Convex hull: Difference between revisions

Revision as of 17:58, 29 June 2022

Revision as of 18:46, 29 June 2022

Line 176:

=== Materials science ===

[[File:Mg–C convex hull.png|thumb|Convex hull of [[Magnesium|Mgmagnesium]]–[[Carbon|Ccarbon]] convex hullcompounds.<ref>{{Cite journalsfnp|last1=Kim|first1=Sooran|last2=Kim|first2=Kyoo|last3=Koo|first3=Jahyun|last4=Lee|first4=Hoonkyung|last5=Il Min|first5=Byung|last6=Kim|first6=Duck Young|date=2019-12-27|title=Pressure-induced phase transitions and superconductivity in magnesium carbides|journal=Scientific Reports|language=en|volume=9|issue=1|pages=20253|doi=10.1038/s41598-019-56497-6|issn=2045-2322|pmc=6934831|pmid=31882982|bibcode=2019NatSR...920253K}}</ref> In this example Mg₂C₃ is expected to be unstable as it layslies above the lower hull.]]

In a set of energies of several [[Stoichiometry|stoichiometries]] of a material, only those measurements laying on the lower convex hull will be stable. When removing a point from the hull and then calculating its distance to the hull, its distance to the new hull represents the degree of stability of the phase.<ref>{{Cite bookharvtxt|last1=Atahan-EvrenkHautier|first1=Sule|url=https://books.google.com/books?id=9nu5BQAAQBAJ&dq=convex+hull+phase&pg=PA143|title=Prediction and Calculation of Crystal Structures: Methods and Applications|last2=Aspuru-Guzik|first2=Alan|date=2014-05-06|publisher=Springer|isbn=978-3-319-05774-3|language=en}}</ref><ref>; {{Cite bookharvtxt|last=Fultz|first=Brent|url=https://books.google.com/books?id=AkbhDwAAQBAJ&dq=convex+hull+phase&pg=PA55|title=Phase Transitions in Materials|date=2020-05-14|publisher=Cambridge University Press|isbn=978-1-108-62255-4|language=en}}</ref>

===Thermodynamics===

Line 424:

| s2cid = 221659506

}}

*{{citation

| last = Fultz | first = Brent

| date = April 2020

| doi = 10.1017/9781108641449

| page = 55

| publisher = Cambridge University Press

| title = Phase Transitions in Materials

| url = https://books.google.com/books?id=AkbhDwAAQBAJ&pg=PA55}}

*{{citation

| last = Gardner | first = L. Terrell

Line 461 ⟶ 469:

| year = 2004}}

*{{citation

| last = Gibbs | first1first = Willard J. Willard | author-link = Josiah Willard Gibbs

| journal = Transactions of the Connecticut Academy of Arts and Sciences

| title = Article II. A method of geometrical representation of the thermodynamic properties of substances by means of surfaces, Scientific Papers of J. Willard Gibbs

| pages = 382–404

| url = https://www.google.com/books/edition/Scientific_Papers_of_J_Willard_Gibbs_in/-neYVEbAm4oC?hl=en&gbpv=1&dq=editions:NpUPvza8FVsC&printsec=frontcover#v=onepage&q&f=false}}

| title = Article II. A method of geometrical representation of the thermodynamic properties of substances by means of surfaces, Scientific Papers of J. Willard Gibbs

| volume = 2

| year = 1873}}; reprinted in ''[https://archive.org/details/scientificpaper00gibbgoog The Scientific Papers of J. Willard Gibbs, Vol. I: Thermodynamics]'', Longmans, Green, & Co., 1906, [https://archive.org/details/scientificpaper00gibbgoog/page/n67 pp. 33–54]

*{{citation

| last1 = Graham | first1 = Ronald L. | author1-link = Ronald Graham

Line 504 ⟶ 515:

| title = Optimizing methods in statistics (Proc. Sympos., Ohio State Univ., Columbus, Ohio, 1971)

| year = 1971}}

*{{citation

| last = Hautier | first = Geoffroy

| editor1-last = Atahan-Evrenk | editor1-first = Sule

| editor2-last = Aspuru-Guzik | editor2-first = Alan

| contribution = Data mining approaches to high-throughput crystal structure and compound prediction

| doi = 10.1007/128_2013_486

| pages = 139–179

| pmid = 24287952

| publisher = Springer International Publishing

| series = Topics in Current Chemistry

| title = Prediction and Calculation of Crystal Structures: Methods and Applications

| volume = 345

| year = 2014}}; see [https://books.google.com/books?id=9nu5BQAAQBAJ&pg=PA143 p. 143]

*{{citation

| last = Herrlich | first = Horst | author-link = Horst Herrlich

Line 558 ⟶ 582:

| title = Radio Tracking and Animal Populations

| year = 2001}}

*{{citation

| last1 = Kim | first1 = Sooran

| last2 = Kim | first2 = Kyoo

| last3 = Koo | first3 = Jahyun

| last4 = Lee | first4 = Hoonkyung

| last5 = Min | first5 = Byung Il

| last6 = Kim | first6 = Duck Young

| bibcode = 2019NatSR...920253K

| date = December 2019

| doi = 10.1038/s41598-019-56497-6

| issue = 1

| journal = Scientific Reports

| page = 20253

| pmc = 6934831 | pmid = 31882982

| title = Pressure-induced phase transitions and superconductivity in magnesium carbides

| volume = 9}}

*{{citation

| last = Kirkpatrick | first = K. A.