[[File:Mg–C convex hull.png|thumb|[[Magnesium|Mg]]–[[Carbon|C]] convex hull.<ref>{{Cite journal|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 Mg<sub>2</sub>C<sub>3</sub> is expected to be unstable as it lays above the 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 book|last1=Atahan-Evrenk|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 book|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> also known as the stability criterion.<ref>{{cite journal |last1=Oses |first1=Corey |last2=Gossett |first2=Eric |last3=Hicks |first3=David |last4=Rose |first4=Frisco |last5=Mehl |first5=Michael J. |last6=Perim |first6=Eric |last7=Takeuchi |first7=Ichiro |last8=Sanvito |first8=Stefano |last9=Scheffler |first9=Matthias |last10=Lederer |first10=Yoav |last11=Levy |first11=Ohad |last12=Toher |first12=Cormac |last13=Curtarolo |first13=Stefano |title=AFLOW-CHULL: Cloud-Oriented Platform for Autonomous Phase Stability Analysis |journal=Journal of Chemical Information and Modeling |date=24 December 2018 |volume=58 |issue=12 |pages=2477–2490 |doi=10.1021/acs.jcim.8b00393}}</ref> This descriptor was used for the discovery of two magnetic Heusler phases.<ref>{{cite journal |last1=Sanvito |first1=Stefano |last2=Oses |first2=Corey |last3=Xue |first3=Junkai |last4=Tiwari |first4=Anurag |last5=Zic |first5=Mario |last6=Archer |first6=Thomas |last7=Tozman |first7=Pelin |last8=Venkatesan |first8=Munuswamy |last9=Coey |first9=Michael |last10=Curtarolo |first10=Stefano |title=Accelerated discovery of new magnets in the Heusler alloy family |journal=Science Advances |date=7 April 2017 |volume=3 |issue=4 |pages=e1602241 |doi=10.1126/sciadv.1602241}}</ref>
