Editing Invar (section)

== Explanation of anomalous properties ==
A detailed explanation of Invar's anomalously low CTE has proven elusive for physicists.

All the iron-rich face-centered cubic Fe–Ni alloys show Invar anomalies in their measured thermal and magnetic properties that evolve continuously in intensity with varying alloy composition. Scientists had once proposed that Invar's behavior was a direct consequence of a high-magnetic-moment to low-magnetic-moment transition occurring in the face centered cubic Fe–Ni series (and that gives rise to the mineral [[antitaenite]]); however, this theory was proven incorrect.<ref>{{cite journal |author1=K. Lagarec |author2=D.G. Rancourt |author3=S.K. Bose |author4=B. Sanyal |author5=R.A. Dunlap |url=http://fizz.phys.dal.ca/~dunlap/index_files/index_files/journal/c210_lagarec.pdf |title=Observation of a composition-controlled high-moment/low-moment transition in the face centered cubic Fe–Ni system: Invar effect is an expansion, not a contraction |journal=Journal of Magnetism and Magnetic Materials |volume=236 |year=2001 |issue=1–2 |pages=107–130 |doi=10.1016/S0304-8853(01)00449-8 |bibcode=2001JMMM..236..107L |url-status=dead |archive-url=https://web.archive.org/web/20120425145000/http://fizz.phys.dal.ca/~dunlap/index_files/index_files/journal/c210_lagarec.pdf |archive-date=25 April 2012 }}</ref> Instead, it appears that the low-moment/high-moment transition is preceded by a high-magnetic-moment [[Geometrically frustrated magnet|frustrated ferromagnetic state]] in which the Fe–Fe magnetic exchange bonds have a large magneto-volume effect of the right sign and magnitude to create the observed thermal expansion anomaly.<ref>{{cite journal|author1=D.G. Rancourt |author2=M.-Z. Dang |title= Relation between anomalous magneto-volume behaviour and magnetic frustration in Invar alloys|journal=Physical Review B|volume= 54|issue= 17|year=1996|pages= 12225–12231|doi=10.1103/PhysRevB.54.12225|pmid=9985084 |bibcode=1996PhRvB..5412225R}}</ref>

Wang et al. considered the statistical mixture between the fully ferromagnetic (FM) configuration and the spin-flipping configurations (SFCs) in {{chem|Fe|3|Pt}} with the free energies of FM and SFCs predicted from first-principles calculations and were able to predict the temperature ranges of negative thermal expansion under various pressures.<ref>Wang, Y., Shang, S. L., Zhang, H., Chen, L.-Q., & Liu, Z.-K. (2010). Thermodynamic fluctuations in magnetic states: Fe 3 Pt as a prototype. Philosophical Magazine Letters, 90(12), 851–859. https://doi.org/10.1080/09500839.2010.508446</ref> It was shown that all individual FM and SFCs have positive thermal expansion, and the negative thermal expansion originates from the increasing populations of SFCs with smaller volumes than that of FM.<ref>{{Cite journal|doi=10.1038/srep07043|pmid=25391631|pmc=4229665|title=Thermal Expansion Anomaly Regulated by Entropy|journal=Scientific Reports|volume=4|pages=7043|year=2014|last1=Liu|first1=Zi-Kui|last2=Wang|first2=Yi|last3=Shang|first3=Shunli|bibcode=2014NatSR...4.7043L}}</ref>