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[[Image:Liquid-liquid.gif|300px|right|thumb|Pressure-temperature [[phase diagram]], including an illustration of the liquid-liquid transition line proposed for several polyamorphous materials. This liquid-liquid [[phase transition]] would be a first order, [[discontinuous]] transition between low and high density liquids (labelled 1 and 2). This is analogous to [[Polymorphism (materials science)|polymorphism]] of crystalline materials, where different stable crystalline states (solid 1, 2 in diagram) of the same substance can exist (e.g. diamond and graphite are two polymorphs of carbon).
[[Image:Liquid-liquid.gif|300px|thumb|Pressure-temperature [[phase diagram]], including an illustration of the liquid-liquid transition line proposed for several polyamorphous materials. This liquid-liquid [[phase transition]] would be a first order, [[discontinuous]] transition between low and high density liquids (labelled 1 and 2). This is analogous to [[Polymorphism (materials science)|polymorphism]] of crystalline materials, where different stable crystalline states (solid 1, 2 in diagram) of the same substance can exist (e.g. diamond and graphite are two polymorphs of carbon). Like the ordinary liquid-gas transition, the liquid-liquid transition is expected to end in a critical point. At temperatures beyond these critical points there is a continuous range of fluid states, i.e. the distinction between liquids and gasses is lost. If crystallisation is avoided the liquid-liquid transition can be extended into the metastable [[supercooled liquid]] regime.]]


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[[Image:Liq-liq-potential2.svg|300px|thumb|Schematic of interatomic pair potentials. The blue line is a typical [[Lennard-Jones potential|Lennard-Jones type potential]], which exhibits the ordinary liquid-gas critical point. The Red line is a double well type potential, which is proposed for polyamorphous systems<ref name=mish1>{{cite journal |last=Mishima |first=O. |title=The relationship between liquid, supercooled and glassy water|journal=Nature |volume=396 |year=1998 |pages=329}}</ref>. The grey line, is a representative of the soft core square well potentials, which in atomisitc simulations exhibit liquid-liquid transitions and a second critical point <ref name=fran>{{cite journal |last=Franzese |first=G. |title=Generic mechanism for generating a liquid-liquid phase transition |journal=Nature |volume=409 |issue= |month= |year=2001 |pages=692 |doi=10.1038/35055514}}</ref>. The numbers 1 and 2 correspond to the 1st and second minima in the potentials.]]
Like the ordinary liquid-gas transition, the liquid-liquid transition is expected to end in a critical point. At temperatures beyond these critical points there is a continuous range of fluid states, i.e. the distinction between liquids and gasses is lost. If crystallisation is avoided the liquid-liquid transition can be extended into the metastable [[supercooled liquid]] regime.]]


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'''Polyamorphism''' is the ability of a substance to exist in several different [[amorphous]] modifications. It is analogous to the [[Polymorphism (materials science)|polymorphism]] of [[crystal]]line materials. Many amorphous substances can exist with different amorphous characteristics (e.g. polymers). However, polyamorphism requires ''two distinct'' amorphous states with a clear phase transition between them. As amorphous solids are sometimes associated with liquid state, polyamorphism is also referred to as '''liquid-liquid phase transition'''. <ref>{{cite journal|pmid=12195833}}</ref>
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[[Image:Liq-liq-potential2.svg|300px|right|thumb|Schematic of interatomic pair potentials. The blue line is a typical [[Lennard-Jones potential|Lennard-Jones type potential]], which exhibits the ordinary liquid-gas critical point. The Red line is a double well type potential, which is proposed for polyamorphous systems<ref name=mish1>{{cite journal |last=Mishima |first=O. |title=The relationship between liquid, supercooled and glassy water|journal=Nature |volume=396 |issue= |month=November |year=1998 |pages=329}}</ref>. The grey line, is a representative of the soft core square well potentials, which in atomisitc simulations exhibit liquid-liquid transitions and a second critical point <ref name=fran>{{cite journal |last=Franzese |first=G. |title=Generic mechanism for generating a liquid-liquid phase transition |journal=Nature |volume=409 |issue= |month= |year=2001 |pages=692 |doi=10.1038/35055514}}</ref>. The numbers 1 and 2 correspond to the 1st and second minima in the potentials.]]

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'''Polyamorphism''' is the ability of a substance to exist in several different [[amorphous]] modifications. It is analogous to the [[Polymorphism (materials science)|polymorphism]] of [[crystal]]line materials. Many amorphous substances can exist with different amorphous characteristics (e.g. polymers). However, polyamorphism requires '''two distinct''' amorphous states with a clear phase transition between them.<ref>http://www.ingentaconnect.com/content/rpsgb/jpp/2002/00000054/00000008/art00019?crawler=true</ref>


==Overview==
==Overview==
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Even though amorphous materials exhibit no [[long-range order|long-range]] periodic atomic ordering, different amorphous phases of the same chemical substance can vary in other properties, such as [[density]]. In several cases sharp transitions have been observed between two different density amorphous states of the same material. [[Amorphous ice]] is one important example (see also examples below).<ref>{{cite journal |last=Mishima |first=O. |title=An apparently 1st-order transition between two amorphous phases of ice induced by pressure|doi=10.1038/314076a0|journal=Nature |volume=314 |issue= |year=1985 |pages=76}}</ref>. Several of these transitions (including water) are expected to end in a second [[critical point (thermodynamics)|critical point]].


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==Liquid-liquid transitions==
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Even though amorphous materials exhibit no [[long-range order|long-range]] periodic atomic ordering, different amorphous phases of the same chemical substance can vary in other properties, such as [[density]]. In several cases sharp transitions have been observed between two different density amorphous states of the same material. [[Amorphous ice]] is one important example <ref>{{cite journal |last=Mishima |first=O. |title=An apparently 1st-order transition between two amorphous phases of ice induced by pressure.|journal=Nature |volume=314 |issue= |month=November |year=1985 |pages=76}}</ref>. Several of these transitions (including water) are expected to end in a second [[critical point (thermodynamics)|critical point]].

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==Liquid-liquid Transitions==


Polyamorphism may apply to all amorphous states, i.e. glasses, other amorphous solids, supercooled liquids, ordinary liquids or fluids. A liquid-liquid transition however, is one that occurs only in the liquid state (red line in the phase diagram, top right). In this article liquid-liquid transitions are defined as transitions between two liquids of the same chemical substance. Elsewhere the term liquid-liquid transition may also refer to the more common transitions between liquid mixtures of different chemical composition.
Polyamorphism may apply to all amorphous states, i.e. glasses, other amorphous solids, supercooled liquids, ordinary liquids or fluids. A liquid-liquid transition however, is one that occurs only in the liquid state (red line in the phase diagram, top right). In this article liquid-liquid transitions are defined as transitions between two liquids of the same chemical substance. Elsewhere the term liquid-liquid transition may also refer to the more common transitions between liquid mixtures of different chemical composition.
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===Rapport's theory===
===Rapport's theory===


Liquid-liquid transitions were originally considered by Rappoport in 1967 in order to explain high pressure melting curve maxima of some liquid metals <ref name=rap>{{cite journal |last=Mishima |first=O. |title=Model for melting curve maxima at high pressure.|journal=J. Chem. Phys. |volume=46 |issue=289 |month=|year=1967 |pages=1–5}}</ref>. Rapoport's theory requires the existence of a melting curve maximum in polyamorphic systems.
Liquid-liquid transitions were originally considered by Rappoport in 1967 in order to explain high pressure melting curve maxima of some liquid metals <ref name=rap>{{cite journal |last=Mishima |first=O. |title=Model for melting curve maxima at high pressure|doi=10.1063/1.1841150|journal=J. Chem. Phys. |volume=46 |issue=289 |year=1967 |pages=1–5}}</ref>. Rapoport's theory requires the existence of a melting curve maximum in polyamorphic systems.


===Double well Potentials===
===Double well potentials===


One physical explanation for polyamorphism is the existence of a double well inter-atomic pair potential (see lower right diagram). It is well known that the ordinary liquid-gas critical point appears when the inter-atomic pair potential contains a minimum. At lower energies (temperatures) particles trapped in this minimum condense into the liquid state. At higher temperatures however, these particles can escape the well and the sharp definition between liquid and gas is lost. [[Molecular modelling]] has shown that addition of a second well produces an additional transition between two different liquids (or fluids) with a second critical point<ref name=fran/>.
One physical explanation for polyamorphism is the existence of a double well inter-atomic pair potential (see lower right diagram). It is well known that the ordinary liquid-gas critical point appears when the inter-atomic pair potential contains a minimum. At lower energies (temperatures) particles trapped in this minimum condense into the liquid state. At higher temperatures however, these particles can escape the well and the sharp definition between liquid and gas is lost. [[Molecular modelling]] has shown that addition of a second well produces an additional transition between two different liquids (or fluids) with a second critical point<ref name=fran/>.


==Examples of polyamorphism==
==Examples of polyamorphism==
The most famous case of polyamorphism is [[amorphous ice]]. Pressurizing conventional hexagonal ice crystals to about 1.6 GPa at [[liquid nitrogen]] temperature (77 K) converts them to the high-density amorphous ice. Upon releasing the pressure, this phase is stable and has density of 1.17 g/cm<sup>3</sup> at 77 K and 1 bar. Consequent warming to 127 K at ambient pressure transforms this phase to a low-density amorphous ice (0.94 g/cm<sup>3</sup> at 1 bar).<ref>{{cite journal|doi=10.1016/S0921-4526(97)00749-7|title=Amorphous polymorphis in ice investigated by inelastic neutron scattering|year=1997|last1=Schober|first1=H|journal=Physica B: Condensed Matter|volume=241-243|pages=897}}</ref> Yet, if the high-density amorphous ice is warmed up to 165 K not at low pressures but keeping the 1.6 GPa compression, and then cooled back to 77 K, then another amorphous ice is produced, which has even higher density of 1.25 g/cm<sup>3</sup> at 1 bar. All those amorphous forms have very different vibrational lattice spectra and intermolecular distances.<ref>{{cite journal|doi=10.1039/b108676f|title=A second distinct structural “state” of high-density amorphous ice at 77 K and 1 bar|year=2001|last1=Loerting|first1=Thomas|last2=Salzmann|first2=Christoph|last3=Kohl|first3=Ingrid|last4=Mayer|first4=Erwin|last5=Hallbrucker|first5=Andreas|journal=Physical Chemistry Chemical Physics|volume=3|pages=5355}}</ref><ref name=r1/>


Another example of polyamorphism is if [[yttria]]-[[alumina]] melts are quenched from about 1900 °C to room temperature at a rate ~400 °C/s, then two co-existing glass phases form at certain initial Y/Al ratio (about 20 mol% Y<sub>2</sub>O<sub>3</sub>). Those phases have the same average composition but different density, molecular structure and hardness.<ref>{{cite journal|doi=10.1038/369633a0|title=Density-driven liquid–liquid phase separation in the
Examples of polyamorphism are the existence of six-coordinated and four-coordinated amorphous [[silicon]], and the different density phases of [[amorphous ice]]. In the case of amorphous ice the transition occurs below zero Celsius, so it is not a true equilibrium transition, the stable crystalline [[ice]]s are the equilibrium phases. There is also continued debate over whether the transformations between the various high density and low density amorphous ices are first order-like or continuous-like transitions.
system
AI2O3–Y2O3|year=1994|last1=Aasland|first1=S.|last2=McMillan|first2=P.
F.|journal=Nature|volume=369|pages=633}}</ref> First-order glass-liquid [[phase transition]] has also been reported for [[silicon]], and continuous changes in density were observed upon cooling [[silicon dioxide]] or [[germanium dioxide]]. Polyamorphism has also been observed in organic compounds, such as liquid [[triphenyl phosphite]] at temperatures about 200 K.<ref name=r1>{{cite book|url=http://books.google.com/books?id=Xk-lYXtqM-4C&pg=PA120|page=120|title=Structural chemistry of glasses|author=K. J. Rao|publisher=Elsevier|year=2002|isbn=0080439586}}</ref><ref>{{cite journal|doi=10.1021/jp9530820|title=Supercooled Liquids and Polyamorphism†|year=1996|last1=Ha|first1=Alice|last2=Cohen|first2=Itai|last3=Zhao|first3=Xiaolin|last4=Lee|first4=Michelle|last5=Kivelson|first5=Daniel|journal=The Journal of Physical Chemistry|volume=100|pages=1}}</ref><ref name=poole>{{cite journal|doi=10.1126/science.275.5298.322|title=Polymorphic Phase Transitions in Liquids and Glasses|year=1997|last1=Poole|first1=P. H.|journal=Science|volume=275|pages=322}}</ref><ref>{{cite book|url=http://books.google.com/books?id=6HQqBtqcy84C&pg=PA65|page=65|title=Disordered materials: an introduction|author=Paolo M. Ossi|publisher=Springer|year=2006|isbn=3540296093}}</ref>


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==References==
Yttria-Aluminates are another system believed to exhibit polyamorphism in the [[supercooled]] liquid and glassy states <ref name=Aasland94>{{cite journal |last=Aasland |first=S. |coauthors=McMillan, P. F. |title=Density driven phase separation in the system Al2O3-Y2O3 |journal=Nature |volume=396 |issue= |month=June |year=1994 |pages=633 |doi=10.1038/369633a0}}</ref>
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{{Reflist|2}}


==Unsolved questions / Future work==

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==References==
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{{Reflist}}
[[Category:Phase changes]]
[[Category:Phase changes]]
[[Category:Phases of matter]]
[[Category:Amorphous solids]]


[[fr:Polyamorphisme]]
[[fr:Polyamorphisme]]

Revision as of 07:26, 26 April 2010

Pressure-temperature phase diagram, including an illustration of the liquid-liquid transition line proposed for several polyamorphous materials. This liquid-liquid phase transition would be a first order, discontinuous transition between low and high density liquids (labelled 1 and 2). This is analogous to polymorphism of crystalline materials, where different stable crystalline states (solid 1, 2 in diagram) of the same substance can exist (e.g. diamond and graphite are two polymorphs of carbon). Like the ordinary liquid-gas transition, the liquid-liquid transition is expected to end in a critical point. At temperatures beyond these critical points there is a continuous range of fluid states, i.e. the distinction between liquids and gasses is lost. If crystallisation is avoided the liquid-liquid transition can be extended into the metastable supercooled liquid regime.
Schematic of interatomic pair potentials. The blue line is a typical Lennard-Jones type potential, which exhibits the ordinary liquid-gas critical point. The Red line is a double well type potential, which is proposed for polyamorphous systems[1]. The grey line, is a representative of the soft core square well potentials, which in atomisitc simulations exhibit liquid-liquid transitions and a second critical point [2]. The numbers 1 and 2 correspond to the 1st and second minima in the potentials.

Polyamorphism is the ability of a substance to exist in several different amorphous modifications. It is analogous to the polymorphism of crystalline materials. Many amorphous substances can exist with different amorphous characteristics (e.g. polymers). However, polyamorphism requires two distinct amorphous states with a clear phase transition between them. As amorphous solids are sometimes associated with liquid state, polyamorphism is also referred to as liquid-liquid phase transition. [3]

Overview

Even though amorphous materials exhibit no long-range periodic atomic ordering, different amorphous phases of the same chemical substance can vary in other properties, such as density. In several cases sharp transitions have been observed between two different density amorphous states of the same material. Amorphous ice is one important example (see also examples below).[4]. Several of these transitions (including water) are expected to end in a second critical point.

Liquid-liquid transitions

Polyamorphism may apply to all amorphous states, i.e. glasses, other amorphous solids, supercooled liquids, ordinary liquids or fluids. A liquid-liquid transition however, is one that occurs only in the liquid state (red line in the phase diagram, top right). In this article liquid-liquid transitions are defined as transitions between two liquids of the same chemical substance. Elsewhere the term liquid-liquid transition may also refer to the more common transitions between liquid mixtures of different chemical composition.

The stable liquid state unlike most glasses and amorphous solids, is a thermodynamically stable equilibrium state. Thus new liquid-liquid or fluid-fluid transitions in the stable liquid (or fluid) states are more easily analysed than transitions in amorphous solids where arguments are complicated by the non-equilibrium, non-ergodic nature of the amorphous state.

Rapport's theory

Liquid-liquid transitions were originally considered by Rappoport in 1967 in order to explain high pressure melting curve maxima of some liquid metals [5]. Rapoport's theory requires the existence of a melting curve maximum in polyamorphic systems.

Double well potentials

One physical explanation for polyamorphism is the existence of a double well inter-atomic pair potential (see lower right diagram). It is well known that the ordinary liquid-gas critical point appears when the inter-atomic pair potential contains a minimum. At lower energies (temperatures) particles trapped in this minimum condense into the liquid state. At higher temperatures however, these particles can escape the well and the sharp definition between liquid and gas is lost. Molecular modelling has shown that addition of a second well produces an additional transition between two different liquids (or fluids) with a second critical point[2].

Examples of polyamorphism

The most famous case of polyamorphism is amorphous ice. Pressurizing conventional hexagonal ice crystals to about 1.6 GPa at liquid nitrogen temperature (77 K) converts them to the high-density amorphous ice. Upon releasing the pressure, this phase is stable and has density of 1.17 g/cm3 at 77 K and 1 bar. Consequent warming to 127 K at ambient pressure transforms this phase to a low-density amorphous ice (0.94 g/cm3 at 1 bar).[6] Yet, if the high-density amorphous ice is warmed up to 165 K not at low pressures but keeping the 1.6 GPa compression, and then cooled back to 77 K, then another amorphous ice is produced, which has even higher density of 1.25 g/cm3 at 1 bar. All those amorphous forms have very different vibrational lattice spectra and intermolecular distances.[7][8]

Another example of polyamorphism is if yttria-alumina melts are quenched from about 1900 °C to room temperature at a rate ~400 °C/s, then two co-existing glass phases form at certain initial Y/Al ratio (about 20 mol% Y2O3). Those phases have the same average composition but different density, molecular structure and hardness.[9] First-order glass-liquid phase transition has also been reported for silicon, and continuous changes in density were observed upon cooling silicon dioxide or germanium dioxide. Polyamorphism has also been observed in organic compounds, such as liquid triphenyl phosphite at temperatures about 200 K.[8][10][11][12]

References

  1. ^ Mishima, O. (1998). "The relationship between liquid, supercooled and glassy water". Nature. 396: 329.
  2. ^ a b Franzese, G. (2001). "Generic mechanism for generating a liquid-liquid phase transition". Nature. 409: 692. doi:10.1038/35055514. {{cite journal}}: Cite has empty unknown parameter: |month= (help)
  3. ^ . PMID 12195833. {{cite journal}}: Cite journal requires |journal= (help); Missing or empty |title= (help)
  4. ^ Mishima, O. (1985). "An apparently 1st-order transition between two amorphous phases of ice induced by pressure". Nature. 314: 76. doi:10.1038/314076a0.
  5. ^ Mishima, O. (1967). "Model for melting curve maxima at high pressure". J. Chem. Phys. 46 (289): 1–5. doi:10.1063/1.1841150.
  6. ^ Schober, H (1997). "Amorphous polymorphis in ice investigated by inelastic neutron scattering". Physica B: Condensed Matter. 241–243: 897. doi:10.1016/S0921-4526(97)00749-7.
  7. ^ Loerting, Thomas; Salzmann, Christoph; Kohl, Ingrid; Mayer, Erwin; Hallbrucker, Andreas (2001). "A second distinct structural "state" of high-density amorphous ice at 77 K and 1 bar". Physical Chemistry Chemical Physics. 3: 5355. doi:10.1039/b108676f.
  8. ^ a b K. J. Rao (2002). Structural chemistry of glasses. Elsevier. p. 120. ISBN 0080439586.
  9. ^ Aasland, S.; McMillan, P. F. (1994). "Density-driven liquid–liquid phase separation in the system AI2O3–Y2O3". Nature. 369: 633. doi:10.1038/369633a0. {{cite journal}}: line feed character in |first2= at position 3 (help); line feed character in |title= at position 53 (help)
  10. ^ Ha, Alice; Cohen, Itai; Zhao, Xiaolin; Lee, Michelle; Kivelson, Daniel (1996). "Supercooled Liquids and Polyamorphism†". The Journal of Physical Chemistry. 100: 1. doi:10.1021/jp9530820.
  11. ^ Poole, P. H. (1997). "Polymorphic Phase Transitions in Liquids and Glasses". Science. 275: 322. doi:10.1126/science.275.5298.322.
  12. ^ Paolo M. Ossi (2006). Disordered materials: an introduction. Springer. p. 65. ISBN 3540296093.
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