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| The '''glass–liquid transition''' (or '''glass transition''' for short) is the reversible transition in [[amorphous solid|amorphous]] materials (or in amorphous regions within [[semicrystalline]] materials) from a hard and relatively brittle state into a molten or [[rubber]]-like state.<ref name=iso11357-2> | | Shaw laminate flooring supplies a lot more choices when it comes to choosing laminate flooring than other manufacturers. The innovative product that Shaw has brought to industry allows you to install new flooring with the appearance of wood in record time. This is the final in glueless laminate floor in order that you dont have any mess to clean-up or do you have to wait before you can go on the floor. You can install Shaw laminate flooring and walk about it immediately. <br><br> |
| [[International Organization for Standardization|ISO]] 11357-2: Plastics – Differential scanning calorimetry (DSC) – Part 2: Determination of glass transition temperature (1999).
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| </ref> An amorphous solid that exhibits a glass transition is called a [[glass]]. Supercooling a [[viscous liquid]] into the glass state is called [[vitrification]], from the [[Latin language|Latin]] ''vitreum'', "glass" via [[French language|French]] ''vitrifier''. | |
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| Despite the massive change in the physical properties of a material through its glass transition, the transition is not itself a [[phase transition]] of any kind; rather it is a laboratory phenomenon extending over a range of temperature and defined by one of several conventions.<ref name="Debenedetti">{{cite journal|doi=10.1038/35065704|last=Debenedetti|first=P. G.|coauthors=Stillinger|title=Supercooled liquids and the glass transition|journal=Nature|year=2001|volume=410|issue=6825|pages=259–267|pmid=11258381|bibcode = 2001Natur.410..259D }}</ref><ref name="Angell">{{cite journal|doi=10.1063/1.1286035|last=Angell|first=C. A.|coauthors=Ngai, K. L.; McKenna, G. B.; McMillan, P. F.; Martin, S. W.|title=Relaxation in glassforming liquids and amorphous solids|journal=App. Phys. Rev.|year=2000|volume=88|issue=6|pages=3113–3157|bibcode = 2000JAP....88.3113A }}</ref> Such conventions include a constant cooling rate (20 K/min)<ref name=iso11357-2/> and a viscosity threshold of 10<sup>12</sup> [[Pa·s]], among others. Upon cooling or heating through this glass-transition range, the material also exhibits a smooth step in the [[thermal expansion|thermal-expansion coefficient]] and in the [[specific heat]], with the location of these effects again being dependent on the history of the material.<ref name=z1/> However, the question of whether some phase transition ''underlies'' the glass transition is a matter of continuing research.<ref name="Debenedetti"/><ref name="Angell"/><ref>{{cite journal|doi=10.1134/1.1790021|title=Glass formation in amorphous SiO<sub>2</sub> as a percolation phase transition in a system of network defects|year=2004|last1=Ojovan|first1=M. I.|journal=Journal of Experimental and Theoretical Physics Letters|volume=79|issue=12|pages=632|bibcode = 2004JETPL..79..632O }}</ref>
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| The '''glass-transition temperature''' ''T''<sub>g</sub> is always lower than the [[melting point|melting temperature]], ''T''<sub>m</sub>, of the crystalline state of the material, if one exists.
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| ==Introduction==
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| The glass transition of a Liquid to a solid-like state may occur with either cooling or compression.<ref name="Hansen&McDonald">{{cite book|last=Hansen|first=J.-P.|title=Theory of Simple Liquids| isbn=0123705355|url=http://books.google.com/books?id=Uhm87WZBnxEC&printsec=frontcover|year=2007|publisher=Elsevier|pages=250–254|coauthors=McDonald, I. R.;}}</ref> The transition comprises a smooth increase in the viscosity of a material by as much as 17{{cn|date=March 2013}} [[order of magnitude|orders of magnitude]] without any pronounced change in material structure. The consequence of this dramatic increase is a [[glass]] exhibiting solid-like mechanical properties on the timescale of practical observation. This transition is in contrast to the [[freezing]] or [[crystallization]] transition, which is a first-order [[phase transition]] in the [[Phase transition#Ehrenfest classification|Ehrenfest classification]] and involves discontinuities in thermodynamic and dynamic properties such as volume, energy, and viscosity. In many materials that normally undergo a freezing transition, rapid cooling will avoid this phase transition and instead result in a glass transition at some lower temperature. Other materials, such as many [[polymers]], lack a well defined crystalline state and easily form glasses, even upon very slow cooling or compression.
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| Below the transition temperature range, the glassy structure does not relax in accordance with the cooling rate used. The expansion coefficient for the glassy state is roughly equivalent to that of the crystalline solid. If slower cooling rates are used, the increased time for structural [[Relaxation (physics)|relaxation]] (or intermolecular rearrangement) to occur may result in a higher density glass product. Similarly, by [[annealing (glass)|annealing]] (and thus allowing for slow structural relaxation) the glass structure in time approaches an equilibrium density corresponding to the supercooled liquid at this same temperature. T<sub>g</sub> is located at the intersection between the cooling curve (volume versus temperature) for the glassy state and the supercooled liquid.<ref name="CM">
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| Moynihan, C. et al. in The Glass Transition and the Nature of the Glassy State, Eds. M. Goldstein and R. Simha, Ann. N.Y. Acad. Sci., Vol. 279 (1976) ISBN 0890720533</ref><ref>
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| {{cite journal|doi=10.1016/0022-3697(88)90002-9|title=Perspective on the glass transition|year=1988|last1=Angell|first1=C. A.|journal=Journal of Physics and Chemistry of Solids|volume=49|issue=8|pages=863|bibcode = 1988JPCS...49..863A }}</ref><ref>{{cite journal|doi=10.1021/jp953538d|title=Supercooled Liquids and Glasses|year=1996|last1=Ediger|first1=M. D.|last2=Angell|first2=C. A.|last3=Nagel|first3=Sidney R.|journal=The Journal of Physical Chemistry|volume=100|issue=31|pages=13200}}</ref><ref>{{cite journal|doi=10.1126/science.267.5206.1924|title=Formation of Glasses from Liquids and Biopolymers|year=1995|last1=Angell|first1=C. A.|journal=Science|volume=267|issue=5206|pages=1924–35|pmid=17770101|bibcode = 1995Sci...267.1924A }}
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| </ref><ref>{{cite journal|doi=10.1126/science.267.5206.1935|title=A Topographic View of Supercooled Liquids and Glass Formation|year=1995|last1=Stillinger|first1=F. H.|journal=Science|volume=267|issue=5206|pages=1935–9|pmid=17770102|bibcode = 1995Sci...267.1935S }}</ref> | |
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| The configuration of the glass in this temperature range changes slowly with time towards the equilibrium structure. The principle of the minimization of the Gibbs free energy provides the thermodynamic driving force necessary for the eventual change. It should be noted here that at somewhat higher temperatures than T<sub>g</sub>, the structure corresponding to equilibrium at any temperature is achieved quite rapidly. In contrast, at considerably lower temperatures, the configuration of the glass remains sensibly stable over increasingly extended periods of time.
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| Thus, the liquid-glass transition is not a transition between states of [[thermodynamic equilibrium]]. It is widely believed that the true equilibrium state is always crystalline. Glass is believed to exist in a kinetically locked state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass transition is primarily a dynamic phenomenon. Time and temperature are interchangeable quantities (to some extent) when dealing with glasses, a fact often expressed in the [[time–temperature superposition]] principle. On cooling a liquid, ''internal degrees of freedom successively fall out of equilibrium''. However, there is a longstanding debate whether there is an underlying second-order phase transition in the hypothetical limit of infinitely long relaxation times.<ref>
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| {{Cite book
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| |author=Nemilov, S. V.,
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| |title= Thermodynamic and Kinetic Aspects of the Vitreous State
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| |publisher=CRC Press
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| |year=1994|isbn=0849337828
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| }}
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| </ref><ref name=z1>
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| {{Cite book|url=http://books.google.com/books?id=D7Z8ywb3QggC&printsec=frontcover|isbn=0521355826
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| |author=Zarzycki, J.
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| |title=Glasses and the Vitreous State|isbn=0521355826
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| |publisher=Cambridge University Press
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| |year=1991
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| }}
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| </ref><ref>
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| {{Cite book
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| |author=J. H. Gibbs
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| |editor=J. D. MacKenzie
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| |title=Modern Aspects of the Vitreous State
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| |publisher=Butterworth
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| |year=1960
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| |oclc=1690554
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| }}
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| </ref><ref>{{cite journal|doi=10.1016/j.jnoncrysol.2010.05.012|title=Connectivity and glass transition in disordered oxide systems|year=2010|last1=Ojovan|first1=Michael I|last2=Lee|first2=William (Bill) E|journal=Journal of Non-Crystalline Solids|volume=356|issue=44–49|pages=2534|bibcode = 2010JNCS..356.2534O }}</ref>
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| ==Transition temperature ''T''<sub>g</sub>==
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| {{anchor|Transition temperature}}
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| {{Refimprove section|date=July 2009}}
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| [[File:Tgdscenglish.svg|thumb|Measurement of ''T''<sub>g</sub> by differential scanning calorimetry]]
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| [[File:Tgdilatometric.gif|thumb|Determination of ''T''<sub>g</sub> by [[Dilatometer|dilatometry]].]]
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| Refer to the figure on the right plotting the heat capacity as a function of temperature. In this context, ''T''<sub>g</sub> is the temperature corresponding to point A on the curve. The linear sections below and above ''T''<sub>g</sub> are colored green. ''T''<sub>g</sub> is the temperature at the intersection of the red regression lines.<ref name=tgmeasurement>[http://www.glassproperties.com/tg/ Tg measurement of glasses]. Glassproperties.com. Retrieved on 2012-06-29.</ref>
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| Different operational definitions of the glass transition temperature ''T''<sub>g</sub> are in use, and several of them are endorsed as accepted scientific standards. Nevertheless, all definitions are arbitrary, and all yield different numeric results: at best, values of ''T''<sub>g</sub> for a given substance agree within a few kelvins. One definition refers to the [[viscosity]], fixing ''T''<sub>g</sub> at a value of 10<sup>13</sup> poise (or 10<sup>12</sup> Pa·s). As evidenced experimentally, this value is close to the [[Annealing (glass)|annealing point]] of many glasses.<ref>[http://old.iupac.org/goldbook/G02641.pdf glass-transition temperature], IUPAC Compendium of Chemical Terminology, 66, 583 (1984)</ref>
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| In contrast to viscosity, the [[thermal expansion]], [[heat capacity]], shear modulus, and many other properties of inorganic [[glass]]es show a relatively sudden change at the glass transition temperature. Any such step or kink can be used to define ''T''<sub>g</sub>. To make this definition reproducible, the cooling or heating rate must be specified.
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| The most frequently used definition of ''T''<sub>g</sub> uses the energy release on heating in [[differential scanning calorimetry]] (DSC, see figure). Typically, the sample is first cooled with 10 K/min and then heated with that same speed.
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| Yet another definition of ''T''<sub>g</sub> uses the kink in [[Dilatometer|dilatometry]] (a.k.a thermal expansion). Here, heating rates of 3–5 K/min are common. Summarized below are ''T''<sub>g</sub> values characteristic of certain classes of materials.
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| ===Polymers===
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| {| class="wikitable sortable"
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| |-
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| ! Material
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| ! ''T''<sub>g</sub> (°C)
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| |-
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| | [[Low-density polyethylene]] (LDPE)
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| | −125<ref name="dm">{{citation
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| |title=Polyethylene|publisher=D&M Plastics|year=2007|location=Canada
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| |quote=The glass transition temperature of polyethylene depends upon the manufacturing process,
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| so the number given is from a particular supplier. | |
| }}</ref>
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| |-
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| | [[Tire]] rubber
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| | −70<ref>
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| {{Cite journal
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| |url=http://patentscope.wipo.int/search/en/WO2003053721
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| |last1=Galimberti
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| |first1=Maurizio
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| |last2=Caprio
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| |first2=Michela
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| |last3=Fino
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| |first3=Luigi
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| |date =2003-03-07
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| |date =2001-12-21
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| |title =Tyre comprising a cycloolefin polymer, tread band and elasomeric composition used therein
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| |quote=country-code =EU, patent-number =WO03053721
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| }}
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| </ref>
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| |-
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| | [[Polyvinylidene fluoride]] (PVDF)
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| | −35<ref name="Ibeh" />
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| |-
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| | [[Polypropylene]] (atactic)
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| | −20<ref name="PVC">
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| {{Cite book|title=PVC Handbook|year=2005|url=http://books.google.com/?id=YUkJNI9QYsUC&pg=PT1&lpg=PT1|author= Wilkes, C. E.|publisher =Hanser Verlag|isbn=1-56990-379-4|display-authors=1}}
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| </ref>
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| |-
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| | [[Polyvinyl fluoride]] (PVF)
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| | -20<ref name="Ibeh">{{cite book | title=THERMOPLASTIC MATERIALS Properties, Manufacturing Methods, and Applications | publisher=CRC Press | author=Christopher C. Ibeh | year=2011 | pages=491–497 | isbn=978-1-4200-9383-4}}</ref>
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| |-
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| | [[Polypropylene]] (isotactic)
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| | 0<ref name="PVC" />
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| |-
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| | [[Poly-3-hydroxybutyrate]] (PHB)
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| | 15<ref name="PVC" />
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| |-
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| | [[Polyvinyl acetate|Poly(vinyl acetate)]] (PVAc)
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| | 30<ref name="PVC" />
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| |-
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| | [[Polychlorotrifluoroethylene]] (PCTFE)
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| | 45<ref name="Ibeh" />
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| |-
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| | [[Polyethylene terephthalate]] (PET)
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| | 70<ref name="PVC" />
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| |-
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| | [[Polyvinyl chloride|Poly(vinyl chloride)]] (PVC)
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| | 80<ref name="PVC" />
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| |-
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| | [[Polyvinyl alcohol|Poly(vinyl alcohol)]] (PVA)
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| | 85<ref name="PVC" />
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| |-
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| | [[Polystyrene]]
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| | 95<ref name="PVC" />
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| |-
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| | [[Poly(methyl methacrylate)]] (atactic)
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| | 105<ref name="PVC" />
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| |-
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| | [[Acrylonitrile butadiene styrene]] (ABS)
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| | 105<ref name="ABS">[http://www.nrri.umn.edu/NLTC/ABS07.pdf ABS] Retrieved 7 May 2010</ref>
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| |-
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| | [[Polytetrafluoroethylene]] (PTFE)
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| | 115<ref>{{cite book | title=The Chemistry of Polymers | publisher=Royal Society of Chemistry | author=John W. Nicholson | year=2011 | pages=50 | isbn=1849733910 |quote=ISBN=9781849733915 | url=http://books.google.co.uk/books?id=5XFsT69cX_YC&printsec=frontcover&dq=polymer+chemistry&hl=en&sa=X&ei=-Wn0T-KZAoflrAfTzv3iBg&ved=0CG0Q6AEwCQ#v=onepage&q=polymer%20chemistry&f=false | edition=4, Revised |deadurl=no |accessdate=10 September 2013}}</ref>
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| |-
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| | [[Polycarbonate|Poly(carbonate)]]
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| | 145<ref name="PVC" />
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| |-
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| | [[Polynorbornene]]
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| | 215<ref name="PVC" />
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| |}
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| Nylon-6 [[Nylon]] has a glass transition temperature of 47 °C.<ref>[http://www.polymerprocessing.com/polymers/PA6.html nylon-6 information and properties]. Polymerprocessing.com (2001-04-15). Retrieved on 2012-06-29.</ref>
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| Whereas [[polyethene]] has a glass transition range of −130 to −80 °C<ref>[http://www.polyesterconverters.com/pcl_apps/stage1/stage2/applications_and_enduses/polyethene.htm PCL | Applications and End Uses | Polythene]. Polyesterconverters.com. Retrieved on 2012-06-29.</ref>
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| It must be kept in mind that the above are only mean values, as the glass transition temperature depends on the cooling rate, molecular weight distribution and could be influenced by additives. Note also that for a semi-crystalline material, such as [[polyethene]] that is 60–80% crystalline at room temperature, the quoted glass transition refers to what happens to the amorphous part of the material upon cooling.
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| ===Silicates and other covalent network glasses===
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| {| class="wikitable sortable"
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| |-
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| ! Material
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| ! ''T''<sub>g</sub> (°C)
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| |-
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| | [[Chalcogenide]] GeSbTe
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| | 150<ref>''[http://www.epcos.org/library/papers/pdf_2007/paper13_Salinga.pdf EPCOS 2007: Glass Transition and Crystallization in Phase Change Materials]'' . Retrieved on 2012-06-29.</ref>
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| |-
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| | [[Chalcogenide]] AsGeSeTe
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| | 245
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| |-
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| | [[ZBLAN]] fluoride glass
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| | 235
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| |-
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| | [[Tellurium dioxide]]
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| | 280
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| |-
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| | Fluoroaluminate
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| | 400
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| |-
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| | [[Soda-lime glass]]
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| | 520–600
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| |-
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| | [[Fused quartz]]
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| | ~1200<ref>{{Cite doi|10.1063/1.1663238}}</ref>
| |
| |}
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| | |
| ==Kauzmann's paradox==
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| [[File:KauzmannParadox.png|thumb|right|Entropy difference between crystal and undercooled melt]]
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| As a liquid is supercooled, the difference in entropy between the liquid and solid phase decreases. By extrapolating the [[heat capacity]] of the supercooled liquid below its [[glass transition temperature]], it is possible to calculate the temperature at which the difference in entropies becomes zero. This temperature has been named the '''Kauzmann temperature'''.
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| If a liquid could be supercooled below its Kauzmann temperature, and it did indeed display a lower entropy than the crystal phase, the consequences would be paradoxical. This '''Kauzmann paradox''' has been the subject of much debate and many publications since it was first put forward by [[Walter Kauzmann]] in 1948.<ref>{{cite journal|doi=10.1021/cr60135a002|title=The Nature of the Glassy State and the Behavior of Liquids at Low Temperatures|year=1948|last1=Kauzmann|first1=Walter|journal=Chemical Reviews|volume=43|issue=2|pages=219}}</ref>
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| One resolution of the Kauzmann paradox is to say that there must be a [[phase transition]] before the entropy of the liquid decreases. In this scenario, the transition temperature is known as the ''calorimetric ideal glass transition temperature'' ''T''<sub>0c</sub>. In this view, the glass transition is not merely a [[Chemical kinetics|kinetic]] effect, i.e. merely the result of fast cooling of a melt, but there is an underlying [[thermodynamic]] basis for glass formation. The glass transition temperature:
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| : <math> T_g \to T_{0c} \text{ as } \frac{dT}{dt} \to 0. </math>
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| There are at least three other possible resolutions to the Kauzmann paradox. It could be that the heat capacity of the supercooled liquid near the Kauzmann temperature smoothly decreases to a smaller value. It could also be that a first order phase transition to another liquid state occurs before the Kauzmann temperature with the heat capacity of this new state being less than that obtained by extrapolation from higher temperature. Finally, Kauzmann himself resolved the entropy paradox by postulating that all supercooled liquids must crystallize before the Kauzmann temperature is reached.
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| ==The glass transition in specific materials==
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| ===Silica, SiO<sub>2</sub>===
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| [[Silica]] (the chemical compound SiO<sub>2</sub>) has a number of distinct [[crystal]]line forms in addition to the quartz structure. Nearly all of the crystalline forms involve [[tetrahedral]] SiO<sub>4</sub> units linked together by ''shared vertices'' in different arrangements. Si-O bond lengths vary between the different crystal forms. For example, in α-quartz the bond length is 161 pm, whereas in α-tridymite it ranges from 154–171 pm. The Si-O-Si bond angle also varies from 140° in α-tridymite to 144° in α-quartz to 180° in β-tridymite. Any deviations from these standard parameters constitute microstructural differences or variations that represent an approach to an [[amorphous solid|amorphous]], vitreous or [[amorphous solid|glassy solid]].
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| The transition temperature ''T''<sub>g</sub> in silicates is related to the energy required to break and re-form covalent bonds in an amorphous (or random network) lattice of [[covalent bond]]s. The ''T''<sub>g</sub> is clearly influenced by the chemistry of the glass. For example, addition of elements such as [[Boron|B]], [[Sodium|Na]], [[Potassium|K]] or [[Calcium|Ca]] to a [[silica glass]], which have a [[valency (chemistry)|valency]] less than 4, helps in breaking up the network structure, thus reducing the ''T''<sub>g</sub>. Alternatively, [[Phosphorus|P]], which has a valency of 5, helps to reinforce an ordered lattice, and thus increases the ''T''<sub>g</sub>.<ref>{{Cite journal|author=Ojovan M.I.|title= Configurons: thermodynamic parameters and symmetry changes at glass transition|journal=Entropy|volume=10|issue=3|pages=334–364|year=2008|url=http://www.mdpi.org/entropy/papers/e10030334.pdf|doi=10.3390/e10030334|bibcode = 2008Entrp..10..334O }}</ref>
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| ''T''<sub>g</sub> is directly proportional to bond strength, e.g. it depends on quasi-equilibrium thermodynamic parameters of the bonds e.g. on the enthalpy ''H''<sub>d</sub> and entropy ''S''<sub>d</sub> of configurons – broken bonds: ''T''<sub>g</sub> = ''H''<sub>d</sub> / [''S''<sub>d</sub> + Rln[(1-''f''<sub>c</sub>)/ ''f''<sub>c</sub>] where R is the gas constant and ''f''<sub>c</sub> is the percolation threshold. For strong melts such as Si''O''<sub>2</sub> the percolation threshold in the above equation is the universal Scher-Zallen critical density in the 3-D space e.g. ''f''<sub>c</sub> = 0.15, however for fragile materials the percolation thresholds are material-dependent and ''f''<sub>c</sub> << 1.<ref>{{cite journal|author=Ojovan, M.I. |title= Configurons: thermodynamic parameters and symmetry changes at glass transition |journal= Entropy|volume=10|pages= 334–364 |year=2008|url= http://www.mdpi.org/entropy/papers/e10030334.pdf|doi=10.3390/e10030334|issue=3 |bibcode=2008Entrp..10..334O}}</ref> The enthalpy ''H''<sub>d</sub> and the entropy ''S''<sub>d</sub> of configurons – broken bonds can be found from available experimental data on viscosity.<ref>{{cite journal|doi=10.1088/0953-8984/19/41/415107|title=Thermodynamic parameters of bonds in glassy materials from viscosity–temperature relationships|year=2007|last1=Ojovan|first1=Michael I|last2=Travis|first2=Karl P|last3=Hand|first3=Russell J|journal=Journal of Physics: Condensed Matter|volume=19|issue=41|pages=415107|bibcode = 2007JPCM...19O5107O }}</ref>
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| ===Polymers===
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| In [[polymer]]s the glass transition temperature, ''T''<sub>g</sub>, is often expressed as the temperature at which the [[Gibbs free energy]] is such that the [[activation energy]] for the cooperative movement of 50 or so elements of the polymer is exceeded {{Citation needed|date=September 2010}}. This allows molecular chains to slide past each other when a force is applied. From this definition, we can see that the introduction of relatively stiff chemical groups (such as [[benzene]] rings) will interfere with the flowing process and hence increase ''T''<sub>g</sub>.<ref>Cowie, J. M. G. and Arrighi, V., Polymers: Chemistry and Physics of Modern Materials, 3rd Edn. (CRC Press, 2007) ISBN 0748740732</ref> | |
| The stiffness of thermoplastics decreases due to this effect (see figure.) When the glass temperature has been reached, the stiffness stays the same for a while, i.e., at or near ''E''<sub>2</sub>, until the temperature exceeds ''T''<sub>m</sub>, and the material melts. This region is called the rubber plateau.
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| [[File:Ironing.jpg|thumb|right|In ironing, a fabric is heated through the glass-rubber transition.]]
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| In [[ironing]], a fabric is heated through this transition so that the polymer chains become mobile. The weight of the iron then imposes a preferred orientation. ''T''<sub>g</sub> can be significantly decreased by addition of [[plasticizer]]s into the polymer matrix. Smaller molecules of plasticizer embed themselves between the polymer chains, increasing the spacing and free volume, and allowing them to move past one another even at lower temperatures. The "[[new car smell|new-car smell]]" is due to the initial [[outgassing]] of [[Volatility (chemistry)|volatile]] small-molecule plasticizers (most commonly known as [[phthalates]]) used to modify interior plastics (e.g., dashboards) to keep them from cracking in the cold of winter weather. The addition of nonreactive [[side chain|side groups]] to a polymer can also make the chains stand off from one another, reducing ''T''<sub>g</sub>. If a plastic with some desirable properties has a ''T''<sub>g</sub> that is too high, it can sometimes be combined with another in a [[copolymer]] or [[composite material]] with a ''T''<sub>g</sub> below the temperature of intended use. Note that some plastics are used at high temperatures, e.g., in automobile engines, and others at low temperatures.<ref name="PVC"/>
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| In [[Viscoelasticity|viscoelastic]] materials, the presence of liquid-like behavior depends on the properties of and so varies with rate of applied load, i.e., how quickly a force is applied. The [[silicone]] toy '[[Silly Putty]]' behaves quite differently depending on the time rate of applying a force: pull slowly and it flows, acting as a heavily viscous liquid; hit it with a hammer and it shatters, acting as a glass.
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| [[File:rubber plateau.svg|thumb|left|Stiffness versus temperature]]
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| On cooling, [[rubber]] undergoes a ''liquid-glass transition'', which has also been called a ''rubber-glass transition''. For example, the [[Space Shuttle Challenger disaster]] was caused by rubber O-rings that were being used well below their glass transition temperature on an unusually cold Florida morning, and thus could not flex adequately to form proper seals between sections of the two [[Space Shuttle Solid Rocket Booster|solid-fuel rocket boosters]].
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| == Mechanics of vitrification ==
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| {{Main|Vitrification}}
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| Molecular motion in condensed matter can be represented by a [[Fourier series]] whose physical interpretation consists of a [[superposition principle|superposition]] of [[longitudinal wave|longitudinal]] and [[transverse wave|transverse]] [[waves]] of atomic displacement with varying directions and wavelengths. In monatomic systems, these waves are called ''[[density]] [[fluctuation]]s''. (In polyatomic systems, they may also include [[wikt:composition|composition]]al [[fluctuation]]s.)<ref>Slater, J.C., Introduction to Chemical Physics (3rd Ed., Martindell Press, 2007) ISBN 1178626598</ref>
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| Thus, [[thermal motion]] in liquids can be decomposed into elementary [[Longitudinal wave|longitudinal vibrations]] (or acoustic [[phonon]]s) while [[transverse wave|transverse vibrations]] (or shear waves) were originally described only in [[elasticity (physics)|elastic]] solids exhibiting the highly ordered crystalline state of matter. In other words, simple liquids cannot support an applied force in the form of a [[shearing stress]], and will yield mechanically via macroscopic [[plastic deformation]] (or viscous flow). Furthermore, the fact that a [[solid]] deforms locally while retaining its [[Stiffness|rigidity]] – while a [[liquid]] yields to macroscopic [[viscous flow]] in response to the application of an applied [[shearing force]] – is accepted by many as the mechanical distinction between the two.<ref>{{cite journal|doi=10.1017/S0305004100017138|title=On the stability of crystal lattices. I|year=2008|last1=Born|first1=Max|journal=Mathematical Proceedings of the Cambridge Philosophical Society|volume=36|issue=2|pages=160|bibcode = 1940PCPS...36..160B }}</ref><ref>{{cite journal| doi=10.1063/1.1750497| title=Thermodynamics of Crystals and Melting| year=1939| last1=Born| first1=Max| journal=The Journal of Chemical Physics| volume=7| issue=8| pages=591|bibcode = 1939JChPh...7..591B }}</ref>
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| The inadequacies of this conclusion, however, were pointed out by Frenkel in his revision of the [[kinetic theory of solids]] and the [[theory of elasticity]] in [[liquid]]s. This revision follows directly from the continuous characteristic of the structural transition from the liquid state into the solid one when this transition is not accompanied by crystallization—ergo the supercooled [[viscous liquid]]. Thus we see the intimate correlation between transverse acoustic phonons (or shear waves) and the onset of rigidity upon [[vitrification]], as described by Bartenev in his mechanical description of the vitrification process.<ref name="D">{{cite book|author=Frenkel, J.|title=Kinetic Theory of Liquids|publisher=Clarendon Press, Oxford|year=1946}}</ref><ref>
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| Bartenev, G. M., Structure and Mechanical Properties of Inorganic Glasses (Wolters – Noordhoof, 1970) ISBN 9001054501</ref>
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| The velocities of longitudinal acoustic phonons in condensed matter are directly responsible for the [[thermal conductivity]] that levels out temperature differentials between [[Compressibility|compressed]] and [[Thermal expansion|expanded]] volume elements. Kittel proposed that the behavior of glasses is interpreted in terms of an approximately constant "[[mean free path]]" for lattice phonons, and that the value of the mean free path is of the [[order of magnitude]] of the scale of disorder in the molecular structure of a liquid or solid. The thermal phonon mean free paths or relaxation lengths of a number of glass formers have been plotted versus the [[glass transition temperature]], indicating a linear relationship between the two. This has suggested a new criterion for glass formation based on the value of the phonon mean free path.<ref>
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| {{cite journal
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| |author=C. L. Reynolds Jr.
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| |title=Correlation between the low temperature phonon mean free path and glass transition temperature in amorphous solids
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| |journal=J. Non-Cryst. Sol.
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| |volume=30
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| |issue=3 |page=371
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| |year=1979
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| |doi=10.1016/0022-3093(79)90174-1|bibcode = 1979JNCS...30..371R }}
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| </ref>
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|
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| It has often been suggested that [[heat conduction|heat transport]] in [[dielectric]] solids occurs through elastic vibrations of the lattice, and that this transport is limited by elastic [[scattering]] of acoustic phonons by lattice defects (e.g. randomly spaced vacancies).<ref>Rosenburg, H. M., Low Temperature Solid State Physics (Clarendon Press, Oxford, 1963)</ref>
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| These predictions were confirmed by experiments on commercial [[glasses]] and glass [[Ceramic engineering|ceramic]]s, where mean free paths were apparently limited by "internal boundary scattering" to length scales of 10–100 micrometers.<ref>{{cite journal|author=Kittel, C.
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| |title=Ultrasonic Propagation in Liquids|journal=J. Chem. Phys.|volume=14|issue=10|page=614|year=1946|doi=10.1063/1.1724073|bibcode = 1946JChPh..14..614K }}
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| </ref><ref>
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| {{cite journal|author=Kittel, C.|title=Interpretation of the Thermal Conductivity of Glasses|journal=Phys. Rev.|volume=75|issue=6|page=972|year=1949|doi=10.1103/PhysRev.75.972|bibcode = 1949PhRv...75..972K }}
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| </ref>
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| The relationship between these transverse waves and the mechanism of vitrification has been described by several authors who proposed that the onset of correlations between such phonons results in an orientational ordering or "freezing" of local shear stresses in glass-forming liquids, thus yielding the glass transition.<ref>{{cite journal|doi=10.1016/0022-3093(85)90256-X|title=Orientational ordering of local shear stresses in liquids: A phase transition?|year=1985|last1=Chen|first1=Shao-Ping|last2=Egami|first2=T.|last3=Vitek|first3=V.|journal=Journal of Non-Crystalline Solids|volume=75|pages=449|bibcode = 1985JNCS...75..449C }}</ref>
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| === Electronic structure ===
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| The influence of [[thermal]] [[phonon]]s and their interaction with [[electron]]ic structure is a topic that was appropriately introduced in a discussion of the [[Electrical resistance|resistance]] of liquid metals. [http://phycomp.technion.ac.il/~phsorkin/thesis/node4.html Lindemann's theory of melting] is referenced, and it is suggested that the drop in [[Electrical resistivity and conductivity|conductivity]] in going from the [[crystal]]line to the liquid state is due to the increased [[scattering]] of conduction electrons as a result of the increased [[amplitude]] of atomic [[vibration]]. Such theories of localization have been applied to transport in [[metallic glass]]es, where the [[mean free path]] of the electrons is very small (on the order of the interatomic spacing).<ref>
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| {{cite journal
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| |author=N. F. Mott
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| |title=The Resistance of Liquid Metals
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| |journal=[[Proceedings of the Royal Society A]]
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| |volume=146
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| |issue=857 |page=465
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| |year=1934
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| |doi=10.1098/rspa.1934.0166
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| |bibcode = 1934RSPSA.146..465M }}</ref><ref>
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| {{cite journal
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| |author=C. Lindemann
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| |title=
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| |journal=Phys. Zeitschr.
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| |volume=11 |page=609
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| |year=1911
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| |doi=
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| }}</ref>
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| The formation of a non-crystalline form of a gold-silicon alloy by the method of [[splat quenching]] from the melt led to further considerations of the influence of electronic structure on glass forming ability, based on the properties of the [[metallic bond]].<ref>{{cite journal|doi=10.1038/187869b0|title=Non-crystalline Structure in Solidified Gold–Silicon Alloys|year=1960|last1=Klement|first1=W.|last2=Willens|first2=R. H.|last3=Duwez|first3=POL|journal=Nature|volume=187|issue=4740|pages=869|bibcode = 1960Natur.187..869K }}</ref><ref>{{cite journal|doi=10.1063/1.1735777|title=Continuous Series of Metastable Solid Solutions in Silver-Copper Alloys|year=1960|last1=Duwez|first1=Pol|last2=Willens|first2=R. H.|last3=Klement|first3=W.|journal=Journal of Applied Physics|volume=31|issue=6|pages=1136|bibcode = 1960JAP....31.1136D }}</ref><ref>{{cite journal|doi=10.1063/1.1735778|title=Metastable Electron Compound in Ag-Ge Alloys|year=1960|last1=Duwez|first1=Pol|last2=Willens|first2=R. H.|last3=Klement|first3=W.|journal=Journal of Applied Physics|volume=31|issue=6|pages=1137|bibcode = 1960JAP....31.1137D }}</ref><ref>{{cite journal|pmid=17841932|year=1978|last1=Chaudhari|first1=P|last2=Turnbull|first2=D|title=Structure and properties of metallic glasses|volume=199|issue=4324|pages=11–21|doi=10.1126/science.199.4324.11|journal=Science|bibcode = 1978Sci...199...11C }}
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| </ref><ref>{{cite journal
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| |author=J. S. Chen
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| |title=Glassy metals
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| |journal=Reports on Progress in Physics
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| |volume=43
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| |issue=4 |page=353
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| |year=1980
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| |doi=10.1088/0034-4885/43/4/001|bibcode = 1980RPPh...43..353C }}
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| </ref>
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|
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| Other work indicates that the [[Electron mobility|mobility]] of localized [[electron]]s is enhanced by the presence of dynamic phonon modes. One claim against such a model is that if [[chemical bonds]] are important, the [[nearly free electron model]]s should not be applicable. However, if the model includes the buildup of a [[charge distribution]] between all pairs of atoms just like a chemical bond (e.g., silicon, when a band is just filled with electrons) then it should apply to [[solid]]s.<ref>
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| {{cite journal
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| |author=M. Jonson, S. M. Girvin
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| |title=Electron-Phonon Dynamics and Transport Anomalies in Random Metal Alloys
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| |journal=Phys. Rev. Lett.
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| |volume=43
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| |issue=19 |page=1447
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| |year=1979
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| |doi=10.1103/PhysRevLett.43.1447
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| |bibcode=1979PhRvL..43.1447J
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| }}</ref>
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| Thus, if the [[electrical conductivity]] is low, the [[mean free path]] of the electrons is very short. The electrons will only be sensitive to the [[short-range order]] in the glass since they do not get a chance to scatter from atoms spaced at large distances. Since the short-range order is similar in glasses and crystals, the electronic energies should be similar in these two states. For alloys with lower resistivity and longer electronic mean free paths, the electrons could begin to sense that there is [[Order and disorder (physics)|disorder]] in the glass, and this would raise their energies and destabilize the glass with respect to crystallization. Thus, the glass formation tendencies of certain alloys may therefore be due in part to the fact that the electron mean free paths are very short, so that only the short-range order is ever important for the energy of the electrons.
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| It has also been argued that glass formation in metallic systems is related to the "softness" of the interaction potential between unlike atoms. Some authors, emphasizing the strong similarities between the local structure of the glass and the corresponding crystal, suggest that chemical bonding helps to stabilize the amorphous structure.<ref>
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| {{cite journal
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| |author=D. Turnbull
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| |title=Amorphous Solid Formation and Interstitial Solution Behavior in Metallic Alloy System
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| |journal=J. Phys. C
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| |volume=35
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| |issue=C4 |page=C4–1
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| |year=1974
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| |doi=10.1051/jphyscol:1974401
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| }}</ref><ref>
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| {{cite journal
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| |author=H. S. Chen, B. K. Park
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| |title=Role of chemical bonding in metallic glasses
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| |journal=Acta Met.
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| |volume=21
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| |issue=4 |page=395
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| |year=1973
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| |doi=10.1016/0001-6160(73)90196-X
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| }}</ref>
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| Other authors have suggested that the electronic structure yields its influence on glass formation through the directional properties of bonds. Non-crystallinity is thus favored in elements with a large number of [[Polymorphism (materials science)|polymorphic]] forms and a high degree of [[Chemical bond|bond]]ing [[anisotropy]]. Crystallization becomes more unlikely as bonding anisotropy is increased from [[isotropic]] [[metallic]] to [[anisotropic]] [[metallic]] to [[covalent]] bonding, thus suggesting a relationship between the [[chemical family|group number]] in the [[periodic table]] and the glass forming ability in [[elemental]] [[solid]]s.<ref>
| |
| {{cite journal
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| |author=R. Wang, D. Merz
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| |title=Polymorphic bonding and thermal stability of elemental noncrystalline solids
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| |journal=Physica Status Solidi (a)
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| |volume=39
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| |issue=2 |page=697
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| |year=1977
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| |doi=10.1002/pssa.2210390240
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| |bibcode = 1977PSSAR..39..697W }}</ref>
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| ==References==
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| {{Reflist|35em}}
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| == External links ==
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| {{commons category|Glass-liquid transitions}}
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| *[http://eprints.iisc.ernet.in/archive/00000257/01/kjrao.pdf Fragility]
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| *[http://www.iop.org/EJ/abstract/0953-8984/12/46/305 VFT Eqn.]
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| *[http://pslc.ws/macrog/tg.htm Polymers I]
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| *[http://www.lasalle.edu/academ/chem/ms/polymersRus/Resources/GlassTrans.htm Polymers II]
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| *[http://www.public.asu.edu/~caangell/Abstracts/395.pdf Angell: Aqueous media]
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| *[http://www.doitpoms.ac.uk/tlplib/glass-transition/index.php DoITPoMS Teaching and Learning Package- "The Glass Transition in Polymers"]
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| {{Glass science}}
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| {{DEFAULTSORT:Glass Transition}}
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| [[Category:Condensed matter physics]]
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| [[Category:Cryobiology]]
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| [[Category:Glass engineering and science]]
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| [[Category:Glass physics]]
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| [[Category:Phase transitions]]
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| [[Category:Polymer chemistry]]
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| [[Category:Proteins]]
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| [[Category:Rubber properties]]
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| [[Category:Threshold temperatures]]
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