilibrium pressure of saturated vapor near a plane liquid surface is given by the fonnula

Psat(T) = Po exp(-co/ T), (A4-2)

and the parameters co, Po of this fonnula for liquids correspond to the temperature range near the melting point. In the Tables below !1Hfus is the specific fusion energy which is spent per atom, and D is the dissociation energy of the diatomic molecule. In Tables AID and All are given values of the Wigner-Seits radius rw, which is detennined by fonnula (2-1) as

rw = ( 3m )1/3, 4np

(A4-3)

A.4 Parameters of Condensed Systems 259

where m is the atomic mass, and p is the bulk density, which is taken for the liquid state at the melting point.

In the case of condensed rare gases, the cohesive energy for the liquid state per atom co, which we find from the dependence (A2.2), must differ from the sublimation energy for the solid state per atom Csub by the fusion energy !1Hfus,

Comparison of these values shows the accuracy of the data. Next, owing to a weak interaction between nearest neighbors, parameters of interaction of neighboring atoms in bulk systems of condensed rare gases are close to those of the diatomic molecule. In particular, the distance between nearest neighbors a in a bulk crystal is close to the equilibrium distance between atoms of the diatomic molecule. Since the crystals of rare gases have a close packed structure, their sublimation energy per atom is close to 6D. For this reason the scaling law is valid for the parameters under consideration, as follows from Table A.I O.

TABLE A.9. Parameters of the pair interaction potential for rare gases, parameters of condensed rare gases and large liquid clusters.

Ne Ar Kr Xe Re. A 3.09 3.76 4.01 4.36

D.meV 3.64 12.3 17.3 24.4 Tm. K 24.6 83.7 115.8 161.2 Tb• K 27.1 87.3 119.8 165.0 a. A 3.156 3.755 3.892 4.335

esub. meV 20 80 116 164 A.meV 15.3 53 73 97

po.104atm 0.34 1.15 1.14 1.28 eo.meV 18.6 68 95 132

!:!.Hjus • meV 3.42 12.3 17.0 23.7

TABLE A.l O. Reduced parameters of condensed rare gases.

Ne Ar Kr Xe Average alRe 1.028 1.000 0.996 0.993 1.004 ± 0.014

Tml D 0.583 0.585 0.576 0.570 0.578 ± 0.006 esubl D 5.50 6.49 6.66 6.71 6.35 ± 0.50 AID 4.20 4.31 4.22 3.98 4.2 ± 0.1

eolD 5.1 5.5 5.5 5.4 5.4 ± 0.2

!:!.Hjusi D 0.955 0.990 0.980 0.977 0.98 ± 0.01

rwlRe 0.601 0.594 0.595 0.589 0.595 ± 0.003

PoR;ID 17 31 27 28 26±6

Ele

men

t Tm

.K

L

i 45

4 B

e 15

60

B

2348

N

a 37

1 M

g 92

3 A

l 93

3 K

33

6 C

a 11

15

Sc

1814

T

i 19

41

V

2183

C

r 21

80

Fe

1812

C

o 27

50

Ni

1728

C

u 13

58

Zn

693

Ga

303

Ge

1211

R

b 31

2 S

r 10

50

Zr

2128

N

b 27

50

Mo

2886

R

h 32

37

Pd

18

28

TA

BL

E A

.ll.

Ene

rget

ic p

aram

eter

s o

f lar

ge l

iqui

d cl

uste

rs.

Tb.

K

rw.

A

So. e

V

A.e

V

t:J.H

/ us•

meV

po

.IO

S atm

16

15

1.75

1.

61

0.99

31

1.

3 27

44

1.28

3.

12

1.4

82

23

4273

1.

27

5.4

1.3

520

20

1156

2.

14

1.08

0.

73

27

0.63

13

63

1.82

1.

44

1.4

88

1.1

2730

1.

65

3.09

2.

0 11

0 11

10

32

2.65

0.

91

0.62

24

0.

37

1757

2.

24

1.67

1.

4 89

0.

72

3103

1.

81

3.57

-

150

8 35

60

1.67

4.

89

3.2

150

300

3680

1.

55

5.1

3.7

223

150

2944

1.

41

3.79

2.

4 21

8 30

30

23

1.47

3.

83

3.0

143

11

5017

1.

45

4.10

3.

1 16

8 3.

5 ~3100

1.44

4.

13

2.9

181

7 28

35

1.47

3.

40

2.2

138

15

1180

1.

58

1.22

1.

5 76

1.

6 26

80

1.65

2.

76

1.5

58

2.0

3106

1.

63

3.70

1.

3 38

0 15

96

1 2.

85

0.82

0.

54

23

0.28

16

55

2.44

1.

5 1.

3 77

0.

32

4650

1.

85

6.12

3.

8 22

0 52

~5100

1.68

7.

35

4.5

310

360

4912

1.

60

6.3

4.5

390

59

3968

1.

55

5.42

3.

8 28

0 7.

7 32

36

1.58

3.

67

2.9

170

6.0

D.e

V

1.05

0.

10

2.8

0.73

0.

053

0.46

0.

55

0.13

1.

7 1.

4 2.

62

1.66

0.

9 0.

9 1.

7 1.

99

0.03

4 1.

18

2.5

0.49

5 0.

13

1.5

5.5

4.1

1.5

0.76

~

o ~ I [ '"

tj I 8- tJ

~

TAB

LE A

.l1.

(con

t.)

Elem

ent

Tm,

K

T h,

K

rwA

A

co, eV

A

,eV

A

g 12

35

2435

1.

66

2.87

2.

0 C

d 59

4 10

40

1.77

1.

06

1.4

In

430

2353

1.

87

2.38

1.

5 Sn

50

5 28

75

1.89

3.

10

1.6

Sb

904

1860

1.

95

1.5

1.04

C

s 30

1 94

4 3.

05

0.78

0.

51

Ba

1000

19

13

2.54

1.

71

1.4

Ta

3290

57

31

1.68

8.

1 4.

7 W

36

95

5830

1.

60

8.59

4.

7 Re

34

59

;:::; 5

880

1.58

7.

62

5.3

Os

;:::;3

100

;:::;5

300

1.55

7.

94

4.7

Ir

2819

;::

:;470

0 1.

58

6.5

4.9

Pt

2041

40

98

1.60

5.

4 3.

6 A

u 13

37

3129

1.

65

3.65

2.

5 H

g 33

4 63

0 1.

80

0.62

1.

23

T1

577

1746

1.

93

1.78

1.

3 Pb

60

0 20

22

1.97

1.

95

1.4

Bi

544

1837

2.

02

1.92

1.

2 U

14

08

4091

1.

77

4.95

3.

8

tlH

jus

, m

eV

po,l

O'a

tm

120

15

290

1.4

34

0.17

73

0.

24

210

0.03

22

0.

24

74

0.17

38

0 25

0 54

0 23

0 63

0 42

60

0 23

0 43

0 13

0 23

0 40

13

0 12

24

7.

7 43

2.

0 23

1.

0 12

0 50

95

5.

4

D,e

V

1.67

0.

04

0.83

2.

0 3.

1 0.

452 - - 6.

9 - - -0.

93

2.31

0.

055

0.00

1 0.

83

2.08

-

> ~

'"0 I g,

()

o 6- I f '" N

0\

TA

BL

E A

.12.

E

ntha

lpie

s o

f for

mat

ion

of g

aseo

us a

tom

s A

Hf

from

met

als

at T

= 29

8K.

The

ent

halp

ies

for

conv

ersi

on o

f sol

ids

in a

mon

atom

ic g

as

are

give

n be

low

for

the

pre

ssur

e I

atm

and

tem

pera

ture

298

K.

Not

e th

at th

e va

lue

80

of T

able

s A

.t 0

and

A.l

l is

the

ene

rgy

of f

orm

atio

n o

f ato

ms

at

the

mel

ting

poi

nt f

rom

the

liqu

id s

tate

, so

that

bot

h va

lues

80

and

AH

f ch

arac

teri

ze th

e at

om b

indi

ng e

nerg

y un

der

diff

eren

t con

diti

ons.

Evi

dent

ly, t

he

valu

e A

Hf

is g

reat

er t

han

80

, be

caus

e it

als

o in

clud

es t

he f

usio

n en

ergy

and

the

ene

rgy

of

heat

ing

of t

his

soli

d ac

coun

ting

for

var

iati

on i

n th

e va

por

pres

sure

. B

ut f

or s

tron

g bo

nds,

as

take

s pl

ace

in m

etal

s, t

his

diff

eren

ce i

s no

t lar

ge.

Hen

ce,

thou

gh t

he r

atio

801 A

Hf

is l

ess

than

uni

ty,

it is

clo

se t

o un

ity. T

able

A.1

2 co

ntai

ns v

alue

s o

f thi

s ra

tio

who

se a

vera

ge v

alue

for

the

elem

ents

incl

uded

in t

he ta

ble

is e

qual

to 0

.94

± 0

.04 .

E

lem

ent

AH

f,e

V

Eo

Ele

men

t A

Hf,

eV

..

.!L

. E

lem

ent

AH

f,e

V

...!

L.

aH

L

aH

, a

H,

Li

1.65

0.

98

Cu

3.50

0.

97

Sb

2.72

0.

55

Be

3.36

0.

92

Zn

1.35

0.

90

Cs

0.80

0.

98

B

5,86

0.

92

Ga

2.82

0.

98

Ba

1.87

0.

91

Na

1.12

0.

96

Ge

3.86

0.

96

Ta

8.12

1.

00

Mg

1.53

0.

94

Rb

0.84

0.

98

W

8.82

0.

97

Al

3.42

0.

90

Sr

I. 71

0.

88

Re

7.99

0.

95

K

0.93

0.

98

Zr

6.31

0.

97

Os

8.16

0.

94

Ca

1.84

0.

91

Nb

7.47

0.

98

Ir

6.93

0.

94

Sc

3.92

0.

91

Mo

6.82

0.

92

Pt

5.87

0.

95

Ti

4.91

0.

99

Rh

5.78

0.

94

Au

3.80

0.

96

V

5.34

0.

96

Pd

3.92

0.

94

Hg

0.63

0.

98

Cr

4.11

0.

92

Ag

2.96

0.

97

TI

1.89

0.

94

Fe

4.32

0.

89

Cd

1.16

0.

91

Pb

2.03

0.

96

Co

4.41

0.

93

In

2.52

0.

94

Bi

2.15

0.

89

Ni

--~.~ _

0.93

Sn

3.

13

0.99

U

5.

53

0.93

-

N ~

~ ? [ i [ ~

TAB

LE A

.l3.

Wor

k fu

nctio

ns (W

o) o

f ele

men

ts in

the

poly

crys

tal s

tate

.

Elem

ent

Wo.

eV

Elem

ent

Wo.

eV

Elem

ent

Wo.

eV

Elem

ent

Li

2.38

C

o 4.

41

In

3.8

Hf

Be

3.92

N

i 4.

50

Sn

4.38

Ta

B

4.

5 C

u 4.

40

Sb

4.08

W

C

4.

7 Zn

4.

24

Te

4.73

R

e N

a 2.

35

Ga

3.96

C

s 1.

81

Os

Mg

3.64

G

e 4.

76

Ba

2.49

Ir

A

l 4.

25

As

5.11

La

3.

3 Pt

Si

4.

8 Se

4.

72

Ce

2.7

Au

S 6.

0 Rb

2.

35

Pr

2.7

Hg

K

2.22

Y

3.

3 N

d 3.

2 TI

C

a 2.

80

Zr

3.9

Sm

2.7

Pb

Sc

3.3

Nb

3.99

C

d 3.

1 B

i Ti

3.

92

Mo

4.3

Tb

3.15

Th

V

4.

12

Ru

4.60

D

y 3.

25

U

Cr

4.58

Pd

4.

8 H

o 3.

22

Mn

3.83

A

g 4.

3 Er

3.

25

Fe

4.31

C

d 4.

1 Tm

3.

10

Wo.

eV

3.53

4.

12

4.54

5.

0 4.

7 4.

7 5.

32

4.30

4.

52

3.7

4.0

4.4

3.3

3.3

>

~

'"C I Q.,

(j 8. [ V

l 1 '" ~

w

264 A. Physical Parameters and Data

TABLE A.14. Debye temperatures for crystals of elements.

Element eD• K Element eD.K Element eD• K Element eD• K Li 344 Mn 410 Nb 275 Hf 252 Be 1440 Fe 470 Mo 450 Ta 240 C 2230 Co 445 Ru 600 W 400 Ne 75 Ni 450 Rh 480 Re 430 Na 158 Cu 343 Pd 274 Os 500 Mg 400 Zn 327 Ag 225 Ir 420 AI 428 Ga 320 Cd 209 Pt 240 Si 645 Ge 374 In \08 Au 165 Ar 92 As 282 Sn 200 Hg 72

K 91 Se 90 Sb 211 TI 78 Ca 230 Kr 72 Te 153 Pb 105 Sc 360 Rb 56 Xe 64 Bi 119 Ti 420 Sr 147 Cs 38 Gd 200 V 380 Y 280 Ba 110 Th 163 Cr 630 Zr 291 La 142 U 207

APPENDIX B

Mechanical and Electrical Parameters of Particles Ellipsoidal and Close Forms

Below we give analytical expressions for symmetric particles that have circular cross sections. The main geometric figure of these particles is an ellipsoid whose surface satisfies the equation

(BI)

where p, z are cylindrical coordinates with the origin at the figure's center, and a, b, b are the lengths of the principal axes of the figure. The case b > a corresponds to a flattened ellipsoid, while b < a corresponds to a stretched ellipsoid, and for the sphere we have a = b.

B.l The Effective Hydrodynamic Radius

The effective radius of a particle of any form Ref is introduced on the basis of the Stokes formula (1-16) such that in the case of a sphere the effective radius coincides with the radius of the sphere

F = 6Jr I1vRef (B2)

Here F is the resistive force that acts on a particle moving in a gas, 11 is the gas viscosity, v is the velocity of the particle, and this formula is valid for small Reynolds numbers and if Ref greatly exceeds the mean free path of gaseous atoms or molecules. Values of Ref are the following

266 B. Mechanical and Electrical Parameters of Particles Ellipsoidal and Close Fonns

B.l.l Aflattened ellipsoid, motion along its axis (z-axis)

8b [2q; 2(1- 2q;2) ~]-I a Ref ="3 1 _ q;2 + (1 _ q;2)3/2 arctan q; , q; = b ~ 1

The limiting cases: Sphere (a = b, q; = l)Ref = a Disk (a = 0, q; = O)Ref = :!

(B3)

B.l.2 Aflattened ellipsoid, motion directed perpendicular to its axis (x-axis)

8b [q; 2q;2 - 3 ~J -I a R f = - - -- - arcsin 1 - m2 m = - < 1 e 3 1 _ q;2 (1 _ q;2)3/2 't'" 't" b-

The limiting cases: Sphere (a = b, q; = 1) Ref = a Disk (a = 0, q; = 0) Ref = 1~

B.l.3 A stretched ellipsoid, motion along its axis (z-axis)

(B4)

8b[ 2q; 2q;2-1 (q;+~)]-I a Ref ="3 - q;2 _ 1 + (q;2 _ 1)3/2 In (rp _~) , q; = b ~ 1 (B5)

The limiting cases: Sphere (a = b, q; = 1) Ref = a

Rod (a »b, q; ---+ 00) Ref = 3In[(2a~~)-1/2l

B.l.4 A stretched ellipsoid, motion directed perpendicular to its axis (x-axis)

8b [q; 2q;2 - 3 ( ~)J -I a Ref ="3 q;2 _ 1 + (q;2 _ 1)3/2 In q; + y q;~ - 1 , q; = b ~ 1

The limiting cases: Sphere (a = b, q; = 1) Ref = a

Rod (a » b, q; ---+ 00) Ref = 3In(2a~~+1/2)

B.l.S Torus (the large radius R, the small radius a, R » a)

Motion directed perpendicular to the plane of the torus

4nR Ref = 3 In (2nRja -0.75)

(B6)

Motion is in the plane the torus

rrR Rf------­

e - 3In (2rr Ria - 2.09)

B.2 Capacity (C)

B.2.1 The ellipsoid's capacity

A flattened ellipsoid (a < b):

The limiting cases: Sphere (a = b) C = a Disk (b »a) C = 2blrr A stretched ellipsoid (a > b):

Jb2 - a2 C=---:----c:-:-

arccos( alb)

Jb2 - a2 Jb2 - a2

B.2 Capacity (C) 267

(B7)

(B8)

C = = 2 Arc ch(alb) In (a+~ -b2 )

(B9)

The limiting cases: Sphere (a = b) C = a Rod (l = 2a, 1 » b) C = II (2 In ~)

B.2.2 Torus (the large radius R, the small radius a, R » a):

(BlO)

B.2.3 Spherical segment (R is the radius, () is the angle between the polar axis and a conic boundary):

C = ~ (sin() + () (Bll) rr

The limiting cases: Sphere «() = rr) C = R Hemisphere C = G + ~) R = 0.818R

268 B. Mechanical and Electrical Parameters ofParticIes Ellipsoidal and Close Forms

B.3 Polarizability

B.3.1 Polarizability of a metallic ellipsoid

Stretched ellipsoid (a > b):

where all, a..L are the components of the polarizability tensor (all = azz , a..L = axx = a yy ), nz + 2np = 1, and

1 - E2 ( 1 + E ) g2 nz = -- In -- - 2E E = 1 - -2E2 1 - E ' a2

The limiting cases: Ball (a = b) all = a..L = a3

Almost ball (a ~ b) all = ab2 (1 - ~E2rl, a..L = ab2 (1 + E2/Sr 1

Rod (a» b)

a3 2ab2

all = 3ln [(2a/b) _ 1]' a..L = -3-

Flattened ellipsoid (a > b): The limiting cases Ball (a = b) all = a..L = a3

Disk (a «b) all = ~~

B.3.2 Polarizability of a dielectric ellipsoid

The relation between the polarizability a of a dielectric particle that occupies a volume V and consists of a material of a dielectric constant £, and the polarizability of the same metallic particle am is given by formula (2-11):

1 1 4Jr -=-+--­a am V(£-l)

This leads to the following values of the polarizability of a particle of the corresponding form: Ball (radius r) all = a..L = r3:~: Rod (the length I, the radius r) all = r2I e-:/; a.l. = r2/:~: Ellipsoid

(2-10a)

where

1-E2 (l+E ) ~ nx + 2ny = 1, nx = w- In 1 _ E - 2E , E = V 1 - [2' (2-lOb)

B.3 Polarizability 269

Here r, I are the lengths of the corresponding axes for a prolate ellipsoid of revo­lution (I > r). In the limiting case when the ellipsoid is close to a ball (l - r « r, E « 1) fonnulas (2-9) give

r21 ( 2E2 ) -1 r21 ( E2 )-1 all = 3 1 - 5 . a~ = 3 1 + "5 .

which are transfonned to the ball polarizability (2-3) if r = I. In the other limiting casel» r(IE -11« I),whichcorrespondstoastretchedcylinder,fromfonnulas (2.9) it follows that

12 1 2 all = 3 [In(21/r) - 1]- , a~ = r I

APPENDIX C

C.I Models of Clusters and Small Particles

Various models can be useful for describing of different properties oflarge clusters and small particles as well as processes involving them. Below we give a list of such models that are used in the book.

1. Model of liquid drop considers a cluster or small particle as a liquid drop for the analysis of collision processes involving clusters and processes of cluster evaporation and atom attachment to the cluster surface (Problems 1.1, 1.2).

2. Model of hard (rigid) sphere for the analysis of elastic collisions of atomic particles with a sharply varied interaction potential. According to this model an elastic collision of particles (atom-cluster or cluster-cluster) is similar to that of billiard balls (Problem 1.5).

3. Metallic cylinder as a model of a chain aggregate is used for the analysis of electric properties of a chain aggregate and the character of its growth as a result of attachment of solid spherical particles to its poles (Problems 2.5-2.8, 5.28, 5.29).

4. Dipole approximationfor radiation assumes that transitions in atomic systems under action of an electromagnetic wave are caused by interaction of the elec­tric field of the wave with an induced dipole moment of the atomic system (problem 2.27).

5. Ball model of an atomic system with a close packed structure assumes atoms in a crystal to be similar to rigid balls (Problem 3.1).

6. Two-shell cluster approximation assumes the presence in the cluster of only two shells or layers that are partially filled (Problems 6.3, 6.4).

7. Model of fixed knots of a cluster assumes that transition of an atom to a new position does not change the positions of surrounding atoms (problem 6.6).

272 C. Appendix

8. Kompaneets model of a finite system of bound atoms assumes that different eigenvibrations in this system have identical frequencies (problem 6.10).

9. Einstein model of oscillations in a finite system of bound atoms assumes that eigenvibrations in this system belong to individual atoms (problem 6.10).

10. Statistical cluster model assumes a random distribution of the cluster excitation energy by cluster vibrational modes (Problem 6.10).

11. Model of a large statistical weight of the liquid state is based on the assumption that the liquid state of a cluster or bulk is an excited state of the system with a large statistical weight compared to the ground state (problem 6.16).

12. Model of heat equilibrium of a cluster with atomic particles assumes that after collision with a cluster an atomic particle takes the average kinetic energy corresponding to the cluster's temperature (problems 7.17).

References

Clusters

I. B.F.G. Johnson. Transition Metal Clusters. Wiley, Chichester, 1980 2. F.A. Cotton. Clusters: Structure and Bonding. Springer-Verlag, Berlin, 1985. 3. M. Moskovits. Metal Clusters. Wiley, New York, 1986 4. S. Sugano. Microcluster Physics. Springer-Verlag, Berlin, 1991 5. B.M. Smimov. Ion Clusters and van der Waals Molecules. Gordon, Philadelphia,

1992. 6. G. Gonzalez-Moraga. Cluster Chemistry: Introduction to the Chemistry of Transition

Metals and Main Group of Elements for Molecular Clusters. Springer-Verlag, Berlin, 1993

7. H. Haberland (Ed.). Cluster of Atoms and Molecules /I (Solvation and Chemistry of Free Clusters, and Embedded, Supported and Compressed Clusters). Springer-Verlag, New York, 1994.

8. U. Kreibig, M. Vollmer. Optical Properties of Metal Clusters. Springer-Verlag, Berlin, 1995

9. H. Haberland (Ed.). Cluster of Atoms and Molecules I (Theory, Experiment, and Clusters of Atoms). Springer-Verlag, Berlin, 1995

10. V. V. Kresin. Collective Resonances and Response Properties of Electrons in Metal Clusters. Phys. Rep. 220 (1992) I

II. T.P. Martin. Cluster Structures. Phys. Rep. 273 (1996) 199 12. U. Naher, S. Bjomholm, S. Frauendorf. Fission of Metal Clusters. Phys. Rep. 285

(1997) 245

Atomic Physics and Collision of Atomic Particles

I. A.S. Kompaneets. Theoretical Physics. Dover, New York, 1961. 2. H.A. Bethe.lntermediate Quantum Mechanics. Benjamin Inc., New York, 1964.

274 References

3. L.D. Landau and E.M. Lifshitz. Quantum Mechanics. Pergamon Press, Oxford, 1965. 4. P. J. Robinson and K.A. Holbrook. Unimolecular Reactions. Wiley, New York 1982. 5. H. Haken. ThePhysics 0/ Atoms and Quanta: Introduction to Experiments and Theory.

Springer, Berlin, 1994 6. F. Harald. Theoretical Atomic Physics. Springer, Berlin, 1991 7. H.S. W. Massey. Atomic and Molecular Collisions. Taylor and Francis, London, 1979.

Crystal Structures

1. L.D. Landau and E.M. Lifshitz. Quantum Mechanics. Pergamon, Oxford, 1965. 2. N.W. Ashcroft and N.D. Merrnin. Solid State Physics. Holt, Rinehart and Wilson,

New York, 1976. 3. Ch. Kittel. Introduction to Solid State Physics. Wiley, New York, 1986

Statistical Physics and Thermodynamics

1. H.B. Callen. Thermodynamics. Wiley, New York, 1960. 2. K.S. Pitzer and L. Brewer. Thermodynamics. McGraw Hill, New York, 1961. 3. A.S. Kompaneets. Theoretical Physics. Dover, New York, 1961. 4. K. Huang. Statistical Mechanics. Wiley, New York, 1963. 5. R. Kubo. Statistical Mechanics. North Holland, Amsterdam, 1965. 6. D. Ter Haar. Elements o/Thermostatics. Addison-Wesley, New York, 1966. 7. G.H. Wannier. Statistical Physics. Wiley, New York, 1966. 8. D. Ter Haar and H.Wergeland. Elements o/Thermodynamics. Addison-Wesley, New

York,1967. 9. R. Kubo. Thermodynamics. North Holland, Amsterdam, 1968.

10. C. Kittel. Thermal Physics. Wiley, New York, 1969. 11. O.Penrose. Foundations 0/ Statistical Mechanics. Pergamon Press, Oxford, 1970. 12. R.P. Feynman. Statistical Mechanics. Benjamin, Massachusetts, 1972. 13. L.D. Landau and E.M. Lifshitz. Statistical Physics. Vol 1. Pergamon Press, Oxford:

1980. 14. L.D. Landau and E.M. Lifshitz. Statistical Physics. Vol. 2, Pergamon Press, Oxford,

1980. 15. K. Stove. Introduction to Statistical Mechanics and Thermodynamics. Wiley, New

York,1984.

Physical Kinetics, Phase Transitions, Nucleation

1. J.P. Hirth and G.M. Pound. Condensation and Evaporation. Pergamon Press,Oxford, 1963.

2. H.S. Green and C.A. Hurst. Order-Disorder Phenomena. Interscience, New York, 1964.

3. R. Brout. Phase Transitions.Benjamin. New York, 1965. 4. P.A. Egelstatf. An Introduction to the Liquid State. Pergamon Press, Oxford, 1967.

References 275

5. H.E. Stanley. Introduction to Phase Transition and Critical Phenomena. Claredon Press, Oxford, 1971

6. F.F. Abraham. Homogeneous Nucleation Theory. Academic Press, New York, 1974. 7. Shang-Keng Ma. Modern Theory of Critical Phenomena. Benjamin, New York, 1976. 8. AR Ubbelohde. The Molten State of Matter. Wiley, Chicester, 1978. 9. J.M. Ziman. Models of Disorder. Cambridge Univ. Press, Cambridge, 1979.

10. E.M. Lifshits and L.P. Pitaevskii. Physical Kinetics, Pergamon Press, Oxford 1981 .

Physics of Ionized Gases and Gas-Discharge Plasma

1. L.B. Loeb. Basic Processes of Gaseous Electronics. Univ. California Press, Berkeley, 1955.

2. J.D. Cobine. Gaseous Conductors. Dover, New York, 1958. 3. S.C. Brown. Introduction to Electrical Discharges in Gases. Wiley, New York and

London, 1966. 4. F. Llewelyn-Jones. The Glow Discharge. Methuen, New York, 1966. 5. M.F. Hoyaux. Arc Physics. Springer, New York, 1968. 6. E. Nasser. Fundamentals of Gaseous Ionization and Plasma Electronics. Wiley, New

York,1971. 7. D.A Frank-Kamenetskii. Plasma-the Fourth State of Matter. Plenum, New York,

1972. 8. E.W. McDaniel and E.A. Mason. The Mobility and DiffUsion of Ions in Gases. Wiley,

New York, 1973. 9. L.G.H. Huxley and RW. Crompton. The Diffusion and Drift of Electrons in Gases.

Wiley, New York, 1974. 10. B. Chapman. Glow Discharge Processes. Wiley, New York, 1980. II. V.E. Golant, AP. Zhilinsky, and I.E. Sakharov. Fundamentals of Plasma Physics.

Wiley, New York, 1980. 12. B.M. Smimov. Physics of Weakly Ionized Gases. Mir, Moscow, 1981. 13. Applyied Atomic Collision Physics. Vol. 1. Atmospheric Physics and Chemistry, ed.

H.S.W. Massey, D.R Bates. Academic Press, New York, 1982. 14. Basis Plasma Physics, ed. AA. Galeev, RN. Sudan. North Holland, Amsterdam,

1983. 15. F.p. Chen. Introduction to Plasma Physics and Controlled Fusion. Plenum, New York

and London, 1984. 16. W. Neuman. The Mechanism of the Thermoemitting Arc Cathode. Academic-Verlag,

Berlin, 1987. 17. V.E. Fortov and I.T. Iakubov. Physics of Non ideal Plasma. Hemisphere, New York,

1990. 18. Y.P. Raizer. Gas Discharge Physics. Springer, Berlin, 1991. 19. P.P.J.M. Schram. Kinetic Theory of Gases and Plasmas. Kluwer, Dordrecht 1991. 20. M.1. Boulos, P. Fauchais and E. Pfender. Thermal Plasmas. Plenum, New York and

London, 1994. 21. Plasma Science: From Fundamental Research to TechnolOgical Applications.

National Academy Press, Washington, 1995

Index

Absorption cross section of a spherical particle 67

Absorption cross section of a cylindrical particle 67

Activation energy 26, 30 Active centers 12,48,52,54,56 Aerogel 181, 182 Aerosol plasma 222, 231 Aggregation in electric field 184, 185 Arrhenius formula 30 Association 161-165 Association in an electric field 165-169 Attachment of atoms to a cluster 145

Ball model 88 Blackbody 68, 76 Block structure of fcc-clusters 105 Bulkness of a particle 199-201

Caloric curve 213, 214 Centered fcc-cluster 105, 106 Chain aggregate 40, 41 Charge separation in the atmosphere

234 Chemical equilibrium of clusters 246,

247 Chemical potential of a cluster 59, 187,

189, 190 Close packed structure 80, 81 Cluster-bulk transition 199-201

Cluster-cluster diffusion limited aggregation 179, 181

Cluster instability 248-250 Cluster plasma 222, 238 Cluster temperature, 59, 239 Coagulation 169 Coexistence of solid and liquid cluster

phases 202, 214 Collision integral for cluster growth

241,242 Combustion process 26, 27 Coordination number 90 Correlation radius 180, 182 Critical radius, size 145, 146, 149, 152,

153, 155,243 Cross section of scattering of radiation

on a small particle 66 Cuboctahedral cluster 109-111 Cuboctahedron 92, 93, 117 Cubic cluster 111, 112

Debye frequency 198 Debye temperature 264 Debye-Hiickel radius 223, 228, 229,

230 Decay of an excited cluster 196-198 Diffusion coefficient for particles in a

gas 6, 7 Diffusion cross section 2

278 Index

Diffusion limited aggregation 179, 180 Diffusion regime of condensation 158 Diffusion regime of particle combustion

32 Diffusion regime of particle evaporation

157, 158 Diffusion regime of quenching 28 Dipole approximation for radiation 65 Distribution function of clusters on size

147,148,149,151,243,244 Distribution of atoms by shells 191,

192 Dusty plasma 222

Equilibrium of clusters with gas 145, 148

Einstein model 196 Einstein relation 6 Electron affinity of atoms 256 Evaporation of clusters 145, 146

Face-centered cubic (fcc) structure 80, 82,103

Facets of a crystalline particle 92 Fee-surfaces 93, 136 Fermi-Dirac distribution 59, 186 Fixed knots model 186, 192 Fractal aggregate 77, 179 Fractal dimensionality 77, 78, 179 Fractal fiber 185 Fragmentation of cluster 197 Free cluster enthalpy 152 Freezing of a cluster 219 Free fall of particles 9 Fuks formula 13

Gas discharge plasma 223 Gauss formula 50 Generation of clusters 150 Grey coefficient 31,68, 74

Hard sphere model I, 5 Heat capacity of a cluster 205 Heat regime of cluster growth 169,

176--178 Hexagonal cluster 116--118 Hexagonal structure 80, 104 Hexahedron 110, 116, 117 Hydrodynamic radius 265

Icosahedral cluster 124, 125, 126, 128, 192-195

Icosahedron 12 I - I 23 Ideality of a plasma 230 Inert gas crystal 89,90 Inert gas liquid 90, 91 Interaction of vacancies 207, 208, 210,

211,212 Ionization equilibrium for a small

particle 48 Ionization potential of atoms, 255

Kinetic regime of quenching 28, 29 Kinetic regime of particle combustion

32,34 Kinetic regime of evaporation 158, 159 Kirchhoff law 68 Knudsen number 8, 14 Kompaneets model 196

Langmuir isoterm 55 Langevin formula 8 Lennard-Jones interaction 83 Lennard-Jones crystal 83-85 Light output 75, 77 Lifetime of excited cluster 196--198 Liquid drop model 2 Liquid state 202, 203, 207 Long-range interaction 79

Magic numbers 103 Mean square displacement of cluster

atoms 204 Mixing of structures 136 Mobility of a small particle 6, 7, 17 Morse interaction potential 86 Morse crystal 86, 87

Noncentered fcc-cluster 105, 106, 107 Nucleation in expanding vapor 172, 174

Octahedral clusters 112, 113 Octahedron 92, 93 Optimization of the cluster energy 124 Optimization of the crystal energy 84,

86 Oscillator strength 72, 73

Pair interaction potential 82

Partition function 187, 191, 192 Plasma crystal 234 Plasmon concept of absorption 70 Polarizability 37 Polarizability of a chain aggregate 41,

43,44 Polarizability of a dielectric particle 39 Polarizability of a metallic particle 37,

38 Polarizability tensor 44 Principle of detailed balance 147

Rate constant of atom attachment to a cluster 147

Rate constant of atom-cluster collision 2 Rate constant, of cluster-cluster

association 162, 163 Rate constant of cluster-cluster collision

3 Rate of cluster evaporation 147 Rate constant of mutual neutralization

of charged clusters 3 Rayleigh problem 46 Rayleigh scattering 66 Recombination of ions on clusters 232,

233 Recombination rate constant 8, 163 Regular fcc-particle 91-93, 113 Regular truncated octahedron 92-94, 96 Resistance force 5, 7, Reynolds number 9 Richardson-Dushman formula 58 Root mean square of bond length

fluctuation 203

Saddle form of the cluster potential energy 195,216,219

Saha formula 4, 49,62 Schottky condition 225 Shells of a cluster 82, 83, 85, 103, 104 Short-range interaction 79, 80 Smoluchowski formula 14,25

Index 279

Sound wave 10, 11 Specific binding energy 83 Specific surface energy 94, 106 Spectral power of radiation 68, 69 Sphericity coefficient of a cluster 107,

109,123 Sphericity of a geometric figure 99, 109 Statistical cluster model 197 Statistical weight of a liquid cluster 211 Statistical weight of a solid cluster 193,

194,195 Stefan-Boltzmann law 69 Structures of small particles in a

discharge plasma 235 Stokes formula 7 Sublimation energy 83 Supersaturation degree 149, 153 Surface energy 88, 91, 92 Surface tension 46, 100

Thermal conductivity of gases 257 Thermal explosion of a particle 29, 33 Thermoemission of electrons 48, 58, 59,

60 Thomson model 60 Three-body process 159 Threshold of particle thermal instability

31,33 Truncated hexahedron 116 Truncated octahedron 113, 114, 115 Twinning 81 Two-level approach 203 Two-shell model 189

Vacancies 186 Viscosity coefficient 258 Vision function 76, 77

Wigner-Seits radius 2, 229, 230, 258, 260,261

Work function 51, 59, Wulf criterion 98, 99

Graduate Texts in Contemporary Physics

(continuedfrom page ii)

B.M. Smimov: Clusters and Small Particles: In Gases and Plasmas

M. Stone: The Physics of Quantum Fields

F.T. Vasko and A.V. Kuznetsov: Electronic States and Optical Transitions in Semiconductor Heterostructures

A.M. Zagoskin: Quantum Theory of Many-Body Systems: Techniques and Applications