Data set for diffusion coefficients of alloying elements in dilute Mg alloys from first-principles
Identifieur interne : 000265 ( Pmc/Corpus ); précédent : 000264; suivant : 000266Data set for diffusion coefficients of alloying elements in dilute Mg alloys from first-principles
Auteurs : Bi-Cheng Zhou ; Shun-Li Shang ; Yi Wang ; Zi-Kui LiuSource :
- Data in Brief [ 2352-3409 ] ; 2015.
Abstract
Diffusion coefficients of alloying elements in Mg are critical for the development of new Mg alloys for lightweight applications. Here we present the data set of the temperature-dependent dilute tracer diffusion coefficients for 47 substitutional alloying elements in hexagonal closed packed (hcp) Mg calculated from first-principles calculations based on density functional theory (DFT) by combining transition state theory and an 8-frequency model. Benchmark for the DFT calculations and systematic comparison with experimental diffusion data are also presented. The data set refers to “Diffusion coefficients of alloying elements in dilute Mg alloys: A comprehensive first-principles study” by Zhou et al.
Url:
DOI: 10.1016/j.dib.2015.10.024
PubMed: 26702419
PubMed Central: 4669471
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Data set for diffusion coefficients of alloying elements in dilute Mg alloys from first-principles</title><author><name sortKey="Zhou, Bi Cheng" sort="Zhou, Bi Cheng" uniqKey="Zhou B" first="Bi-Cheng" last="Zhou">Bi-Cheng Zhou</name></author><author><name sortKey="Shang, Shun Li" sort="Shang, Shun Li" uniqKey="Shang S" first="Shun-Li" last="Shang">Shun-Li Shang</name></author><author><name sortKey="Wang, Yi" sort="Wang, Yi" uniqKey="Wang Y" first="Yi" last="Wang">Yi Wang</name></author><author><name sortKey="Liu, Zi Kui" sort="Liu, Zi Kui" uniqKey="Liu Z" first="Zi-Kui" last="Liu">Zi-Kui Liu</name></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">26702419</idno><idno type="pmc">4669471</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4669471</idno><idno type="RBID">PMC:4669471</idno><idno type="doi">10.1016/j.dib.2015.10.024</idno><date when="2015">2015</date><idno type="wicri:Area/Pmc/Corpus">000265</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Data set for diffusion coefficients of alloying elements in dilute Mg alloys from first-principles</title><author><name sortKey="Zhou, Bi Cheng" sort="Zhou, Bi Cheng" uniqKey="Zhou B" first="Bi-Cheng" last="Zhou">Bi-Cheng Zhou</name></author><author><name sortKey="Shang, Shun Li" sort="Shang, Shun Li" uniqKey="Shang S" first="Shun-Li" last="Shang">Shun-Li Shang</name></author><author><name sortKey="Wang, Yi" sort="Wang, Yi" uniqKey="Wang Y" first="Yi" last="Wang">Yi Wang</name></author><author><name sortKey="Liu, Zi Kui" sort="Liu, Zi Kui" uniqKey="Liu Z" first="Zi-Kui" last="Liu">Zi-Kui Liu</name></author></analytic><series><title level="j">Data in Brief</title><idno type="eISSN">2352-3409</idno><imprint><date when="2015">2015</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>Diffusion coefficients of alloying elements in Mg are critical for the development of new Mg alloys for lightweight applications. Here we present the data set of the temperature-dependent dilute tracer diffusion coefficients for 47 substitutional alloying elements in hexagonal closed packed (hcp) Mg calculated from first-principles calculations based on density functional theory (DFT) by combining transition state theory and an 8-frequency model. Benchmark for the DFT calculations and systematic comparison with experimental diffusion data are also presented. The data set refers to “Diffusion coefficients of alloying elements in dilute Mg alloys: A comprehensive first-principles study” by Zhou et al. <xref rid="bib1" ref-type="bibr">[1]</xref>.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Zhou, Bi Cheng" uniqKey="Zhou B">Bi-Cheng Zhou</name></author><author><name sortKey="Shang, Shun Li" uniqKey="Shang S">Shun-Li Shang</name></author><author><name sortKey="Wang, Yi" uniqKey="Wang Y">Yi Wang</name></author><author><name sortKey="Liu, Zi Kui" uniqKey="Liu Z">Zi-Kui Liu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Kresse, G" uniqKey="Kresse G">G. Kresse</name></author><author><name sortKey="Joubert, D" uniqKey="Joubert D">D. Joubert</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Perdew, J P" uniqKey="Perdew J">J.P. Perdew</name></author><author><name sortKey="Ruzsinszky, A" uniqKey="Ruzsinszky A">A. Ruzsinszky</name></author><author><name sortKey="Csonka, G I" uniqKey="Csonka G">G.I. Csonka</name></author><author><name sortKey="Vydrov, O A" uniqKey="Vydrov O">O.A. Vydrov</name></author><author><name sortKey="Scuseria, G E" uniqKey="Scuseria G">G.E. Scuseria</name></author><author><name sortKey="Constantin, L A" uniqKey="Constantin L">L.A. Constantin</name></author><author><name sortKey="Zhou, X L" uniqKey="Zhou X">X.L. Zhou</name></author><author><name sortKey="Burke, K" uniqKey="Burke K">K. Burke</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Kresse, G" uniqKey="Kresse G">G. Kresse</name></author><author><name sortKey="Furthmuller, J" uniqKey="Furthmuller J">J. Furthmuller</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Janot, C" uniqKey="Janot C">C. Janot</name></author><author><name sortKey="Mallejac, D" uniqKey="Mallejac D">D. Mallejac</name></author><author><name sortKey="George, B" uniqKey="George B">B. George</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Hautoj Rvi, P" uniqKey="Hautoj Rvi P">P. Hautojärvi</name></author><author><name sortKey="Johansson, J" uniqKey="Johansson J">J. Johansson</name></author><author><name sortKey="Vehanen, A" uniqKey="Vehanen A">A. Vehanen</name></author><author><name sortKey="Ylikauppila, J" uniqKey="Ylikauppila J">J. Ylikauppila</name></author><author><name sortKey="Hillairet, J" uniqKey="Hillairet J">J. Hillairet</name></author><author><name sortKey="Tzanetakis, P" uniqKey="Tzanetakis P">P. Tzanetakis</name></author></analytic></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Combronde, J" uniqKey="Combronde J">J. Combronde</name></author><author><name sortKey="Brebec, G" uniqKey="Brebec G">G. Brebec</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Yerko, V F" uniqKey="Yerko V">V.F. Yerko</name></author><author><name sortKey="Zelenskiy, V F" uniqKey="Zelenskiy V">V.F. Zelenskiy</name></author><author><name sortKey="Krasnorustskiy, V S" uniqKey="Krasnorustskiy V">V.S. Krasnorustskiy.</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Pavlinov, L V" uniqKey="Pavlinov L">L.V. Pavlinov</name></author><author><name sortKey="Gladyshev, A M" uniqKey="Gladyshev A">A.M. Gladyshev</name></author><author><name sortKey="Bykov, V N" uniqKey="Bykov V">V.N. Bykov.</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Stloukal, I" uniqKey="Stloukal I">I. Stloukal</name></author><author><name sortKey=" Ermak, J" uniqKey=" Ermak J">J. Čermák</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Fujikawa, S I" uniqKey="Fujikawa S">S.I. Fujikawa</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Das, S K" uniqKey="Das S">S.K. Das</name></author><author><name sortKey="Kang, Y B" uniqKey="Kang Y">Y.B. Kang</name></author><author><name sortKey="Ha, T" uniqKey="Ha T">T. Ha</name></author><author><name sortKey="Jung, I H" uniqKey="Jung I">I.H. Jung</name></author></analytic></biblStruct></listBibl></div1></back></TEI><pmc article-type="other"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">Data Brief</journal-id><journal-id journal-id-type="iso-abbrev">Data Brief</journal-id><journal-title-group><journal-title>Data in Brief</journal-title></journal-title-group><issn pub-type="epub">2352-3409</issn><publisher><publisher-name>Elsevier</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">26702419</article-id><article-id pub-id-type="pmc">4669471</article-id><article-id pub-id-type="publisher-id">S2352-3409(15)00272-3</article-id><article-id pub-id-type="doi">10.1016/j.dib.2015.10.024</article-id><article-categories><subj-group subj-group-type="heading"><subject>Data Article</subject></subj-group></article-categories><title-group><article-title>Data set for diffusion coefficients of alloying elements in dilute Mg alloys from first-principles</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Zhou</surname><given-names>Bi-Cheng</given-names></name><email>zhoubicheng@gmail.com</email><email>bicheng.zhou@psu.edu</email><xref rid="cor1" ref-type="corresp">⁎</xref></contrib><contrib contrib-type="author"><name><surname>Shang</surname><given-names>Shun-Li</given-names></name></contrib><contrib contrib-type="author"><name><surname>Wang</surname><given-names>Yi</given-names></name></contrib><contrib contrib-type="author"><name><surname>Liu</surname><given-names>Zi-Kui</given-names></name></contrib></contrib-group><aff id="aff0005">Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA</aff><author-notes><corresp id="cor1"><label>⁎</label>Corresponding author. <email>zhoubicheng@gmail.com</email><email>bicheng.zhou@psu.edu</email></corresp></author-notes><pub-date pub-type="pmc-release"><day>01</day><month>11</month><year>2015</year></pub-date><pmc-comment> PMC Release delay is 0 months and 0 days and was based on .</pmc-comment>
<pub-date pub-type="collection"><month>12</month><year>2015</year></pub-date><pub-date pub-type="epub"><day>01</day><month>11</month><year>2015</year></pub-date><volume>5</volume><fpage>900</fpage><lpage>912</lpage><history><date date-type="received"><day>13</day><month>10</month><year>2015</year></date><date date-type="accepted"><day>19</day><month>10</month><year>2015</year></date></history><permissions><copyright-statement>© 2015 The Authors</copyright-statement><copyright-year>2015</copyright-year><license license-type="CC BY" xlink:href="http://creativecommons.org/licenses/by/4.0/"><license-p>This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).</license-p></license></permissions><abstract><p>Diffusion coefficients of alloying elements in Mg are critical for the development of new Mg alloys for lightweight applications. Here we present the data set of the temperature-dependent dilute tracer diffusion coefficients for 47 substitutional alloying elements in hexagonal closed packed (hcp) Mg calculated from first-principles calculations based on density functional theory (DFT) by combining transition state theory and an 8-frequency model. Benchmark for the DFT calculations and systematic comparison with experimental diffusion data are also presented. The data set refers to “Diffusion coefficients of alloying elements in dilute Mg alloys: A comprehensive first-principles study” by Zhou et al. <xref rid="bib1" ref-type="bibr">[1]</xref>.</p></abstract></article-meta></front><body><p><bold>Specifications Table</bold><table-wrap id="t0010" position="float"><alt-text id="at0100">Table</alt-text><table frame="hsides" rules="groups"><tbody><tr><td>Subject area</td><td><italic>Materials science</italic></td></tr><tr><td>More specific subject area</td><td><italic>Magnesium alloys</italic></td></tr><tr><td>Type of data</td><td><italic>Tables, Figures, Excel data sheet</italic></td></tr><tr><td>How data was acquired</td><td><italic>Density functional theory calculations using Vienna Ab initio simulation package (VASP)</italic></td></tr><tr><td>Data format</td><td><italic>Analyzed</italic></td></tr><tr><td>Experimental factors</td><td><italic>Not applicable</italic></td></tr><tr><td>Experimental features</td><td><italic>Not applicable</italic></td></tr><tr><td>Data source location</td><td><italic>State college, PA, USA</italic></td></tr><tr><td>Data accessibility</td><td><italic>Data are available here with this article</italic></td></tr></tbody></table></table-wrap></p><p><bold>Value of the data</bold><list list-type="simple"><list-item id="u0005"><label>•</label><p>The comprehensive database of diffusion coefficients of 47 solutes in hcp Mg can be used by alloy designers to design better cast and wrought Mg alloys.</p></list-item><list-item id="u0010"><label>•</label><p>The calculated diffusion data can be used to develop CALPHAD-type diffusion mobility databases for multi-component Mg alloys.</p></list-item><list-item id="u0015"><label>•</label><p>The solute diffusion data in Mg can be used as the input for the microstructure level simulations such as phase-field simulations and finite element modeling.</p></list-item></list></p><sec id="s0005"><label>1</label><title>Computational methods</title><p>We used first-principles calculations based on DFT coupled with transition state theory and the 8-frequency model to calculate the dilute solute tracer diffusion coefficients in hcp Mg. Forty-seven substitutional alloying elements have been considered herein, namely Ag, Al, As, Au, Be, Bi, Ca, Cd, Co, Cr, Cu, Fe, Ga, Ge, Hf, Hg, In, Ir, Li, Mn, Mo, Na, Nb, Ni, Os, Pb, Pd, Pt, Re, Rh, Ru, Sb, Sc, Se, Si, Sn, Sr, Ta, Tc, Te, Ti, Tl, V, W, Y, Zn, and Zr.</p><p>First-principles calculations based on DFT were employed to calculate the free energies needed in the diffusion equations and the 8-frequency model. The finite temperature vibrational contributions to the free energies were calculated using the quasi-harmonic approximations from phonon or Debye model. The ion–electron interaction was described by the projector augmented plane-wave (PAW) method <xref rid="bib2" ref-type="bibr">[2]</xref> and the X-C functional was described by an improved GGA of PBEsol <xref rid="bib3" ref-type="bibr">[3]</xref>, as implemented in the VASP 5.3.2 code <xref rid="bib4" ref-type="bibr">[4]</xref>. The PAW potentials (POTCAR files) used in the present work were released by VASP on April 19, 2012. The recommended core configurations by VASP were adopted for each element in the present work. Due to the magnetic nature of V, Cr, Mn, Fe, Co, and Ni, first-principles calculations containing these elements were performed with the spin polarization approach. An energy cut-off of 350 eV was used for the plane-wave expansion of the electronic wave functions. For the complete description of the diffusion theory used in the present work and more computational details, the reader can refer to the main article <xref rid="bib1" ref-type="bibr">[1]</xref>.</p></sec><sec id="s0010"><label>2</label><title>Benchmark of the DFT calculations</title><sec id="s0015"><label>2.1</label><title>Supercell size convergence test</title><p>Solute–vacancy binding energies were calculated for Zn and Y in different supercell sizes of 36 (3×3×2 conventional hcp unit cells), 64 (4×4×2), 96 (4×4×3) and 150 (5×5×3) atoms in order to test the convergence of supercell size. Δ<italic>V</italic><sub><italic>X</italic></sub> is the volume difference induced by placing a single solute into pure Mg, which is a quantitative measure of the atomic size of each solute. Zn and Y represent solutes with negative and positive Δ<italic>V</italic><sub><italic>X</italic></sub>, respectively. From the test results as shown in <xref rid="t0005" ref-type="table">Table 1</xref>, we can conclude that the supercell size of Zn converges at 64 atoms and the supercell size of Y converges at 96 atoms. Therefore, for elements with large Δ<italic>V</italic><sub><italic>X</italic></sub> (Ba, Bi, Ca, K, Pb, Sr, and Y), 96-atom supercell was used. 64-atom supercell was adopted in calculations for all the rest of the elements.</p></sec><sec id="s0020"><label>2.2</label><title><italic>K</italic>-point convergence test</title><p>An 8×8×9 Γ-centered <italic>k</italic>-point mesh was used for the 64-atom supercell for the electronic integration in the Brillouin zone. For calculations using 96-atom supercells, a 5×5×4 Γ-centered <italic>k</italic>-point mesh was used in structural relaxation and a 7×7×7 Γ-centered <italic>k</italic>-point mesh in subsequent static calculations. <xref rid="f0005" ref-type="fig">Fig. 1</xref> shows the energy convergence test as a function of KPOINTS in VASP for both supercells used in the calculations.</p></sec><sec id="s0025"><label>2.3</label><title>Thermodynamic properties of pure hcp Mg</title><p>In order to validate the applicability of quasi-harmonic Debye model, thermodynamic properties (heat capacity Cp and entropy <italic>S</italic>) were predicted using both quasi-harmonic Debye and phonon model and were compared with experimental data, as shown in <xref rid="f0010" ref-type="fig">Fig. 2</xref>. Excellent agreement was achieved between computation and experiments.</p></sec><sec id="s0030"><label>2.4</label><title>Vacancy formation in pure hcp Mg</title><p>The thermodynamic properties of vacancy formation in pure hcp Mg were predicted using the quasi-harmonic Debye model and were compared with experimental data, as shown in <xref rid="f0015" ref-type="fig">Fig. 3</xref>.</p></sec></sec><sec id="s0035"><label>3</label><title>Diffusion data</title><sec id="s0040"><label>3.1</label><title>Plots of the calculated diffusion coefficients compared with experiments</title><p><xref rid="f0020" ref-type="fig">Fig. 4</xref>, <xref rid="f0025" ref-type="fig">Fig. 5</xref>, <xref rid="f0030" ref-type="fig">Fig. 6</xref>, <xref rid="f0035" ref-type="fig">Fig. 7</xref>, <xref rid="f0040" ref-type="fig">Fig. 8</xref>, <xref rid="f0045" ref-type="fig">Fig. 9</xref>, <xref rid="f0050" ref-type="fig">Fig. 10</xref>, <xref rid="f0055" ref-type="fig">Fig. 11</xref>, <xref rid="f0060" ref-type="fig">Fig. 12</xref>, <xref rid="f0065" ref-type="fig">Fig. 13</xref> show the plots of the calculated diffusion coefficients of solutes compared with available experimental data besides Al, Zn, and Sn shown in the main article <xref rid="bib1" ref-type="bibr">[1]</xref>.</p></sec><sec id="s0045"><label>3.2</label><title>Plots of the calculated diffusion coefficients with strong correlation effects</title><p><xref rid="f0070" ref-type="fig">Fig. 14</xref>, <xref rid="f0075" ref-type="fig">Fig. 15</xref>, <xref rid="f0080" ref-type="fig">Fig. 16</xref>, <xref rid="f0085" ref-type="fig">Fig. 17</xref>, <xref rid="f0090" ref-type="fig">Fig. 18</xref> show the plots of the calculated diffusion coefficients with strong correlation effects, i.e. diffusion coefficients of Na, Se, Sr, Te, and Y in Mg (Ca in Mg in the main article <xref rid="bib1" ref-type="bibr">[1]</xref>).</p></sec><sec id="s0050"><label>3.3</label><title>Diffusion data file</title><p>All the diffusion plots shown in the present work were plotted using the calculated data directly from first-principles, not the fitted Arrhenius equation. The original calculated diffusion data sets and other physical properties for each element can be found in the Excel worksheet file in the <xref rid="s0060" ref-type="sec">Supplementary data</xref> associated with this article.</p><p>In the diffusion data Excel worksheet file , there are the following six parts:<list list-type="simple"><list-item id="o0020"><label>(1)</label><p>D_basal (D<sub>⊥</sub>): a plot of all the predicted basal impurity diffusion coefficients in Mg for each solute.</p></list-item><list-item id="o0025"><label>(2)</label><p>D_normal (D<sub>||</sub>): a plot of all the predicted normal impurity diffusion coefficients in Mg for each solute.</p></list-item><list-item id="o0030"><label>(3)</label><p>Ratio: a plot of the ratio of basal diffusion coefficients over normal diffusion coefficients for each solute.</p></list-item><list-item id="o0035"><label>(4)</label><p>Diffusion data from DFT: the original calculated diffusion data sets for each solute</p></list-item><list-item id="o0040"><label>(5)</label><p>Properties from DFT: the original calculated diffusion related physical properties:<list list-type="simple"><list-item id="o0045"><label>a.</label><p>Δ<italic>V<sub>X</sub></italic>: the volume difference induced by placing a single solute into pure Mg</p></list-item><list-item id="o0050"><label>b.</label><p><italic>B</italic>: the bulk modulus of the Mg63X dilute alloys (Mg95X for Ba, Bi, Ca, K, Pb, Sr, and Y)</p></list-item><list-item id="o0055"><label>c.</label><p>Ebind_basal: the solute–vacancy binding energies of solute and vacancy on the same basal plane of hcp Mg</p></list-item><list-item id="o0060"><label>d.</label><p>Ebind_normal: the solute–vacancy binding energies of solute and vacancy between adjacent basal planes of hcp Mg</p></list-item><list-item id="o0065"><label>e.</label><p>Ex: the solute migration barriers for solute–vacancy exchange within the basal plane</p></list-item><list-item id="o0070"><label>f.</label><p>Ex׳: the solute migration barriers for solute–vacancy exchange between adjacent basal planes</p></list-item><list-item id="o0075"><label>g.</label><p>Emix: the dilute mixing energy given in units of eV per atom of solute</p></list-item><list-item id="o0080"><label>h.</label><p>D<sub>0</sub>_basal (<italic>D</italic><sub>0⊥</sub>): the fitted diffusion pre-factors for the diffusion component perpendicular to the <italic>c</italic> axis</p></list-item><list-item id="o0085"><label>i.</label><p> <italic>Q</italic>_basal (<italic>Q</italic><sub>⊥</sub>): the fitted diffusion activation energies for the diffusion component perpendicular to the <italic>c</italic> axis</p></list-item><list-item id="o0090"><label>j.</label><p>D<sub>0</sub>_normal (<italic>D</italic><sub>0||</sub>): the fitted diffusion pre-factors for the diffusion component parallel to the <italic>c</italic> axis</p></list-item><list-item id="o0095"><label>k.</label><p><italic>Q</italic>_normal (<italic>Q</italic><sub>||</sub>): the fitted diffusion activation energies for the diffusion component parallel to the <italic>c</italic> axis</p></list-item></list></p></list-item><list-item id="o0100"><label>(6)</label><p><italic>E</italic>–<italic>V</italic> fitting results: the equilibrium properties of Mg<sub>63</sub>X (Mg<sub>95</sub>X for Ba, Bi, Ca, K, Pb, Sr, and Y): volume (<italic>V</italic><sub>0</sub>), energy (<italic>E</italic><sub>0</sub>), bulk modulus (<italic>B</italic><sub>0</sub>) and its pressure derivative (<italic>B</italic><sub>0</sub>′) for use in the Debye–Grüneisen model were obtained from an energy vs. volume equation of state (EOS) calculated from first-principles using the equilibrium volume at 0 K and at least five additional volumes (0.96, 0.98, 1.02, 1.04, and 1.06 with respect to <italic>V</italic><sub>0</sub>).</p></list-item></list></p></sec></sec></body><back><ref-list><title>References</title><ref id="bib1"><label>1</label><element-citation publication-type="journal" id="sbref1"><person-group person-group-type="author"><name><surname>Zhou</surname><given-names>Bi-Cheng</given-names></name><name><surname>Shang</surname><given-names>Shun-Li</given-names></name><name><surname>Wang</surname><given-names>Yi</given-names></name><name><surname>Liu</surname><given-names>Zi-Kui</given-names></name></person-group><article-title>“Diffusion coefficients of alloying elements in dilute Mg alloys: A comprehensive first-principles study”</article-title><source>Acta Mater.</source><volume>103</volume><year>2016</year><fpage>573</fpage><lpage>586</lpage></element-citation></ref><ref id="bib2"><label>2</label><element-citation publication-type="journal" id="sbref2"><person-group person-group-type="author"><name><surname>Kresse</surname><given-names>G.</given-names></name><name><surname>Joubert</surname><given-names>D.</given-names></name></person-group><article-title>From ultrasoft pseudopotentials to the projector augmented-wave method</article-title><source>Phys. 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Light Met.</source><volume>42</volume><year>1992</year><fpage>826</fpage><lpage>827</lpage></element-citation></ref><ref id="bib13"><label>13</label><element-citation publication-type="journal" id="sbref12"><person-group person-group-type="author"><name><surname>Das</surname><given-names>S.K.</given-names></name><name><surname>Kang</surname><given-names>Y.B.</given-names></name><name><surname>Ha</surname><given-names>T.</given-names></name><name><surname>Jung</surname><given-names>I.H.</given-names></name></person-group><article-title>Thermodynamic modeling and diffusion kinetic experiments of binary Mg–Gd and Mg–Y systems</article-title><source>Acta Mater.</source><volume>71</volume><year>2014</year><fpage>164</fpage><lpage>175</lpage></element-citation></ref></ref-list><sec id="s0060" sec-type="supplementary-material"><label>Appendix A</label><title>Supplementary material</title><p><supplementary-material content-type="local-data" id="ec0005"><caption><p>Supplementary material</p></caption><media xlink:href="mmc1.xlsx"></media></supplementary-material></p></sec><ack id="ack0005"><title>Acknowledgments</title><p>The present work was funded by the <funding-source id="gs1">National Science Foundation</funding-source> (NSF) through Grant no. DMR-1006557. First-principles calculations were carried out partially on the LION clusters at the Pennsylvania State University supported by the Materials Simulation Center and the Research Computing and Cyberinfrastructure unit at the Pennsylvania State University, partially on the resources of NERSC supported by the Office of Science of the <funding-source id="gs2">US Department of Energy</funding-source> under Contract no. DE-AC02-05CH11231, and partially on the resources of XSEDE supported by NSF with Grant no. ACI-1053575. Calculations were also carried out on the CyberSTAR cluster funded by NSF through Grant no. OCI-0821527. B.C.Z would like to thank Dr. Huazhi Fang for his helpful discussion.</p></ack><fn-group><fn id="s0055" fn-type="supplementary-material"><label>Appendix A</label><p>Supplementary data associated with this article can be found in the online version at <ext-link ext-link-type="uri" xlink:href="http://dx.doi.org/10.1016/j.dib.2015.10.024" id="ir0005">doi:10.1016/j.dib.2015.10.024</ext-link>.</p></fn></fn-group></back><floats-group><fig id="f0005"><label>Fig. 1</label><caption><p>Energy convergence as a function of KPOINTS for (a) a 64 atom supercell and (b) a 96 atom supercell.</p></caption><alt-text id="at0005">Fig. 1</alt-text><graphic xlink:href="gr1"></graphic></fig><fig id="f0010"><label>Fig. 2</label><caption><p>Predicted (a) heat capacity Cp and (b) entropy <italic>S</italic> of pure hcp Mg using Debye and phonon model in comparison with SGTE experimental data.</p></caption><alt-text id="at0010">Fig. 2</alt-text><graphic xlink:href="gr2"></graphic></fig><fig id="f0015"><label>Fig. 3</label><caption><p>Vacancy formation (a) enthalpy, (b) free energy, (c) entropy, and (d) vacancy concentration as a function of temperature in pure hcp Mg calculated by the X-C functional of PBEsol using the quasi-harmonic Debye model. Experimental vacancy concentration data of Mg are taken from Janot et al. <xref rid="bib5" ref-type="bibr">[5]</xref> and Hautojärvi et al. <xref rid="bib6" ref-type="bibr">[6]</xref>.</p></caption><alt-text id="at0015">Fig. 3</alt-text><graphic xlink:href="gr3"></graphic></fig><fig id="f0020"><label>Fig. 4</label><caption><p>Predicted Ag diffusion coefficients in Mg with available experimental data taken from Lal <xref rid="bib7" ref-type="bibr">[7]</xref> and Combronde and Brebec <xref rid="bib8" ref-type="bibr">[8]</xref>.</p></caption><alt-text id="at0020">Fig. 4.</alt-text><graphic xlink:href="gr4"></graphic></fig><fig id="f0025"><label>Fig. 5</label><caption><p>Predicted Be diffusion coefficients in Mg with available experimental data taken from Yerko et al. <xref rid="bib9" ref-type="bibr">[9]</xref>.</p></caption><alt-text id="at0025">Fig. 5</alt-text><graphic xlink:href="gr5"></graphic></fig><fig id="f0030"><label>Fig. 6</label><caption><p>Predicted Cd diffusion coefficients in Mg with available experimental data taken from Combronde and Brebec <xref rid="bib8" ref-type="bibr">[8]</xref>.</p></caption><alt-text id="at0030">Fig. 6</alt-text><graphic xlink:href="gr6"></graphic></fig><fig id="f0035"><label>Fig. 7</label><caption><p>Predicted in diffusion coefficients in Mg with available experimental data taken from Lal <xref rid="bib7" ref-type="bibr">[7]</xref> and Combronde and Brebec <xref rid="bib8" ref-type="bibr">[8]</xref>.</p></caption><alt-text id="at0035">Fig. 7</alt-text><graphic xlink:href="gr7"></graphic></fig><fig id="f0040"><label>Fig. 8</label><caption><p>Predicted Fe diffusion coefficients in Mg with available experimental data taken from Pavlinov et al. <xref rid="bib10" ref-type="bibr">[10]</xref>.</p></caption><alt-text id="at0040">Fig. 8</alt-text><graphic xlink:href="gr8"></graphic></fig><fig id="f0045"><label>Fig. 9</label><caption><p>Predicted Ga diffusion coefficients in Mg with available experimental data taken from Stloukal and Čermák <xref rid="bib11" ref-type="bibr">[11]</xref>.</p></caption><alt-text id="at0045">Fig. 9</alt-text><graphic xlink:href="gr9"></graphic></fig><fig id="f0050"><label>Fig. 10</label><caption><p>Predicted Mn diffusion coefficients in Mg with available experimental data taken from Fujikawa <xref rid="bib12" ref-type="bibr">[12]</xref>.</p></caption><alt-text id="at0050">Fig. 10.</alt-text><graphic xlink:href="gr10"></graphic></fig><fig id="f0055"><label>Fig. 11</label><caption><p>Predicted Ni diffusion coefficients in Mg with available experimental data taken from Pavlinov et al. <xref rid="bib10" ref-type="bibr">[10]</xref>.</p></caption><alt-text id="at0055">Fig. 11.</alt-text><graphic xlink:href="gr11"></graphic></fig><fig id="f0060"><label>Fig. 12</label><caption><p>Predicted Sb diffusion coefficients in Mg with available experimental data taken from Combronde and Brebec <xref rid="bib8" ref-type="bibr">[8]</xref>.</p></caption><alt-text id="at0060">Fig. 12.</alt-text><graphic xlink:href="gr12"></graphic></fig><fig id="f0065"><label>Fig. 13</label><caption><p>Predicted Y diffusion coefficients in Mg with available experimental data taken from Das et al. <xref rid="bib13" ref-type="bibr">[13]</xref>.</p></caption><alt-text id="at0065">Fig. 13.</alt-text><graphic xlink:href="gr13"></graphic></fig><fig id="f0070"><label>Fig. 14</label><caption><p>Predicted Na diffusion coefficients in Mg with and without correlation effects considered, together with the calculated correlation factors <inline-formula><mml:math id="M1" altimg="si0001.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula><mml:math id="M2" altimg="si0002.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> , and <inline-formula><mml:math id="M3" altimg="si0003.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>.</p></caption><alt-text id="at0070">Fig. 14</alt-text><graphic xlink:href="gr14"></graphic></fig><fig id="f0075"><label>Fig. 15</label><caption><p>Predicted Se diffusion coefficients in Mg with and without correlation effects considered, together with the calculated correlation factors <inline-formula><mml:math id="M4" altimg="si0001.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula><mml:math id="M5" altimg="si0002.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and <inline-formula><mml:math id="M6" altimg="si0003.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>.</p></caption><alt-text id="at0075">Fig. 15</alt-text><graphic xlink:href="gr15"></graphic></fig><fig id="f0080"><label>Fig. 16</label><caption><p>Predicted Sr diffusion coefficients in Mg with and without correlation effects considered, together with the calculated correlation factors <inline-formula><mml:math id="M7" altimg="si0001.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula><mml:math id="M8" altimg="si0002.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and <inline-formula><mml:math id="M9" altimg="si0003.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>.</p></caption><alt-text id="at0080">Fig. 16</alt-text><graphic xlink:href="gr16"></graphic></fig><fig id="f0085"><label>Fig. 17</label><caption><p>Predicted Te diffusion coefficients in Mg with and without correlation effects considered, together with the calculated correlation factors <inline-formula><mml:math id="M10" altimg="si0001.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula><mml:math id="M11" altimg="si0002.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and <inline-formula><mml:math id="M12" altimg="si0003.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>.</p></caption><alt-text id="at0085">Fig. 17</alt-text><graphic xlink:href="gr17"></graphic></fig><fig id="f0090"><label>Fig. 18</label><caption><p>Predicted Y diffusion coefficients in Mg with and without correlation effects considered, together with the calculated correlation factors <inline-formula><mml:math id="M13" altimg="si0001.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula><mml:math id="M14" altimg="si0002.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and <inline-formula><mml:math id="M15" altimg="si0003.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. The experimental data are taken from Das et al. <xref rid="bib13" ref-type="bibr">[13]</xref>. Note that <inline-formula><mml:math id="M16" altimg="si0002.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula><mml:math id="M17" altimg="si0003.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> almost overlap with each other.</p></caption><alt-text id="at0090">Fig. 18</alt-text><graphic xlink:href="gr18"></graphic></fig><table-wrap id="t0005" position="float"><label>Table 1</label><caption><p>Supercell size convergence of basal and normal solute–vacancy binding energies for Zn and Y. <inline-formula><mml:math id="M18" altimg="si0004.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula>and <inline-formula><mml:math id="M19" altimg="si0005.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> are the solute–vacancy binding energies of solute and vacancy on the same basal plane and between adjacent basal planes of hcp Mg, respectively.</p></caption><alt-text id="at0095">Table 1</alt-text><table frame="hsides" rules="groups"><thead><tr><th colspan="2">Solute</th><th colspan="4">Solute–vacancy binding energy (eV)<hr></hr></th></tr><tr><th>36 atoms</th><th>64 atoms</th><th>96 atoms</th><th>150 atoms</th></tr></thead><tbody><tr><td>Zn</td><td><inline-formula><mml:math id="M20" altimg="si0004.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula></td><td align="char">0.065</td><td align="char">0.054</td><td align="char">0.055</td><td align="char"></td></tr><tr><td></td><td><inline-formula><mml:math id="M21" altimg="si0005.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula></td><td align="char">0.047</td><td align="char">0.038</td><td align="char">0.039</td><td align="char"></td></tr><tr><td>Y</td><td><inline-formula><mml:math id="M22" altimg="si0004.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula></td><td align="char">−0.112</td><td align="char">−0.081</td><td align="char">−0.051</td><td align="char">−0.051</td></tr><tr><td></td><td><inline-formula><mml:math id="M23" altimg="si0005.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula></td><td align="char">−0.096</td><td align="char">−0.065</td><td align="char">−0.055</td><td align="char">−0.045</td></tr></tbody></table><table-wrap-foot><fn><p><italic>Note:</italic> the solute–vacancy binding energies listed here were obtained from full structural relaxations without static calculations. For accurate values of solute–vacancy binding energies in Mg, the reader should refer to Table 2 in the main article <xref rid="bib1" ref-type="bibr">[1]</xref>.</p></fn></table-wrap-foot></table-wrap></floats-group></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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