alexander stukowski ATOMIC-SCALE MODELING OF NANOSTRUCTURED METALS AND ...

185 Pages·2010·26.77 MB·English

alexander stukowski
ATOMIC-SCALE MODELING OF NANOSTRUCTURED
METALS AND ALLOYS
Zur Erlangung des akademischen Grades des Doktors der
Naturwissenschaften (Dr. rer. nat.) genehmigte Dissertation
vorgelegt von Dipl.-Phys. Alexander Stukowski aus Seeheim-Jugenheim
Fachgebiet Materialmodellierung
Fachbereich Material- und Geowissenschaften
Technische Universität Darmstadt
Referent: Prof. Dr. Karsten Albe
Korreferent: Prof. Dr. Horst Hahn
12 2010
Tag der Einreichung: . Mai
2 2010
Tag der Prüfung: . Juli
2010
Darmstadt,
17
D

ATOMIC-SCALE MODELING OF
NANOSTRUCTURED METALS AND ALLOYS
alexander stukowski
Dissertation
2010
Mai
On the cover: Nanocrystalline microstructure loaded with dislocations and
twin boundaries after tensile deformation. The visualization has been de-
rived from an atomistic simulation with the help of a new analysis method
described in this thesis.
Alexander Stukowski: Atomic-scale modeling of nanostructured metals and alloys,
2010
Dissertation, © Mai
CONTENTS
Abstract xi
i introduction 1
1 introduction 3
11 3
. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12 8
. Plasticity of nanocrystalline materials . . . . . . . . . . . . . .
121 8
. . Non-dislocation based deformation mechanisms . . . .
122 10
. . Dislocations in nanocrystalline metals . . . . . . . . . .
13 13
. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
131 13
. . Molecular dynamics . . . . . . . . . . . . . . . . . . . .
132 17
. . Structure preparation . . . . . . . . . . . . . . . . . . . .
133 18
. . Studying mechanical behavior . . . . . . . . . . . . . .
ii characterization of nanocrystalline structures 21
2 visualization and analysis software for atomistic sim
-
ulation data 23
21 23
. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22 23
. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23 24
. Processing pipeline concept . . . . . . . . . . . . . . . . . . . .
24 25
. Additional features . . . . . . . . . . . . . . . . . . . . . . . . .
25 27
. Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26 29
. Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27 30
. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 microstrain fields in nanocrystalline metals 31
31 31
. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32 32
. Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
321 32
. . Molecular dynamics simulation . . . . . . . . . . . . . .
322 33
. . Analysis of atomic level strain . . . . . . . . . . . . . .
323 35
. . Virtual diffractograms . . . . . . . . . . . . . . . . . . .
33 36
. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
331 36
. . Microstrain from virtual diffractograms . . . . . . . . .
332 36
. . Direct analysis of atomic level strain . . . . . . . . . . .
34 41
. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35 43
. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iii dislocations in nanotwinned metals 45
4 dislocation detection methods 47
41 47
. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
contents
42 48
. On-the-fly dislocation detection algorithm (ODDA) . . . . . .
421 50
. . Description of the algorithm . . . . . . . . . . . . . . .
422 60
. . Limitations . . . . . . . . . . . . . . . . . . . . . . . . . .
423 60
. . Implementation and performance . . . . . . . . . . . .
424 61
. . Examples . . . . . . . . . . . . . . . . . . . . . . . . . . .
43 63
. Dislocation extraction algorithm (DXA) . . . . . . . . . . . . .
431 65
. . Dislocation network extraction . . . . . . . . . . . . . .
432 65
. . Analysis of crystalline atoms . . . . . . . . . . . . . . .
433 67
. . The interface mesh . . . . . . . . . . . . . . . . . . . . .
434 68
. . Elastic Burgers circuits . . . . . . . . . . . . . . . . . . .
435 69
. . Transition to a network of one-dimensional lines . . . .
436 70
. . Extraction of other crystal defects . . . . . . . . . . . .
437 70
. . Examples . . . . . . . . . . . . . . . . . . . . . . . . . . .
438 73
. . Additional remarks . . . . . . . . . . . . . . . . . . . . .
44 74
. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 nanotwinned fcc metals strengthening vs softening
: .
mechanisms 77
51 77
. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52 79
. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
521 79
. . Simulation procedure . . . . . . . . . . . . . . . . . . .
522 81
. . Analysis techniques . . . . . . . . . . . . . . . . . . . .
53 81
. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
531 84
. . Planar fault densities . . . . . . . . . . . . . . . . . . . .
532 84
. . Dislocation densities . . . . . . . . . . . . . . . . . . . .
54 86
. Dislocation plasticity in nanocrystalline copper and palladium
55 89
. Dislocation–twin boundary interactions . . . . . . . . . . . . .
56 92
. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57 97
. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iv nanocrystalline alloys 99
6 modeling techniques for alloys at the atomic scale 101
61 101
. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62 101
. Hybrid MD/MC simulation technique . . . . . . . . . . . . . .
621 102
. . The semi-grandcanonical ensemble . . . . . . . . . . .
622
. . Parallelization strategies for semi-grandcanonical MC
102
simulations . . . . . . . . . . . . . . . . . . . . . . . . .
623 104
. . Optimal spatial decomposition . . . . . . . . . . . . . .
624 105
. . Sampling structural and vibrational degrees of freedom
63 105
. Concentration-dependent potentials . . . . . . . . . . . . . . .
631
. . The concentration-dependent embedded atom method
107
(CD-EAM) . . . . . . . . . . . . . . . . . . . . . . . . . .
632 108
. . Derivation of forces for the CD-EAM model . . . . . .
vi
contents
633 111
. . Molecular dynamics performance . . . . . . . . . . . .
634
. . From the two-site concentration model to the one-site
112
concentration model . . . . . . . . . . . . . . . . . . . .
635 115
. . Derivation of forces for the one-site CD-EAM model .
636 117
. . MD/MC performance of the one-site CD-EAM . . . .
64 119
. Summary and conclusions . . . . . . . . . . . . . . . . . . . . .
7 nanocrystalline palladium gold alloy 121
–
71 121
. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72 123
. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
721 123
. . Interatomic potential . . . . . . . . . . . . . . . . . . . .
722 125
. . Alloying . . . . . . . . . . . . . . . . . . . . . . . . . . .
723 125
. . Preparation of nanocrystalline model structures . . . .
724 126
. . Loading . . . . . . . . . . . . . . . . . . . . . . . . . . .
73 126
. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
731 126
. . Structure characterization . . . . . . . . . . . . . . . . .
732 128
. . Stress-strain behavior – compositional effects . . . . . .
733 131
. . Re-straining and strain softening . . . . . . . . . . . . .
734 133
. . Chemical GB relaxation . . . . . . . . . . . . . . . . . .
74 136
. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75 137
. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
139
Conclusions
143
Outlook
147
Erklärung – Disclaimer
149
Danksagung – Acknowledgments
151
Curriculum vitae
153
Bibliography
vii
LIST OF FIGURES
1 11
Figure Deformation mechanism maps for nanocrystalline metals
2 19
Figure Workflow of MD simulations . . . . . . . . . . . . . . .
3 vito 24
Figure O ’s processing pipeline . . . . . . . . . . . . . . . .
4 vito 26
Figure Screenshot of the main window of O . . . . . . . .
5 vito 28
Figure Working with O : A case study . . . . . . . . . . . .
6
Figure Microstrain in nanocrystalline samples as a function of
37
grain size . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 38
Figure Distribution of the atomic strain values . . . . . . . . .
8 38
Figure Strain and stress fields in a nanocrystalline sample . .
9
Figure Average distortions as a function of distance from the
40
grain boundaries . . . . . . . . . . . . . . . . . . . . . .
10
Figure Measurements of intrinsic microstrain of a single grain
41
using the virtual XRD method . . . . . . . . . . . . . .
11 49
Figure Illustration of the dislocation detection method . . . .
12 53
Figure Burgers circuit around a twinning partial . . . . . . . .
13 55
Figure Burgers circuits around two Shockley partials . . . . .
14 56
Figure Dislocation in an fcc crystal with small splitting distance
15
Figure Detection of a screw dislocation in a crystal with free
58
surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16 61
Figure Simulation of a Frank-Read dislocation source . . . . .
17
Figure Large-scale simulation of the failure of a cracked fcc
62
aluminum single crystal under tension . . . . . . . . .
18 63
Figure Close-up view of a dislocation network . . . . . . . . .
19 64
Figure Quantitative analysis of the dislocation density . . . .
20
Figure Schematic illustration of the dislocation extraction algo-
65
rithm (DXA) . . . . . . . . . . . . . . . . . . . . . . . . .
21 66
Figure Construction of the interface mesh around crystal defects
22 67
Figure The halfedge data structure . . . . . . . . . . . . . . . .
23 69
Figure Tracing of dislocations on the interface mesh . . . . . .
24 71
Figure Dislocation analyis of a nanoindentation simulation . .
25 72
Figure Dislocation analysis of a nanocrystalline model structure
26 79
Figure Nanocrystalline model structure used for MD simulations
27 82
Figure Stress-strain curves for twinned and twin-free Cu and Pd
28 83
Figure Cross sections of nanotwinned Cu and Pd . . . . . . .
29
Figure Dislocation density and planar fault densities in nano-
85
twinned metals . . . . . . . . . . . . . . . . . . . . . . .
30 87
Figure Cross sections of deformed nanocrystalline Cu and Pd
viii
List of Figures
31 88
Figure Dislocation embryos in nanocrystalline Cu . . . . . . .
32 89
Figure Lomer dislocation in nanocrystalline Pd . . . . . . . . .
33
Figure Formation and dissolving of a stacking fault ribbon in
91
nanotwinned copper. . . . . . . . . . . . . . . . . . . . .
34 92
Figure Relative atomic displacement map of nanotwinned Cu
35 93
Figure Twin-mediated cross-slip of a screw dislocation . . . .
36 94
Figure Generalized planar fault energy curves for Cu and Pd
37
Figure Schmidfactorhistogramofdislocationsinnanotwinned
95
metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
Figure Schematic illustration of the preferred glide systems in
96
nanotwinned Cu and Pd . . . . . . . . . . . . . . . . . .
39 103
Figure Parallelization of the semi-grandcanonical MC method
40 104
Figure Optimal spatial decomposition of the SGC-MC method
41
Figure Performancecomparison betweenthe CD-EAMandthe
112
standard EAM model . . . . . . . . . . . . . . . . . . .
42 114
Figure Formation energy of the Fe–Cr random alloy . . . . . .
Figure 43 The h(x) polynomial of the Fe–Cr potential . . . . . . . 115
44
Figure Comparison of the timing in a MC simulation of a
50 119
Fe–Cr alloy at % composition . . . . . . . . . . . . . .
45 123
Figure Enthalpy of mixing of the Pd–Au binary alloy. . . . . .
46 124
Figure Generalized planar fault energies of Pd–Au . . . . . . .
47 126
Figure Distribution of elements in grain boundaries of nc Pd–Au
48 128
Figure Grain boundary excess concentration . . . . . . . . . .
49
Figure Stress-strain curves, dislocation and stacking fault den-
129
sity, and GB free volume of Pd–Au . . . . . . . . . . . .
50 131
Figure MaximumyieldstressasafunctionofPd–Aucomposition
51 132
Figure Preloading effects of Pd–Au . . . . . . . . . . . . . . . .
52 134
Figure Strain-rate and cycling effects of Pd–Au . . . . . . . . .
53 135
Figure Structural vs. chemical equilibration of Pd–Au alloys .
54 136
Figure Elastic stress-strain behavior of Pd–Au . . . . . . . . .
ix