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Density Functional Study of Elastic Properties of Metallic Alloys
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Applied Material Physics.
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Special quasi-random structure (SQS) and coherent potential approximation (CPA) are techniques widely employed in the first-principles calculations of random alloys. The aim of the thesis is to study these approaches by focusing on the local lattice distortion (LLD) and the crystal symmetry effects. We compare the elastic parameters obtained from SQS and CPA calculations. For the CPA and SQS calculations, we employ the Exact Muffin-Tin Orbitals (EMTO) method and the pseudopotential method as implemented in the Vienna Ab initio Simulation Package (VASP), respectively. We compare the predicted trends of the VASP-SQS and EMTO-CPA parameters against composition.

As a first case study, we investigate the elastic parameters of face centered cubic (fcc) Ti1−xAlx(0≤x≤100at.%) random solid solutions as a function of Al content (x). The EMTO-CPA and VASP-SQS results are in good agreement with each other. Comparing the lattice constants from SQS calculations with and without local lattice relaxations, we find that in Ti-rich (Al-rich) side the lattice constants remain almost unchanged (slightly increase) upon atomic relaxations. Taking local lattice distortions into consideration decreases the C11 and C44 elastic parameters, but their trends are not significantly affected. The C12 elastic constant, on the other hand, is almost unchanged when atomic relaxations are included. In general, the uncertainties in the elastic parameters associated with the symmetry lowering in supercell studies turn out to be superior to the differences between the two alloy techniques including the effect of LLD.

We also investigate the elastic properties of random fcc Cu1−xAux(0≤x≤100 at.%) alloys as a function of Au content employing the CPA and SQS approaches. It is found that the CPA and SQS values forC11andC12 are consistent with each other no matter whether the atomic relaxations are taken into account or not. On the other hand, the EMTO-CPA values for C44 are slightly larger than those from SQS calculations especially for Cu-rich alloys which we ascribe to the differences in the DFT solvers rather than the differences between CPA and SQS.

The Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation term in density functional theory (DFT) is a mature approach and have been adopted routinely to investigate the properties of metallic alloys. In most of the cases, PBE provides theoretical results in good agreement with experiments. However, the ordered Cu-Au system turned out to be a special case where large deviations between the PBE predictions and observations occur. In this work, we make use of a recently developed exchange-correlation functional, the so-called quasi-non-uniform exchange-correlation approximation (QNA), to calculate the lattice constants and formation energies for ordered Cu-Au alloys as a function of composition. The calculations are performed using the EMTO method. We find that the QNA functional leads to excellent agreement betweent heory and experiment. The PBE strongly overestimates the lattice constants for ordered Cu3Au, CuAu, CuAu3 compounds and also for the pure metals which is nicely corrected by the QNA approach. The errors in the formation energies of Cu3Au, CuAu, CuAu3relative to the experimental data decrease from 38-45% obtained with PBE to 5-9% calculated for QNA.

 

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. , viii, 40 p.
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:kth:diva-179336ISBN: 978-91-7595-787-6 (print)OAI: oai:DiVA.org:kth-179336DiVA: diva2:882617
Presentation
2015-12-14, Sal Sefström M131, Brinellvägen 23, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20151216

Available from: 2015-12-16 Created: 2015-12-15 Last updated: 2015-12-16Bibliographically approved
List of papers
1. Elastic constants of random solid solutions by SQS and CPA approaches: the case of fcc Ti-Al
Open this publication in new window or tab >>Elastic constants of random solid solutions by SQS and CPA approaches: the case of fcc Ti-Al
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2015 (English)In: Journal of Physics: Condensed Matter, ISSN 0953-8984, E-ISSN 1361-648X, Vol. 27, no 31, 315702Article in journal (Refereed) Published
Abstract [en]

Special quasi-random structure (SQS) and coherent potential approximation (CPA) are techniques widely employed in the first-principles calculations of random alloys. Here we scrutinize these approaches by focusing on the local lattice distortion (LLD) and the crystal symmetry effects. We compare the elastic parameters obtained from SQS and CPA calculations, taking the random face-centered cubic (fcc) Ti1-xAlx (0 <= x <= 1) alloy as an example of systems with components showing different electronic structures and bonding characteristics. For the CPA and SQS calculations, we employ the Exact Muffin-Tin Orbitals (EMTO) method and the pseudopotential method as implemented in the Vienna Ab initio Simulation Package (VASP), respectively. We show that the predicted trends of the VASP-SQS and EMTO-CPA parameters against composition are in good agreement with each other. The energy associated with the LLD increases with x up to x = 0.625 similar to 0.750 and drops drastically thereafter. The influence of the LLD on the lattice constants and C12 elastic constant is negligible. C-11 and C-44 decrease after atomic relaxation for alloys with large LLD, however, the trends of C-11 and C-44 are not significantly affected. In general, the uncertainties in the elastic parameters associated with the symmetry lowering turn out to be superior to the differences between the two techniques including the effect of LLD.

Keyword
random solid solution, elastic constant, density functional theory
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-172673 (URN)10.1088/0953-8984/27/31/315702 (DOI)000358595500012 ()26202339 (PubMedID)2-s2.0-84937808999 (Scopus ID)
Funder
Swedish Research CouncilSwedish Foundation for Strategic Research
Note

QC 20150901

Available from: 2015-09-01 Created: 2015-08-27 Last updated: 2017-12-04Bibliographically approved
2. CPA description of random Cu-Au alloys in comparison with SQS approach
Open this publication in new window or tab >>CPA description of random Cu-Au alloys in comparison with SQS approach
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(English)Manuscript (preprint) (Other academic)
Identifiers
urn:nbn:se:kth:diva-179404 (URN)
Note

QS 2015

Available from: 2015-12-16 Created: 2015-12-16 Last updated: 2015-12-16Bibliographically approved
3. Density Functional description of Cu-Au Intermetallic Alloy
Open this publication in new window or tab >>Density Functional description of Cu-Au Intermetallic Alloy
(English)Manuscript (preprint) (Other academic)
Identifiers
urn:nbn:se:kth:diva-179405 (URN)
Note

QS 2015

Available from: 2015-12-16 Created: 2015-12-16 Last updated: 2015-12-16Bibliographically approved

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