Stress and strain in solids: a formalism for the LAPW method
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Aachen
Shaker
2001
|
| Series: | Berichte aus der Physik
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Graz, Univ., Diss., 2001 |
| Physical Description: | X, 146 S. graph. Darst. |
| ISBN: | 3826596900 |
Staff View
MARC
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| 100 | 1 | |a Thonhauser, Timo |d 1972- |e Verfasser |0 (DE-588)123546273 |4 aut | |
| 245 | 1 | 0 | |a Stress and strain in solids |b a formalism for the LAPW method |c Timo Thonhauser |
| 264 | 1 | |a Aachen |b Shaker |c 2001 | |
| 300 | |a X, 146 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Berichte aus der Physik | |
| 500 | |a Zugl.: Graz, Univ., Diss., 2001 | ||
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Record in the Search Index
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| adam_text |
CONTENTS
1
INTRODUCTION
1
1.1
HISTORICAL
REVIEW
.
1
1.2
MOTIVATION
.
3
1.3
STRUCTURING
.
3
2
THE
STRAIN
AND
STRESS
TENSOR
5
2.1
SCALARS,
VECTORS,
AND
TENSORS
.
5
2.2
TRANSFORMATION
AND
DEFINITION
OF
A
TENSOR
.
8
2.3
SYMMETRY
AND
SECOND-RANK
TENSORS
.
9
2.4
THE
STRAIN
TENSOR
.
12
2.4.1
ONE
DIMENSIONAL
STRAIN
.
12
2.4.2
TWO-DIMENSIONAL
STRAIN
.
12
2.4.3
THREE
DIMENSIONAL
STRAIN
.
16
2.5
THE
STRAIN
TRANSFORMATION
.
17
2.6
THE
STRESS
TENSOR
.
19
2.6.1
INTERPRETATION
.
19
2.6.2
PROOF
THAT
A
FORMS
A
TENSOR
.
20
2.6.3
SPECIAL
FORMS
OF
STRESS
.
21
2.7
RELATION
BETWEEN
STRESS
AND
STRAIN
.
22
2.8
ELASTIC
CONSTANTS
.
22
2.8.1
DEFINITION
.
22
2.8.2
GEOMETRICAL
INTERPRETATION
AND
CALCULATION
.
23
2.8.3
CONNECTION
TO
STRESS
.
25
3
DENSITY
FUNCTIONAL
THEORY
27
3.1
BASIC
THEOREMS
.
27
3.2
LOCAL
DENSITY
APPROXIMATION
.
28
3.3
TOTAL
ENERGY
.
29
4
THE
LAPW
METHOD
33
4.1
LAPW
BASICS
.
33
4.2
REPRESENTATION
OF
P
AND
V
.
38
4.3
SOLVING
INTEGRALS
.
40
VIII
CONTENTS
4.3.1
INTEGRALS
OVER
THE
INTERSTITIAL
.
40
4.3.2
INTEGRALS
OVER
THE
MUFFIN-TIN
REGION
.
42
4.4
WHY
LAPW?
.
43
5
STRESS
WITHIN
THE
LAPW
METHOD
45
5.1
STRESS
DEFINITION
FOR
SOLIDS
.
45
5.2
ION-ION
INTERACTION
.
47
5.3
ION-ELECTRON
INTERACTION
.
49
5.4
ELECTRON
ELECTRON
INTERACTION
.
50
5.5
KINETIC
ENERGY
CONTRIBUTION
.
50
5.5.1
INTERSTITIAL
CONTRIBUTION
.
52
5.5.2
VALENCE
CONTRIBUTION
OF
THE
SPHERES
.
53
5.5.3
CORE
CONTRIBUTION
.
53
5.6
EXCHANGE-CORRELATION
CONTRIBUTION
.
54
5.7
INFINITIES
.
56
5.7.1
INTERSTITIAL
CONTRIBUTION
.
57
5.7.2
SPHERES
CONTRIBUTION
.
58
5.7.3
MADELUNG
TERM
.
61
5.8
PULAY-LIKE
TERMS
.
61
5.9
CORE
CORRECTION
.
62
5.10
VALENCE
CORRECTION
.
64
5.10.1
INTERSTITIAL
CONTRIBUTION
.
67
5.10.2
SPHERES
CONTRIBUTION
.
68
5.10.3
CHANGE
IN
AI
M
AND
BI
M
.
71
5.11
KINETIC
ENERGY
DISCONTINUITY
.
73
5.11.1
SPHERICAL-HARMONICS
CONTRIBUTION
.
75
5.11.2
PLANE-WAVE
CONTRIBUTION
.
76
6
SIMPLE
PRESSURE
FORMULA
79
6.1
PRESSURE
AS
PART
OF
THE
STRESS
.
79
6.1.1
SIMPLE
COULOMB
PRESSURE
.
80
6.1.2
SIMPLE
KINETIC
PRESSURE
.
82
6.2
THE
VIRIAL
THEOREM
.
82
7
STRESS
IN
DIFFERENT
MATERIALS
85
7.1
ALUMINUM
.
85
7.1.1
PRESSURE
IN
ALUMINUM
.
86
7.1.2
CONVERGENCE
WITH
SELF-CONSISTENCY
CYCLES
.
94
7.1.3
CONVERGENCE
WITH
K
MESH
.
100
7.1.4
CONVERGENCE
WITH
7?G
MAX
.
105
7.1.5
CHANGING
SPHERE
RADII
.
110
7.2
SILICON
.
ILL
7.2.1
PRESSURE
IN
SILICON
.
ILL
CONTENTS
IX
A
YI
M
MACHINERY
115
A.L
DEFINITION
OF
THE
BASICS
.
115
A.2
DERIVATIVES
OF
SPHERICAL
HARMONICS
.
117
A.
3
COUPLING
OF
SPHERICAL
HARMONICS
.
121
B
IMPROVEMENTS
AND
EXTENSIONS
127
B.L
LOCAL
ORBITALS
.
127
B.2
RELATIVISTIC
MODIFICATIONS
.
128
B.3
SIMPLIFYING
SUMS
.
129
B.3.1
SUMS
OVER
ATOMS
.
129
B.3.
2
SUMS
OVER
THE
FIRST
BRILLOUIN
ZONE
.
130
ACKNOWLEDGMENTS
131
SYMBOLS
AND
ABBREVIATIONS
133
LIST
OF
FIGURES
135
LIST
OF
TABLES
137
BIBLIOGRAPHY
139
INDEX
143 |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV014086755 |
| illustrated | Illustrated |
| indexdate | 2024-11-22T17:30:11Z |
| institution | BVB |
| isbn | 3826596900 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009649686 |
| oclc_num | 52216571 |
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| physical | X, 146 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Shaker |
| record_format | marc |
| series2 | Berichte aus der Physik |
| spelling | Thonhauser, Timo 1972- Verfasser (DE-588)123546273 aut Stress and strain in solids a formalism for the LAPW method Timo Thonhauser Aachen Shaker 2001 X, 146 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Berichte aus der Physik Zugl.: Graz, Univ., Diss., 2001 Verzerrungstensor (DE-588)4316421-3 gnd rswk-swf Spannungstensor (DE-588)4316422-5 gnd rswk-swf Festkörper (DE-588)4016918-2 gnd rswk-swf LAPW-Methode (DE-588)4381621-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Festkörper (DE-588)4016918-2 s LAPW-Methode (DE-588)4381621-6 s Spannungstensor (DE-588)4316422-5 s Verzerrungstensor (DE-588)4316421-3 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009649686&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Thonhauser, Timo 1972- Stress and strain in solids a formalism for the LAPW method Verzerrungstensor (DE-588)4316421-3 gnd Spannungstensor (DE-588)4316422-5 gnd Festkörper (DE-588)4016918-2 gnd LAPW-Methode (DE-588)4381621-6 gnd |
| subject_GND | (DE-588)4316421-3 (DE-588)4316422-5 (DE-588)4016918-2 (DE-588)4381621-6 (DE-588)4113937-9 |
| title | Stress and strain in solids a formalism for the LAPW method |
| title_auth | Stress and strain in solids a formalism for the LAPW method |
| title_exact_search | Stress and strain in solids a formalism for the LAPW method |
| title_full | Stress and strain in solids a formalism for the LAPW method Timo Thonhauser |
| title_fullStr | Stress and strain in solids a formalism for the LAPW method Timo Thonhauser |
| title_full_unstemmed | Stress and strain in solids a formalism for the LAPW method Timo Thonhauser |
| title_short | Stress and strain in solids |
| title_sort | stress and strain in solids a formalism for the lapw method |
| title_sub | a formalism for the LAPW method |
| topic | Verzerrungstensor (DE-588)4316421-3 gnd Spannungstensor (DE-588)4316422-5 gnd Festkörper (DE-588)4016918-2 gnd LAPW-Methode (DE-588)4381621-6 gnd |
| topic_facet | Verzerrungstensor Spannungstensor Festkörper LAPW-Methode Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009649686&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT thonhausertimo stressandstraininsolidsaformalismforthelapwmethod |