книги из ГПНТБ / Немошкаленко В.В. Теоретические основы рентгеновской эмиссионной спектроскопии

C O N T E N T S

P re fa c e ........................................................................................

3

G

h a p

t e г l

ELEMENTS OF BAND THEORY

Elements of Abstract Group Theory......................................

8

Definition of Group and Subgroup...............................

8

Conjugate Elements and C la sse s ..................................

10

Invariant

Subgroup

(Normal

D iv iso r).....................

11

Factor-Group

..................................................................

11

Group

Isomorphism

and

Homomorphism . . .

12

Representations of Finite Groups

......................................

14

Matrix

Representation..................................................

14

Reducible

and

Irreducible Representations . . .

17

Orthogonality

Relation

for

Matrix

Elements

of

Irreducible

Representations.....................................

21

Character

of

Representations

......................................

23

Regular Representations..............................................

25

Number of Irreducible Representations.....................

25

Direct

Product of Group

Representations . . . .

28

Representations

of

Schrodinger

Equation

Symmetry

G roup..........................................................................................

29

Plotting of Basic Functions for Irreducible Representa­

tions

...........................................................................................

32

Projection

Operators ..................................................

32

Orthogonality

of Basic F u n ctio n s.............................

35

Selection

R u le s ..............................................................

36

Symmetry

Transformations..................................................

37

Point

G roups..........................................................................

42

Euclidian G roup ......................................................................

48

Brave’s L a ttic e s ......................................................................

50

Discrete Vector Groups..................................................

50

Symmetry

of Brave’s Lattices......................................

52

Types of

Brave’s Lattices..............................................

54

Crystalline

Classes

......................................................

56

Space

Groups

......................................................................

57

Representations of Space Groups..........................................

59

Translation

G ro u p s ......................................................

59

Irreducible Representations of Symmorphic Space

G ro u p s

..........................................................................

64

Irreducible

Representations

of

Nonsymmorphic

Space

G roups..................................................................

67

Dependence of

Group Irreducible

Representations

on Choosing Origin of Coordinates

.........................

71

Continuous

Groups..................................................................

71

Linear

Transformations..............................................

71

Three-dimensional Group of Pure Rotations 0+ (3)

72

Metals

with FCC

L a t t ic e .......................................

275

Metals

with BCC

L a tt ic e .......................................

280

Metals

with HCP L a t t ic e .......................................

283

Peculiarities

of

Electronic Structure in

Transition

M e ta ls ....................................................................................

285

Rare-Earth

M e ta ls ..............................................................

288

Compounds

of TransitionMetals

...................................

289

Alloys of

TransitionM e ta ls .............................................

297

Dielectrics

and

Semiconductors..................................

302

C h a p t

e r

4

UNIELECTRONIC AND MULTIELECTRONIC

APPROXIMATIONS IN THE THEORY

OF X-RAY EMISSION SPECTRUM

Calculation of Intensity Distribution in X-Ray

Emis­

sion Bands

in Unielectronic Approximation .

. .

.

313

Calculations

of Intensity

Distribution

in

X-Ray

317

Emission

Bands of Light-Weight Elements

. .

.

Calculations

of Intensity

Distribution

in X-Ray

326

Emission Bands of Transition

M etals.....................

Emission X-Ray Spectra of Disordered Alloys .

. .

.

335

Plasma Satellites

in Soft

X-Ray Emission

Spectra

of

M etals......................................................................................

345

Unielectronic

Density

of States

of System

of

Interac­

ting Electrons and Its

Relation with X-Ray

Emission

Spectra

. ■..............................................................................

352

Emission

Spectra

Shape

in Low-energetic

and

High-

energetic

R e g io n s ..............................................................

358

References..............................................................................

363

Su m m ary ..............................................................................

375