Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Elastic constants of random solid solutions by SQS and CPA approaches: the case of fcc Ti-Al
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Applied Material Physics. Key Laboratory of Materials Modification by Laser, Ion and Electron Beams of Ministry of Education, Dalian University of Technology, Dalian, China.
Show others and affiliations
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.

Place, publisher, year, edition, pages
2015. Vol. 27, no 31, 315702
Keyword [en]
random solid solution, elastic constant, density functional theory
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:kth:diva-172673DOI: 10.1088/0953-8984/27/31/315702ISI: 000358595500012PubMedID: 26202339Scopus ID: 2-s2.0-84937808999OAI: oai:DiVA.org:kth-172673DiVA: diva2:850333
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
In thesis
1. Density Functional Study of Elastic Properties of Metallic Alloys
Open this publication in new window or tab >>Density Functional Study of Elastic Properties of Metallic Alloys
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:nbn:se:kth:diva-179336 (URN)978-91-7595-787-6 (ISBN)
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
2. Density Functional Theory Study of Bulk Properties of Metallic Alloys and Compounds
Open this publication in new window or tab >>Density Functional Theory Study of Bulk Properties of Metallic Alloys and Compounds
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

First-principles methods based on Density functional theory (DFT) are now adopted routinely to calculate the properties of materials. However, one of the biggest challenges of DFT is to describe the electronic behaviors of random alloys. One of the aims of this thesis is to study binary alloys, e.g. Ti-Al, Cu-Au, and multi-component alloys by using two models for chemically random structures: the special quasi-random structure (SQS) and coherent potential approximation (CPA).

I investigate these approaches by focusing on the local lattice distortion (LLD) and the crystal symmetry effects. Within the SQS approach, the LLD effect can be modeled in a straightforward manner by relaxing the positions of atoms in the supercell. However, within this approach, it is difficult to model the random multi-components alloys due to the large size of the supercells. On the other hand, the CPA approach uses single-site approximation and thus it is not limited by the number of alloy components. But CPA suffers from the neglect of the local lattice relaxation effect, which in some systems and for some properties could be of significant importance.

In my studies, the SQS and CPA approaches are combined with the pseudopotential method as implemented in the Vienna Ab-initio Simulation Package (VASP) and the Exact Muffin-Tin Orbitals (EMTO) methods, respectively. The mixing energies or formation enthalpies and elastic parameters of fcc Ti1-xAlx and Cu1-xAux (0 =< x =< 1) random solid solutions and high-entropy multicomponent TiZrVNb, TiZrNbMo and TiZrVNbMo alloys are calculated as a function of concentration. By comparing the results with and without local lattice relaxations, we find that the LLD effect is negligible for the elastic constants C11, C12, and C44. 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. However, the LLD effect on the mixing energies or formation enthalpies is significant and depends on the degree of size mismatch between alloy constituents. In the cases of random Cu-Au and high-entropy alloys, the formation enthalpies and mixing energies are significantly decreased when the LLD effect is considered. This finding sets the limitations of CPA for the mixing energies or formation enthalpies of alloys with large atomic size differences.

The other goal of the thesis is to study the effect of exchange-correlation functionals on the formation energies of ordered alloys. For this investigation, we select the Cu-Au binary system which has for many years been in the focus of DFT and beyond DFT schemes. The Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation term in DFT is a mature approach and have been adopted routinely to investigate the properties of metallic alloys. In most 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-nonuniform 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 and verified by a full-potential method. We find that the QNA functional leads to an excellent agreement between theory and experiment. The PBE strongly overestimates the lattice constants for ordered Cu3Au, CuAu, CuAu3 compounds and also for the pure metals which are nicely corrected by the QNA approach. The errors in the formation energies of Cu3Au, CuAu, CuAu3 relative to the experimental data decrease from 38-45% obtained with PBE to 5-9% calculated for QNA. This excellent result demonstrates that one can reach superior accuracy within DFT for the formation energies and there is no need to go beyond DFT. Furthermore, it shows that error cancellation can be very effective for the formation energies as well and that the main DFT errors obtained at PBE or LDA levels originate from the core-valence overlap region, which is correctly captured by QNA due to its particular construction. Our findings are now extended to disordered alloys, which is briefly discussed already in one of my published papers.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2017. 76 p.
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-210305 (URN)978-91-7729-350-7 (ISBN)
Public defence
2017-06-02, F3, Lindstedtsvägen 26, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

Qc 20170630

Available from: 2017-06-30 Created: 2017-06-30 Last updated: 2017-06-30Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textPubMedScopus

Authority records BETA

Vitos, Levente

Search in DiVA

By author/editor
Tian, Li-YunJohansson, BörjeVitos, Levente
By organisation
Applied Material Physics
In the same journal
Journal of Physics: Condensed Matter
Condensed Matter Physics

Search outside of DiVA

GoogleGoogle Scholar

doi
pubmed
urn-nbn

Altmetric score

doi
pubmed
urn-nbn
Total: 123 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf