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SSSuuummmmmmeeerrr SSSccchhhoooooolll:::
CCCooommmpppuuutttaaatttiiiooonnnaaalll
MMMaaattteeerrriiiaaalllsss SSSccciiieeennnccceee
Miramar Palace, San Sebastian, Spain
June 28th – July 3th, 2010
CONTRIBUTIONS
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SUMMER SCHOOL ORGANIZED BY
IGOR ABRIKOSOV, [email protected] JÖRG NEUGEBAUER,
[email protected] ANDRÉS AYUELA, [email protected] PEPA
CABRERA-SANFELIX, [email protected]
INVITED SPEAKERS
ABRIKOSOV IGOR
ALFE DARIO
ALONSO MARTIN JULIO ALFONSO
ASTA MARK
AYUELA ANDRES
BURKE KIERON
DIEZ-MUIÑO RICARDO
DRAUTZ RALF
DUDAREV SERGEI L.
GRABOWSKI BLAZEJ
HICKEL TILMANN
KORZHAVYI PAVEL
LECHERMANN FRANK
NEUGEBAUER JÖRG
ORDEJON PABLO
OZOLINS VIDVUDS
RAEBIGER HANNES
RINKE PATRICK
RUBAN ANDREI V.
SANCHEZ-PORTAL DANIEL
SIMAK SEGEI
VAN DE WALLE CHRIS
ORGANIZING COMMITTEE
PEDRO MIGUEL ECHENIQUE IGOR ABRIKOSOV
JÖRG NEUGEBAUER ANDRÉS AYUELA
PEPA CABRERA-SANFELIX
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PREFACE
We would like to welcome all participants to the Summer School:
Computational Materials
Science, being held in San Sebastian, from June 28 to July
third, 2010. This Summer School
aims at the identification and promotion of the common elements
developed in theoretical and
computational studies of materials properties across materials
types, metals, ceramics,
materials for new energy technologies, electronic materials and
minerals. To accomplish this
goal, the School brings together leading experts from a wide
spectrum of materials
simulations including theory, modeling, and computation, engaged
in the study of a broad
range of materials properties.
Therefore, this School provides a forum for exposing young
researchers and students to most
recent state-of-the-art theoretical and computational
developments in studying, understanding,
and predicting the properties of materials. Also, the School
encourages interdisciplinary
contributions, such as between the fields of condensed matter
physics and applied materials
sciences, chemistry, metallurgy, etc.
The attendance of the school has been kept below 100
participants so that active
communication between all members could be guaranteed. We are
confident that the activity
of all the participants will result in a lively and successful
school and, in addition, we hope
you will find the time to enjoy the surroundings and gastronomy
of San Sebastian.
Igor Abrikosov Andrés Ayuela Jörg Neugebauer Pepa
Cabrera-Sanfelix
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Time Schedule
Monday, June 28th
(2010)
8:30 – 9:00 Registration
9:00 – 9:40 Basic class: J. Neugebauer, “Introduction to
DFT”
9:50 – 10:30 Basic class: J. Neugebauer, “Introduction to DFT ”.
Second part
10:30 – 11:00 Coffee break
11:00 – 11:40 Basic class: I. Abrikosov, “Ab initio theory of
substitutional disorder: the
coherent potential approximation and beyond”
11:50 – 12:30 Basic class: I. Abrikosov, “Ab initio theory of
substitutional disorder: the
coherent potential approximation and beyond”. Second part
12:30 – 15:00 Lunch
15:00 – 16:30 Poster Introduction Section (3 – 5 minutes
talks)
1. A. Allard, “Tuning The Kohn Anomaly In The Phonon Dispersion
Of Graphene By
Interaction With A Metallic Substrate.”
2. A. Glensk, “Ab initio prediction of thermodynamic data for
selected phases of the Al-Mg-Si-
Cu system”.
3. A. Stroppa, “HYBRID FUNCTIONAL STUDIES OF MULTIFERROICS”.
4. M.S. Rakitin, “Effect of palladium and titanium impurities on
hydrogen solubility in bcc
iron”.
5. G. M. Thomas, “SELF-ASSEMBLY OF DNA BASE THYMINE ON Cu(110)
STUDY”.
6. E. Kabliman, “Mechanism Of Stabilization Of The Misfit Layer
Compound (PbS)1.13TaS2”.
7. M. Rohrmüller, “Analysis of paramagnetic and ferromagnetic
surface states in µc-Si:H via
the orbital magnetization”.
8. I. Errea, “Superconductivity and Novel Structures of Calcium
Under Pressure from ab intio
Calculations”.
9. J. Ibañez, “Spin-Orbit Coupling in Tl/Si(1,1,1) surface”.
10. Z. Wang, “Thermoelectric transport properties of silicon
from first principles”.
11. M. Certain, “Phase field crystal modelling of liquid-crystal
and reconstructive phase
transitions with FCC and BCC lattices”.
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12. A. Maître, “MODELING OF OF Co/IrMn BILAYER : PHASE
TRANSITIONS AND
HYSTERESIS LOOPS”.
13. F. Gallino, “Characterization of nitrogen defective centers
in zinc oxide”.
14. C. Motta, “Study of electronic transport in metal-metal
junctions within the embedding
approach”.
15. L. Bläckberg, “Noble gas diffusion barriers for improved
Nuclear-Test-Ban treaty
verification detection systems”.
16. G. Hautier, “A High-Throughput Computational Search for New
Lithium-Ion Battery
Cathode Materials”.
17. M. Dahlqvist, “Stability trends of Mn+1AXn phases”.
18. L. Bjerg, “The Hunt For N-type ZnSb”.
19. S.S. Tsirkin, “Scattering of electrons and holes in surface
states on Cu(110) and Ag(110)”.
20. Hemant Dixit, “Quasiparticle bandstructure of zincblende and
rocksalt ZnO”.
16:30 – 17:00 Coffee break
17:00 – 18:30 Master Class: S. Simak, “Using VASP for materials
simulations”.
18:30 – 19:00 Poster Introduction Section (3 – 5 minutes
talks)
1. M. Amini, “Hydrogen impurities and oxygen vacancies in
CdO”.
2. M.G. Vergniory, “Calculation Of Complex Band Structure Fro
Plane-wave Pseudopotential
Hamiltonian”.
3. I. Etxebarria, “Condensation Of Several Structural
Instabilities Via Secondary Distortions:
The Case Of Sr2MWO6 (M= Zn, Mg And Ni) Double Perovskites”.
4. D. Costa, “Towards an Atomistic kinetic Monte Carlo
simulation of Iron Chromium
phasedecomposition based on an ab initio parameterisation”.
5. N. Tillack, “Ab initio study of nano-precipitate nucleation
and growth in ferritic steels”.
6. E. Wachowicz, “Effect of impurities on structural, cohesive,
and magnetic properties of grain
boundaries in α-Fe”.
7. B. Lange, “Constructing optimized atomic basis-sets with PW
accuracy”.
8. D. Ma, “Solid solution strengthening investigated by first
principles”.
9. I. Ulfat, “Annealing Induced Modifications in (GaMn)As:
Electron Spectroscopic Studies”
10. A. Cammarata, “Local Structure Of Octahedral Site In Y-doped
BaCeO3 And BaZrO3
Perovskite Compounds: A New Tetravalent Cation Substitution
Model”
11. T. Pabisiak, “DFT study of formation and stability of Au
nanostructure on rutile TiO2(110)”
19:00 – 21:00 Poster Session (and Refreshments)
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Tuesday, June 29th
(2010)
9:00 – 9:40 Basic class: A. Ruban, “Alloys and magnetism”
9:50 – 10:30 Basic class: A. Ruban, “Alloys and magnetism”.
Second Part
10:30 – 11:00 Coffee break
11:00 – 11:40 Basic class: M. Asta, “First-Principles Modeling
of Configurational
Thermodynamics in Crystalline Alloys and Compounds”
11:50 – 12:30 Basic class: M. Asta, “First-Principles Modeling
of Configurational
Thermodynamics in Crystalline Alloys and Compounds”. Second
Part
12:30 – 15:00 Lunch
15:00 – 15:45 Special Class: A. Ayuela, “Magnetically driven
shape memory alloys”
15:45– 16:30 Special Class: L-W.Wang, “Ab initio simulations for
semiconductor
nanostructures and alloys for solar cell applications”
16:30 – 17:00 Coffee break
17:00 – 18:30 Master Class: A. V. Ruban, “Effective cluster
interactions”
18:30 – 19:00 Poster Introduction Section (3 – 5 minutes
talks)
1. K. Özdoğan, “The overview of the half-metallic Heusler
alloys”.
2. P. Elstnerová, “Ab initio study of thermodynamic, structural,
and elastic properties of Mg-
substituted crystalline calcite”.
3. M. Colakogullari, “An Investigation On The Covalent-like
Transformation Of Undercooled
Liquid Silicon Using Orbital-Free Ab-initio Molecular Dynamics
Method”.
4. U. Aydin, “Ab initio investigation of hydrogen solubility in
3d metals”.
5. A. Saracibar, “Molecular Dynamics In Zirconium Phosphates
Systems”.
6. P. Rejmak, “QM/MM Studies On Ethene Adsorption On Cu(I)
Exchanged Zeolites”.
7. J-B. Piochaud, “Microstructural evolution of austenitic
alloys under irradiation modelled by an ab initio based Atomic
Kinetic Monte Carlo (AKMC) model”.
8. S. Rigamonte, “√7x√3 Indium on Si(111): one or two In
layers?” 9. B. Grabowski, “Ab initio concepts for an efficient and
accurate determination of
thermodynamic properties up to the melting point”
10. H. Sener Sen, “ELECTRONIC PROPERTIES OF GRAPHENE
NANO-RIBBONS”.
11. C. M. Ulrich, “Modeling Diffusion in the Al-Au System with
Parameters from Ab-Initio Calculations”
19:00 – 21:00 Poster Session (and Refreshments)
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Wednesday, June 30th
(2010)
9:00 – 9:40 Basic class: A. Drautz, “Bond-Order Potentials: from
the electronic
structure to interatomic potentials”
9:50 – 10:30 Basic class: A. Drautz, “Bond-Order Potentials:
from the electronic
structure to interatomic potentials”. Second Part
10:30 – 11:00 Coffee break
11:00 – 11:40 Basic class: S. Dudarev, “structure and dynamics
of nano-defects in IRON
and OTHER BCC Metals”
11:50 – 12:30 Basic class: S. Dudarev, “structure and dynamics
of nano-defects in IRON
and OTHER BCC Metals”. Second Part
12:30 – 15:00 Lunch
15:00 – … Guided tour or free afternoon
Thursday, July 1st (2010)
9:00 – 9:40 Basic class: K. Burke, “New functionals”
9:50 – 10:30 Basic class: K. Burke, “New functionals”. Second
Part
10:30 – 11:00 Coffee break
11:00 – 11:40 Basic class: F. Lechermann, “An introduction to
Dynamical Mean-Field
Theory and its application to strongly correlated materials”
11:50 – 12:30 Basic class: F. Lechermann, “An introduction to
Dynamical Mean-Field
Theory and its application to strongly correlated materials”.
Second Part
12:30 – 15:00 Lunch
15:00 – 16:30 Basic Class: C. van de Walle, “First-principles
Investigations of Point
Defects”
16:30 – 17:00 Coffee break
17:00 – 18:30 Master Class: K. Burke, “Time-dependent DFT”.
18:30 – 19:15 Master Class: H. Raebiger, “Impurity States”.
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Friday, July 2st (2010)
9:00 – 9:40 Basic class: V. Ozolins, “First-principles
calculations of vibrational
thermodynamics at high temperatures”
9:50 – 10:30 Basic class: V. Ozolins, “First-principles
calculations of vibrational
thermodynamics at high temperatures”. Second Part
10:30 – 11:00 Coffee break
11:00 – 11:40 Basic class: P. Ordejon, “Linear scaling methods
in electronic structure
calculations”.
11:50 – 12:30 Basic class: D. Sánchez-Portal, “The SIESTA
method: an efficient tool in
materials science”.
12:30 – 15:00 Lunch
15:00 – 15:45 Special Class: J. A. Alonso, “Hydrogen Storage in
Nanoporous Carbons”
15:45 – 16:30 Special Class: P. Rinke, “GW Quasiparticle
Calculations”
16:30 – 17:00 Coffee break
17:00 – 17:45 Master Class: P. Ordejon, “Advanced concepts in
SIESTA”
17:45 – 18:30 Master Class: R. Diez-Muiño, “Theory of
gas/surface dynamics”
21:00 Conference dinner
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Saturday, July 3st (2010)
9:00 – 9:40 Basic class: P. Korzhavyi, “Interaction between ab
initio and Calphad
approaches”
9:50 – 10:30 Basic class: P. Korzhavyi, “Interaction between ab
initio and Calphad
approaches”. Second Part
10:30 – 11:00 Coffee break
11:00 – 11:40 Basic class: D. Alfe, “Liquids”.
11:50 – 12:30 Basic class: D. Alfe, “Liquids”. Second part
12:30 – 15:45 Lunch
15:45 – 16:30 Special Class: T. Hickel, “Using ab initio methods
to predict thermodynamic
properties of metals”
16:30 – 17:00 Coffee break
17:00 – 18:30 Master Class: B. Grabowski, “Master Class on
thermodynamics: How to
derive electronic and vibronic free energy surfaces from ab
initio?”
(Close)
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MONDAY
June 28th
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Introduction into Density Functional Theory
Jörg Neugebauer
Max-Planck-Institut für Eisenforschung, Düsseldorf, Germany
In this lecture a brief introduction into key concepts of
various popular ab initio methods will be given,
advantages and present limitations will be discussed, and
examples with respect to applications in
material science will be given. An important aspect to address
real world problems is the limitation of
ab initio techniques to rather small system sizes of typically a
few hundred atoms, which makes it
necessary to combine them with simulation techniques on the
meso- and/or macroscale. Recent
developments and perspectives of such multiscale approaches will
be given with specific focus on the
requirements on the ab initio side such as accuracy, efficiency
etc.
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Ab initio theory of substitutional disorder: the coherent
potential approximation and beyond
I. A. Abrikosov Department of Physics, Chemistry and Biology,
Linköping University, Sweden
We review recent developments in the field of ab initio
electronic structure theory and its application for studies of
complex alloy systems. Basic ideas behind state-of-the-art
techniques for first-principles theoretical calculations of the
electronic structure and properties of intermetallic compounds and
alloys based on the density functional theory are outlined. We
concentrate on methods that allow for an efficient treatment of
disorder effects [1,2], and illustrate their predictive power by
numerous examples.
In general, a solution to the quantum mechanical problem for a
solid is provided by the electronic structure theory [3]. However,
a serious problem with its application occurs if a configuration of
the solution phase, say A1-xBx, does not have any translational
periodicity, which is the most common situation in practice. In
this case the group theory, which is the corner stone of the modern
electronic structure calculations, cannot be used directly. We will
present modern approaches for solving the electronic structure
problem and calculating the total energy for systems with
substitutional disorder.
One obvious way to deal with a disordered system is to consider
its fragment(s), to impose periodic boundary conditions, and to
solve the KS problem for such “supercells”. As an alternative to
the supercell approach one can reconstruct three-dimensional
periodicity of the substitutionally disordered system by mapping
the latter onto a suitably chosen ordered lattice of “effective”
atoms, which describe the original system on the average. In terms
of the electronic structure problem, one is ultimately interested
in processes of electron scattering off the atoms in the system,
the so-called multiple-scattering. The simplest mean field method,
the coherent potential approximation (CPA), is constructed by
placing effective scatterers at the sites of the original system.
Scattering properties of these effective atoms have to be
determined self-consistently from the condition that the scattering
of electrons off the alloy components, embedded in the effective
medium as impurities, vanishes on the average. The CPA is currently
one of the most popular techniques to deal with substitutional
disorder. However, CPA gives an approximate, mean-field description
of the scattering properties of a system. A way beyond the
mean-field theory in electronic structure calculations for solution
phases is associated with the development of so-called O(N) methods
[3]. Unfortunately, most of them can not deal with metallic systems
at present. However, the locally self-consistent Green’s function
method (LSGF) based on a concept of local self-consistency within
the multiple scattering theory, has been applied for metals with
considerable success. The basic ideas behind the LSGF method will
be discussed. [1] I A. V. Ruban and I. A. Abrikosov, Rep. Prog.
Phys. 71, 046501 (2008). [2] P. E. A. Turchi, I. A. Abrikosov, B.
Burton, S. G. Fries, G. Grimvall, L. Kaufman, P. A. Korzhavyi, V.
Rao Manga, M. Ohno, A. Pisch, A. Scott, and W. Zhang, CALPHAD 31, 4
(2007). [3] R. M. Martin, Electronic structure. Basic Theory and
Practical Methods (Cambridge University Press, Cambridge, 2004)
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Using VASP for materials simulations
S. I. Simak Theoretical Physics, IFM, Linköping University,
SE-58183 Linköping (Sweden)
Practical aspects of materials simulation employing Vienna Ab
Initio Simulation Package (VASP)1 will be addressed. VASP is a
package for performing ab-initio quantum-mechanical simulations
using pseudopotentials or the projector-augmented wave (PAW)2
method and a plane wave basis set. Basic techniques and choice of
input parameters including potentials, density functional
approximations, basis sets, k-point sampling etc. will be discussed
in more detail, with a number of corresponding examples.
References
1 G. Kresse and J. Hafner. Ab initio molecular dynamics for
liquid metals. Phys. Rev. B 47, 558, 1993; G. Kresse and J. Hafner.
Ab initio molecular-dynamics simulation of the
liquid-metal-amorphous-semiconductor transition in germanium. Phys.
Rev. B 49, 14251, 1994; G. Kresse and J. Furthmüller. Efficiency of
ab-initio total energy calculations for metals and semiconductors
using a plane-wave basis set. Comput. Mat. Sci. 6, 15, 1996; G.
Kresse and J. Furthmüller. Efficient iterative schemes for ab
initio total-energy calculations using a plane-wave basis set.
Phys. Rev. B 54, 11169, 1996. 2 P. E. Blochl. Projector
augmented-wave method. Phys. Rev. B 50, 17953, 1994; G. Kresse and
D. Joubert. From ultrasoft pseudopotentials to the projector
augmented-wave method. Phys. Rev. B 59, 1758, 1999.
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TUESDAY
June 29th
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“Alloys and magnetism”
A.V. Ruban Materials Science and Engineering Department, KTH,
Stockholm
(basic class)
Magnetism and bonding have the same origin in the case of
3d-metals and their alloys: valence
d-electrons. This determines their complex interplay, when, on
one hand, magnetic interactions
can be extremely sensitive as to the local atomic structure and
local chemical environment, and,
on the other hand, magnetic exchange interactions and local and
global magnetic structure can
modify substantially chemical interactions between alloy
components. This is also a
consequence of the fact that effective chemical and magnetic
exchange interactions are on the
same energy scale.
This lecture is an introduction to the first-principles
description of these phenomena and their
modeling on the atomic scale, which can be used in the
statistical simulations of the phase
equilibria as magnetic as well as chemical. The ab initio
methods for calculating effective
magnetic and chemical interactions, such as magnetic force
theorem and generalized
perturbation methods will be introduced. Their application to
the different alloy system
illustrating the above mention phenomena will be given.
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First-Principles Modeling of Configurational Thermodynamics
in
Crystalline Alloys and Compounds
Cluster Expansions and Related Approaches
Mark Asta1,2, Vitaly Alexandrov2, and Axel van de Walle3
1Department of Materials Science and Engineering, University of
California, and Materials
Sciences Division, Lawrence Berkeley National Laboratory,
Berkeley, CA, USA
2NEAT ORU, University of California, Davis, CA, USA
3Materials Science and Engineering, California Institute of
Technology, Pasadena, CA, USA
This lecture will cover first-principles methods for modeling
the structure and thermodynamic
properties of substitutionally disordered crystalline materials,
including alloys and ionic
compounds, within the framework of the so-called cluster
expansion formalism.
Technologically-relevant materials are typically multicomponent
systems, with solute species
added intentionally to enhance properties, or present as
impurities originating from processing
or service. To impact the design of such materials, and to
optimize their properties for
technological applications, it is generally critical to
understand the thermodynamic stability of
competing phases as well as the ways in which aging of the
materials can lead to changes in
atomic structure that can ultimately affect properties and
performance. First-principles
computational methods, based on electronic density-functional
theory, have found growing
applications in this area over the past decade owing to advances
in methods, algorithms and
computational power. The lecture will begin with an introduction
to the class of problems
that can be modeled by cluster expansion techniques, and will go
on to describe the statistical-
mechanical foundation underlying the approach. After a review of
the mathematical
formalism of cluster expansions, we will describe approaches
used to fit the expansion
-
coefficients in this approach, including strategies used to
account for long
interactions arising from, e.g., size mismatch between
constituent species. N
the use of cluster-expansion models in Monte
of short and long-range order, and associated thermodynamic
properties. The lecture will end
with a discussion of a few case studies taken from a
structured oxide compounds.
Figure 1: The figure on the right shows a schematic of the
coupleddisorder present on an aliovalently doped fluorite crystal
structsnapshot of a cluster-expansion based Monteright) and dopants
(shown in red) display ordering along 110 planes in the fluorite
structure.
coefficients in this approach, including strategies used to
account for long
interactions arising from, e.g., size mismatch between
constituent species. N
expansion models in Monte-Carlo simulations to derive
equilibrium states
range order, and associated thermodynamic properties. The
lecture will end
with a discussion of a few case studies taken from applications
in Al alloys and fluorite
structured oxide compounds.
: The figure on the right shows a schematic of the
coupled-sublattice configurational disorder present on an
aliovalently doped fluorite crystal structure. The figure on the
left is a
expansion based Monte-Carlo simulation where the vacancies
(shown in right) and dopants (shown in red) display ordering along
110 planes in the fluorite structure.
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coefficients in this approach, including strategies used to
account for long-ranged interatomic
interactions arising from, e.g., size mismatch between
constituent species. Next we will cover
Carlo simulations to derive equilibrium states
range order, and associated thermodynamic properties. The
lecture will end
pplications in Al alloys and fluorite-
sublattice configurational ure. The figure on the left is a
Carlo simulation where the vacancies (shown in right) and
dopants (shown in red) display ordering along 110 planes in the
fluorite structure.
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Magnetically driven shape memory alloys
A. Ayuela*
Centro de Física de Materiales CSIC UPV EHU, MPC, San Sebastian
20080, Spain
DIPC, San Sebastian 20018, Spain
* Work done in collaboration with Enkovaara J, Zayak AT, Entel
P, Nordstrom L, Dube M,
Jalkanen J, Impola J, Nieminen RM.
Significant progress has been made both in experimentation and
theoretical modelling of the
magnetic shape memory (MSM) effect, where magnetic field can
induce strains of 10%. The
theoretical models used to analyze and interpret the different
experiments provide reliable
information and insight into the physical changes involved in
the magnetically driven shape
memory alloys. The aim of this talk is to discuss the present
status of the computational
modelling we have done. First, the basic MSM requirements [1-2]
and a brief summary of the
experimental results for the prototype material Ni-Mn-Ga are
given. Then, in the context of
atomic-scale calculations, we focus primarily on the
understanding of the structural variants
[1], magnetic anisotropy [2], and Curie temperatures [3]. Also
we see an approach to describe
doping out of the stoichiometric alloys where we see the
antiferromagnetic coupling of extra
Mn [4]. Finally, we bring into contact our modelling with recent
results [5].
[1] Ayuela A, Enkovaara J, Ullakko K, et al. J. Phys-Condens
Matter 11, 2017 (1999); Ayuela
A, Enkovaara J, Nieminen RM J. Phys-Condens Matter 14, 5325
(2002); Zayak AT, Entel P,
Enkovaara J, et al. J Phys-Condens Matter 15, 159 (2003); Zayak
AT, Entel P, Enkovaara J,
et al. Phys. Rev. B 68, 132402 (2003).
[2] Enkovaara J, Ayuela A, Nordstrom L, et al Phys. Rev B 65,
134422 (2002); Enkovaara J,
Ayuela A, Nordstrom L, et al. J. App. Phys. 91, 7798 (2002).
[3] Enkovaara J, Ayuela A, Jalkanen J, et al. Phys Rev B 67,
054417 (2003).
[4] Enkovaara J, Heczko O, Ayuela A, et al.Phys. Rev. B 67,
212405 (2003).
[5] Ye, M. et al Phys. Rev. Lett. 104, 176401 (2010); Uijttewaal
MA, Hickel T, Neugebauer
J, et al Phys. Rev. Lett. 102, 035702 (2009).
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Ab initio simulations for semiconductor nanostructures and
alloys
for solar cell applications
Lin-Wang Wang
Lawrence Berkeley National Laboratory
Inorganic semiconductor nanocrystals and alloys are often
proposed to be used as active solar
cell materials. In this talk, I will present our recent ab
initio simulations on such systems.
First, the binding
energy of the charge transfer exciton at CdTe/CdSe nanowire
interface has been calculated. It
is found that the exciton binding energy can be as high as 0.4
eV, which poses a problem for
exciton dissociation. Second the electronic structure of GaN/ZnO
alloy has been studied using
the ab initio method. A Hamiltonian model has been developed to
describe the configuration
energy of this system. Monte Carlo simulation based on this
model Hamiltonian is used to
study the atomic structures of the alloy. The electronic
structure is then calculated after the
density functional theory band gap error has been corrected.
Third, the electronic structures of
ZnTe:O has been calculated using the linear scaling three
dimensional fragment method. This
material has been proposed to be used as an band gap
intermediate state solar cell. The solar
cell efficiency has been calculated based on the absorption
spectrum. Theoretical solar cell
efficiency as high as 60% has been predicted.
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“Effective cluster interactions”
A.V. Ruban
Materials Science and Engineering Department, KTH,
Stockholm.
(master class)
This class is intended as a guide to the practical use of two
methods: screened generalized
perturbation method (SGPM) for calculating effective chemical
interactions in metallic alloys
and magnetic force theorem method for magnetic exchange
interaction parameters of the
Heisenberg magnetic Hamiltonian. The practical examples will be
given showing how to
apply this method and check the consistency of the calculated
interactions with the
configurational energetics of the corresponding systems. The
calculated interactions will be
consequently used in the Monte Carlo simulations of the chemical
order-disorder transition as
well as magnetic transition in real systems.
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WEDNESDAY June 30th
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Bond-Order Potentials: from the electronic structure to
interatomic
potentials
Ralf Drautz¹, Bernhard Seiser², Thomas Hammerschmidt¹, David G.
Pettifor²
¹ ICAMS, Ruhr-Universität Bochum, Germany
² Department of Materials, University of Oxford
Although quantum mechanics provides a fundamental and highly
accurate basis for materials
science, it is rarely used as the basis for the development of a
new material. This is due to the
hierarchical structure of materials, where several orders in
length and time need to be bridged
between the electronic structure and the mechanical behaviour on
the component scale. A
critical step for a systematic modelling of materials is the
derivation of classical, effective
interatomic interactions from a quantum mechanical treatment of
bond formation. For the
derivation of robust interatomic potentials we coarse grain the
electronic structure at two
levels of approximation. In a first step, the description of the
electronic structure is simplified
to the tight-binding approximation.
In a second step, a moments expansion of the tight-binding
Hamiltonian results in a classical,
effective interatomic interaction, the analytic bond-order
potential (BOP). The format of the
potential includes charge transfer and magnetic contributions to
the binding energy. The BOP
reproduces the structural trend across the non-magnetic 4d and
5d TM series and displays the
experimental trend from anti-ferromagnetic order to
ferromagnetic order across the 3d
transition metal series. For iron, the potential correctly
predicts a large magnetic energy for
the alpha phase whereas the close-packed gamma and epsilon
phases exhibit only a small
magnetic contribution to the binding energy. We will discuss the
application of the bond-
order potentials to the prediction of phase stability in complex
phases.
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23
structure and dynamics of nano-defects in IRON and OTHER
BCC Metals1
S.L. Dudarev EURATOM/CCFE Fusion Association, Culham Centre for
Fusion Energy,
Oxfordshire OX14 3DB, UK, [email protected]
The need to formulate a rational knowledge-based strategy for
the development of fusion and fission materials has stimulated a
renewed interest in fundamental materials modelling methodology.
Recent developments show that modelling can indeed provide
quantitative interpretation of experimentally observed changes in
physical and mechanical properties of materials occurring under
irradiation, make predictions needed for optimizing experimental
tests, and even suggest routes for designing new alloys.
This presentation gives examples showing how multiscale
mathematical modelling was successfully applied to solving
practical problems of nuclear materials science. The examples
include an ab initio study of small radiation defects in bcc
transition metals [1], which for the first time explained the
origin of low-temperature mobility of defects in tungsten, and
highlighted the unusual effect of atomic magnetism on the structure
of defects in iron; the development of a ‘magnetic’ interatomic
potential for molecular dynamics simulations [2,3,4], its
generalization to spin-lattice dynamics, where equations of motion
follow the evolution of atomic coordinates and directions of
magnetic moments [5], and the application of Magnetic Cluster
Expansion (MCE) to the treatment of magnetic thermal fluctuations,
and bcc-fcc α-γ-δ phase transitions in iron-based alloys [6].
Figure 1: Left: the magnetic (violet) and phonon (orange)
fcc-bcc free energy differences for pure iron calculated using the
Magnetic Cluster Expansion model [6]. Centre: the trajectory of a
magnetic moment of an iron atom simulated using the spin-lattice
dynamics algorithm [5]. Right: the real-space trajectory of the
same atom simulated using spin-lattice dynamics [5].
Interpreting experimental observations requires algorithms for
treating macroscopic time and length scales. The two papers [7,8],
addressing the dynamical behaviour of ensembles of interacting
defects, illustrate the complexity of the problem. To interpret
in-situ electron microscope observations of migrating defects, it
is necessary to formulate an alternative (to the well-established
kinetic Monte Carlo) model for simulating the long-time-scale
evolution of radiation-induced microstructures. The need for a new
algorithm stems from the fact that understanding microscopic
processes driving microstructural evolution, and matching
simulations to experiment, requires modelling particular
configurations of evolving defect
1This work was funded partly by the United Kingdom Engineering
and Physical Sciences Research Council
under grant EP/G003955 and the European Communities under the
contract of Association between EURATOM and CCFE.
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24
structures. Some properties of irradiated materials depend on
the statistics of their microstructure, formed by many defects and
dislocations, and representing self-averaging quantities. At the
same time, a microstructural evolution model requires understanding
the dynamics of particular configurations of interacting defects,
and comparing the results of simulations with local experimental
observations, involving only a few defects, where no statistical
averaging is possible. Langevin dynamics [8] is a new method for
treating long-time-scale evolution of ensembles of interacting
defects, which provides a conceptually consistent and
computationally efficient framework for matching simulations to
real-time experimental observations.
Figure 2: In-situ electron microscope observation (left) and a
matching real-time Langevin dynamics simulation (right) showing
correlated stochastic motion of two interacting nano-scale
dislocation loops formed in pure iron under irradiation [8].
REFERENCES
1. D. Nguyen-Manh, A.P. Horsfield, and S.L. Dudarev,
Self-interstitial atom defects in bcc transition metals:
group-specific trends. Phys. Rev. B73 (2006) 020101.
2. S.L. Dudarev and P.M. Derlet, A ‘magnetic’ interatomic
potential for molecular dynamics simulations. J. Phys.: Cond. Mat.
17 (2005) 7097; ibid. 19 (2007) 239001.
3. P.M. Derlet and S.L. Dudarev, Million-atom molecular dynamics
simulations of magnetic iron. Progress in Materials Science 52
(2007) 299.
4. S. Chiesa, P.M. Derlet and S.L. Dudarev, Free energy of a 110
dumbbell interstitial defect in bcc Fe: harmonic and anharmonic
contributions. Phys. Rev. B79 (2009) 214109
5. P.-W. Ma, C.H. Woo, and S.L. Dudarev, Large-scale simulations
of the spin-lattice dynamics in ferromagnetic iron. Phys. Rev. B78
(2008) 024434.
6. M.Y. Lavrentiev, D. Nguyen-Manh, and S.L. Dudarev, Magnetic
Cluster Expansion model for bcc-fcc transitions in Fe and Fe-Cr
alloys. Phys. Rev. B81 (2010) 184202.
7. T.S. Hudson, S.L. Dudarev, M.J. Caturla, and A.P. Sutton,
Effects of elastic interactions on post-cascade radiation damage
evolution in kinetic Monte Carlo simulations. Philosophical
Magazine 85 (2005) 661.
8. S.L. Dudarev, M.R. Gilbert, K. Arakawa, H. Mori, Z. Yao, M.L.
Jenkins, and P.M. Derlet, A Langevin model for real-time Brownian
dynamics of interacting nano-defects in irradiated metals. Phys.
Rev. B81 (2010) in press, June 2010 issue of the journal
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25
THURSDAY
July 1st
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26
"New functionals"
Kieron Burke
UC Irvine, Depts of Physics and of Chemistry
In this talk, I will review basics of DFT, using material from
my online book, ABC of DFT,
and elsewhere. I will discuss standard functionals, including
both successes and failures, and
the current state-of-the-art. There will be a quiz at the end,
including prizes.
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An introduction to Dynamical Mean-Field Theory and its
application to
strongly correlated materials
Frank Lechermann I. Institut für Theoretische Physik,
Universität Hamburg, 22303 Hamburg, Germany
The celebrated density functional theory (DFT), e.g., within the
local-density approximation (LDA), achieves for many weakly
correlated materials excellent agreement between theory and
experiment regarding the band structure, phase stability, static
relaxation, phonon spectrum or ordered magnetic moments. However,
materials with strong local electronic correlations cannot be
described in this way. Focusing on the energy-band aspect, the LDA
provides a conceptually invalid description in that case. For
instance, the correlation induced Mott insulating state amounts to
an electron localization in real space, which implies the overall
breakdown of band theory. Thus strongly correlated systems require
an explicit inclusion of many-body effects in order to capture the
coherent quasiparticle excitations at low energy (i.e., close to
the Fermi level) and the incoherent atomic-like excitations at
higher energies. Inherent features like e.g, band-narrowing,
spectral-weight transfer or the loss of coherency due to finite
temperature are important results of such a manifest many-body
nature. The dynamical mean-field theory (DMFT), developed 20 years
ago, is the most comprehensive approach to describe such strongly
correlated systems. Initially constructed for Hubbard-like model
systems, DMFT becomes exact in the limit of high spatial dimensions
or lattice coordination number. It corresponds to a mapping of the
interacting lattice problem to the problem of a single quantum
impurity subject to a mean-field given by an effective bath. In
contrast to Hartree-Fock-type theories the mean field here is
energy dependent and can thus cope with retardation effects,
whereby the local quantum fluctuations on the impurity are fully
taken into account. The self-consistent determination of the
dynamical mean-field corresponds then to the solution of the
original lattice problem with a local self energy. Hence the DMFT
approximation amounts to the neglect of explicit spatial
correlations. The actual numerical solution of the DMFT problem
implies the use of quantum-impurity solvers, such as Quantum
Monte-Carlo methods, exact diagonalization, slave-particle
representations, etc…
Figure 1: DMFT construction. Lattice problem with on-site
Coulomb interaction U is mapped onto the problem of a single
interacting site in an effective mean field ζ0(τ− τ ′).
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Figure 2: Possible scheme for an LDA+DMFT calculation.
By combining DFT with DMFT within the so-called “LDA+DMFT”
approach one ends up with a powerful approach to tackle strongly
correlated materials on a realistic level. Several physical as well
as technical aspects need however to be clarified and worked out in
order to successfully merge electronic band-structure calculations
with the DMFT method. For instance, the interacting Hamiltonian has
to be defined and a suitable local-basis representation for the
description of the local self-energy has to be introduced.
Concerning the latter, Wannier-like techniques and projection
methods have been applied, reinforcing the chemistry viewpoint in
modern electronic structure calculations. In this talk, we will
provide an introduction to the DMFT method as well as the relevant
phenomenology of realistic many-body systems. Starting from the
fundamental single-orbital Hubbard model Hamiltonian, we will
elaborate on the DMFT description towards the application to
demanding strong correlation problems in realistic materials
systems. Recent developments in this very active field of research
in theoretical condensed matter physics will be presented.
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First-principles Investigations of Point Defects
Chris G. Van de Walle
Materials Department, University of California, Santa Barbara,
CA 93103, USA
[email protected] Defects and impurities are often
decisive in determining the physical properties of most materials.
They control the conductivity of the material, and point defects
also mediate diffusion. Experimental defect identification and
characterization is typically difficult and indirect, usually
requiring an ingenious combination of different techniques.
First-principles calculations have emerged as a powerful approach
that complements experiments and can even serve as a predictive
tool. In these lectures I will describe the general methodology for
performing defect calculations [1], addressing issues of geometry
(supercells versus clusters), choice of first-principles technique,
and computational issues such as convergence with respect to
various parameters. Density functional theory (DFT), usually in
conjunction with pseudopotential or projector augmented wave
potentials, has emerged as the most commonly used first-principles
approach for defects. Figure 1 shows the charge density of the
defect state for an oxygen vacancy in ZnO.
Figure 1: Charge density of the defect-induced gap state for an
oxygen vacancy in ZnO. In the neutral charge state, the defect
state is occupied with two electrons. The isosurface corresponds to
10% of the maximum. The background shows the ZnO wurtzite
lattice.
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This approach has proven its value as an immensely powerful
technique for assessing the structural properties of defect.
Minimization of the total energy as a function of atomic positions
yields the stable structure, including all relaxations of the host
atoms, and most functionals [including the still most widely used
local density approximation (LDA)] all yield results within
reasonable error bars. Quite frequently, however, information about
electronic structure is required, i.e., the position of defect
levels that are introduced in the band gap of semiconductors or
insulators. Since DFT in the LDA or generalized gradient
approximation (GGA) severely underestimates the gap, the position
of defect levels is subject to large error bars and cannot be
directly compared with experiment. In turn, this affects the
calculated formation energy of the defect, which determines its
concentration. I will discuss particular methods that improve the
description of band gaps, leading to results that can be directly
compared to experiments on a quantitative level. These include
LDA+U, screened hybrid functionals, the quasiparticle GW method,
and the use of modified pseudopotentials. Advantages and
limitations of these methods will be illustrated with examples and
comparisons with experiment. Another issue that may occur in defect
calculations is related to the geometry in which the calculations
are performed. Typically, one wishes to address the dilute limit in
which the defect concentration is low and defect-defect
interactions are negligible. When performing calculations for
charged defects in the supercell approach, long-range interactions
may affect the calculated formation energies and transition levels.
We have recently developed an approach based on a rigorous
treatment of the electrostatic problem that outlines the conditions
of validity of certain approximations and provides explicit
expression for the quantities to be evaluated [2]. Work performed
in collaboration with C. Freysoldt, A. Janotti, G. Kresse, J.
Lyons, J. Neugebauer, P. Rinke, M. Scheffler, A. Singh, J. Varley,
and J. Weber. [1] C. G. Van de Walle and J. Neugebauer, J. Appl.
Phys. 95, 3851 (2004). [2] C. Freysoldt, J. Neugebauer, and C.G.
Van de Walle, Phys. Rev. Lett. 102, 016402 (2009).
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"Time-dependent DFT"
Kieron Burke
UC Irvine, Depts of Physics and of Chemistry
In this short class, I will quickly review basics of TDDFT, with
an emphasis on excitations.
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Impurity States
Hannes Raebiger Yokohama National University, Yokohama,
Japan
[email protected] While defects and impurities semantically
convey a somewhat negative meaning of ‘dirty’ or ‘imperfect’,
semiconductor applications, including computer processors,
photovoltaic cells, and various sensor devices etc. would be
completely useless without such ‘dirt’ and ‘imperfections’. What
makes semiconductors unique compared with metals or insulators is
that tiny amounts of imperfections (around 1 ppm) can dramatically
alter their conductive, optical, and even magnetic properties.
Moreover, the abundance of such defects and impurities is rather
simple to control via tuning the chemical environment during
growth, and the thermochemical formation of various defects can be
accurately predicted from quantum mechanical calculations. To asses
the relevance of certain defect types, I will give an overview of
density-functional theories to calculate defect formation
enthalpies. Ideally, it would be desirable to carry out such
calculations within self-interaction free total energy functionals,
but in practice this is rarely possible. To this end, I will
discuss both ‘post-processor’ corrections and simple nonlocal
corrections to local-density approximations (LDA), which yield
accurate thermochemical quantities for a similar CPU cost as an
LDA-calculation. This is followed by a description of the relevant
thermodynamics in order to actually assess the defect abundancies
together with induced carrier concentrations. The main focus of
this lecture is in understanding the electronic spectra of various
impurity configurations, and how these impurity states ultimately
affect the electronic, optical, and magnetic properties of the
samples. While first principles calculations can be used to
accurately predict these spectra, this does not entail
understanding the physical mechanisms that lead to the specific
electronic configurations. Here, symmetry considerations, together
with simple tight binding theories are a useful tool – in parallel
to ab initio calculations – to provide an in-depth understanding of
the origin of specific impurity states. Here, I give an overview of
the different types of defects one encounters. First of all, it is
customary to distinguish between intrinsic and extrinsic defects,
which further can be classified as shallow or deep. I will discuss
in terms of simple LCAO models under what conditions intrinsic
defects are shallow or deep [1], and show examples of oxide
materials relevant in the design of photovoltaic cells. Finally, I
will discuss the microscopic theory of charge regulation [2], which
enables deep defects to exhibit multiple ‘charged states’, thus
providing e.g. transparent materials with new catalytic
functionalities relevant for photoelectrochemical water splitting
for hydrogen fuel production, and is a driving force for
microscopic phase separation (see e.g. Ref. 3) and defect
gettering. [1] H. Raebiger, S. Lany, and A. Zunger, Phys. Rev. B
76, 045209 (2007). [2] H. Raebiger, S. Lany, and A. Zunger, Nature
453, 763 (2008). [3] H. Raebiger, A. Ayuela, and R. M. Nieminen, J.
Phys.: Condens. matter 16, L457 (2004).
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33
FRIDAY
July 2st
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First-principles calculations of vibrational thermodynamics at
high
temperatures
Vidvuds Ozolins
Department of Materials Science and Engineering,
University of California, Los Angeles, California 90095-1595,
USA
E-mail: [email protected]
We will review the basic principles and methods of calculating
vibrational contributions to the
free energies of solids at high temperatures. The harmonic and
quasiharmonic phonon
theories, both within the linear response and supercell force
constant method, will be
introduced together with the key applications from the
literature. In the strongly anharmonic
limit where the quasiharmonic theory becomes inadequate, we will
explain the most popular
state-of-the-art methods based on thermodynamic integration
techniques. The case of high-
temperature metastable phases and relation to the CALPHAD
calculations of phase diagrams
will be covered in detail. The lecture is expected to be useful
for those who are interested in
modeling the thermodynamic properties of solid phases and
thermodynamic driving forces for
structural transformations in pure elements and alloys using
first-principles density-functional
theory techniques.
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Linear scaling methods in electronic structure calculations
Pablo Ordejón
Centre d’Investigació en Nanociència i Nanotecnologia-CIN2
(CSIC-ICN), Campus UAB,
08193 Bellaterra, Spain
I will review the basic ideas behind the so-called "linear
scaling" or Order-N methods for
electronic structures [1]. These methods were developed to
speed-up the calculation of
electronic properties of large systems, overcoming the
superlinear scaling imposed by the
standard diagonalization methods in solving a one-electron
Hamiltonian. These linear scaling
methods always involve physically motivated approximations
(mainly, localization ideas),
which imply that the solutions are approximate and that,
therefore, errors must be carefully
tested and controlled. Linear scaling methods have also been
developed to compute the
Hamiltonian matrix in Density Functional methods, and these will
also be presented in this
talk.
[1] A review of some of these methodologies can be found, for
example, in the articles: P. Ordejón, “Order-N tight-binding
methods for electronic-structure and molecular dynamics”, Comp.
Mat. Sci. 12, 157 (1998); and S. Goedecker,“Linear scaling
electronic structure methods”, Rev. Mod. Phys. 71, 1085 (1999)
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The SIESTA method: an efficient tool in materials science
Daniel Sánchez-Portal
Centro de Física de Materiales CSIC-UPV/EHU, Materials Physics
Center (MPC, and
Donostia International Physics Center (DIPC),
Paseo Manuel de Lardizabal 4-5, 20018 Donostia, Spain
Email: [email protected]
The SIESTA method is an approach to compute the electronic
properties and perform atomistic simulations of complex materials
from first principles [1-7]. Large systems, with an unprecedented
number of atoms, can be studied while keeping the computational
cost at a reasonable level. The SIESTA code is freely available for
the academic community (visit http://www.icmab.es/siesta), and this
has made it a widely used tool for the study of materials. It has
been applied to a large variety of systems including surfaces,
adsorbates, nanotubes, nanoclusters, biological molecules,
amorphous semiconductors, ferroelectric films, low-dimensional
metals, etc. Here I will briefly present some of the ideas and
algorithms behind the capabilities of the code, and present some
recent applications in materials science. The capabilities of
SIESTA are exemplified in Figure 1, where the distribution of the
highest occupied molecular orbital (HOMO) of a short DNA chain
(polyA-polyT) coupled to two carbon nanotubes has been plotted. The
simulation cell contains 580 atoms. The output of this calculation
will be used as an input to calculate transport using the
TranSIESTA utility as will be explained by P. Ordejón in his talk.
[1] The main team of SIESTA developers is composed by E. Artacho,
J. M. Cela, J. Gale, A. García, J. Junquera, R. M. Martin, P.
Ordejón, D. Sánchez-Portal and J. M. Soler. It is also necessary to
acknowledge the generous work of many people who have contributed
to the development of the code over the years with their
implementations, ideas, suggestions and bug reports. [2] P.
Ordejón, E. Artacho, and J. M. Soler, Self-consistent order-N
density-functional calculations for very large systems, Phys. Rev.
B 53, R10441 (1996) [3] D. Sánchez Portal, P. Ordejón, E. Artacho,
J. M. Soler, Density-functional method for very large systems with
LCAO basis sets, Int. J. Quantum Chem. 63, 453 (1997) [4] J. M.
Soler, E. Artacho, J. D. Gale, A. García, J. Junquera, P. Ordejón,
D. Sánchez-Portal, The SIESTA method for ab initio order-N
materials simulations, Journal of Physics: Condensed Matter 14,
2745 (2002) [5] J. Junquera, O. Paz, D. Sánchez-Portal, E. Artacho,
Numerical orbitals for linear-scaling calculations, Physical Review
B 64, 235111 (2001) [6] D. Sánchez-Portal, P. Ordejón, E. Canadell,
Computing the properties of materials from first principles with
SIESTA, Bonding and Structure 113, 103 (2004) [7] E. Artacho , E
Anglada , O Diéguez , J D Gale , A García , J Junquera , R M Martin
, P Ordejón , J M Pruneda , D Sánchez-Portal and J M Soler, The
SIESTA method; developments and applicability, J. Phys.: Condens.
Matter 20 064208 (2008)
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Figure 1. Distribution of the highest occupied molecular orbital
(HOMO) of a short DNA chain (polyA-polyT) coupled to two carbon
nanotubes as calculated with SIESTA. The simulation cell contains
580 atoms. Later on, the output of this calculation will be used as
the input to calculate electronic transport in this system using
the TranSIESTA utility. (Courtesy of Prof. P. Ordejón)
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38
Hydrogen Storage in Nanoporous Carbons
Julio A. Alonso Departamento de Física Teórica, Atómica y
Optica
University of Valladolid 47011 Valladolid, Spain
Hydrogen is a candidate to replace gasoline as a fuel in cars.
Prototypes of electric cars in which the electric power is
generated by the reaction of hydrogen with atmospheric oxygen in a
fuel cell have already been built. The process is noncontaminant
and only produces water. Hydrogen has a high energy density by
mass, 120 MegaJoules/gram, nearly three times that of gasoline.
However, hydrogen is a gas, and consequently its energy density by
volume is much smaller than the value of 35 MegaJoules/liter of
gasoline. Even liquid hydrogen has a volumetric energy density that
is only about one fourth of that value. In the present prototype
cars hydrogen is stored as a compressed gas in the tank of the car.
This storage method is not very efficient. A few years ago the U.S.
Department of Energy (DOE) established a hydrogen storage target
for the year 2010 of 6 per cent of the storage system weight for
onboard automotive applications. This has motivated a lot of
research on light materials that could store enough hydrogen to
fulfill the target. Computational materials science can help
experimentalists in searching for materials with promising storage
properties. One type of materials that is currently investigated,
and which is the focus here, is the class of porous carbons. These
light materials, cheap and easy to produce, contain a network of
interconnected pores of nanometric size. Molecular dynamics
simulations using effective many-atom potentials indicate that the
walls of the pores have the form of planar and curved graphitized
ribbons with many defects and open terminations [1]. Nanoporous
carbons have large specific surface areas, several 100 m2 per gram.
The potential of nanoporous carbons to store hydrogen is based on
the physisorption of molecular hydrogen on the graphitic surface.
The conditions for automotive applications require reversible
adsorption/desorption cycles, and this establishes strict
conditions on the adsorption enthalpies.
Figure 1. Potential energy curves for the interaction of a
hydrogen molecule with a graphene layer, clean and
doped with lithium [2].
A graphene slitpore, consisting in two parallel graphene layers
separated a certain distance d, gives a simple model for the pores
existing in nanoporous carbons. The measured storage capacities of
nanoporous carbons are often analyzed by assuming the pores in the
material to have the form of slitpores. The adsorption of H2 on a
planar graphene layer has been studied
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39
using DFT. Figure 1 shows the interaction potential calculated
using the LDA approximation. The binding energy is 70 - 90
meV/molecule. The interaction energy arises from two main
contributions, one attractive and one repulsive. The sharp
repulsive wall is due to the short-range repulsion that develops
when the closed electronic shell of the hydrogen molecule overlaps
substantially with the electron gas of the substrate. This
contribution is sensitive to the local electron density sampled by
the hydrogen molecule in its approach to the graphene layer, and
consequently, it is sensitive to the adsorption site. The
attractive contribution is mainly due to electronic exchange and
correlation effects. The minimum of the interaction
potential energy in Fig. 1 occurs at 2.75o
A ; then, in a slitpore of width about 6o
A the hydrogen molecule interacts optimally with the two
parallel surfaces, increasing the binding energy by a factor of
two. That is, the binding energy of the molecule in a slitpore of
that size will be Eb = 150 - 200 meV. Cylindrical nanopores can be
modelled as the inner channel of a single wall carbon nanotube
(SWCNT). The interaction potential between a hydrogen molecule and
a (5, 5) nanobube,
whose radius is 6.44 a.u. (1o
A = 1.88 a.u.), is plotted in Figure 2. The different curves
correspond to several orientations of the molecule relative to the
nanotube. The largest binding energy, 170 meV, occurs for the
molecule inside the SWNT, and this is due to the curvature effect.
The binding for the molecule inside is sensitive to the radius. For
instance, Eb = 120 meV for a (6, 6) nanotube. The difference gives
a hint that narrow cylindrical pores may enhance the storage of
hydrogen.
Figure 2. Interaction energy of a hydrogen molecule and a (5, 5)
single wall carbon nanotube as a function of the
distance to the nanotube axis. The vertical line represents the
nanotube wall. The left curves correspond to the molecule inside
the nanotube, and the right curves to the molecule outside.
Different curves indicate different
orientations and sites of approach.
The storage capacity of planar slitpores can be calculated using
a quantum thermodynamical model [3, 4]. The model takes into
account the quantum behavior of the hydrogen molecules confined in
the volume of the slitpore and uses the experimental equation of
state of hydrogen. The results of the model for storage at 298 K
are in good agreement with measurements for activated carbons [5].
The conclusion from the theoretical calculations is that the DOE
goal for the gravimetric storage capacity appears to be accessible
for nanoporous carbons at 77 K, that is, at low temperatures. Of
course, those temperatures prevent applications in the car
industry, although other applications requiring low temperatures
may be possible. At room temperature and for optimized slitpore
sizes, a gravimetric storage capacity of 3.1 % is predicted at
pressures of 10 MPa (see Fig. 3). The curves in this Figure
indicate that the DOE target is not reached at room
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40
temperature. However, the storage capacity increases with the
external pressure and this indicates a possible path to enhance the
storage.
Figure 3. Calculated gravimetric capacities of graphene
slitpores as a function of the pore width at 300 K, and different
pressures: 0.1, 1, 5 and 10 MPa [4]. The DOE target is indicated by
he continuous horizontal line. The
dashed horizontal line represents a coverage of one H2 molecule
per two hexagons.
Doping with some impurities represents a promising strategy to
enhance the adsorption binding energies of molecular hydrogen to
graphitized surfaces. Cabria et al. [2] have performed calculations
comparing the physisorption of H2 on pure and Li-doped planar and
curved graphitic surfaces. The Li atom transfers electronic charge
to the carbon layer, and the presence of the partially charged Li
atom polarizes the nearby H2 molecules, enhancing their adsorption
binding energies in a factor of 2. This is shown in Figure 1 for
the case of a planar graphene layer. The combination of the
confinement effect of the pore and the polarization effect due to
impurities increases the adsorption binding energies, which reach
values of more than 300 meV per molecule [6], already approaching
the magnitude required for efficient cyclic adsorption-desorption
under normal operating conditions. This may be a promising line of
research. Acknowledgements: This work was supported by MICINN
(Grant MAT2008-06483-C03-01) and Junta de Castilla y León (Grants
VA017A08 and GR23). References 1. M. J. López, I. Cabria and J. A.
Alonso, manuscript in preparation. 2. I. Cabria, M J. López and J.
A. Alonso, J. Chem. Phys. 123, 204721 (2005) 3. S. Patchkovskii, J.
S. Tse, S. N. Yurchenko, L. Zhechkov, T. Hrine and G. Seifert,
Proc. Nat. Acad. Sci. USA 102, 10439 (2005). 4. I. Cabria, M. J.
López and J. A. Alonso, Carbon 45, 2649 (2007). 5. M.
Jorda-Beneyto, F. Suarez-García, D. Lozano-Castelló, D.
Cazorla-Amorós and A. Linares-Solano, Carbon 45, 293 (2007). 6. I.
Cabria, M J. López and J. A. Alonso, J. Chem. Phys. 128, 144704
(2008).
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GW Quasiparticle Calculations
Patrick Rinke
Fritz-Haber-Institut der Max-Planck-Gesellschaft
Faradayweg 4–6, 14195 Berlin
In material science excited states are ubiquitous. For certain
applications such as
optoelectronic devices the excitation process is of primary
concern. More generally, our
understanding of the response of a material to an external
perturbation such as excitation by
light or electrons is fundamental for characterizing its
properties and utilizing its potential for
new applications.
In this lecture I will focus on photoemission spectroscopy (PES)
and its inverse counterpart
(IPES). The success of PES and IPES owes much to the
interpretation of the photo-electron
spectra in terms of single-particle-like excitations or
quasiparticles. I will introduce the
connection between photoemission spectroscopy and many-body
perturbation theory
(MBPT). For solids MBPT in Hedin’s GW approximation, where G
refers to the Green’s
function and W to the dynamically screened Coulomb interaction,
has become the method of
choice for an ab initio calculation of the quasiparticle energy
spectrum. The GW approach is
best know for ameliorating the band-gap problem of Kohn-Sham
density-functional theory,
but is of course not restricted to the calculation of
quasiparticle band gaps. I will review the
current state of the art and illustrate practical aspects of GW
calculations before discussing
open questions and future developments.
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Advanced concepts in SIESTA
Pablo Ordejón
Centre d’Investigació en Nanociència i Nanotecnologia-CIN2
(CSIC-ICN), Campus UAB,
08193 Bellaterra, Spain
In this talk, I will describe some of the less standard
calculations which are available in the
SIESTA package [1]. In particular, I will describe the
TranSIESTA utility [2], which allows
the calculation of non-equilibrium transport properties in
nanoscale devices. I will also
present a QM/MM methodology [3,4] that has been recently
implemented in SIESTA, in
which the full DFT description of a part of the system is
combined with classical potentials
for the rest of the atoms. This technique is useful for the
study of very large systems in which
chemical reactions only take place in a small region, which must
be treated at the QM level.
[1] J. M. Soler, E. Artacho, J. D. Gale, A. García, J. Junquera,
P. Ordejón, D. Sánchez-Portal, The
SIESTA method for ab initio order-N materials simulations,
Journal of Physics: Condensed Matter 14,
2745 (2002)
[2] Mads Brandbyge, José-Luis Mozos, Pablo Ordejón, Jeremy
Taylor, and Kurt Stokbro,
Density-functional method for non-equilibrium electron
transport, Phys. Rev. B 65, 165401 (2002)
[3] A. Crespo, D. A. Scherlis, M. A. Marti, P. Ordejón, A. E.
Roitberg and D. A. Estrin, A DFT based
QM-MM Approach Designed for the Treatment of Large Molecular
Systems: Application to
Chorismate Mutase, J. Phys. Chem. B 107, 13728 (2003)
[4] C. Sanz, A. García, P. Ordejón, to be published.
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Theory of gas/surface dynamics
Ricardo Díez Muiño
Centro de Física de Materiales, Centro Mixto CSIC-UPV/EHU, San
Sebastián, Spain, and
Donostia International Physics Center DIPC, San Sebastián,
Spain
Understanding and mastering the dynamics of elementary reactive
processes at surfaces is a
basic ingredient to control many physical and chemical
processes. In particular, metal
surfaces are effective chemical agents capable of adsorbing
and/or dissociating molecules
impinging from the gas phase. When the molecules approach the
surface, intramolecular
chemical bonds can break down and new ones be formed with the
surface. Over the last years,
the combination of experimental molecular-beam techniques and
refined theoretical
calculations based on ab-initio methods have led research on the
field to a new stage, in which
detailed investigations of the kinetics and dynamics of
molecular reactivity at surfaces are
possible.
In this talk, we will describe the use of first-principles
electronic structure calculations to
describe the details of the interaction between small diatomic
molecules and metal surfaces.
We will cover different methodologies to build accurate
multidimensional potential energy
surfaces (PESs), based on the adiabatic approximation. Once the
PES of the system is known,
we will show how the dynamics of several processes can be
analyzed by solving classical or
quantum equations of motion. Finally, we will discuss the
possible relevance of non-adiabatic
effects in elementary reactive processes at surfaces, with
special emphasis on the excitation of
electron-hole pairs in the metal surface.
.
References
[1] M. Alducin, R. Díez Muiño, H.F. Busnengo and A. Salin, Phys.
Rev. Lett. 97 056102
(2006).
[2] J.I. Juaristi, M. Alducin, R. Díez Muiño, H.F. Busnengo and
A. Salin, Phys. Rev. Lett.
100 116102 (2008).
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SATURDAY
July 3st
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45
Interaction between ab initio and Calphad approaches
Pavel A. Korzhavyi
Department of Materials Science and Engineering
Royal Institute of Technology (KTH)
100 44 Stockholm, SWEDEN
Abstract
Density functional theory enables one to obtain the ground-state
energy of any given atomic
configuration (static as well as dynamic) through
self-consistent ab initio calculations. This
possibility is of direct interest for the scientific community
working with CALculations of
PHAse Diagrams (CALPHAD) and other types of empirically-based
thermodynamic
modeling. However, the interaction between the two communities,
one doing ab initio
calculations and the other performing Calphad modeling is not
limited to a straightforward
use of ab initio-calculated total energies in place of
experimental data. A mutually enriching
information exchange is actually taking place, and that involves
several levels of abstraction:
Plain numerical data, their interpretation in the form of
physical and mathematical models, as
well as general concepts and approaches in modeling are being
exchanged, discussed and
developed jointly. Some examples of such collaborative projects,
dealing with modeling of
industrially-relevant materials, will be discussed.
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46
Liquids
Dario Alfè
This lecture will focus on how to obtain various properties of
liquids using computer simulations, and in particular how to
calculate melting properties. The initial part of the lecture will
introduce the main concepts that help to characterise liquids, and
how to distinguish liquids from solids and gases. These will
include importance of collisional processes and short range
correlations, as well as lack of long range order. It will be
mentioned that the strong repulsions at short distances, caused by
the overlap of the valence electronic charges, is the main
ingredient in the determining the structure of liquids. Long range,
smoother, attractive forces play a minor role for the structure,
although they of course provide cohesive energy. I will briefly
mention the source of these long range interactions, which in some
cases are due to dispersive multipole-multipole interactions caused
by spontaneous fluctuations in the electron densities. Combining
these concepts I will introduce the Lennard-Jones potential. I will
introduce the concepts of reduced density and reduced temperature,
in terms of typical internuclear distances and internuclear
energies, and mention that in liquids these two quantities are both
of order ~ 1. Many properties of liquids can be obtained by a
detailed microscopic analysis of the motion of the constituents
atoms. The computer simulation of liquids goes back to the
pioneering molecular dynamics (MD) work of Alder and Wainwright
(1959). I will recall the basis concepts of molecular dynamics,
including the solution of the Newton’s equation of motion, and how
to solve them numerically on a computer: the Verlet algorithm.
Simulation boxes, periodic boundary conditions to reduce surface
effects. Thermodynamic properties of a system can be expressed as
averages of appropriate functions of the coordinates and momenta of
the constituent particles (with some important exceptions).
Averages can be taken along MD trajectories. For example, the
temperature of the system is proportional to the time average of
the kinetic energy of the constituent particles, averaged over the
total number of particles. Alternatively, ensemble averages are
taken by generating a collection of imaginary systems, all
representative of the system of interest in the sense that they
have the same macroscopic properties, in which the position and the
momenta of the particles are distributed according to some
appropriate probability density. Recall the most important
ensembles. Microcanonical (NVE), constant number of particles N,
volume V and energy E. This ensemble is the natural outcome of a MD
simulation for an isolated system, where the Hamiltonian is a
constant of the motion. It is defined by the hypersurface in phase
space of constant energy E. Canonical (NVT), constant N, V and
temperature T. Isothermal-isobaric (NpT), constant N, pressure p
and T. All these ensembles can be generated using Monte Carlo
methods, or MD with appropriately modified Lagrangians. Introduce
the concept of extended systems to include barostats and
thermostats in MD. Under the hypothesis of ergodicity (after a long
enough time a trajectory will have visited an equal number of times
all points on the appropriate hyper-surface in phase space), time
averages are equivalent to ensemble averages, and therefore it is
possible to use MD to
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47
evaluate thermodynamic properties in each of the ensembles
mentioned above. The advantage of MD over the Monte Carlo method is
that with MD one has access also to dynamical properties, like
diffusion and correlation functions. Main ingredients in MD are
forces on the atoms and energy of the system. Classical potentials
versus ab-initio methods (density functional theory, quantum Monte
Carlo). Brief mention of the Car-Parrinello method (1985), extended
system to include the electronic degrees of freedom in the
Lagrangian and perform ab-initio molecular dynamics (AIMD)
simulations. Born-Oppenheimer AIMD. Example of static and dynamical
properties of liquids calculated with AIMD: radial distribution
functions, structure factors, diffusion coefficients, viscosity.
Introduction to melting. Methods to calculate melting curves,
including free energy calculations and coexistence of phases.
Discussion of advantages and disadvantages of the methods:
coexistence is fairly straightforward, but it needs large
simulation cells (~ 1000 atoms), only recently become possible with
AIMD. Show examples: Al, MgO (important for the mantle of the
Earth), Fe (important for the Earth’s core) and Li (peculiar
behaviour of the melting curve which displays a maximum). The free
energy method is more involved and intricate, but has the advantage
that can be used on fairly small systems (64 atoms) if the
reference systems are good. Moreover, free energies also give
access to a wealth of thermodynamic properties. I will discuss the
method of thermodynamic integration to calculate free energies, and
the importance of building a hierarchy of good reference systems,
which are at the base for the success of the method. Methods to
construct good reference systems. Free energies can be calculated
for a range of pressures and temperatures, and therefore give
access to whole melting curves, rather than to a set of melting
points obtained in each coexistence simulation. In the spirit of
building a hierarchy of reference systems, I will discuss recent
applications of the quantum Monte Carlo method to the calculation
of free energies, and in particular to the calculation of the
melting temperature of iron at Earth’s core conditions.
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48
Using ab initio methods to predict thermodynamic properties
of
metals
T. Hickel, B. Grabowski, F, Körmann, A. Dick, J. Neugebauer
Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Str. 1,
40237 Düsseldorf, Germany
[email protected]
Although density functional theory (DFT) was originally
developed as a ground state theory, recent
methodological developments extend it to predict thermodynamic
properties of materials at
temperatures T > 0K. The key quantity for this purpose is the
Helmholtz free energy, since its
knowledge provides not only access to derived properties like
the heat capacity, but also to phase
transition temperatures. Within this presentation we will
therefore discuss the capabilities and
accuracy of present day implementations (xc-functionals) of DFT
in determining all relevant
contributions to free energies of metals. We will repeat the
concepts of the quasiharmonic
approximation [1], which yield the dominant contribution to the
free energy, and of extensions to
include anharmonic lattice vibrations [2]. For magnetic
materials such as iron proper quantum-
mechanical treatments of magnetic excitation will be presented,
pointing also out that classical
simulations are often not sufficient [3]. The focus of the talk
will be on realistic material systems, for
which we will show that an integrated approach, combining these
effects, leads to highly accurate free
energies. It will be shown that the predictive power of the
approach can be estimated by comparing the
deviations between different xc-functionals. For the examples
aluminum, cementite and a shape
memory alloy [4] we will demonstrate that the introduced ab
initio methods can be extremely helpful
to identify the relevance of the individual free energy
contributions for thermodynamic trends and
phase transitions.
[1] B. Grabowski, T. Hickel and J. Neugebauer, Phys. Rev. B 76,
024309 (2007).
[2] B. Grabowski, L. Ismer, T. Hickel and J. Neugebauer, Phys.
Rev. B 79, 134106 (2009).
[3] F. Körmann, A. Dick, B. Grabowski, B. Hallstedt, T. Hickel,
J. Neugebauer, Phys. Rev. B
78, 235302 (2008).
[4] M.A. Uijttewaal, T. Hickel, J. Neugebauer, M.E. Gruner, P.
Entel, Phys. Rev. Lett. 102,
035702 (2009).
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49
Master Class on thermodynamics: How to derive electronic and
vibronic
free energy surfaces from ab initio?
Blazej Grabowski
Max-Planck-Institut für Eisenforschung, Düsseldorf, Germany
An accurate description of thermodynamic quantities at finite
temperatures is a key ingredient in designing and processing new
materials with optimized properties. Traditional approaches to
describe thermodynamic quantities have been based on physical
understanding derived from the meso- and macroscopic scale. Due to
the high complexity real materials can exhibit at microscopic
scales, it became clear that such approaches, although extremely
valuable, are facing fundamental limits and that further progress
is only possible by a combination with ab initio based methods. One
such ab initio method, the density functional theory (DFT), has
turned to be very accurate yet computationally efficient in
describing material properties at T=0 K. The extension to finite
temperatures is however accompanied by conceptual and computational
challenges. The conceptual difficulty arises from the fact that
classical DFT calculations provide only ground-state properties and
neglect thermodynamic excitations. The additional computational
effort to treat these excitations is significant due to cumbersome
calculations required to sample the enlarged phase space with high
demands on the accuracy. It is therefore of crucial importance to
provide and advance efficient statistical concepts that allow to
obtain DFT based finite temperature properties efficiently but
still with a high numerical accuracy. In this master class, we will
provide an interactive introduction to the current state-of-the-art
methods to calculate finite temperature material properties based
on DFT. We will focus on the calculation of the central
thermodynamic quantity, the free energy surface, which contains all
thermodynamic information needed to derive any other quantity. In
particular, we will discuss the practical procedures developed to
include electronic and vibronic excitations and show that these
contributions constitute a dominant part of the free energy. For
the latter, the quantized harmonic lattice vibrations (phonons)
play a decisive role and their computation will be therefore
discussed intensively. We will also show how one can go beyond the
usually applied non-interacting phonon description by the inclusion
of so called anharmonic effects. It is particularly in this domain
where efficient statistical methods are crucial and where still a
lot of space for improvement exists. Based on a flexible
interactive format of the master class, practical knowledge will be
provided to the participants allowing them to make first steps in
the quickly developing yet challenging field of ab initio finite
temperature calculations.
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50
Posters
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51
Tuning The Kohn Anomaly In The Phonon Dispersion Of Graphene
By
Interaction With A Metallic Substrate.
Adrien ALLARD1, Ludger Wirtz1
1 Institute for Electronics, Microelectronics, and
Nanotechnology // CNRS-UMR 8520 // Lille,
France
The phonon dispersion of graphene is known to display two strong
Kohn Anomalies (kinks) in the highest optical branch (HOB) at the
high-symmetry points Gamma and K. The phonon slope around the Kohn
anomalies is related to the electron-phonon-coupling (EPC) with the
graphene Pi bands. We show that this EPC which has strong impact,
e.g., on Raman scattering and electron transport can be strongly
modified due to interaction with a metallic substrate. For graphene
grown on a Ni(111) surface, a total suppression of the Kohn anomaly
occurs: the HOB around Gamma and K becomes completely flat. This is
due to the strong hybridization of the graphene Pi bands with the
Nickel d bands which lifts the linear crossing of the Pi bands at
K. For other metallic substrates, where the distance between the
graphene sheet and the substrate is larger, hybridization is much
less pronounced and the Kohn anomaly is only weakly perturbed. From
experimental phonon dispersions one can therefore draw conclusions
about the interaction strength between graphene and its different
substrates.
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52
Ab initio prediction of thermodynamic data for selected phases
of the Al-
Mg-Si-Cu system
Albert Glensk1, Blazej Grabowski1, Tilmann Hickel1, Jörg
Neugebauer1
1Max-Planck Institut für Eisenforschung GmbH, Max-Planck-Strasse
1, D-40237 Düsseldorf, Germany
Al-Mg-Si-Cu alloys are widely used in engineering applications
due to their excellent mechanical properties. The adjustment of
processing routes is one of the most decisive steps for tailoring
properties to specific needs and can e.g. significantly increase
the strength of Al-Mg-Si-Cu alloys [1]. To address this challenge
quantitative simulations (like the CALPHAD approach) need exact
thermodynamic potentials, which are nowadays mostly gained from
experiment. First principles theoretical calculations emerge as an
alternative for reliable thermodynamic functions in cases of
non-existent experimental data or in regions of phase boundaries
where the reliability of experiments is limited due to the
transient nature of metastable phases. The primary goal of this
project is to provide highly accurate ab initio free energies as a
function of temperature and molar volume for selected binary,
ternary and quaternary phases of the Al-Mg-Si-Cu system. Based on
this thermodynamic potential Helmholtz and Gibbs free energies,
heat capacities, thermal expansion and vacancy concentrations will
be derived. In particular finite temperature effects due to lattice
vibrations will be considered. Our results show that converged
phonon dispersions are indispensable in order to gain highly
accurate free energies: Compared to total energies though, phonon
energies respond much more sensitive to changes in relevant
parameters. Systematic studies of these dependencies for hcp Mg
will be presented. For complex phases, such as GP-zones, ß'' and ß
phases , static total energy calculations and enthalpies of
formation have been obtained and will be discussed.
[1] H. Zhang, Y. Wang, S.L. Shanbg, C.Ravi, C. Wolverton, L.Q.
Chen, Z.K. Liu,
CALPHAD 34 (2010) 20 - 25
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53
HYBRID FUNCTIONAL STUDIES OF MULTIFERROICS Alessandro Stroppa1*,
Silvia Picozzi1
1 SPIN-CNR, University of l'Aquila, Italy *Email address:
[email protected]
Multiferroics, i.e. materials where ferroelectricity and
magnetism coexist, are considered as a "hot topic" in condensed
matter physics (h-index for multiferroics: 49; almost 400 published
articles in 2009). From the computational point of view, their
description poses serious problems. These compounds are often
(strongly) correlated materials, involving d- and f-electronic
charge with significant spatial localization. First-principles
density functional theory (DFT) calculations in the most commonly
applied approximations (LDA, GGA) are not accurate enough to
describe the complex electronic structure of these materials, where
spin-charge-lattice degrees of freedom are strongly linked.
Recently, hybrid Fock exchange/density functional theory
functionals have received great attention in the solid state
community. In particular, the HSE (Heyd-Scuseria-Ernzerhof)
screened hybrid functional, widely applied in solid state
calculations[1],is becoming a new computational paradigm for
accurate electronic structure calculations of complex materials. In
fact, HSE has been recently applied to solid states systems and has
shown good results with respect to standard local DFT approaches,
especially for insulating and correlated systems. Despite this,
very few studies exist in the multiferroic field, and clearly much
work is needed in order to assess the performance of HSE in this
recent field of material research. In this framework, we focus on
two prototypical systems such as BiFeO3 (BFO) and HoMnO3 (HMO). We
perform an accurate study of the structural, electronic, magnetic
and ferroelectric properties based on the comparison of the
performance of standard DFT approaches, and more advanced and
recent hybrid-DFT, such HSE. For BFO and HMO, by comparing our
calculations with available experimental data, our study points
towards a truly realistic description of multifunctional materials,
such as multiferroics. For BFO, we also included state-of-the-art
GW calculations, which, to the best of our knowledge, have not yet
been done. ACKNOWLEDGEMENTS The research leading to these results
has received funding from the European Research Council under the
European-Community, 7th Framework Programme – FP7 (20072013)/ERC
Grant Agreement n. 203523. Computational support by Caspur
Supercomputing Center in Roma is gratefully acknowledged.
REFERENCES [1] Heyd, J. Scuseria, G.E. and Ernzerhof, M. (2003)
Hybrid functionals based on a screened Coulomb potential. J. Chem.
Phys.,118, 8207-8216 [2] Stroppa, A. and Picozzi, S (2010), Hybrid
functional study of proper and improper multiferroics, Phys. Chem.
Chem. Phys., 12, 5405-5416
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Effect of palladium and titanium impurities
on hydrogen solubility in bcc iron
M.S. Rakitin, A.A. Mirzoev South Ural State University,
Chelyabinsk, Russia
E-mail: [email protected] Hydrogen is known to cause some
types of structural defects in iron and steels which can lead to
cracks and embrittlement of the materials. Solubility of hydrogen
decreases with cooling. As a result high pressure inside the
materials can cause their failure. One of the ways to avoid such
negative effect is to add impurities of Pd or Ti during steel
production, so hydrogen atoms can be trapped by them. We have made
an attempt to understand the nature of the phenomenon and eliminate
disagreements about preferable position of the impurities to trap
hydrogen. Several series of ab initio calculations have been
performed for ferromagnetic bcc iron with hydrogen and small
impurities of Pd and Ti with structural relaxation. We used WIEN2k
[1] program realization of DFT method within the generalized
gradient approximation of the PBE form for electron exchange and
correlation. We employed LAPW method, which is an all-electron DFT
technique. According to our convergence tests, we used a kinetic
energy cutoff of 340 eV for all calculations. Structural
relaxations were performed until forces on each atom were below 1
Ry/a.u. We used a k-point sampling of 24 for the Fe53MeH supercell
(Me=Pd, Ti) and experimental lattice parameter of bcc Fe (5.4169
a.u.). In our earlier work we simulated dissolution of hydrogen in
pure Fe54 with almost identical parameters and obtained results
which are in good agreement with the results of Jiang and Carter
[2]. Namely, we found the tetrahedral site of bcc iron to be more
stable than the octahedral site for hydrogen dissol
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