Glass transition - Knowledge

17: 1081: 375: 2598: 2100: 428: 447: 258:. 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 2803:, where mean free paths were apparently limited by "internal boundary scattering" to length scales of 10–100 micrometres (0.00039–0.00394 in). 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 2538: 2152:, which is still amorphous, but has a long-range amorphous order which decreases its overall entropy to that of the crystal. The ideal glass would be a true phase of matter. The ideal glass is hypothesized, but cannot be observed naturally, as it would take too long to form. Something approaching an ideal glass has been observed as "ultrastable glass" formed by 166:

the two phases, i.e., the melt and the glass, are equal, while the heat capacity and the expansivity are discontinuous. However, the glass transition is generally not regarded as a thermodynamic transition in view of the inherent difficulty in reaching equilibrium in a polymer glass or in a polymer melt at temperatures close to the glass-transition temperature.

1822: 1235:. This was explained by the two-level system hypothesis, which states that a glass is populated by two-level systems, which look like a double potential well separated by a wall. The wall is high enough such that resonance tunneling does not occur, but thermal tunneling does occur. Namely, if the two wells have energy difference 270:

decreasing. As a result of the fluctuating input of thermal energy into the liquid matrix, the harmonics of the oscillations are constantly disturbed and temporary cavities ("free volume") are created between the elements, the number and size of which depend on the temperature. The glass transition temperature

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Phenomena occurring at the glass transition of polymers are still subject to ongoing scientific investigation and debate. The glass transition presents features of a second-order transition since thermal studies often indicate that the molar Gibbs energies, molar enthalpies, and the molar volumes of

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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. Addition of plasticizer can effectively take control over polymer chain dynamics and

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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

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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

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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

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Glass is a nonequilibrium, non-crystalline condensed state of matter that exhibits a glass transition. The structure of glasses is similar to that of their parent supercooled liquids (SCL), and they spontaneously relax toward the SCL state. Their ultimate fate is to solidify, i.e., crystallize.

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In a more recent model of glass transition, the glass transition temperature corresponds to the temperature at which the largest openings between the vibrating elements in the liquid matrix become smaller than the smallest cross-sections of the elements or parts of them when the temperature is

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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

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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

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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, this would be paradoxical, as the liquid phase should have the same vibrational entropy, but much higher positional entropy, as the crystal phase. This is the

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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

214:, lack a well defined crystalline state and easily form glasses, even upon very slow cooling or compression. The tendency for a material to form a glass while quenched is called glass forming ability. This ability depends on the composition of the material and can be predicted by the 942:

has a glass transition range of −130 to −80 °C (−202 to −112 °F) The above are only mean values, as the glass transition temperature depends on the cooling rate and molecular weight distribution and could be influenced by additives. For a semi-crystalline material, such as

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for the cooperative movement of 50 or so elements of the polymer is exceeded . 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

3750:"Microscopic-Phenomenological Model of Glass Transition I. Foundations of the model (Revised and enhanced version) (Former title: Microscopic Model of Glass Transformation and Molecular Translations in Liquids I. Foundations of the Model-October 2015)" 1297:

is randomly distributed but fixed ("quenched disorder"), then as temperature drops, more and more of these two-level levels are frozen out (meaning that it takes such a long time for a tunneling to occur, that they cannot be experimentally observed).

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10 in). 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

251:, 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. 336:

Glasses are thermodynamically non-equilibrium kinetically stabilized amorphous solids, in which the molecular disorder and the thermodynamic properties corresponding to the state of the respective under-cooled melt at a temperature

135:; rather it is a phenomenon extending over a range of temperature and defined by one of several conventions. Such conventions include a constant cooling rate (20 kelvins per minute (36 °F/min)) and a viscosity threshold of 10 1817:{\displaystyle {\bar {E}}\sim \int _{0}^{O(1/\beta )}{\frac {\beta \Delta E}{e^{\beta \Delta E}-1}}\beta ^{-1}\;n(\Delta E)d\Delta E=\beta ^{-2}\int _{0}^{O(1)}{\frac {a}{e^{a}-1}}n(a/\beta )da\propto \beta ^{-2}n(0)} 1417: 2924:

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

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Perhaps 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.

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defined in this way is a fixed material constant of the disordered (non-crystalline) state that is dependent only on the pressure. As a result of the increasing inertia of the molecular matrix when approaching

2256: 147:, with the location of these effects again being dependent on the history of the material. The question of whether some phase transition underlies the glass transition is a matter of ongoing research. 76:

of a material characterizes the range of temperatures over which this glass transition occurs (as an experimental definition, typically marked as 100 s of relaxation time). It is always lower than the

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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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The glass transition of a liquid to a solid-like state may occur with either cooling or compression. The transition comprises a smooth increase in the viscosity of a material by as much as 17

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materials) from a hard and relatively brittle "glassy" state into a viscous or rubbery state as the temperature is increased. An amorphous solid that exhibits a glass transition is called a

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in diameter that move in a two-state fashion on a time scale of minutes. This is much faster than dynamics in the bulk, but in agreement with models that compare bulk and surface dynamics.

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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

2520:. 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 1866: 1345: 1274:, then a particle in one well can tunnel to the other well by thermal interaction with the environment. Now, imagine that there are many two-level systems in the glass, and their 230:(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. 1272: 3315: 1559: 4298: 550:(a.k.a. thermal expansion): refer to the figure on the top right. Here, heating rates of 3–5 K/min (5.4–9.0 °F/min) are common. The linear sections below and above 1229: 285:, the setting of the thermal equilibrium is successively delayed, so that the usual measuring methods for determining the glass transition temperature in principle deliver 169:

In the case of polymers, conformational changes of segments, typically consisting of 10–20 main-chain atoms, become infinitely slow below the glass transition temperature.

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has a glass transition temperature of 47 °C (117 °F). Nylon-6,6 in the dry state has a glass transition temperature of about 70 °C (158 °F). Whereas

87:, of the crystalline state of the material, if one exists, because the glass is a higher energy state (or enthalpy at constant pressure) than the corresponding crystal. 4522: 1498: 1443: 1295: 266:. However, there is a longstanding debate whether there is an underlying second-order phase transition in the hypothetical limit of infinitely long relaxation times. 333:

Glass is a "frozen liquid” (i.e., liquids where ergodicity has been broken), which spontaneously relax towards the supercooled liquid state over a long enough time.

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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

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Swallen, Stephen F.; Kearns, Kenneth L.; Mapes, Marie K.; Kim, Yong Seol; McMahon, Robert J.; Ediger, M. D.; Wu, Tian; Yu, Lian; Satija, Sushil (2007-01-19).

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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

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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.

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Kauzmann himself resolved the entropy paradox by postulating that all supercooled liquids must crystallize before the Kauzmann temperature is reached.

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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.

4023: 3338: 2315:, is the main exception). Si-O bond lengths vary between the different crystal forms. For example, in α-quartz the bond length is 161 picometres (6.3 2091:, that is, a straight line with slope showing the typical Debye-like heat capacity, and a vertical intercept showing the anomalous linear component. 161:(in polymer science): process in which a polymer melt changes on cooling to a polymer glass or a polymer glass changes on heating to a polymer melt. 151: 4192: 2549:, a fabric is heated through this transition so that the polymer chains become mobile. The weight of the iron then imposes a preferred orientation. 5129:

Reynolds, C. L. Jr. (1979). "Correlation between the low temperature phonon mean free path and glass transition temperature in amorphous solids".

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solids exhibiting the highly ordered crystalline state of matter. In other words, simple liquids cannot support an applied force in the form of a

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dominate the amounts of the associated free volume so that the increased mobility of polymer ends is not apparent. The addition of nonreactive

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from the melt led to further considerations of the influence of electronic structure on glass forming ability, based on the properties of the

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is directly proportional to bond strength, e.g. it depends on quasi-equilibrium thermodynamic parameters of the bonds e.g. on the enthalpy

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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

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of acoustic phonons by lattice defects (e.g. randomly spaced vacancies). These predictions were confirmed by experiments on commercial

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values that are too high. In principle, the slower the temperature change rate is set during the measurement, the closer the measured

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is located at the intersection between the cooling curve (volume versus temperature) for the glassy state and the supercooled liquid.

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The definition of the glass and the glass transition are not settled, and many definitions have been proposed over the past century.

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prevents free flow of their molecules, thus endowing rubber with a set shape at room temperature (as opposed to a viscous liquid).

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crossover from the liquid state into the solid one when the transition is not accompanied by crystallization—ergo the supercooled

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in silicates is related to the energy required to break and re-form covalent bonds in an amorphous (or random network) lattice of

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Meille Stefano, V.; Allegra, G.; Geil Phillip, H.; He, J.; Hess, M.; Jin, J.-I.; Kratochvíl, P.; Mormann, W.; Stepto, R. (2011).

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Chen, Shao-Ping; Egami, T.; Vitek, V. (1985). "Orientational ordering of local shear stresses in liquids: A phase transition?".

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within a temperature range of 500 K without any pronounced change in material structure. This transition is in contrast to the

4738: 4680: 16: 4136: 4086: 3986: 3417: 139:, among others. Upon cooling or heating through this glass-transition range, the material also exhibits a smooth step in the 131:

Despite the change in the physical properties of a material through its glass transition, the transition is not considered a

4514: 3208: 3385: 2752:. Thus we see the intimate correlation between transverse acoustic phonons (or shear waves) and the onset of rigidity upon 2261:

Perhaps the heat capacity of the supercooled liquid near the Kauzmann temperature smoothly decreases to a smaller value.

4056:, "TYRE COMPRISING A CYCLOOLEFIN POLYMER, TREAD BAND AND ELASTOMERIC COMPOSITION USED THEREIN", issued 2003-03-07 5335: 3674: 3379: 3202: 330:: Glass is a topologically disordered network, with short range order equivalent to that in the corresponding crystal. 259: 1871: 20:

Two-dimensional, schematic, representation of the lattices of quartz (a), silica (b), and of silica based glasses (c).

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11357-2: Plastics – Differential scanning calorimetry – Part 2: Determination of glass transition temperature (1999).

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the percolation threshold in the above equation is the universal Scher–Zallen critical density in the 3-D space e.g.

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volume elements. Kittel proposed that the behavior of glasses is interpreted in terms of an approximately constant "

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Ojovan, Michael I; Lee, William (Bill) E (2010). "Connectivity and glass transition in disordered oxide systems".

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Phillips, J.C. (1979). "Topology of covalent non-crystalline solids I: Short-range order in chalcogenide alloys".

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Refer to the figure on the bottom right plotting the heat capacity as a function of temperature. In this context,

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Cowie, J. M. G. and Arrighi, V., Polymers: Chemistry and Physics of Modern Materials, 3rd Edn. (CRC Press, 2007)

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show a relatively sudden change at the glass transition temperature. Any such step or kink can be used to define

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provides the thermodynamic driving force necessary for the eventual change. At somewhat higher temperatures than

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Klement, W.; Willens, R. H.; Duwez, POL (1960). "Non-crystalline Structure in Solidified Gold–Silicon Alloys".

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of configurons – broken bonds can be found from available experimental data on viscosity. On the surface of SiO

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In experimental measurements, the specific heat capacity of glass is measured at different temperatures, and a

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Turnbull, D. (1974). "Amorphous Solid Formation and Interstitial Solution Behavior in Metallic Alloy System".

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Jonson, M.; Girvin, S. M. (1979). "Electron-Phonon Dynamics and Transport Anomalies in Random Metal Alloys".

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of atomic displacement with varying directions and wavelengths. In monatomic systems, these waves are called

536:(DSC, see figure). Typically, the sample is first cooled with 10 K/min and then heated with that same speed. 4007: 206: 6073: 5747:

Wang, R.; Merz, D. (1977). "Polymorphic bonding and thermal stability of elemental noncrystalline solids".

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Kauzmann, Walter (1948). "The Nature of the Glassy State and the Behavior of Liquids at Low Temperatures".

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In a partially crystalline polymer the glass transition occurs only in the amorphous parts of the material.

5801: 3056: 1829: 1304: 324:: Glass is a rigid material obtained from freezing-in a supercooled liquid in a narrow temperature range. 98:

are used well below their glass transition temperatures, i.e., when they are in their glassy state. Their

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before the entropy of the liquid decreases. In this scenario, the transition temperature is known as the

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discovered that when glass is at a very low temperature ~1K, its specific heat has a linear component:

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Jones, A (2014). "Supplementary Materials for Artificial Muscles from Fishing Line and Sewing Thread".

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solids occurs through elastic vibrations of the lattice, and that this transport is limited by elastic

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As a liquid is supercooled, the difference in entropy between the liquid and solid phase decreases. By

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Bartenev, G. M., Structure and Mechanical Properties of Inorganic Glasses (Wolters – Noordhoof, 1970)

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The velocities of longitudinal acoustic phonons in condensed matter are directly responsible for the

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of liquid metals. Lindemann's theory of melting is referenced, and it is suggested that the drop in

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The inadequacies of this conclusion, however, were pointed out by Frenkel in his revision of the

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is enhanced by the presence of dynamic phonon modes. One claim against such a model is that if

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is clearly influenced by the chemistry of the glass. For example, addition of elements such as

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at a value of 10 poise (or 10 Pa·s). As evidenced experimentally, this value is close to the

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Capponi, S.; Alvarez, F.; Racko, D. (2020), "Free Volume in a PVME Polymer–Water Solution",

4885:"A universal origin for secondary relaxations in supercooled liquids and structural glasses" 4126: 2452:= 0.15, however for fragile materials the percolation thresholds are material-dependent and 6404: 6333: 6207: 6119: 5955: 5945: 5756: 5649: 5606: 5555: 5506: 5450: 5400: 5344: 5266: 5231: 5186: 5138: 5070: 5027: 4959: 4778: 4720: 4662: 4604: 4557: 4449: 4410: 4345: 4242: 3941: 3855: 3816: 3722: 3623: 3614:

Stillinger, F. H. (1995). "A Topographic View of Supercooled Liquids and Glass Formation".

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Ediger, M. D.; Angell, C. A.; Nagel, Sidney R. (1996). "Supercooled Liquids and Glasses".

2389:, which has a valency of 5, helps to reinforce an ordered lattice, and thus increases the 8: 6353: 6280: 6275: 6197: 6172: 6139: 6000: 5435: 4790: 2889: 2800: 2706: 2375: 1080: 178:

The commonly used term “glass-rubber transition” for glass transition is not recommended.

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Debenedetti, P. G.; Stillinger (2001). "Supercooled liquids and the glass transition".

3019: 2978: 2776: 2756:, as described by Bartenev in his mechanical description of the vitrification process. 2584: 2292:

forms in addition to the quartz structure. Nearly all of the crystalline forms involve

788: 659: 522:. To make this definition reproducible, the cooling or heating rate must be specified. 190: 5097: 4592: 3968: 6338: 6308: 6265: 6202: 6187: 6099: 5990: 5796: 5733: 5626: 5618: 5571: 5278: 5150: 5113: 5047: 5002: 4989: 4934: 4916: 4865: 4794: 4763: 4628: 4620: 4573: 4465: 4379: 4378:(Report). Cornell Univ., Ithaca, N.Y. (USA). Lab. of Atomic and Solid State Physics. 4258: 4213: 4182: 4132: 4082: 4053: 3982: 3953: 3910: 3871: 3828: 3734: 3695: 3670: 3639: 3588: 3522: 3484: 3466: 3413: 3375: 3262: 3198: 3109: 3023: 2908: 2873: 2768: 2686: 2655: 2505: 2501: 2177:

effect, i.e. merely the result of fast cooling of a melt, but there is an underlying

2174: 2153: 1023: 804: 707: 504: 497: 241: 227: 140: 5706: 4806: 4270: 4033: 3651: 3348: 3311: 3282:"Definitions of terms relating to crystalline polymers (IUPAC Recommendations 2011)" 6129: 6114: 5764: 5729: 5694: 5657: 5614: 5583: 5563: 5514: 5458: 5420: 5408: 5352: 5274: 5239: 5202: 5194: 5146: 5078: 5035: 4975: 4967: 4906: 4896: 4855: 4847: 4786: 4728: 4705: 4670: 4647: 4612: 4565: 4492: 4457: 4418: 4398: 4353: 4250: 4037: 4028: 3974: 3949: 3902: 3890: 3863: 3824: 3757: 3730: 3631: 3580: 3545: 3518: 3462: 3352: 3343: 3299: 3278: 3250: 3159: 3138:

Angell, C. A.; Ngai, K. L.; McKenna, G. B.; McMillan, P. F.; Martin, S. W. (2000).

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Chaudhari, P; Turnbull, D (1978). "Structure and properties of metallic glasses".

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Chen, H. S.; Park, B. K. (1973). "Role of chemical bonding in metallic glasses".

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Slater, J.C., Introduction to Chemical Physics (3rd Ed., Martindell Press, 2007)

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The formation of a non-crystalline form of a gold-silicon alloy by the method of

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Nguyen, Huy; Lia, Can; Wallum, Alison; Lyding, Joseph; Gruebele, Martin (2019).

4706:"Configurons: thermodynamic parameters and symmetry changes at glass transition" 4648:"Configurons: thermodynamic parameters and symmetry changes at glass transition" 3761: 2936:. Crystallization becomes more unlikely as bonding anisotropy is increased from 6285: 6255: 6250: 5698: 4336:

Bucaro, J. A. (1974). "High-temperature Brillouin scattering in fused quartz".

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criterion for glass formation based on the value of the phonon mean free path.

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Consider a single two-level system that is not frozen-out, whose energy gap is

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for a given substance agree within a few kelvins. One definition refers to the

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structure is a topic that was appropriately introduced in a discussion of the

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Lindemann, C. (1911). "On the calculation of molecular natural frequencies".

4624: 4577: 4469: 4032:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " 3914: 3875: 3347:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " 3303: 3027: 2930: 2866: 2753: 2641: 2344: 2178: 2112: 2108: 886: 675: 643: 508: 321: 144: 77: 60: 44: 5995: 5768: 5222:

Kittel, C. (1949). "Interpretation of the Thermal Conductivity of Glasses".

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The Vitreous State: Thermodynamics, Structure, Rheology, and Crystallization

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of the electrons is very short. The electrons will only be sensitive to the

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THERMOPLASTIC MATERIALS Properties, Manufacturing Methods, and Applications

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Angell, C. A. (1995). "Formation of Glasses from Liquids and Biopolymers".

3113: 2804: 2745: 2744:. This revision follows directly from the continuous characteristic of the 2722: 2565:

to a polymer can also make the chains stand off from one another, reducing

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less than 4, helps in breaking up the network structure, thus reducing the

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DoITPoMS Teaching and Learning Package- "The Glass Transition in Polymers"

4438:"Anomalous low-temperature thermal properties of glasses and spin glasses" 4316:

EPCOS 2007: Glass Transition and Crystallization in Phase Change Materials

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should not be applicable. However, if the model includes the buildup of a

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of the electrons is very small (on the order of the interatomic spacing).

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graph, showing linear dependence component in the low-temperature regime.

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Measurement of Moisture Effects on the Mechanical Properties of 66 Nylon

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Thus, the liquid-glass transition is not a transition between states of

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films, scanning tunneling microscopy has resolved clusters of ca. 5 SiO

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10 in), whereas in α-tridymite it ranges from 154–171 pm (6.1

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Now, assume that the two-level systems are all quenched, so that each

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Different operational definitions of the glass transition temperature

5412: 4004: 3843: 3105: 2937: 2847: 2843: 2729:– is accepted by many as the mechanical distinction between the two. 2714: 2580: 2363: 739: 486: 457:(the temperature at the point A) by differential scanning calorimetry 106: 3483:, M. Goldstein and R. Simha (Eds.), Ann. N.Y. Acad. Sci., Vol. 279. 2534:, and the material melts. This region is called the rubber plateau. 1826:

The effect is that the average energy in these two-level systems is

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is the temperature at the intersection of the red regression lines.

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as a percolation phase transition in a system of network defects".

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In ironing, a fabric is heated through the glass-rubber transition.

211: 194: 124:, that is, in the rubbery state, where they are soft and flexible; 2850:. Such theories of localization have been applied to transport in 2513:

rings) will interfere with the flowing process and hence increase

2251:{\displaystyle T_{g}\to T_{0c}{\text{ as }}{\frac {dT}{dt}}\to 0.} 2148:

Perhaps at the Kauzmann temperature, glass reaches an ideal glass

2099: 6083: 4399:"Thermal Conductivity and Specific Heat of Noncrystalline Solids" 2835: 2796: 2667: 2597: 2579:

that is too high, it can sometimes be combined with another in a

2546: 2510: 2490: 2367: 2289: 427: 3844:"Zum Prinzip von der Unerreichbarkeit des absoluten Nullpunktes" 1564:

Then, the total energy contributed by those two-level systems is

264:

internal degrees of freedom successively fall out of equilibrium

136: 6159: 5965: 5020:

Mathematical Proceedings of the Cambridge Philosophical Society

4436:

Anderson, P. w.; Halperin, B. I.; Varma, c. M. (January 1972).

4181:(4, Revised ed.). Royal Society of Chemistry. p. 50. 3973:. Berlin, Heidelberg: Springer Berlin Heidelberg. p. 124. 3060: 2819: 2741: 2718: 2690: 2621: 2359: 2281: 950: 446: 4223:. Polymerprocessing.com (2001-04-15). Retrieved on 2012-06-29. 3805:"The glassy state of matter: Its definition and ultimate fate" 3409:

Chalcogenide Glasses: Preparation, Properties and Applications

2807:

in glass-forming liquids, thus yielding the glass transition.

2142:

There are many possible resolutions to the Kauzmann paradox.

6078: 6045: 5879: 5864: 5018:

Born, Max (2008). "On the stability of crystal lattices. I".

3501:

Angell, C. A. (1988). "Perspective on the glass transition".

2966: 2947: 2940: 2893: 2710: 2646:

Molecular motion in condensed matter can be represented by a

2355: 2181:

basis for glass formation. The glass transition temperature:

1009: 935: 512: 48: 5061:

Born, Max (1939). "Thermodynamics of Crystals and Melting".

105:

values are both at around 100 °C (212 °F). Rubber

4762:

Ojovan, Michael I; Travis, Karl P; Hand, Russell J (2007).

2816: 2662: 1445:

varies little with temperature. In that case, we can write

1347:. It is in a Boltzmann distribution, so its average energy 1084:

Specific heat of several noncrystalline solids, plotted as

611: 4286:. TA Instruments Thermal Analysis Application Brief TA-133 2537: 468:

is the temperature corresponding to point A on the curve.

3140:"Relaxation in glassforming liquids and amorphous solids" 2438:

is the percolation threshold. For strong melts such as Si

310:

can be used to measure the glass transition temperature.

5177:

Kittel, C. (1946). "Ultrasonic Propagation in Liquids".

4374:

Pohl, R. O.; Love, W. F.; Stephens, R. B. (1973-08-01).

511:, shear modulus, and many other properties of inorganic 5639: 3667:

Thermodynamic and Kinetic Aspects of the Vitreous State

3481:

The Glass Transition and the Nature of the Glassy State

3235:

Journal of Experimental and Theoretical Physics Letters

3229:

Ojovan, M. I. (2004). "Glass formation in amorphous SiO

2103:

Entropy difference between crystal and undercooled melt

574:

values characteristic of certain classes of materials.

5719: 3930:"Non-crystalline solids: glasses and amorphous solids" 5303:(MSc). Israel Institute of Technology. pp. 5–8. 4833: 4590: 4546:"Nature of the Glass Transition and the Glassy State" 4435: 3367: 3083: 2842:

of conduction electrons as a result of the increased

2500:, is often expressed as the temperature at which the 2190: 2173:. In this view, the glass transition is not merely a 2033: 1974: 1927: 1874: 1832: 1570: 1538: 1506: 1483: 1451: 1428: 1353: 1307: 1280: 1241: 1204: 1145: 1090: 4544:

Gibbs, Julian H.; DiMarzio, Edmund A. (1958-03-01).

4076: 3803:

Zanotto, Edgar D.; Mauro, John C. (September 2017).

3274: 3272: 2954:

bonding, thus suggesting a relationship between the

2572:. If a plastic with some desirable properties has a 5489: 5433: 5390: 5128: 4949: 4836:"Multi-scale dynamics at the glassy silica surface" 4515:"Ideal Glass Would Explain Why Glass Exists at All" 4305:. Polyesterconverters.com. Retrieved on 2012-06-29. 3361: 2697:(or shear waves) were originally described only in 4174: 3405: 3280: 2763:that levels out temperature differentials between 2250: 2083: 2019: 1960: 1905: 1860: 1816: 1553: 1524: 1492: 1469: 1437: 1411: 1339: 1289: 1266: 1223: 1190: 1123: 5545: 3535: 3269: 3059:. Polymer Science Learning Center. Archived from 3004:"SUMMARY OF WORK ON ATOMIC ARRANGEMENT IN GLASS*" 6396: 5746: 5490:Duwez, Pol; Willens, R. H.; Klement, W. (1960). 5434:Duwez, Pol; Willens, R. H.; Klement, W. (1960). 4882: 4761: 4373: 4000: 3998: 2709:(or viscous flow). Furthermore, the fact that a 2674:. (In polyatomic systems, they may also include 1906:{\displaystyle \partial _{T}{\bar {E}}\propto T} 4014:. Glassproperties.com. Retrieved on 2012-06-29. 3966: 2165:calorimetric ideal glass transition temperature 5492:"Metastable Electron Compound in Ag-Ge Alloys" 5256: 3967:Gutzow, Ivan S.; Schmelzer, Jürn W.P. (2013). 2912:electrons could begin to sense that there is 2705:, and will yield mechanically via macroscopic 2556:can be significantly decreased by addition of 2431: / where R is the gas constant and 6304:Conservation and restoration of glass objects 5849: 5371: 4543: 4124: 3995: 3690:Gibbs, J. H. (1960). MacKenzie, J. D. (ed.). 3079: 3077: 2725:in response to the application of an applied 2685:in liquids can be decomposed into elementary 2635: 175:The definition is different from that in ref. 5674: 5301:Point Defects, Lattice Structure and Melting 4703: 3802: 3689: 3438: 3190: 3039: 3037: 2921:helps to stabilize the amorphous structure. 2838:to the liquid state is due to the increased 2650:whose physical interpretation consists of a 951:Silicates and other covalent network glasses 356: 24:Reversible transition in amorphous materials 5829:Glass Transition Temperature short overview 5596: 5328: 5095: 4645: 4376:Lattice vibrations in noncrystalline solids 4296:PCL | Applications and End Uses | Polythene 3888: 3776:"What is Dynamic Mechanical Testing (DMA)?" 2917:important for the energy of the electrons. 2084:{\displaystyle c/T\approx c_{1}+c_{3}T^{2}} 5856: 5842: 5221: 5176: 4396: 3613: 3503:Journal of Physics and Chemistry of Solids 3074: 2020:{\displaystyle c\approx c_{1}T+c_{3}T^{3}} 1670: 1191:{\displaystyle c\approx c_{1}T+c_{3}T^{3}} 43:materials (or in amorphous regions within 5688: 5356: 5206: 4979: 4910: 4900: 4859: 4732: 4674: 4512: 4397:Zeller, R. C.; Pohl, R. O. (1971-09-15). 3712: 3406:Adam, J-L; Zhang, X. (14 February 2014). 3034: 1477:as the density of states with energy gap 415:Learn how and when to remove this message 5863: 4482: 3895:Journal of the American Chemical Society 3444: 3133: 3131: 2596: 2536: 2268: 2098: 1079: 445: 426: 15: 4120: 4118: 4072: 4070: 4068: 3664: 3368:Hansen, J.-P.; McDonald, I. R. (2007). 3008:Journal of the American Ceramic Society 2810: 2137: 1075: 525:The most frequently used definition of 6397: 5291: 4335: 4116: 4114: 4112: 4110: 4108: 4106: 4104: 4102: 4100: 4098: 3562: 3500: 3228: 3001: 532:uses the energy release on heating in 51:. The reverse transition, achieved by 5837: 5597:Chen, J. S. (1980). "Glassy metals". 4508: 4506: 4369: 4367: 4232: 3927: 3841: 3798: 3796: 3747: 3128: 2094: 313: 5060: 5017: 4771:Journal of Physics: Condensed Matter 4513:Wolchover, Natalie (11 March 2020). 4065: 3692:Modern Aspects of the Vitreous State 3186: 3184: 2713:deforms locally while retaining its 2115:of the supercooled liquid below its 1916: 1861:{\displaystyle {\bar {E}}\sim T^{2}} 1340:{\displaystyle \Delta E=O(1/\beta )} 397:adding citations to reliable sources 368: 345:differs from the actual temperature 5310:from the original on 19 August 2019 5165:Low Temperature Solid State Physics 4883:Wolynes, PG; Stevenson, JD (2009). 4156: 4095: 3928:Gupta, Prabhat K. (February 1996). 3889:Zachariasen, W. H. (October 1932). 2134:, still not definitively resolved. 1267:{\displaystyle \Delta E\sim k_{B}T} 201:transition, which is a first-order 13: 5336:Proceedings of the Royal Society A 4503: 4364: 4214:nylon-6 information and properties 4195:from the original on 10 April 2022 4029:Compendium of Chemical Terminology 3793: 3473: 3344:Compendium of Chemical Terminology 3020:10.1111/j.1151-2916.1941.tb14858.x 2493:the glass transition temperature, 1876: 1689: 1677: 1640: 1624: 1539: 1513: 1484: 1458: 1429: 1379: 1363: 1308: 1281: 1242: 184: 14: 6446: 5778: 5331:"The Resistance of Liquid Metals" 5259:Journal of Non-Crystalline Solids 5089: 4525:from the original on 7 April 2020 3934:Journal of Non-Crystalline Solids 3891:"The Atomic Arrangement in Glass" 3809:Journal of Non-Crystalline Solids 3715:Journal of Non-Crystalline Solids 3538:The Journal of Physical Chemistry 3447:Journal of Non-Crystalline Solids 3426:from the original on 17 July 2017 3181: 2962:and the glass forming ability in 2783:It has often been suggested that 1554:{\displaystyle \Delta E\approx 0} 534:differential scanning calorimetry 3829:10.1016/j.jnoncrysol.2017.05.019 3735:10.1016/j.jnoncrysol.2010.05.012 3412:. Elsevier Science. p. 94. 2527:, until the temperature exceeds 1968:graph is plotted. Assuming that 373: 262:principle. On cooling a liquid, 59:into the glass state, is called 6374:Radioactive waste vitrification 6329:Glass fiber reinforced concrete 5740: 5713: 5668: 5633: 5590: 5539: 5528:from the original on 2020-04-18 5483: 5472:from the original on 2017-12-02 5427: 5384: 5365: 5322: 5285: 5250: 5215: 5170: 5157: 5122: 5106: 5063:The Journal of Chemical Physics 5054: 5011: 4995: 4943: 4927: 4876: 4827: 4816:from the original on 2018-07-25 4755: 4744:from the original on 2009-07-11 4697: 4686:from the original on 2009-07-11 4639: 4584: 4550:The Journal of Chemical Physics 4537: 4476: 4429: 4390: 4329: 4308: 4289: 4277: 4226: 4207: 4168: 4145:from the original on 2022-04-03 4081:. CRC Press. pp. 491–497. 4046: 4017: 3960: 3921: 3882: 3835: 3782:from the original on 2020-11-17 3768: 3741: 3706: 3683: 3658: 3607: 3556: 3529: 3494: 3399: 3388:from the original on 2013-09-21 3321:from the original on 2018-06-25 3211:from the original on 2020-08-02 3170:from the original on 2020-03-07 2628:, which has also been called a 2417:of configurons – broken bonds: 2273: 854:Acrylonitrile butadiene styrene 384:needs additional citations for 306:approaches. Techniques such as 5599:Reports on Progress in Physics 4791:10.1088/0953-8984/19/41/415107 3479:Moynihan, C. et al. (1976) in 3374:. Elsevier. pp. 250–254. 3332: 3222: 3197:. Cambridge University Press. 3194:Glasses and the Vitreous State 3049: 2995: 2872:Other work indicates that the 2242: 2201: 1955: 1928: 1891: 1839: 1811: 1805: 1777: 1763: 1730: 1724: 1683: 1674: 1613: 1599: 1577: 1519: 1510: 1464: 1455: 1334: 1320: 1224:{\displaystyle c\propto T^{3}} 1118: 1091: 503:In contrast to viscosity, the 260:time–temperature superposition 1: 6410:Glass engineering and science 6241:Chemically strengthened glass 4077:Ibeh, Christopher C. (2011). 3636:10.1126/science.267.5206.1935 3585:10.1126/science.267.5206.1924 3002:Warren, B. E. (August 1941). 2989: 2484: 2459: ≪ 1. The enthalpy 2336:. The transition temperature 141:thermal-expansion coefficient 6074:Glass-ceramic-to-metal seals 5734:10.1016/0001-6160(73)90196-X 5279:10.1016/0022-3093(85)90256-X 5151:10.1016/0022-3093(79)90174-1 4972:10.1021/acs.macromol.0c00472 4034:glass-transition temperature 3954:10.1016/0022-3093(95)00502-1 3523:10.1016/0022-3697(88)90002-9 3467:10.1016/0022-3093(79)90033-4 2601:Stiffness versus temperature 2117:glass transition temperature 1532:is positive and smooth near 68:glass-transition temperature 7: 5662:10.1103/PhysRevLett.43.1447 5568:10.1126/science.199.4324.11 5292:Sorkin, Viacheslav (2005). 4175:Nicholson, John W. (2011). 3842:Simon, Franz (1927-04-01). 3762:10.13140/RG.2.2.19831.73121 3748:Sturm, Karl Günter (2017). 2972: 2929:forms and a high degree of 2886:nearly free electron models 2822:and their interaction with 2304:in different arrangements ( 2288:) has a number of distinct 1961:{\displaystyle (T^{2},c/T)} 1525:{\displaystyle n(\Delta E)} 1470:{\displaystyle n(\Delta E)} 1124:{\displaystyle (T^{2},c/T)} 724:Polychlorotrifluoroethylene 577: 308:dynamic mechanical analysis 10: 6451: 5619:10.1088/0034-4885/43/4/001 5499:Journal of Applied Physics 5443:Journal of Applied Physics 5167:. Clarendon Press, Oxford. 5102:. Clarendon Press, Oxford. 4338:Journal of Applied Physics 4326:. Retrieved on 2012-06-29. 3291:Pure and Applied Chemistry 2639: 2636:Mechanics of vitrification 2284:(the chemical compound SiO 773:Polyethylene terephthalate 539:Yet another definition of 6294: 6226: 6158: 6105:Chemical vapor deposition 6092: 6054: 6026:Ultra low expansion glass 5916:Borophosphosilicate glass 5898: 5872: 5099:Kinetic Theory of Liquids 5040:10.1017/S0305004100017138 4462:10.1080/14786437208229210 4178:The Chemistry of Polymers 4005:Tg measurement of glasses 3979:10.1007/978-3-642-34633-0 2300:units linked together by 837:Poly(methyl methacrylate) 256:thermodynamic equilibrium 96:poly(methyl methacrylate) 6344:Glass-reinforced plastic 6006:Sodium hexametaphosphate 5699:10.1051/jphyscol:1974401 5163:Rosenburg, H. M. (1963) 3371:Theory of Simple Liquids 3304:10.1351/PAC-REC-10-11-13 2734:kinetic theory of solids 2308:, composed of linked SiO 2159:Perhaps there must be a 2027:, the graph should show 1493:{\displaystyle \Delta E} 1438:{\displaystyle \Delta E} 1290:{\displaystyle \Delta E} 210:materials, such as many 207:Ehrenfest classification 6236:Anti-reflective coating 6110:Glass batch calculation 5991:Photochromic lens glass 5769:10.1002/pssa.2210390240 5749:Physica Status Solidi A 4617:10.1126/science.1135795 4423:10.1103/PhysRevB.4.2029 4255:10.1126/science.1246906 4042:10.1351/goldbook.G02641 3357:10.1351/goldbook.G02640 2901:electrical conductivity 2687:longitudinal vibrations 2630:rubber-glass transition 2626:liquid-glass transition 870:Polytetrafluoroethylene 628:Polyvinylidene fluoride 357:Transition temperature 29:glass–liquid transition 6435:Threshold temperatures 5358:10.1098/rspa.1934.0166 5244:10.1103/PhysRev.75.972 4442:Philosophical Magazine 4125:Wilkes, C. E. (2005). 3848:Zeitschrift für Physik 3057:"The Glass Transition" 2721:yields to macroscopic 2602: 2542: 2252: 2104: 2085: 2021: 1962: 1907: 1862: 1818: 1555: 1526: 1500:. We also assume that 1494: 1471: 1439: 1413: 1341: 1291: 1268: 1225: 1192: 1132: 1125: 692:Poly-3-hydroxybutyrate 458: 443: 341:are frozen-in. Hereby 181: 21: 6369:Prince Rupert's drops 6218:Transparent materials 6178:Gradient-index optics 5986:Phosphosilicate glass 5819:Angell: Aqueous media 5294:"Lindemann criterion" 4704:Ojovan, M.I. (2008). 3191:Zarzycki, J. (1991). 2695:transverse vibrations 2600: 2540: 2269:In specific materials 2253: 2102: 2086: 2022: 1963: 1908: 1863: 1819: 1556: 1527: 1495: 1472: 1440: 1414: 1342: 1292: 1269: 1226: 1193: 1126: 1083: 567:Summarized below are 449: 430: 156: 117:are used above their 35:, is the gradual and 19: 6334:Glass ionomer cement 6208:Photosensitive glass 6135:Liquidus temperature 5956:Fluorosilicate glass 5329:Mott, N. F. (1934). 5131:J. Non-Cryst. Solids 5096:Frenkel, J. (1946). 4646:Ojovan M.I. (2008). 2811:Electronic structure 2761:thermal conductivity 2738:theory of elasticity 2188: 2138:Possible resolutions 2031: 1972: 1925: 1872: 1830: 1568: 1536: 1504: 1481: 1449: 1426: 1351: 1305: 1278: 1239: 1202: 1143: 1135:In 1971, Zeller and 1088: 1076:Linear heat capacity 789:Poly(vinyl chloride) 393:improve this article 6354:Glass-to-metal seal 6276:Self-cleaning glass 6198:Optical lens design 5761:1977PSSAR..39..697W 5654:1979PhRvL..43.1447J 5611:1980RPPh...43..353C 5560:1978Sci...199...11C 5511:1960JAP....31.1137D 5455:1960JAP....31.1136D 5405:1960Natur.187..869K 5349:1934RSPSA.146..465M 5271:1985JNCS...75..449C 5236:1949PhRv...75..972K 5191:1946JChPh..14..614K 5143:1979JNCS...30..371R 5075:1939JChPh...7..591B 5032:1940PCPS...36..160B 4964:2020MaMol..53.4770C 4783:2007JPCM...19O5107O 4725:2008Entrp..10..334O 4667:2008Entrp..10..334O 4609:2007Sci...315..353S 4562:1958JChPh..28..373G 4497:10.1021/cr60135a002 4454:1972PMag...25....1A 4415:1971PhRvB...4.2029Z 4350:1974JAP....45.5324B 4247:2014Sci...343..868H 3946:1996JNCS..195..158G 3907:10.1021/ja01349a006 3860:1927ZPhy...41..806S 3821:2017JNCS..471..490Z 3727:2010JNCS..356.2534O 3665:Nemilov SV (1994). 3628:1995Sci...267.1935S 3577:1995Sci...267.1924A 3515:1988JPCS...49..863A 3459:1979JNCS...34..153P 3247:2004JETPL..79..632O 3156:2000JAP....88.3113A 3098:2001Natur.410..259D 2890:charge distribution 2884:are important, the 2707:plastic deformation 1734: 1617: 848:Plexiglas, Perspex 805:Poly(vinyl alcohol) 708:Poly(vinyl acetate) 557:are colored green. 191:orders of magnitude 90:Hard plastics like 78:melting temperature 6339:Glass microspheres 6261:Hydrogen darkening 6183:Hydrogen darkening 5931:Chalcogenide glass 5921:Borosilicate glass 5812:2010-01-11 at the 5790:2007-06-28 at the 4321:2011-07-26 at the 4301:2013-06-05 at the 4219:2012-01-10 at the 4010:2009-04-17 at the 3868:10.1007/BF01395487 2979:Gardner transition 2834:in going from the 2777:order of magnitude 2603: 2585:composite material 2543: 2248: 2105: 2095:Kauzmann's paradox 2081: 2017: 1958: 1903: 1858: 1814: 1711: 1586: 1551: 1522: 1490: 1467: 1435: 1409: 1337: 1287: 1264: 1221: 1188: 1133: 1121: 660:Polyvinyl fluoride 459: 444: 314:Formal definitions 22: 6430:Rubber properties 6425:Polymer chemistry 6420:Phase transitions 6392: 6391: 6309:Glass-coated wire 6281:sol–gel technique 6266:Insulated glazing 6203:Photochromic lens 6188:Optical amplifier 6140:sol–gel technique 5519:10.1063/1.1735778 5463:10.1063/1.1735777 5199:10.1063/1.1724073 5083:10.1063/1.1750497 4958:(12): 4770–4782, 4902:10.1063/1.5123228 4852:10.1038/nphys1432 4734:10.3390/e10030334 4676:10.3390/e10030334 4603:(5810): 353–356. 4570:10.1063/1.1744141 4403:Physical Review B 4358:10.1063/1.1663238 4344:(12): 5324–5329. 4138:978-1-56990-379-7 4131:. Hanser Verlag. 4088:978-1-4200-9383-4 3988:978-3-642-34632-3 3901:(10): 3841–3851. 3571:(5206): 1924–35. 3550:10.1021/jp953538d 3419:978-0-85709-356-1 3255:10.1134/1.1790021 3164:10.1063/1.1286035 3092:(6825): 259–267. 2909:short-range order 2815:The influence of 2506:activation energy 2504:is such that the 2502:Gibbs free energy 2385:. Alternatively, 2240: 2220: 1917:Experimental data 1894: 1842: 1758: 1655: 1580: 1394: 1073: 1072: 1024:Tellurium dioxide 932: 931: 546:uses the kink in 505:thermal expansion 500:of many glasses. 431:Determination of 425: 424: 417: 242:Gibbs free energy 6442: 6130:Ion implantation 5885:Glass transition 5858: 5851: 5844: 5835: 5834: 5773: 5772: 5744: 5738: 5737: 5717: 5711: 5710: 5692: 5672: 5666: 5665: 5637: 5631: 5630: 5594: 5588: 5587: 5543: 5537: 5536: 5534: 5533: 5527: 5496: 5487: 5481: 5480: 5478: 5477: 5471: 5440: 5431: 5425: 5424: 5413:10.1038/187869b0 5388: 5382: 5381: 5369: 5363: 5362: 5360: 5326: 5320: 5319: 5317: 5315: 5309: 5298: 5289: 5283: 5282: 5254: 5248: 5247: 5219: 5213: 5212: 5210: 5174: 5168: 5161: 5155: 5154: 5126: 5120: 5110: 5104: 5103: 5093: 5087: 5086: 5058: 5052: 5051: 5015: 5009: 4999: 4993: 4992: 4983: 4947: 4941: 4931: 4925: 4924: 4914: 4904: 4880: 4874: 4873: 4863: 4831: 4825: 4824: 4822: 4821: 4815: 4768: 4759: 4753: 4752: 4750: 4749: 4743: 4736: 4710: 4701: 4695: 4694: 4692: 4691: 4685: 4678: 4652: 4643: 4637: 4636: 4588: 4582: 4581: 4541: 4535: 4534: 4532: 4530: 4510: 4501: 4500: 4485:Chemical Reviews 4480: 4474: 4473: 4433: 4427: 4426: 4409:(6): 2029–2041. 4394: 4388: 4387: 4371: 4362: 4361: 4333: 4327: 4312: 4306: 4293: 4287: 4281: 4275: 4274: 4241:(6173): 868–72. 4230: 4224: 4211: 4205: 4204: 4202: 4200: 4172: 4166: 4160: 4154: 4153: 4151: 4150: 4122: 4093: 4092: 4074: 4063: 4062: 4061: 4057: 4050: 4044: 4021: 4015: 4002: 3993: 3992: 3964: 3958: 3957: 3940:(1–2): 158–164. 3925: 3919: 3918: 3886: 3880: 3879: 3839: 3833: 3832: 3800: 3791: 3790: 3788: 3787: 3772: 3766: 3765: 3745: 3739: 3738: 3710: 3704: 3703: 3687: 3681: 3680: 3662: 3656: 3655: 3622:(5206): 1935–9. 3611: 3605: 3604: 3560: 3554: 3553: 3533: 3527: 3526: 3498: 3492: 3477: 3471: 3470: 3442: 3436: 3435: 3433: 3431: 3403: 3397: 3396: 3394: 3393: 3365: 3359: 3349:glass transition 3336: 3330: 3329: 3327: 3326: 3320: 3287: 3284: 3276: 3267: 3266: 3226: 3220: 3219: 3217: 3216: 3188: 3179: 3178: 3176: 3175: 3150:(6): 3113–3157. 3135: 3126: 3125: 3106:10.1038/35065704 3081: 3072: 3071: 3069: 3068: 3053: 3047: 3041: 3032: 3031: 2999: 2852:metallic glasses 2466:and the entropy 2326: 2322: 2318: 2257: 2255: 2254: 2249: 2241: 2239: 2231: 2223: 2221: 2218: 2216: 2215: 2200: 2199: 2161:phase transition 2154:vapor deposition 2132:Kauzmann paradox 2090: 2088: 2087: 2082: 2080: 2079: 2070: 2069: 2057: 2056: 2041: 2026: 2024: 2023: 2018: 2016: 2015: 2006: 2005: 1990: 1989: 1967: 1965: 1964: 1959: 1951: 1940: 1939: 1912: 1910: 1909: 1904: 1896: 1895: 1887: 1884: 1883: 1867: 1865: 1864: 1859: 1857: 1856: 1844: 1843: 1835: 1823: 1821: 1820: 1815: 1801: 1800: 1773: 1759: 1757: 1750: 1749: 1736: 1733: 1719: 1710: 1709: 1669: 1668: 1656: 1654: 1647: 1646: 1630: 1619: 1616: 1609: 1594: 1582: 1581: 1573: 1560: 1558: 1557: 1552: 1531: 1529: 1528: 1523: 1499: 1497: 1496: 1491: 1476: 1474: 1473: 1468: 1444: 1442: 1441: 1436: 1418: 1416: 1415: 1410: 1408: 1407: 1395: 1393: 1386: 1385: 1369: 1358: 1346: 1344: 1343: 1338: 1330: 1296: 1294: 1293: 1288: 1273: 1271: 1270: 1265: 1260: 1259: 1230: 1228: 1227: 1222: 1220: 1219: 1197: 1195: 1194: 1189: 1187: 1186: 1177: 1176: 1161: 1160: 1130: 1128: 1127: 1122: 1114: 1103: 1102: 1036:Fluoroaluminate 955: 954: 606:Commercial name 582: 581: 420: 413: 409: 406: 400: 377: 369: 203:phase transition 159:Glass transition 133:phase transition 33:glass transition 6450: 6449: 6445: 6444: 6443: 6441: 6440: 6439: 6395: 6394: 6393: 6388: 6324:Glass electrode 6319:Glass databases 6296: 6290: 6228: 6222: 6154: 6088: 6064:Bioactive glass 6050: 6036:Vitreous enamel 6021:Thoriated glass 6016:Tellurite glass 6001:Soda–lime glass 5971:Gold ruby glass 5941:Cranberry glass 5894: 5868: 5862: 5814:Wayback Machine 5792:Wayback Machine 5781: 5776: 5745: 5741: 5718: 5714: 5690:10.1.1.596.7462 5673: 5669: 5642:Phys. Rev. Lett 5638: 5634: 5595: 5591: 5554:(4324): 11–21. 5544: 5540: 5531: 5529: 5525: 5494: 5488: 5484: 5475: 5473: 5469: 5438: 5432: 5428: 5389: 5385: 5370: 5366: 5327: 5323: 5313: 5311: 5307: 5296: 5290: 5286: 5255: 5251: 5220: 5216: 5175: 5171: 5162: 5158: 5127: 5123: 5111: 5107: 5094: 5090: 5059: 5055: 5016: 5012: 5000: 4996: 4948: 4944: 4932: 4928: 4881: 4877: 4832: 4828: 4819: 4817: 4813: 4766: 4760: 4756: 4747: 4745: 4741: 4708: 4702: 4698: 4689: 4687: 4683: 4650: 4644: 4640: 4589: 4585: 4542: 4538: 4528: 4526: 4519:Quanta Magazine 4511: 4504: 4481: 4477: 4434: 4430: 4395: 4391: 4372: 4365: 4334: 4330: 4323:Wayback Machine 4313: 4309: 4303:Wayback Machine 4294: 4290: 4282: 4278: 4231: 4227: 4221:Wayback Machine 4212: 4208: 4198: 4196: 4189: 4173: 4169: 4161: 4157: 4148: 4146: 4139: 4123: 4096: 4089: 4075: 4066: 4059: 4052: 4051: 4047: 4022: 4018: 4012:Wayback Machine 4003: 3996: 3989: 3965: 3961: 3926: 3922: 3887: 3883: 3840: 3836: 3801: 3794: 3785: 3783: 3774: 3773: 3769: 3746: 3742: 3721:(44–49): 2534. 3711: 3707: 3694:. Butterworth. 3688: 3684: 3677: 3663: 3659: 3612: 3608: 3561: 3557: 3534: 3530: 3499: 3495: 3478: 3474: 3443: 3439: 3429: 3427: 3420: 3404: 3400: 3391: 3389: 3382: 3366: 3362: 3337: 3333: 3324: 3322: 3318: 3285: 3277: 3270: 3241:(12): 632–634. 3232: 3227: 3223: 3214: 3212: 3205: 3189: 3182: 3173: 3171: 3144:Appl. Phys. Rev 3136: 3129: 3082: 3075: 3066: 3064: 3055: 3054: 3050: 3042: 3035: 3000: 2996: 2992: 2984:Glass formation 2975: 2863:splat quenching 2813: 2703:shearing stress 2678:fluctuations.) 2644: 2638: 2593: 2578: 2571: 2555: 2533: 2526: 2519: 2499: 2487: 2480: 2476: 2472: 2465: 2458: 2451: 2444: 2437: 2430: 2423: 2416: 2409: 2402: 2395: 2384: 2374:, which have a 2353: 2342: 2324: 2320: 2316: 2311: 2302:shared vertices 2299: 2287: 2279: 2277: 2271: 2232: 2224: 2222: 2217: 2208: 2204: 2195: 2191: 2189: 2186: 2185: 2172: 2140: 2097: 2075: 2071: 2065: 2061: 2052: 2048: 2037: 2032: 2029: 2028: 2011: 2007: 2001: 1997: 1985: 1981: 1973: 1970: 1969: 1947: 1935: 1931: 1926: 1923: 1922: 1919: 1886: 1885: 1879: 1875: 1873: 1870: 1869: 1868:, leading to a 1852: 1848: 1834: 1833: 1831: 1828: 1827: 1793: 1789: 1769: 1745: 1741: 1740: 1735: 1720: 1715: 1702: 1698: 1661: 1657: 1636: 1632: 1631: 1620: 1618: 1605: 1595: 1590: 1572: 1571: 1569: 1566: 1565: 1537: 1534: 1533: 1505: 1502: 1501: 1482: 1479: 1478: 1450: 1447: 1446: 1427: 1424: 1423: 1400: 1396: 1375: 1371: 1370: 1359: 1357: 1352: 1349: 1348: 1326: 1306: 1303: 1302: 1279: 1276: 1275: 1255: 1251: 1240: 1237: 1236: 1215: 1211: 1203: 1200: 1199: 1182: 1178: 1172: 1168: 1156: 1152: 1144: 1141: 1140: 1110: 1098: 1094: 1089: 1086: 1085: 1078: 1048:Soda-lime glass 1012:fluoride glass 975: 966: 953: 887:Poly(carbonate) 839:(PMMA atactic) 757:Polylactic acid 678:(PP isotactic) 602: 593: 580: 573: 563: 556: 545: 531: 521: 498:annealing point 495: 484: 477: 467: 456: 450:Measurement of 437: 421: 410: 404: 401: 390: 378: 365: 363: 316: 305: 298: 291: 284: 276: 250: 236: 216:rigidity theory 199:crystallization 187: 185:Characteristics 182: 155: 123: 115:polyisobutylene 104: 86: 75: 45:semicrystalline 25: 12: 11: 5: 6448: 6438: 6437: 6432: 6427: 6422: 6417: 6412: 6407: 6390: 6389: 6387: 6386: 6381: 6376: 6371: 6366: 6361: 6356: 6351: 6346: 6341: 6336: 6331: 6326: 6321: 6316: 6311: 6306: 6300: 6298: 6292: 6291: 6289: 6288: 6286:Tempered glass 6283: 6278: 6273: 6268: 6263: 6258: 6256:DNA microarray 6253: 6251:Dealkalization 6248: 6243: 6238: 6232: 6230: 6224: 6223: 6221: 6220: 6215: 6210: 6205: 6200: 6195: 6190: 6185: 6180: 6175: 6170: 6164: 6162: 6156: 6155: 6153: 6152: 6147: 6142: 6137: 6132: 6127: 6125:Glass modeling 6122: 6117: 6112: 6107: 6102: 6096: 6094: 6090: 6089: 6087: 6086: 6081: 6076: 6071: 6066: 6060: 6058: 6056:Glass-ceramics 6052: 6051: 6049: 6048: 6043: 6038: 6033: 6028: 6023: 6018: 6013: 6008: 6003: 5998: 5996:Silicate glass 5993: 5988: 5983: 5978: 5973: 5968: 5963: 5958: 5953: 5948: 5943: 5938: 5933: 5928: 5923: 5918: 5913: 5908: 5902: 5900: 5896: 5895: 5893: 5892: 5887: 5882: 5876: 5874: 5870: 5869: 5867:science topics 5861: 5860: 5853: 5846: 5838: 5832: 5831: 5826: 5821: 5816: 5804: 5799: 5794: 5780: 5779:External links 5777: 5775: 5774: 5739: 5712: 5667: 5632: 5589: 5538: 5482: 5426: 5383: 5364: 5321: 5284: 5249: 5214: 5169: 5156: 5121: 5105: 5088: 5069:(8): 591–603. 5053: 5026:(2): 160–172. 5010: 4994: 4952:Macromolecules 4942: 4926: 4889:Nature Physics 4875: 4826: 4777:(41): 415107. 4754: 4719:(3): 334–364. 4696: 4661:(3): 334–364. 4638: 4583: 4556:(3): 373–383. 4536: 4502: 4491:(2): 219–256. 4475: 4428: 4389: 4363: 4328: 4307: 4288: 4276: 4225: 4206: 4187: 4167: 4165:. nrri.umn.edu 4155: 4137: 4094: 4087: 4064: 4045: 4016: 3994: 3987: 3959: 3920: 3881: 3854:(4): 806–809. 3834: 3792: 3767: 3740: 3705: 3682: 3676:978-0849337826 3675: 3657: 3606: 3555: 3528: 3509:(8): 863–871. 3493: 3472: 3437: 3418: 3398: 3381:978-0123705358 3380: 3360: 3331: 3268: 3230: 3221: 3204:978-0521355827 3203: 3180: 3127: 3073: 3048: 3033: 3014:(8): 256–261. 2993: 2991: 2988: 2987: 2986: 2981: 2974: 2971: 2960:periodic table 2905:mean free path 2882:chemical bonds 2856:mean free path 2812: 2809: 2805:shear stresses 2785:heat transport 2773:mean free path 2750:viscous liquid 2727:shearing force 2683:thermal motion 2648:Fourier series 2640:Main article: 2637: 2634: 2591: 2576: 2569: 2553: 2531: 2524: 2517: 2497: 2486: 2483: 2478: 2474: 2470: 2463: 2456: 2449: 2442: 2435: 2428: 2421: 2414: 2407: 2400: 2393: 2382: 2351: 2345:covalent bonds 2340: 2332:, vitreous or 2309: 2297: 2285: 2278: 2275: 2272: 2270: 2267: 2259: 2258: 2247: 2244: 2238: 2235: 2230: 2227: 2219: as 2214: 2211: 2207: 2203: 2198: 2194: 2170: 2139: 2136: 2096: 2093: 2078: 2074: 2068: 2064: 2060: 2055: 2051: 2047: 2044: 2040: 2036: 2014: 2010: 2004: 2000: 1996: 1993: 1988: 1984: 1980: 1977: 1957: 1954: 1950: 1946: 1943: 1938: 1934: 1930: 1918: 1915: 1902: 1899: 1893: 1890: 1882: 1878: 1855: 1851: 1847: 1841: 1838: 1813: 1810: 1807: 1804: 1799: 1796: 1792: 1788: 1785: 1782: 1779: 1776: 1772: 1768: 1765: 1762: 1756: 1753: 1748: 1744: 1739: 1732: 1729: 1726: 1723: 1718: 1714: 1708: 1705: 1701: 1697: 1694: 1691: 1688: 1685: 1682: 1679: 1676: 1673: 1667: 1664: 1660: 1653: 1650: 1645: 1642: 1639: 1635: 1629: 1626: 1623: 1615: 1612: 1608: 1604: 1601: 1598: 1593: 1589: 1585: 1579: 1576: 1550: 1547: 1544: 1541: 1521: 1518: 1515: 1512: 1509: 1489: 1486: 1466: 1463: 1460: 1457: 1454: 1434: 1431: 1406: 1403: 1399: 1392: 1389: 1384: 1381: 1378: 1374: 1368: 1365: 1362: 1356: 1336: 1333: 1329: 1325: 1322: 1319: 1316: 1313: 1310: 1286: 1283: 1263: 1258: 1254: 1250: 1247: 1244: 1218: 1214: 1210: 1207: 1185: 1181: 1175: 1171: 1167: 1164: 1159: 1155: 1151: 1148: 1120: 1117: 1113: 1109: 1106: 1101: 1097: 1093: 1077: 1074: 1071: 1070: 1067: 1064: 1063:(approximate) 1057: 1056: 1053: 1050: 1044: 1043: 1040: 1037: 1033: 1032: 1029: 1026: 1020: 1019: 1016: 1013: 1006: 1005: 1002: 999: 992: 991: 988: 985: 978: 977: 973: 968: 964: 959: 952: 949: 930: 929: 927: 924: 921: 919:Polynorbornene 915: 914: 912: 909: 906: 900: 899: 896: 893: 890: 883: 882: 879: 876: 873: 866: 865: 863: 860: 857: 850: 849: 846: 843: 840: 833: 832: 830: 827: 824: 817: 816: 814: 811: 808: 801: 800: 798: 795: 792: 785: 784: 782: 779: 776: 769: 768: 766: 763: 760: 753: 752: 749: 746: 743: 736: 735: 733: 730: 727: 720: 719: 717: 714: 711: 704: 703: 701: 698: 695: 688: 687: 685: 682: 679: 672: 671: 669: 666: 663: 656: 655: 653: 650: 647: 640: 639: 637: 634: 631: 624: 623: 621: 618: 615: 608: 607: 604: 600: 595: 591: 586: 579: 576: 571: 561: 554: 543: 529: 519: 493: 482: 475: 465: 454: 435: 423: 422: 381: 379: 372: 364: 361: 355: 315: 312: 303: 296: 289: 282: 274: 248: 234: 186: 183: 180: 179: 176: 173: 170: 167: 150: 149: 121: 102: 84: 73: 57:viscous liquid 39:transition in 23: 9: 6: 4: 3: 2: 6447: 6436: 6433: 6431: 6428: 6426: 6423: 6421: 6418: 6416: 6415:Glass physics 6413: 6411: 6408: 6406: 6403: 6402: 6400: 6385: 6382: 6380: 6377: 6375: 6372: 6370: 6367: 6365: 6362: 6360: 6357: 6355: 6352: 6350: 6347: 6345: 6342: 6340: 6337: 6335: 6332: 6330: 6327: 6325: 6322: 6320: 6317: 6315: 6312: 6310: 6307: 6305: 6302: 6301: 6299: 6293: 6287: 6284: 6282: 6279: 6277: 6274: 6272: 6269: 6267: 6264: 6262: 6259: 6257: 6254: 6252: 6249: 6247: 6244: 6242: 6239: 6237: 6234: 6233: 6231: 6225: 6219: 6216: 6214: 6211: 6209: 6206: 6204: 6201: 6199: 6196: 6194: 6193:Optical fiber 6191: 6189: 6186: 6184: 6181: 6179: 6176: 6174: 6171: 6169: 6166: 6165: 6163: 6161: 6157: 6151: 6150:Vitrification 6148: 6146: 6143: 6141: 6138: 6136: 6133: 6131: 6128: 6126: 6123: 6121: 6120:Glass melting 6118: 6116: 6115:Glass forming 6113: 6111: 6108: 6106: 6103: 6101: 6098: 6097: 6095: 6091: 6085: 6082: 6080: 6077: 6075: 6072: 6070: 6067: 6065: 6062: 6061: 6059: 6057: 6053: 6047: 6044: 6042: 6039: 6037: 6034: 6032: 6031:Uranium glass 6029: 6027: 6024: 6022: 6019: 6017: 6014: 6012: 6011:Soluble glass 6009: 6007: 6004: 6002: 5999: 5997: 5994: 5992: 5989: 5987: 5984: 5982: 5979: 5977: 5974: 5972: 5969: 5967: 5964: 5962: 5959: 5957: 5954: 5952: 5949: 5947: 5944: 5942: 5939: 5937: 5934: 5932: 5929: 5927: 5926:Ceramic glaze 5924: 5922: 5919: 5917: 5914: 5912: 5909: 5907: 5904: 5903: 5901: 5897: 5891: 5888: 5886: 5883: 5881: 5878: 5877: 5875: 5871: 5866: 5859: 5854: 5852: 5847: 5845: 5840: 5839: 5836: 5830: 5827: 5825: 5822: 5820: 5817: 5815: 5811: 5808: 5805: 5803: 5800: 5798: 5795: 5793: 5789: 5786: 5783: 5782: 5770: 5766: 5762: 5758: 5754: 5750: 5743: 5735: 5731: 5727: 5723: 5716: 5708: 5704: 5700: 5696: 5691: 5686: 5682: 5678: 5671: 5663: 5659: 5655: 5651: 5647: 5643: 5636: 5628: 5624: 5620: 5616: 5612: 5608: 5604: 5600: 5593: 5585: 5581: 5577: 5573: 5569: 5565: 5561: 5557: 5553: 5549: 5542: 5524: 5520: 5516: 5512: 5508: 5504: 5500: 5493: 5486: 5468: 5464: 5460: 5456: 5452: 5448: 5444: 5437: 5430: 5422: 5418: 5414: 5410: 5406: 5402: 5399:(4740): 869. 5398: 5394: 5387: 5379: 5375: 5368: 5359: 5354: 5350: 5346: 5342: 5338: 5337: 5332: 5325: 5306: 5302: 5295: 5288: 5280: 5276: 5272: 5268: 5264: 5260: 5253: 5245: 5241: 5237: 5233: 5229: 5225: 5218: 5209: 5204: 5200: 5196: 5192: 5188: 5184: 5180: 5179:J. Chem. Phys 5173: 5166: 5160: 5152: 5148: 5144: 5140: 5136: 5132: 5125: 5119: 5115: 5109: 5101: 5100: 5092: 5084: 5080: 5076: 5072: 5068: 5064: 5057: 5049: 5045: 5041: 5037: 5033: 5029: 5025: 5021: 5014: 5008: 5004: 4998: 4991: 4987: 4982: 4977: 4973: 4969: 4965: 4961: 4957: 4953: 4946: 4940: 4936: 4930: 4922: 4918: 4913: 4908: 4903: 4898: 4894: 4890: 4886: 4879: 4871: 4867: 4862: 4857: 4853: 4849: 4845: 4841: 4840:J. Chem. Phys 4837: 4830: 4812: 4808: 4804: 4800: 4796: 4792: 4788: 4784: 4780: 4776: 4772: 4765: 4758: 4740: 4735: 4730: 4726: 4722: 4718: 4714: 4707: 4700: 4682: 4677: 4672: 4668: 4664: 4660: 4656: 4649: 4642: 4634: 4630: 4626: 4622: 4618: 4614: 4610: 4606: 4602: 4598: 4594: 4587: 4579: 4575: 4571: 4567: 4563: 4559: 4555: 4551: 4547: 4540: 4524: 4520: 4516: 4509: 4507: 4498: 4494: 4490: 4486: 4479: 4471: 4467: 4463: 4459: 4455: 4451: 4447: 4443: 4439: 4432: 4424: 4420: 4416: 4412: 4408: 4404: 4400: 4393: 4385: 4381: 4377: 4370: 4368: 4359: 4355: 4351: 4347: 4343: 4339: 4332: 4325: 4324: 4320: 4317: 4311: 4304: 4300: 4297: 4292: 4285: 4280: 4272: 4268: 4264: 4260: 4256: 4252: 4248: 4244: 4240: 4236: 4229: 4222: 4218: 4215: 4210: 4194: 4190: 4188:9781849733915 4184: 4180: 4179: 4171: 4164: 4159: 4144: 4140: 4134: 4130: 4129: 4121: 4119: 4117: 4115: 4113: 4111: 4109: 4107: 4105: 4103: 4101: 4099: 4090: 4084: 4080: 4073: 4071: 4069: 4055: 4054:EU WO03053721 4049: 4043: 4039: 4035: 4031: 4030: 4025: 4020: 4013: 4009: 4006: 4001: 3999: 3990: 3984: 3980: 3976: 3972: 3971: 3963: 3955: 3951: 3947: 3943: 3939: 3935: 3931: 3924: 3916: 3912: 3908: 3904: 3900: 3896: 3892: 3885: 3877: 3873: 3869: 3865: 3861: 3857: 3853: 3850:(in German). 3849: 3845: 3838: 3830: 3826: 3822: 3818: 3814: 3810: 3806: 3799: 3797: 3781: 3777: 3771: 3763: 3759: 3755: 3751: 3744: 3736: 3732: 3728: 3724: 3720: 3716: 3709: 3701: 3697: 3693: 3686: 3678: 3672: 3669:. 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