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E-raamat: Computational Materials Science: An Introduction, Second Edition

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(Korea Institute of Science and Technology, Seoul, South Korea)
  • Formaat: 376 pages
  • Ilmumisaeg: 25-Nov-2016
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781498749756
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Computational Materials Science: An Introduction, Second EditionSuurem pilt
  • Formaat: 376 pages
  • Ilmumisaeg: 25-Nov-2016
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781498749756
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This book covers the essentials of Computational Science and gives tools and techniques to solve materials science problems using molecular dynamics (MD) and first-principles methods. The new edition expands upon the density functional theory (DFT) and how the original DFT has advanced to a more accurate level by GGA+U and hybrid-functional methods. It offers 14 new worked examples in the LAMMPS, Quantum Espresso, VASP and MedeA-VASP programs, including computation of stress-strain behavior of Si-CNT composite, mean-squared displacement (MSD) of ZrO2-Y2O3, band structure and phonon spectra of silicon, and Mo-S battery system. It discusses methods once considered too expensive but that are now cost-effective. New examples also include various post-processed results using VESTA, VMD, VTST, and MedeA.

Arvustused

"The delightful and pragmatic style of this book is irresistible. It intrigues the reader to start using the leading methods in computational materials science, to simulate interesting systems, and to become excited about the remarkable capabilities of todays computational methods." Erich Wimmer, Materials Design, Inc., Angel Fire, New Mexico, USA

"Books such as this allow my students the new generation - to catch up with our fast progressing knowledge and technology. Definitely, this book has help me to teach density functional theory to my students and mentees. I will continually use this book for my class and research. " Al Rey Villagracia, De La Salle University, Manila, Philippines

"This text takes you on a working tour of the most important computational methods available to materials scientist today. You get to know the underlying theory with enough detail to manage understanding, and it projects you to the next stages of employing particular codes to solve problems and predict properties. Better than a Hitchhikers guide through the materials computational galaxy because its intentionally a guide not a random one." Rene Corrales, University of Arizona, USA

"The second edition of Computational Materials Science: An Introduction improves upon the first version of the textbook. It includes examples designed to be used with Open Source Computational Codes. This opens the book to many more students worldwide. I commend the author for this outstanding addition. The second edition continues the well written explanations present in the first. It covers the mechanics of calculations in enough detail so that the techniques are understood by the reader. The examples highlight important problems in condensed matter physics. They also go into detail where the calculations have problems. I find that this helps students to understand the limitations of the techniques. The author has really written an excellent textbook for computational materials science." Jeff Terry, Illinois Institute of Technology, USA

"Simulation remains a discipline that is usually acquired in a research lab. This is particularly true in a chemistry department. How do the students then get knowledge of the simulation techniques? One response is a book like Computational Materials Science where theory is simply explained, and several exercises are shown. Moreover, materials are currently important in science, and simulation will play an increasingly important role. More and more publications are published where a simulation part needs to be inserted. However, most of the time, it has been carried out by non-expert persons! This book is certainly intended for them." Armand Soldera, University of Sherbrooke, Quebec, Canada

"This is a book designed with a beginning practitioner in mind. It presents key insights in a format that is highly accessible. The author uses plenty of analogies and everyday examples and draw parallels with the subject matter. The presentation of the material is not overly burdened by equations and formulae. Even so, the author does a remarkable job of helping the reader make choices that are faced in practice." Sachin Shanbhag, Florida State University, USA

"....a good text. It suites well for Engineering students." Oleg Rubel, McMaster University, Hamilton, Ontario, Canada

Preface xix
Author xxiii
Chapter 1 Introduction 1(10)
1.1 Computational materials science
1(3)
1.1.1 Human beings versus matter
1(2)
1.1.2 Computational materials science
3(1)
1.1.2.1 Goals
3(1)
1.1.2.2 Our approach
3(1)
1.2 Methods in computational materials science
4(4)
1.2.1 Basic procedures of computational materials science
5(1)
1.2.2 Finite element analysis
5(1)
1.2.3 Monte Carlo method
6(1)
1.2.4 Molecular dynamics
7(1)
1.2.5 First-principles methods (ab initio methods)
7(1)
1.2.6 Remarks
7(1)
1.3 Computers
8(1)
Reference
9(2)
Chapter 2 Molecular dynamics 11(36)
2.1 Introduction
12(3)
2.1.1 Atomic model in MD
12(1)
2.1.2 Classical mechanics
13(1)
2.1.3 Molecular dynamics
14(1)
2.2 Potentials
15(9)
2.2.1 Pair potentials
17(2)
2.2.2 Embedded atom method potentials
19(3)
2.2.3 Tersoff potential
22(1)
2.2.4 Potentials for ionic solids
23(1)
2.2.5 Reactive force field potentials
24(1)
2.3 Solutions for Newton's equations of motion
24(5)
2.3.1 N-atom system
24(2)
2.3.2 Verlet algorithm
26(1)
2.3.3 Velocity Verlet algorithm
27(1)
2.3.4 Predictor-corrector algorithm
27(2)
2.4 Initialization
29(7)
2.4.1 Pre-setups
29(3)
2.4.1.1 Potential cutoff
29(2)
2.4.1.2 Periodic boundary conditions
31(1)
2.4.1.3 Neighbor lists
32(1)
2.4.2 Initialization
32(4)
2.4.2.1 Number of atoms (system size)
33(1)
2.4.2.2 Initial positions and velocities
33(1)
2.4.2.3 Timestep
33(1)
2.4.2.4 Total simulation time
34(1)
2.4.2.5 Type of ensemble
34(2)
2.5 Integration/equilibration
36(2)
2.5.1 Temperature and pressure control
36(1)
2.5.2 Minimization in a static MD run
37(1)
2.5.2.1 Steepest-descent method
37(1)
2.5.2.2 Conjugate gradients method
38(1)
2.6 Data production
38(6)
2.6.1 Run analysis
38(2)
2.6.1.1 Conservation of energy
38(1)
2.6.1.2 Confirmation of global minimum
39(1)
2.6.1.3 Time averages under the ergodic hypothesis
39(1)
2.6.1.4 Errors
40(1)
2.6.2 Energies
40(1)
2.6.3 Structural properties
41(2)
2.6.3.1 Equilibrium lattice constant, cohesive energy
41(1)
2.6.3.2 Bulk modulus
41(1)
2.6.3.3 Thermal expansion coefficient
42(1)
2.6.3.4 Radial distribution function
42(1)
2.6.4 Mean-square displacement
43(1)
2.6.5 Energetics, thermodynamic properties, and others
44(1)
Homework
44(1)
References
45(1)
Further reading
46(1)
Chapter 3 MD exercises with XMD and LAMMPS 47(52)
3.1 Potential curve of Al
47(5)
3.1.1 Input files
48(2)
3.1.1.1 Run file
48(1)
3.1.1.2 Potential file
49(1)
3.1.2 Run
50(1)
3.1.3 Results
50(2)
3.1.3.1 Potential energy curve
51(1)
3.2 Melting of Ni cluster
52(3)
3.2.1 Run file
52(1)
3.2.2 Results
53(2)
3.2.2.1 Visualization with MDL ChimeSP6
54(1)
3.3 Sintering of Ni nanoparticles
55(3)
3.3.1 Input file
55(2)
3.3.2 Results
57(1)
3.4 Speed distribution of Ar gas: A computer experiment
58(4)
3.4.1 Input file
60(1)
3.4.2 Results
61(1)
3.5 SiC deposition on Si(001)
62(4)
3.5.1 Input file
62(3)
3.5.2 Results
65(1)
3.6 Yield mechanism of an Au nanowire
66(3)
3.6.1 Input file
67(1)
3.6.2 Results
68(1)
3.6.2.1 Snapshots
68(1)
3.6.3 Conclusions
69(1)
3.7 Nanodroplet of water wrapped by a graphene nanoribbon
69(5)
3.7.1 Input files
69(3)
3.7.1.1 Positions file (data.C-H2O)
70(1)
3.7.1.2 Input file
71(1)
3.7.2 Results
72(1)
3.7.3 Conclusions
73(1)
3.8 Carbon nanotube tension
74(5)
3.8.1 Introduction
74(1)
3.8.2 Input file
75(1)
3.8.3 readdata.CNT
76(1)
3.8.4 CH.old.airebo
77(1)
3.8.5 Results
78(1)
3.9 Si-tension
79(4)
3.9.1 Introduction
79(1)
3.9.2 Input file
79(3)
3.9.3 Results
82(1)
3.10 Si-CNT composite under tension
83(8)
3.10.1 Introduction
83(2)
3.10.2 Potentials
85(1)
3.10.3 Input files
85(4)
3.10.4 Run
89(1)
3.10.5 Results
89(1)
3.10.6 Conclusions
90(1)
3.11 ZrO2-Y2O3-MSD
91(4)
3.11.1 Introduction
91(1)
3.11.2 Input files
92(2)
3.11.3 Run
94(1)
3.11.4 Results
94(1)
Homework
95(1)
References
96(3)
Chapter 4 First-principles methods 99(32)
4.1 Quantum mechanics: The beginning
100(7)
4.1.1 Niels Bohr and the quantum nature of electrons
101(2)
4.1.2 De Broglie and the dual nature of electrons
103(1)
4.1.3 Schrodinger and the wave equation
104(1)
4.1.4 Heisenberg and the uncertain nature of electrons
105(1)
4.1.5 Remarks
106(1)
4.2 Schrodinger wave equation
107(13)
4.2.1 Simplifying the problem
107(2)
4.2.1.1 Forget about gravity, relativity, and time
107(1)
4.2.1.2 Forget about nuclei and spin
108(1)
4.2.1.3 Forget about the excited states
109(1)
4.2.1.4 Use of atomic units
109(1)
4.2.2 Time-independent electronic wave equation
109(1)
4.2.3 Energy operator: Hamiltonian H
110(2)
4.2.4 Waves and wave function
112(3)
4.2.4.1 Plane wave
113(1)
4.2.4.2 Standing wave
114(1)
4.2.4.3 Superposition principle of waves
114(1)
4.2.4.4 Indistinguishability of electrons
115(1)
4.2.5 Energy E
115(1)
4.2.6 Solutions of Schrodinger wave equation: An electron in a well
116(4)
4.2.6.1 An electron in a one-dimensional infinite well
116(3)
4.2.6.2 An electron in a one-dimensional well with a finite potential
119(1)
4.2.6.3 Hydrogen atom
119(1)
4.2.6.4 Degenerate states
120(1)
4.3 Early first-principles calculations
120(8)
4.3.1 n-electron problem
120(1)
4.3.2 Hartree method: One-electron model
121(1)
4.3.3 Hartree-Fock method
122(10)
4.3.3.1 Expression for Psi(r)
122(1)
4.3.3.2 Orthonormality of wave functions
123(1)
4.3.3.3 Expression for E
124(2)
4.3.3.4 Calculation for E
126(1)
4.3.3.5 Variational approach to the search for the ground-state energy
127(1)
4.3.3.6 Self-consistent procedure
127(1)
4.3.3.7 Remarks
128(1)
Homework
128(1)
References
129(1)
Further reading
129(2)
Chapter 5 Density functional theory 131(42)
5.1 Introduction
132(6)
5.1.1 Electron density
133(2)
5.1.1.1 Electron density in DFT
135(1)
5.1.2 Hohenberg-Kohn theorems
135(3)
5.1.2.1 Electron density as central player
135(1)
5.1.2.2 Search for the ground-state energy
136(2)
5.2 Kohn-Sham approach
138(2)
5.2.1 One-electron representations
138(1)
5.2.2 One-electron system replacing n-electron system
139(1)
5.3 Kohn-Sham equations
140(9)
5.3.1 Energy terms
141(4)
5.3.1.1 Kinetic energy
141(1)
5.3.1.2 External energy
142(1)
5.3.1.3 Hartree energy
142(1)
5.3.1.4 Exchange-correlation energy
143(1)
5.3.1.5 Magnitudes of each energy term
144(1)
5.3.2 Functional derivatives
145(2)
5.3.3 Kohn-Sham equations
147(2)
5.3.3.1 KS orbitals
148(1)
5.3.3.2 KS eigenvalues
149(1)
5.4 Exchange-correlation functionals
149(13)
5.4.1 Exchange-correlation hole
150(3)
5.4.1.1 Exchange hole
151(1)
5.4.1.2 Correlation hole
152(1)
5.4.1.3 Exchange-correlation hole
152(1)
5.4.2 Local density approximation
153(3)
5.4.2.1 Homogeneous electron gas
154(1)
5.4.2.2 Exchange energy
154(1)
5.4.2.3 Correlation energy
154(1)
5.4.2.4 XC energy
155(1)
5.4.2.5 Remarks
156(1)
5.4.3 Generalized gradient approximation
156(3)
5.4.3.1 PW91
158(1)
5.4.3.2 PBE
158(1)
5.4.4 Other XC functionals
159(1)
5.4.5 Remarks
160(2)
5.4.5.1 General trends of GGA
160(1)
5.4.5.2 Limitations of GGA: Strongly correlated systems
161(1)
5.4.5.3 Limitations of GGA: Band gap underestimation
161(1)
5.5 Solving Kohn-Sham equations
162(4)
5.5.1 Introduction
162(2)
5.5.1.1 Self-consistency
162(1)
5.5.1.2 Variational principle
163(1)
5.5.1.3 Constraints
163(1)
5.5.2 Direct diagonalization
164(1)
5.5.3 Iterative diagonalization
164(2)
5.5.3.1 Total energy and other properties
165(1)
5.6 DFT extensions and limitations
166(4)
5.6.1 DFT extensions
166(3)
5.6.1.1 Spin-polarized DFT
167(1)
5.6.1.2 DFT with fractional occupancies
167(1)
5.6.1.3 DFT for excited states
167(1)
5.6.1.4 Finite-temperature DFT
168(1)
5.6.1.5 Time-dependent DFT
168(1)
5.6.1.6 Linear scaling of DFT
169(1)
5.6.2 DFT limitations
169(1)
Homework
170(1)
References
171(1)
Further reading
172(1)
Chapter 6 Treating solids 173(44)
6.1 Pseudopotential approach
174(7)
6.1.1 Freezing the core electrons
175(1)
6.1.1.1 Core electrons
175(1)
6.1.1.2 Valence electrons
175(1)
6.1.1.3 Frozen-core approximation
176(1)
6.1.2 Pseudizing the valence electrons
176(3)
6.1.2.1 Pseudizing procedure
177(1)
6.1.2.2 Benefits
178(1)
6.1.3 Various pseudopotentials
179(2)
6.1.3.1 Norm-conserving PPs
179(1)
6.1.3.2 Ultrasoft PPs
179(1)
6.1.3.3 PAW potentials
180(1)
6.2 Reducing the calculation size
181(8)
6.2.1 Supercell approach under periodic boundary conditions
182(1)
6.2.2 First Brillouin zone and irreducible Brillouin zone
183(4)
6.2.2.1 Reciprocal lattice
183(3)
6.2.2.2 The first Brillouin zone
186(1)
6.2.2.3 Irreducible Brillouin zone
186(1)
6.2.3 k-points
187(2)
6.2.3.1 k-point sampling
188(1)
6.2.3.2 Monkhorst-Pack method
189(1)
6.2.3.3 k-point
189(1)
6.3 Bloch theorem
189(6)
6.3.1 Electrons in solid
190(1)
6.3.2 Bloch expression with periodic function
190(2)
6.3.3 Bloch expression with Fourier expansions
192(3)
6.3.3.1 Fourier expansions
192(1)
6.3.3.2 Fast Fourier transformation
193(1)
6.3.3.3 Matrix expression for the KS equations
193(2)
6.4 Plane wave expansions
195(8)
6.4.1 Basis set
195(1)
6.4.1.1 Local basis set
195(1)
6.4.1.2 Plane wave basis set
195(1)
6.4.2 Plane wave expansions for KS quantities
196(3)
6.4.2.1 Charge density
196(2)
6.4.2.2 Kinetic energy
198(1)
6.4.2.3 Effective potential
198(1)
6.4.2.4 KS equations
198(1)
6.4.3 KS orbitals and bands
199(4)
6.4.3.1 Band structure of free electron
200(1)
6.4.3.2 Band structure of electrons in solids
200(2)
6.4.3.3 Density of states
202(1)
6.5 Some practical topics
203(3)
6.5.1 Energy cutoff
203(1)
6.5.1.1 Cutoff energy
203(1)
6.5.2 Smearing
204(2)
6.5.2.1 Gaussian smearing
205(1)
6.5.2.2 Fermi smearing
205(1)
6.5.2.3 Methfessel-Paxton smearing
205(1)
6.5.2.4 Tetrahedron method with Blochl corrections
206(1)
6.6 Practical algorithms for DFT runs
206(8)
6.6.1 Electronic minimizations
206(3)
6.6.1.1 Direct diagonalization
207(1)
6.6.1.2 Iterative Davidson method
207(1)
6.6.1.3 RMM-DIIS method
207(2)
6.6.2 Ionic minimizations
209(1)
6.6.2.1 Hellmann-Feynman forces
209(1)
6.6.2.2 Minimization methods
210(1)
6.6.3 Born-Oppenheimer molecular dynamics
210(1)
6.6.4 Car-Parrinello molecular dynamics
211(2)
6.6.4.1 CPMD for electronic minimization
211(1)
6.6.4.2 CPMD for ionic minimization
212(1)
6.6.5 Multiscale methods
213(4)
6.6.5.1 Crack propagation in silicon
213(1)
Homework
214(1)
References
214(1)
Further reading
215(2)
Chapter 7 DFT exercises with Quantum Espresso 217(26)
7.1 Quantum espresso
217(1)
7.1.1 General features
217(1)
7.1.2 Installation
218(1)
7.2 Sit
218(5)
7.2.1 Introduction
218(1)
7.2.2 Si2.in
218(2)
7.2.3 Si.pbe-rrkj.UPF
220(1)
7.2.4 Run
221(1)
7.2.5 Si2.out
221(2)
7.3 Si2-convergence test
223(4)
7.3.1 Introduction
223(1)
7.3.2 Si2-conE.in
223(1)
7.3.3 Results
223(1)
7.3.4 Further runs
224(3)
7.4 Si2-band
227(3)
7.4.1 Introduction
227(1)
7.4.2 Si2-scf
227(1)
7.4.3 Si2-bands
228(1)
7.4.4 Results and discussion
229(1)
7.5 Si7-vacancy
230(5)
7.5.1 Introduction
230(1)
7.5.2 Si8-scf
231(1)
7.5.3 Si7v-relax
232(3)
7.6 Si7-vacancy diffusion
235(6)
7.6.1 Introduction
235(1)
7.6.2 Calculation method
235(1)
7.6.3 Step 1: First image
236(1)
7.5.4 Step 2: Last image
236(1)
7.6.5 Step 3: Si7v.NEB20.in
237(4)
Homework
241(1)
References
242(1)
Chapter 8 DFT exercises with VASP 243(56)
8.1 VASP
245(2)
8.1.1 General features of VASP
245(1)
8.1.2 Flow of VASP
245(2)
8.1.2.1 Ten things you should not do in a VASP run
246(1)
8.2 Pt-atom
247(5)
8.2.1 Input files
247(2)
8.2.1.1 INCAR
247(1)
8.2.1.2 KPOINTS
248(1)
8.2.1.3 POSCAR
248(1)
8.2.1.4 POTCAR
249(1)
8.2.2 Run
249(1)
8.2.3 Results
250(2)
8.2.3.1 OSZICAR
250(1)
8.2.3.2 OUTCAR
251(1)
8.2.3.3 Continuous run
251(1)
8.3 Pt-FCC
252(5)
8.3.1 Input files
252(3)
8.3.1.1 INCAR
252(2)
8.3.1.2 KPOINTS
254(1)
8.3.1.3 POSCAR
254(1)
8.3.2 Run
255(1)
8.3.2.1 run.vasp
255(1)
8.3.2.2 nohup.out
255(1)
8.3.3 Results
256(1)
8.3.3.1 CONTCAR
256(1)
8.3.3.2 OUTCAR
257(1)
8.4 Convergence tests
257(5)
8.4.1 Encut convergence
257(4)
8.4.1.1 Shell script run.lattice
258(1)
8.4.1.2 Run
259(1)
8.4.1.3 Results
259(2)
8.4.2 k-points convergence
261(1)
8.5 Pt-bulk
262(6)
8.5.1 Cohesive energy of solid Pt
262(3)
8.5.1.1 Cohesive energy
264(1)
8.5.2 Vacancy formation energy of Pt
265(3)
8.5.2.1 Vacancy formation energy
265(1)
8.5.2.2 CHGCAR plot
266(2)
8.6 Pt(111)-surface
268(9)
8.6.1 Pt(111)-slab
268(4)
8.6.1.1 INCAR
268(1)
8.6.1.2 KPOINTS
269(1)
8.6.1.3 POSCAR
269(2)
8.6.1.4 Results
271(1)
8.6.2 Adsorption energy
272(3)
8.6.2.1 POSCAR
272(2)
8.6.2.2 POTCAR
274(1)
8.6.2.3 Results
274(1)
8.6.3 Work function and dipole correction
275(2)
8.6.3.1 Work function
275(1)
8.6.3.2 Results
276(1)
8.7 Nudged elastic band method
277(7)
8.7.1 Principle of NEB method
278(1)
8.7.2 Procedure of the NEB method
278(2)
8.7.2.1 Initial and final states
278(1)
8.7.2.2 Initial band
279(1)
8.7.2.3 Nudging the band
279(1)
8.7.2.4 Force calculation
279(1)
8.7.2.5 NEB method with climb
279(1)
8.7.3 Pt(111)-O-NEB
280(4)
8.7.3.1 Pt(111)-slab-O-HCP
280(1)
8.7.3.2 Run NEB with VTST scripts
281(1)
8.7.3.3 Results
282(2)
8.8 Pt(111)-catalyst
284(3)
8.8.1 Catalyst
284(1)
8.8.2 Density of states
285(1)
8.8.3 Pt(111)-slab-O-DOS
285(2)
8.8.3.1 Static run
285(1)
8.8.3.2 DOS run
285(1)
8.8.3.3 Results
286(1)
8.9 Band structure of silicon
287(6)
8.9.1 Static run for Si
288(2)
8.9.2 Run for band structure of Si
290(3)
8.9.2.1 INCAR
290(1)
8.9.2.2 KPOINTS
290(1)
8.9.2.3 EIGENVAL
291(2)
8.10 Phonon calculation for silicon
293(4)
8.10.1 Input files
293(1)
8.10.2 Phonon calculations
294(5)
8.10.2.1 INPHON
295(2)
Homework
297(1)
References
297(2)
Chapter 9 DFT exercises with MedeA-VASP 299(20)
9.1 MedeA-VASP
299(1)
9.1.1 General features
299(1)
9.2 Si2-band-HSE06
300(4)
9.2.1 Introduction
300(1)
9.2.2 Run steps
301(1)
9.2.3 Results
302(2)
9.3 Si16-phonon
304(3)
9.3.1 Introduction
304(1)
9.3.2 Ionic relaxation for supercell with displacements
304(1)
9.3.3 Results
304(3)
9.4 W12C9-Co28-interface
307(4)
9.4.1 Introduction
307(1)
9.4.2 Surface models for WC and Co
308(1)
9.4.3 Interface model for WC-Co
308(1)
9.4.4 Results
309(2)
9.5 Mg4(Mo6S8)3-barrier energy
311(3)
9.5.1 Introduction
311(3)
9.5.2 NEB run
314(1)
9.5.3 Results
314(1)
9.6 Si14-H2-ab initio MD
314(4)
9.6.1 Introduction
314(2)
9.6.2 Run steps
316(1)
9.6.3 Results
317(1)
References
318(1)
Appendix A: List of symbols and abbreviations 319(4)
Appendix B: Linux basic commands 323(2)
Appendix C: Convenient scripts 325(12)
Appendix D: The Greek alphabet 337(2)
Appendix E: SI prefixes 339(2)
Appendix F: Atomic units 341(2)
Index 343
June Gunn Lee is an emeritus research fellow in the Computational Science Center at the Korea Institute of Science and Technology, where he has worked for 28 years. Currently, he is also lecturing at the University of Seoul. He has published about 70 papers on engineering ceramics and computational materials science. He received his M.S. and Ph.D. in Materials Science and Engineering from the University of Utah, U.S.A.
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