Editing Phase transition (section)

===Phase coexistence===
A disorder-broadened  first-order transition occurs over a finite range of temperatures where the fraction of the low-temperature equilibrium phase grows from zero to one (100%) as the temperature is lowered. This continuous variation of the coexisting fractions with temperature raised interesting possibilities. On cooling, some liquids vitrify into a glass rather than transform to the equilibrium crystal phase. This happens if the cooling rate is faster than a critical cooling rate, and is attributed to the molecular motions becoming so slow that the molecules cannot rearrange into the crystal positions.<ref>{{cite journal | year = 1995 | title =  Metallic Glasses| journal = Science | volume = 267 | issue = 5206| pages = 1947–1953 |bibcode = 1995Sci...267.1947G |doi = 10.1126/science.267.5206.1947 | pmid =  17770105| last1 =  Greer| first1 =  A. L.| s2cid = 220105648}}</ref> This slowing down happens below a glass-formation temperature ''T''<sub>g</sub>, which may depend on the applied pressure.<ref name="J. Non-Cryst 2013"/><ref>{{cite journal | last1 = Tarjus | first1 = G. | year = 2007 | title =  Materials science: Metal turned to glass| journal = Nature | volume = 448 | issue = 7155| pages = 758–759 | doi=10.1038/448758a| pmid = 17700684 |bibcode = 2007Natur.448..758T | s2cid = 4410586 | doi-access = free }}</ref> If the first-order freezing transition occurs over a range of temperatures, and ''T''<sub>g</sub> falls within this range, then there is an interesting possibility that the transition is arrested when it is partial and incomplete. Extending these ideas to first-order magnetic transitions being arrested at low temperatures, resulted in the observation of incomplete magnetic transitions, with two magnetic phases coexisting, down to the lowest temperature. First reported in the case of a ferromagnetic to anti-ferromagnetic transition,<ref name="ManekarChaudhary2001">{{cite journal |last1=Manekar |first1=M. A. |last2=Chaudhary |first2=S. |last3=Chattopadhyay |first3=M. K. |last4=Singh |first4=K. J. |last5=Roy |first5=S. B. |last6=Chaddah |first6=P. |title=First-order transition from antiferromagnetism to ferromagnetism inCe(Fe<sub>0.96</sub>Al<sub>0.04</sub>)<sub>2</sub> |journal=Physical Review B |volume=64 |issue=10 |page=104416 |year=2001 |issn=0163-1829 |doi=10.1103/PhysRevB.64.104416 |arxiv=cond-mat/0012472 |bibcode=2001PhRvB..64j4416M|s2cid=16851501 }}</ref> such persistent phase coexistence has now been reported across a variety of first-order magnetic transitions. These include colossal-magnetoresistance manganite materials,<ref>{{cite journal|doi=10.1088/0953-8984/18/49/L02|arxiv = cond-mat/0611152 |bibcode = 2006JPCM...18L.605B |title = Coexisting tunable fractions of glassy and equilibrium long-range-order phases in manganites |journal = Journal of Physics: Condensed Matter |volume = 18 |issue = 49 |pages = L605 |year = 2006 |last1 = Banerjee |first1 = A. |last2 = Pramanik |first2 = A. K. |last3 = Kumar |first3 = Kranti |last4 = Chaddah |first4 = P. |s2cid = 98145553 }}</ref><ref>{{cite journal |author=Wu W. |author2=Israel C. |author3=Hur N. |author4=Park S. |author5=Cheong S. W. |author6=de Lozanne A. | year = 2006 | title =  Magnetic imaging of a supercooling glass transition in a weakly disordered ferromagnet| journal = Nature Materials | volume = 5 | issue = 11| pages = 881–886 |bibcode = 2006NatMa...5..881W |doi = 10.1038/nmat1743 | pmid = 17028576 | s2cid = 9036412 }}</ref> magnetocaloric materials,<ref name="RoyChattopadhyay2006">{{cite journal |last1=Roy |first1=S. B. |last2=Chattopadhyay |first2=M. K. |last3=Chaddah |first3=P. |last4=Moore |first4=J. D. |last5=Perkins |first5=G. K. |last6=Cohen |first6=L. F. |last7=Gschneidner |first7=K. A. |last8=Pecharsky |first8=V. K. |title=Evidence of a magnetic glass state in the magnetocaloric material Gd<sub>5</sub>Ge<sub>4</sub> |journal=Physical Review B |volume=74 |issue=1 |page=012403 |year=2006 |issn=1098-0121 |doi=10.1103/PhysRevB.74.012403 |bibcode = 2006PhRvB..74a2403R }}</ref> magnetic shape memory materials,<ref name="LakhaniBanerjee2012">{{cite journal |last1=Lakhani |first1=Archana |last2=Banerjee |first2=A. |last3=Chaddah |first3=P. |last4=Chen |first4=X. |last5=Ramanujan |first5=R. V. |title=Magnetic glass in shape memory alloy: Ni<sub>45</sub>Co<sub>5</sub>Mn<sub>38</sub>Sn<sub>12</sub> |journal=Journal of Physics: Condensed Matter |volume=24 |issue=38 |year=2012 |page=386004 |issn=0953-8984 |doi=10.1088/0953-8984/24/38/386004 |pmid=22927562 |arxiv = 1206.2024 |bibcode = 2012JPCM...24L6004L |s2cid=206037831 }}</ref> and other materials.<ref name="KushwahaLakhani2009">{{cite journal |last1=Kushwaha |first1=Pallavi |last2=Lakhani |first2=Archana |last3=Rawat |first3=R. |last4=Chaddah |first4=P. |title=Low-temperature study of field-induced antiferromagnetic-ferromagnetic transition in Pd-doped Fe-Rh |journal=Physical Review B |volume=80 |issue=17 |page=174413 |year=2009 |issn=1098-0121 |doi=10.1103/PhysRevB.80.174413 |arxiv=0911.4552 |bibcode=2009PhRvB..80q4413K|s2cid=119165221 }}</ref>
The interesting feature of these observations of ''T''<sub>g</sub> falling within the temperature range over which the transition occurs is that the first-order magnetic transition is influenced by magnetic field, just like the structural transition is influenced by pressure. The relative ease with which magnetic fields can be controlled, in contrast to pressure, raises the possibility that one can study the interplay between ''T''<sub>g</sub> and ''T''<sub>c</sub> in an exhaustive way. Phase coexistence across first-order magnetic transitions will then enable the resolution of outstanding issues in understanding glasses.