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Atomistic simulations of lattice defects
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theory of Materials.
2005 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Mechanical properties of solids are governed by crystal imperfections. Computational materials science is largely concerned with the modelling of such defects, e.g. their formation, migration, and interaction energies. Atomistic simulations of systems containing lattice defects are inherently difficult because of the generally complicated geometrical structure of the defects, the need for large simulation cells, etc.

In this thesis, the role of lattice defects in the mechanism behind homogeneous melting is demonstrated. Also, a generic calculational scheme for studying atomic vibrations close to extended defects (applied to a dislocation) has been considered. Furthermore, heat capacities in the solid and liquid phases of aluminium have been calculated, as well as various thermophysical defect properties.

The work was carried out using classical atomistic simulations, mainly molecular dynamics, of aluminium and copper. The interatomic forces were modelled with effective interactions of the embedded-atom type.

The main results of this thesis are the following:

• The thermal fluctuation initiating melting is an aggregate typically with 6-7 interstitials and 3-4 vacancies.

• In the initial stage of melting, no signs of a shear modulus melting mechanism, or the presence of line-like defects (dislocations), can be seen.

• The typical time interval from when melting initiates to the time at which the liquid phase is fully developed is of the order of 1000τ, where the period τ corresponds to the maximum vibrational frequency in the solid.

• The solid-liquid boundary advances at a pace comparable to that of thermal transport by vibrating atoms in the crystal at high temperatures.

• The seemingly small anharmonic effect in the heat capacity of aluminium is caused by a partial cancellation of the low-order term linear in the temperature and anharmonic terms of higher order in the temperature.

• The core region of an edge dislocation in face-centred cubic aluminium has compressed and expanded regions. The excess volume associated with the dislocation core is small, about 6 percent of the atomic volume, as a result of a partial cancellation between the volume changes of the compressed and expanded regions.

• The compressed and expanded regions of the edge dislocation core give negative and positive contributions, respectively, to the excess vibrational entropy. The overall effect is a positive vibrational excess entropy of the dislocation core which is about 2kB per atomic repeat length along the dislocation core.

• The atomic vibrations near the dislocation core are modelled by considering an atomic cluster with about 500-1000 atoms containing the core of dislocation, embedded in a large discrete, but relaxed, lattice of about 23 000 atoms. An atomic region that is four atomic layers thick and about 18 atomic diameters long in the direction parallel to the Burgers vector, accounts for most of the excess entropy.

• The constant-pressure heat capacity of aluminium shows a minimum as a function of temperature in the liquid phase.

Place, publisher, year, edition, pages
Stockholm: KTH , 2005. , vii, 64 p.
Series
Trita-FYS, ISSN 0280-316X ; 2005:26
Keyword [en]
Theoretical physics
Keyword [sv]
Teoretisk fysik
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-253ISBN: 91-7178-042-4 (print)OAI: oai:DiVA.org:kth-253DiVA: diva2:8147
Public defence
2005-06-07, Sal FB42, AlbaNova, Roslagstullsbacken 21, Stockholm, 13:00
Opponent
Supervisors
Note
QC 20101013Available from: 2005-06-01 Created: 2005-06-01 Last updated: 2010-10-13Bibliographically approved
List of papers
1. Vibrational entropy of dislocations in Al
Open this publication in new window or tab >>Vibrational entropy of dislocations in Al
2004 (English)In: Philosophical Magazine, ISSN 1478-6435, E-ISSN 1478-6443, Vol. 84, no 6, 521-532 p.Article in journal (Refereed) Published
Abstract [en]

The region nearest to a lattice defect must be described by an atomistic model, while a continuum model suffices further away from the defect. We study such a separation into two regions for an edge dislocation. In particular we focus on the excess defect energy and vibrational entropy, when the dislocation core is described by a cluster of about 500-100 atoms, embedded in a large discrete and relaxed, but static, lattice. The interaction between the atoms is given by a potential of the embedded-atom model type referring to Al. The dynamic matrix of the vibrations in the cluster is fully diagonalized. The excess entropy DeltaS near the core has positive and negative contributions, depending on the sign of the local strain. Typically, DeltaS/k(B) approximate to 2 per atomic repeat length along the dislocation core in fcc Al. In the elastic continuum region far from the dislocation core the excess entropy shows the same logarithmic divergence as the elastic energy. Although the work refers to a specific material and defect type, the results are of a generic nature.

Keyword
1st-principles calculations, aluminum, potentials, metals, copper
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-23106 (URN)10.1080/14786430310001635422 (DOI)000188327500002 ()2-s2.0-1242352398 (Scopus ID)
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved
2. Anharmonic effects in the heat capacity of Al
Open this publication in new window or tab >>Anharmonic effects in the heat capacity of Al
2004 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 69, no 16, 165106-1-165106-6 p.Article in journal (Refereed) Published
Abstract [en]

The vibrational heat capacity of aluminum at fixed volume is studied in molecular dynamics and Monte Carlo simulations, using effective interactions due to Ercolessi and Adams, Mishin , and Mei and Davenport. When experimental data are reduced to represent the classical vibrational heat capacity at fixed volume, the result is within about +/-2 % of 3k(B)/atom up to the melting temperature of Al, thus suggesting small anharmonic effects. Our simulations of the heat capacity are in good agreement with experiments, but also show that anharmonic effects are in fact large, with a cancellation between the low-order linear term in the temperature T and higher-order terms.

Keyword
thermodynamic properties, interatomic potentials, high-temperatures, melting-point, aluminum, crystal, derivation, vacancies, pressure, tungsten
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-23413 (URN)10.1103/PhysRevB.69.165106 (DOI)000221427100018 ()2-s2.0-37649031570 (Scopus ID)
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved
3. How superheated crystals melt
Open this publication in new window or tab >>How superheated crystals melt
2005 (English)In: Nature Materials, ISSN 1476-1122, E-ISSN 1476-4660, Vol. 4, no 5, 388-390 p.Article in journal (Refereed) Published
Abstract [en]

The melting of superheated crystalline solids through the penetration of intense radiation within at a temperature above the equilibrium melting temperature was investigated. The atomistic simulations, relevant for aluminum, was used to show that the thermal fluctuation initiating melting is an aggregate typically with 6-7 interstitials and 3-4 vacancies. Vacancy-interstital pairs were created through thermal fluctuation and interstitial-vacancy pairs were created close to the interstitial aggregate. It was found that when a defect aggregate contains more than about 10 point defects, it usually grows rapidly and irreversibly.

Keyword
Computational complexity, Computer simulation, Crystal defects, Crystal lattices, Crystal structure, Elastic moduli, Mathematical models, Melting, Molecular dynamics, Thermal effects, Melting temperature, Thermal fluctuation, Vacancy-interstitial pairs, Wigner-Seitz cells
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-5249 (URN)10.1038/nmat1375 (DOI)000228834000011 ()2-s2.0-17644420346 (Scopus ID)
Note
QC 20101012Available from: 2005-06-01 Created: 2005-06-01 Last updated: 2017-12-04Bibliographically approved
4. Homogeneous melting of superheated crystals: Molecular dynamics simulations
Open this publication in new window or tab >>Homogeneous melting of superheated crystals: Molecular dynamics simulations
2005 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 72, no 5, 054107- p.Article in journal (Refereed) Published
Abstract [en]

The homogeneous melting mechanism in a superheated fcc lattice is studied through molecular dynamics simulations, usually for about 20 000 atoms, with the Ercolessi and Adams interaction that represents aluminum. The periodic boundary conditions for the simulation cell suppress the usual surface-initiated melting at T-m=939 K, and the solid-to-liquid transition takes place at the temperature T-s=1.3T(m). By logging the position of each atom at every time step in the simulation, we can follow the melting process in detail at the atomic level. Thermal fluctuations close to T-s create interstitial-vacancy pairs, which occasionally separate into mobile interstitials and almost immobile vacancies. There is an attraction between two interstitials, with a calculated maximum interaction energy of about 0.7 eV. When three to four migrating interstitials have come close enough to form a bound aggregate of point defects, and a few thermally created interstitial-vacancy pairs have been added to the aggregate, such a defect configuration usually continues to grow irreversibly to the liquid state. For 20 000 atoms in the simulation cell, the growth process takes about 10(2)tau to be completed, where tau is the period of a typical atomic vibration in the solid phase. This melting mechanism involves fewer atoms in its crucial initial phase than has been suggested in other melting models. The elastic shear moduli c(44) and c(')=(c(11)-c(12))/2 were calculated as a function of temperature and were shown to be finite at the onset of melting.

Keyword
INTERATOMIC POTENTIALS, ELASTIC-CONSTANTS, POINT-DEFECTS, METALS, TEMPERATURE, MODEL, LINDEMANN, ALUMINUM, SOLIDS
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-25208 (URN)10.1103/PhysRevB.72.054107 (DOI)000231564300044 ()2-s2.0-33644955479 (Scopus ID)
Note
QC 20101012Available from: 2010-10-12 Created: 2010-10-12 Last updated: 2017-12-12Bibliographically approved
5. Heat capacity of liquid Al: Molecular dynamics simulations
Open this publication in new window or tab >>Heat capacity of liquid Al: Molecular dynamics simulations
2005 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 72, no 13, 132204- p.Article in journal (Refereed) Published
Abstract [en]

The heat capacities at constant pressure, c(P), at constant volume and at fixed volume, and the isothermal bulk modulus, are calculated for liquid Al over a wide range of temperatures using molecular dynamics simulations with interactions due to Ercolessi and Adams and Mei and Davenport. c(P) has only a weak temperature dependence, with a shallow minimum that results from the opposing effects of a gradual loss of shear resistance and thermal expansion.

Keyword
thermodynamic properties, melting-point, aluminum, model, potentials, crystal, metals
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-25212 (URN)10.1103/PhysRevB.72.132204 (DOI)000232933700007 ()2-s2.0-29744435700 (Scopus ID)
Note
QC 20101013. Uppdaterad från submitted till published (20101013).Available from: 2010-10-13 Created: 2010-10-13 Last updated: 2017-12-12Bibliographically approved

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