A theoretical investigation into some properties of ionic crystals: a quantum mechanical treatment of the cohesive energy, the interionic distance, the elastic constants, and the compression at high pressures with numerical applications to some alkali halides
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Uppsala
Almqvist & Wiksells Boktryckeri
1948
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 2 Bl., XI, 126 S. graph. Darst. |
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| 245 | 1 | 0 | |a A theoretical investigation into some properties of ionic crystals |b a quantum mechanical treatment of the cohesive energy, the interionic distance, the elastic constants, and the compression at high pressures with numerical applications to some alkali halides |c Per-Olov Löwdin |
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Datensatz im Suchindex
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|---|---|
| adam_text | A THEORETICAL INVESTIGATION
INTO
SOME PROPERTIES OF
IONIC CRYSTALS
A QUANTUM MECHANICAL TREATM ENT OF THE COHESIVE
ENERGY, THE INTERIONIC DISTANCE THE ELASTIC CONSTANTS,
AND THE COMPRESSION AT HIGH PRESSURES
WITH
NUMERICAL APPLICATIONS TO SOME
ALKALI HALIDES
By
JPER-OLOY10WDIN
^;t
tj ;
UPPSALA 1948
ALMQVIST amp; WIKSELLS BOK fRYCKERI A I!
INTRODUCTION
CONTENTS
PART I
INVESTIGATION OF THE COHESIVE ENERGY OF A SYSTEM OF
IONS HAVING COMPLETE ELECTRON SHELLS
WITH A DESCRIPTION OF A METHOD OF NUMERICAL CALCULATION
I THE COHESIVE ENERGY OF A SYSTEM OF IONS
1 The Hamiltonian Operator and the One-elertron Approximation 11
2 The Free-ion Wave Functions; The Cohesive Energy in the First Ap
proximation 13
II THE ONE-ELECTRON WAVE FUNCTIONS AND THEIR EXPANSION IN
SPHERICAL HARMONICS
3 The One-electron Wave Functions and the Separation of the Spin 17
4 A Theorem concerning the Orientation of i he Axes of Quantization 18
o Expansion of the Wave Functions in Spherical Harmonics 18
0 Some Kemarks on the Numerical Calculation of the Coefficient Functions
a k (NLM | a, r)22
Method I 22
Method II A 22
7 The Coefficient Functions (N LM a,r) in the Nearest Range of r — 0
A Second Method (II B) of Calculating the Quantities x k h {XL M a ) 25
Method III 25
III THE ELECTROSTATIC ENERGY
„ 8 An Integration Formula 29
9 The Electrostatic Energy 29
10 Numerical Calculation of the Coulomb Correction 31
IV THE EXCHANGE ENERGY
11 A Formula of the Exchange Energy for a Pair of Tons Having Complete
Electron Shells 33
12 Numerical Calculation of the Exchange Energy 35
Method I 35
Method II 36
V THE S-ENERGY
•13 Approximate Treatment of the S-energy b Neglecting Terms Small of
the Third or Higher Orders in the Overlap Integrals S/ir 38
14 Treatment of B fiv and 40
The Many-Body Potential B]l , 41
The Two-body Potentials and 43
The Many-body Potential D/n 44
IX —
15 Some Remarks on the Numerical Calculation of the S-energy 45
Method I 45
Method II: Applications to Ionic Crystals 45
A Simplified Formula of the S-cm-rgy for Ionic Crystals of the
NaCl-type 47
PART II
APPLICATIONS TO IONIC CRYSTALS
A CALCULATION OF THE COHESIVE ENERGY, HIE INTERIONIC DISTANCE, THE
ELASTIC CONSTANTS, AND THE COMPRESSIONS AT HIGH PRESSURES OF SOME
CRYSTALS OF THE NSCI-TYPE
VI THE FORMULAE FOR THE COHESIVE ENERGY AND THE ELASTIC CON
STANTS FOR IONIC CRYSTALS OF THE NaCl-TvPE
16 The Energy Formula : 51
17 The Elastic Constants 52
18 The Failure of the Cauchv Relations 59
VII TREATMENT OF THE NEGATIVE IONS F AND CI
19 Approximation of the Numerically Given Radial Wave-functions/ jYJ (2? )
by Anah tic Functions 64
20 The Functions a k {NL] [ a,r) and yk{ SLM |a,r) 65
Some Remarks on Our Numerical Integrations 69
21 A More Detailed Investigation of the I Miction «0(310 |ar) Associated
with the Chlorine Ion; A Comparison between Different Methods of
Calculation 69
22 The Quantities 1^ and Jg;/,(a r) in i;he Coulomb Correction 70
VIII TREATMENT OF THE POSITIVE IONS Li , Na , AND K
23 Calculation of the Simple and Double Integrals Connected with the
Positive Ions by Numerical Integrations 72
24 Analytical Treatment of Certain Integrals Connected with Na+ 74
IX NUMERICAL CALCULATIONS OF THE COHESIVE ENERGY, THE INTER-
IONIC DISTANCE, AND THE ELASTIC CONSTANTS OF SOME IONIC
CRYSTALS
25 NaCl 76
LANDSHOFF S Calculations Concerning NaCl 76
A Preliminary Calculation Concerning NaCl ; 76
Calculation of the Cohesive liner m v and the Elastic Constants
AccordingtoMethodII77
26 Li CI 82
27 KC1 84
28 LiF 88
29 NaF SO
30 The Elastic Constants c12 and c44 of K F 92
— X —
X THE COMPRESSION OF THE ALKALI HALIDKS AT HIGH PRESSURES;
TRANSITIONS BETWEEN DIFFERENT TYPES OF LATTICES
31 Quantum-mechanical Treatment of KC1 ami NaCl 94
32 Semi-empirical Treatment of the Alkali Hnlides 99
The Correction Depending on the Many body Potentials in the Case
of RbF, RhCI, CsF, and CsCl 103
XI DISCUSSIONS OF THE METHODS OF INVESTIGATION AND OF THE
NUMERICAL RESULTS
33 Survey of the Methods of Investigation and of the Approximations and
Neglections Introduced 106
34 Discussion of the Numerical Results 113
*
APPENDIX TO SECTION 17
35 A Derivation of the Stress-strain Law for Finite Sirains; Definition of
the Elastic Constants 118
* SYMBOLS
— XJ: —
|
| any_adam_object | 1 |
| author | Löwdin, Per Olov 1916-2000 |
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| author_facet | Löwdin, Per Olov 1916-2000 |
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| ctrlnum | (OCoLC)8517392 (DE-599)BVBBV014965639 |
| dewey-full | 548.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 548 - Crystallography |
| dewey-raw | 548.7 |
| dewey-search | 548.7 |
| dewey-sort | 3548.7 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Physik |
| format | Thesis Book |
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| indexdate | 2024-07-09T19:08:53Z |
| institution | BVB |
| language | English |
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| spelling | Löwdin, Per Olov 1916-2000 Verfasser (DE-588)124396747 aut A theoretical investigation into some properties of ionic crystals a quantum mechanical treatment of the cohesive energy, the interionic distance, the elastic constants, and the compression at high pressures with numerical applications to some alkali halides Per-Olov Löwdin Uppsala Almqvist & Wiksells Boktryckeri 1948 2 Bl., XI, 126 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Uppsala, Univ., Phil. Fak., Diss., 1948 Crystallography, Mathematical Ionenkristall (DE-588)4162318-6 gnd rswk-swf Physikalische Eigenschaft (DE-588)4134738-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Ionenkristall (DE-588)4162318-6 s Physikalische Eigenschaft (DE-588)4134738-9 s DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010087162&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Löwdin, Per Olov 1916-2000 A theoretical investigation into some properties of ionic crystals a quantum mechanical treatment of the cohesive energy, the interionic distance, the elastic constants, and the compression at high pressures with numerical applications to some alkali halides Crystallography, Mathematical Ionenkristall (DE-588)4162318-6 gnd Physikalische Eigenschaft (DE-588)4134738-9 gnd |
| subject_GND | (DE-588)4162318-6 (DE-588)4134738-9 (DE-588)4113937-9 |
| title | A theoretical investigation into some properties of ionic crystals a quantum mechanical treatment of the cohesive energy, the interionic distance, the elastic constants, and the compression at high pressures with numerical applications to some alkali halides |
| title_auth | A theoretical investigation into some properties of ionic crystals a quantum mechanical treatment of the cohesive energy, the interionic distance, the elastic constants, and the compression at high pressures with numerical applications to some alkali halides |
| title_exact_search | A theoretical investigation into some properties of ionic crystals a quantum mechanical treatment of the cohesive energy, the interionic distance, the elastic constants, and the compression at high pressures with numerical applications to some alkali halides |
| title_full | A theoretical investigation into some properties of ionic crystals a quantum mechanical treatment of the cohesive energy, the interionic distance, the elastic constants, and the compression at high pressures with numerical applications to some alkali halides Per-Olov Löwdin |
| title_fullStr | A theoretical investigation into some properties of ionic crystals a quantum mechanical treatment of the cohesive energy, the interionic distance, the elastic constants, and the compression at high pressures with numerical applications to some alkali halides Per-Olov Löwdin |
| title_full_unstemmed | A theoretical investigation into some properties of ionic crystals a quantum mechanical treatment of the cohesive energy, the interionic distance, the elastic constants, and the compression at high pressures with numerical applications to some alkali halides Per-Olov Löwdin |
| title_short | A theoretical investigation into some properties of ionic crystals |
| title_sort | a theoretical investigation into some properties of ionic crystals a quantum mechanical treatment of the cohesive energy the interionic distance the elastic constants and the compression at high pressures with numerical applications to some alkali halides |
| title_sub | a quantum mechanical treatment of the cohesive energy, the interionic distance, the elastic constants, and the compression at high pressures with numerical applications to some alkali halides |
| topic | Crystallography, Mathematical Ionenkristall (DE-588)4162318-6 gnd Physikalische Eigenschaft (DE-588)4134738-9 gnd |
| topic_facet | Crystallography, Mathematical Ionenkristall Physikalische Eigenschaft Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010087162&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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