The
liquid-glass transition (or
glass transition for short) is the reversible transition in
amorphousIn condensed matter physics, an amorphous or non-crystalline solid is a solid that lacks the long-range order characteristic of a crystal....
materials (or in amorphous regions within semicrystalline materials) from a hard and relatively brittle state into a molten or
rubberNatural rubber, also called India rubber or caoutchouc, is an elastomer that was originally derived from latex, a milky colloid produced by some plants. The plants would be ‘tapped’, that is, an incision made into the bark of the tree and the sticky, milk colored latex sap collected and refined...
-like state. An amorphous solid that exhibits a glass transition is called a
glassGlass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...
. Supercooling a
viscous liquidIn condensed matter physics and physical chemistry, the terms viscous liquid, supercooled liquid, and glassforming liquid are often used interchangeably to designate liquids that are at the same time highly viscous , supercooled, and able to form a glass.- Working points in glass processing :The...
into the glass state is called
vitrificationVitrification is the transformation of a substance into a glass. Usually, it is achieved by rapidly cooling a liquid through the glass transition. Certain chemical reactions also result in glasses...
, from the Latin
vitreum, "glass" via
FrenchFrench is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...
vitrifier.
Despite the massive change in the physical properties of a material through its glass transition, the transition is not itself a
phase transitionA phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
of any kind; rather it is a laboratory phenomenon extending over a range of temperature and defined by one of several conventions. Such conventions include a constant cooling rate (20 K/min) and a viscosity threshold of 10
12 Pa·s, among others. Upon cooling or heating through this glass transition range, the material also exhibits a smooth step in the thermal expansion coefficient and in the specific heat, with the location of these effects again being dependent on the history of the material. However, the question of whether some phase transition
underlies the glass transition is a matter of continuing research.
The
glass transition temperature Tg is always lower than the
melting temperatureThe melting point of a solid is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends on pressure and is usually specified at standard atmospheric pressure...
,
Tm, of the crystalline state of the material, if one exists.
Introduction
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
orders of magnitudeAn order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...
without any pronounced change in material structure. The consequence of this dramatic increase is a
glassGlass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...
exhibiting solid-like mechanical properties on the timescale of practical observation. This transition is in contrast to the
freezingFreezing or solidification is a phase change in which a liquid turns into a solid when its temperature is lowered below its freezing point. The reverse process is melting....
or
crystallizationCrystallization is the process of formation of solid crystals precipitating from a solution, melt or more rarely deposited directly from a gas. Crystallization is also a chemical solid–liquid separation technique, in which mass transfer of a solute from the liquid solution to a pure solid...
transition, which is a first-order
phase transitionA phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
in the 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.
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 (or intermolecular rearrangement) to occur may result in a higher density glass product. Similarly, by
annealingAnnealing may refer to:*Annealing , a heat treatment that alters the microstructure of a material causing changes in properties such as strength and hardness and ductility*Annealing , heating a piece of glass to remove stress...
(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
g is located at the intersection between the cooling curve (volume versus temperature) for the glassy state and the supercooled liquid.
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
g, 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.
Thus, the liquid-glass transition is not a transition between states of
thermodynamic equilibriumIn thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...
. 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 superpositionThe Time–temperature superposition principle is a concept in polymer physics and in the physics of glass-forming liquids. Some materials, polymers in particular, show a strong dependence of viscoelastic properties on the temperature at which they are measured...
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.
,
Transition temperature Tg
Refer to the figure on the right plotting the heat capacity as a function of temperature. In this context, T
g is the temperature corresponding to point A on the curve. The linear sections below and above T
g are colored green. T
g is the temperature at the intersection of the red regression lines.
Different operational definitions of the glass transition temperature T
g 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
g for a given substance agree within a few kelvins. One definition refers to the
viscosityViscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
, fixing T
g at a value of 10
13 poise (or 10
12 Pa·s). As evidenced experimentally, this value is close to the
annealing pointAnnealing is a process of slowly cooling glass to relieve internal stresses after it was formed. The process may be carried out in a temperature-controlled kiln known as a Lehr. Glass which has not been annealed is liable to crack or shatter when subjected to a relatively small temperature change...
of many glasses.
In contrast to viscosity, the
thermal expansionThermal expansion is the tendency of matter to change in volume in response to a change in temperature.When a substance is heated, its particles begin moving more and thus usually maintain a greater average separation. Materials which contract with increasing temperature are rare; this effect is...
,
heat capacityHeat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...
, and many other properties of inorganic
glassGlass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...
es show a relatively sudden change at the glass transition temperature. Any such step or kink can be used to define
Tg. To make this definition reproducible, the cooling or heating rate must be specified.
The most frequently used definition of
Tg uses the energy release on heating in
differential scanning calorimetryDifferential scanning calorimetry or DSC is a thermoanalytical technique in which the difference in the amount of heat required to increase the temperature of a sample and reference is measured as a function of temperature. Both the sample and reference are maintained at nearly the same temperature...
(DSC, see figure). Typically, the sample is first cooled with 10 K/min and then heated with that same speed.
Yet another definition of
Tg uses the kink in
dilatometryA dilatometer is a scientific instrument that measures volume changes caused by a physical or chemical process. A familiar application of a dilatometer is the mercury-in-glass thermometer, in which the change in volume of the liquid column is read from a graduated scale...
. Here, heating rates of 3-5 K/min are common. Summarized below are
Tg values characteristic of certain classes of materials.
Polymers
| Material | Tg (°C) |
|---|
| Tyre A tire or tyre is a ring-shaped covering that fits around a wheel rim to protect it and enable better vehicle performance by providing a flexible cushion that absorbs shock while keeping the wheel in close contact with the ground...
rubber | −70 |
PolypropylenePolypropylene , also known as polypropene, is a thermoplastic polymer used in a wide variety of applications including packaging, textiles , stationery, plastic parts and reusable containers of various types, laboratory equipment, loudspeakers, automotive components, and polymer banknotes...
(atactic) | −20 |
PolypropylenePolypropylene , also known as polypropene, is a thermoplastic polymer used in a wide variety of applications including packaging, textiles , stationery, plastic parts and reusable containers of various types, laboratory equipment, loudspeakers, automotive components, and polymer banknotes...
(isotactic) | 0 |
| Poly-3-hydroxybutyrate (PHB) | 15 |
| Poly(vinyl acetate) Polyvinyl acetate, PVA, PVAc, poly, is a rubbery synthetic polymer with the formula n. It belongs to the polyvinyl esters family with the general formula -[RCOOCHCH2]-...
(PVAc) | 30 |
| Polyethylene terephthalate Polyethylene terephthalate , commonly abbreviated PET, PETE, or the obsolete PETP or PET-P, is a thermoplastic polymer resin of the polyester family and is used in synthetic fibers; beverage, food and other liquid containers; thermoforming applications; and engineering resins often in combination...
(PET) | 70 |
Poly(vinyl chloride)Polyvinyl chloride, commonly abbreviated PVC, is a thermoplastic polymer. It is a vinyl polymer constructed of repeating vinyl groups having one hydrogen replaced by chloride. Polyvinyl chloride is the third most widely produced plastic, after polyethylene and polypropylene. PVC is widely used in...
(PVC) | 80 |
| Poly(vinyl alcohol) Polyvinyl alcohol is a water-soluble synthetic polymer .-Properties:...
(PVA) | 85 |
PolystyrenePolystyrene ) also known as Thermocole, abbreviated following ISO Standard PS, is an aromatic polymer made from the monomer styrene, a liquid hydrocarbon that is manufactured from petroleum by the chemical industry...
| 95 |
| Poly(methylmethacrylate) (atactic) | 105 |
Poly(carbonate)PolycarbonatePhysical PropertiesDensity 1.20–1.22 g/cm3Abbe number 34.0Refractive index 1.584–1.586FlammabilityV0-V2Limiting oxygen index25–27%Water absorption – Equilibrium0.16–0.35%Water absorption – over 24 hours0.1%...
| 145 |
| Polynorbornene | 215 |
These 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 polyethylene 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.
Silicates and other covalent network glasses
| Material | Tg (°C) |
|---|
| Chalcogenide A chalcogenide is a chemical compound consisting of at least one chalcogen ion and at least one more electropositive element. Although all group 16 elements of the periodic table are defined as chalcogens, the term is more commonly reserved for sulfides, selenides, and tellurides, rather than...
GeSbTe | 150 |
| Chalcogenide A chalcogenide is a chemical compound consisting of at least one chalcogen ion and at least one more electropositive element. Although all group 16 elements of the periodic table are defined as chalcogens, the term is more commonly reserved for sulfides, selenides, and tellurides, rather than...
AsGeSeTe | 245 |
| ZBLAN Heavy metal fluoride glasses were accidentally discovered in 1975 by Poulain and Lucas at the University of Rennes in France, including a family of glasses ZBLAN with a composition ZrF4-BaF2-LaF3-AlF3-NaF....
fluoride glass | 235 |
| Tellurium dioxide Tellurium dioxide is a solid oxide of tellurium. It is encountered in two different forms, the yellow orthorhombic mineral tellurite, β-TeO2, and the synthetic, colourless tetragonal , α-TeO2...
| 280 |
| Fluoroaluminate | 400 |
Soda-lime glassSoda-lime glass, also called soda-lime-silica glass, is the most prevalent type of glass, used for windowpanes, and glass containers for beverages, food, and some commodity items...
| 520-600 |
| Fused quartz Fused quartz and fused silica are types of glass containing primarily silica in amorphous form. They are manufactured using several different processes...
| ~1200 |
Kauzmann's paradox
As a liquid is supercooled, the difference in entropy between the liquid and solid phase decreases. By extrapolating the
heat capacityHeat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...
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.
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 KauzmannWalter J. Kauzmann was an American chemist and professor emeritus of Princeton University. He was noted for his work in both physical chemistry and biochemistry. His most important contribution was recognizing that the hydrophobic effect plays a key role in determining the three-dimensional...
in 1948.
One resolution of the Kauzmann paradox is to say that there must be a phase change before the entropy of the liquid decreases. In this scenario, the transition temperature is known as the
calorimetric ideal glass transition temperature T0c. In this view, the glass transition is not merely a
kineticChemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition...
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:
-
-
-
-
-
-
- Tg → T0c as dT⁄dt → 0.
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.
Silica, SiO2
Silica (the chemical compound SiO
2) has a number of distinct
crystalA crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
line forms in addition to the quartz structure. Nearly all of the crystalline forms involve tetrahedral SiO
4 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 which represent an approach to an
amorphousIn condensed matter physics, an amorphous or non-crystalline solid is a solid that lacks the long-range order characteristic of a crystal....
, vitreous or
glassy solidIn condensed matter physics, an amorphous or non-crystalline solid is a solid that lacks the long-range order characteristic of a crystal....
.
The transition temperature
Tg in silicates is related to the energy required to break and re-form covalent bonds in an amorphous (or random network) lattice of
covalent bondA covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....
s. The
Tg is clearly influenced by the chemistry of the glass. For example, addition of elements such as
BBoron is the chemical element with atomic number 5 and the chemical symbol B. Boron is a metalloid. Because boron is not produced by stellar nucleosynthesis, it is a low-abundance element in both the solar system and the Earth's crust. However, boron is concentrated on Earth by the...
,
NaSodium is a chemical element with the symbol Na and atomic number 11. It is a soft, silvery-white, highly reactive metal and is a member of the alkali metals; its only stable isotope is 23Na. It is an abundant element that exists in numerous minerals, most commonly as sodium chloride...
,
KPotassium is the chemical element with the symbol K and atomic number 19. Elemental potassium is a soft silvery-white alkali metal that oxidizes rapidly in air and is very reactive with water, generating sufficient heat to ignite the hydrogen emitted in the reaction.Potassium and sodium are...
or
CaCalcium is the chemical element with the symbol Ca and atomic number 20. It has an atomic mass of 40.078 amu. Calcium is a soft gray alkaline earth metal, and is the fifth-most-abundant element by mass in the Earth's crust...
to a silica glass, which have a valency less than 4, helps in breaking up the network structure, thus reducing the
Tg. Alternatively,
PPhosphorus is the chemical element that has the symbol P and atomic number 15. A multivalent nonmetal of the nitrogen group, phosphorus as a mineral is almost always present in its maximally oxidized state, as inorganic phosphate rocks...
which has a valency of 5, helps to reinforce an ordered lattice, and thus increases the
Tg.
Tg is directly proportional to bond strength, e.g. it depends on quasi-equilibrium thermodynamic parameters of the bonds e.g. on the enthalpy
Hd and entropy
Sd of configurons – broken bonds:
Tg =
Hd / [
Sd + Rln[(1-
fc)/
fc]
where R is the gas constant and
fc is the percolation threshold. For strong melts such as Si
O2 the percolation threshold in the above equation is the universal Scher-Zallen critical density in the 3-D space e.g.
fc = 0.15, however for fragile materials the percolation thresholds are material-dependent and
fc << 1. The enthalpy
Hd and the entropy
Sd of configurons – broken bonds can be found from available experimental data on viscosity.
Polymers
In
polymerA polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...
s the glass transition temperature,
Tg, is often expressed as the temperature at which the
Gibbs free energyIn thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure...
is such that the
activation energyIn chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius that is defined as the energy that must be overcome in order for a chemical reaction to occur. Activation energy may also be defined as the minimum energy required to start a chemical reaction...
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
benzeneBenzene is an organic chemical compound. It is composed of 6 carbon atoms in a ring, with 1 hydrogen atom attached to each carbon atom, with the molecular formula C6H6....
rings) will interfere with the flowing process and hence increase
Tg.
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
E2, until the temperature exceeds
Tm, and the material melts. This region is called the rubber plateau.
In
ironingIroning is the use of a heated tool to remove wrinkles from fabric. The heating is commonly done to a temperature of 180-220 °Celsius, depending on the fabric. Ironing works by loosening the bonds between the long-chain polymer molecules in the fibers of the material...
, a fabric is heated through this transition so that the polymer chains become mobile. The weight of the iron then imposes a preferred orientation.
Tg can be significantly decreased by addition of
plasticizerPlasticizers or dispersants are additives that increase the plasticity or fluidity of the material to which they are added; these include plastics, cement, concrete, wallboard, and clay. Although the same compounds are often used for both plastics and concretes the desired effects and results are...
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 smellNew-car smell is the common term for the odor that comes from the combination of materials found in new automobiles. Some people regard it as a pleasant and desirable smell. However, there is some question about whether the chemicals in the odour pose a health risk.- Chemical composition :Both the...
" is due to the initial
outgassingOutgassing is the release of a gas that was dissolved, trapped, frozen or absorbed in some material. As an example, research has shown how the concentration of carbon dioxide in the Earth's atmosphere has sometimes been linked to ocean outgassing...
of
volatileIn chemistry and physics, volatility is the tendency of a substance to vaporize. Volatility is directly related to a substance's vapor pressure. At a given temperature, a substance with higher vapor pressure vaporizes more readily than a substance with a lower vapor pressure.The term is primarily...
small-molecule plasticizers used to modify interior plastics (e.g., dashboards) to keep them from cracking in the cold of winter weather. The addition of nonreactive
side groupsIn organic chemistry and biochemistry, a side chain is a chemical group that is attached to a core part of the molecule called "main chain" or backbone. The placeholder R is often used as a generic placeholder for alkyl group side chains in chemical structure diagrams. To indicate other non-carbon...
to a polymer can also make the chains stand off from one another, reducing
Tg. If a plastic with some desirable properties has a
Tg which is too high, it can sometimes be combined with another in a copolymer or
composite materialComposite materials, often shortened to composites or called composition materials, are engineered or naturally occurring materials made from two or more constituent materials with significantly different physical or chemical properties which remain separate and distinct at the macroscopic or...
with a
Tg 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.
In
viscoelasticViscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like honey, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain instantaneously when stretched and just...
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
siliconeSilicones are inert, synthetic compounds with a variety of forms and uses. Typically heat-resistant and rubber-like, they are used in sealants, adhesives, lubricants, medical applications , cookware, and insulation....
toy '
Silly PuttySilly Putty , is the Crayola-owned trademark name for a class of silicone polymers. It is marketed today as a toy for children, but was originally created by accident during research into potential rubber substitutes for use by the United States in World War II...
' 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.
On cooling,
rubberNatural rubber, also called India rubber or caoutchouc, is an elastomer that was originally derived from latex, a milky colloid produced by some plants. The plants would be ‘tapped’, that is, an incision made into the bark of the tree and the sticky, milk colored latex sap collected and refined...
undergoes a
liquid-glass transition, which has also been called a
rubber-glass transition. For example, the
Space Shuttle ChallengerSpace Shuttle Challenger was NASA's second Space Shuttle orbiter to be put into service, Columbia having been the first. The shuttle was built by Rockwell International's Space Transportation Systems Division in Downey, California...
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
solid-fuel rocket boostersThe Space Shuttle Solid Rocket Boosters were the pair of large solid rockets used by the United States' NASA Space Shuttle during the first two minutes of powered flight. Together they provided about 83% of liftoff thrust for the Space Shuttle. They were located on either side of the rusty or...
.
Mechanics of vitrification
Molecular motion in condensed matter can be represented by a
Fourier seriesIn mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...
whose physical interpretation consists of a
superpositionSuperposition can refer to:* The superposition principle in physics, mathematics, and engineering, describes the overlapping of waves. Particular applications include :** Quantum superposition, in quantum physics** Superposition theorem, in electronics....
of
longitudinalLongitudinal may refer to:* Longitudinal engine, an internal combustion engine in which the crankshaft is oriented along the long axis of the vehicle, front to back...
and
transverseTransverse may refer to:*Transversality, a concept related to the intersection of manifolds in topology*Transverse City, an album by Warren Zevon...
wavesThe WAVES were a World War II-era division of the U.S. Navy that consisted entirely of women. The name of this group is an acronym for "Women Accepted for Volunteer Emergency Service" ; the word "emergency" implied that the acceptance of women was due to the unusual circumstances of the war and...
of atomic displacement with varying directions and wavelengths. In monatomic systems, we call these waves:
densityThe mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
fluctuations. (In polyatomic systems, they may also include
compositionComposition may refer to:* Composition , in which one assumes that a whole has a property solely because its various parts have that property* Compounding is also known as composition in linguistic literature* in computer science...
al fluctuations.)
Thus, thermal motion in liquids can be decomposed into elementary
longitudinal vibrationsLongitudinal waves, as known as "l-waves", are waves that have the same direction of vibration as their direction of travel, which means that the movement of the medium is in the same direction as or the opposite direction to the motion of the wave. Mechanical longitudinal waves have been also...
(or acoustic
phononIn physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...
s) while
transverse vibrationsA transverse wave is a moving wave that consists of oscillations occurring perpendicular to the direction of energy transfer...
(or shear waves) were originally described only in
elasticIn physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....
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
solidSolid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...
deforms locally while retaining its
rigidityRigid or rigidity may refer to:*Stiffness, the property of a solid body to resist deformation, which is sometimes referred to as rigidity*Structural rigidity, a mathematical theory of the stiffness of ensembles of rigid objects connected by hinges...
-- while a
liquidLiquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...
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.
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
liquidLiquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...
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 liquidIn condensed matter physics and physical chemistry, the terms viscous liquid, supercooled liquid, and glassforming liquid are often used interchangeably to designate liquids that are at the same time highly viscous , supercooled, and able to form a glass.- Working points in glass processing :The...
. Thus we see the intimate correlation between transverse acoustic phonons (or shear waves) and the onset of
rigidityRigid or rigidity may refer to:*Stiffness, the property of a solid body to resist deformation, which is sometimes referred to as rigidity*Structural rigidity, a mathematical theory of the stiffness of ensembles of rigid objects connected by hinges...
upon
vitrificationVitrification is the transformation of a substance into a glass. Usually, it is achieved by rapidly cooling a liquid through the glass transition. Certain chemical reactions also result in glasses...
, as described by Bartenev in his mechanical description of the vitrification process.
The velocities of longitudinal acoustic phonons in condensed matter are directly responsible for the
thermal conductivityIn physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....
which levels out temperature differentials between
compressed and
expandedThermal expansion is the tendency of matter to change in volume in response to a change in temperature.When a substance is heated, its particles begin moving more and thus usually maintain a greater average separation. Materials which contract with increasing temperature are rare; this effect is...
volume elements. Kittel proposed that the behavior of glasses is interpreted in terms of an approximately constant "
mean free pathIn physics, the mean free path is the average distance covered by a moving particle between successive impacts which modify its direction or energy or other particle properties.-Derivation:...
" for lattice phonons, and that the value of the mean free path is of the
order of magnitudeAn order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...
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.
It has often been suggested that
heat transportHeat transport may refer to:* Heat* Heat pipe* Heat conduction* Convection* Coolant* Cogeneration...
in
dielectricA dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...
solids occurs through elastic vibrations of the lattice, and that this transport is limited by elastic
scatteringScattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
of acoustic phonons by lattice defects (e.g. randomly spaced vacancies).
These predictions were confirmed by experiments on commercial
glassesGlasses, also known as eyeglasses , spectacles or simply specs , are frames bearing lenses worn in front of the eyes. They are normally used for vision correction or eye protection. Safety glasses are a kind of eye protection against flying debris or against visible and near visible light or...
and glass
ceramicCeramic engineering is the science and technology of creating objects from inorganic, non-metallic materials. This is done either by the action of heat, or at lower temperatures using precipitation reactions from high purity chemical solutions...
s, where mean free paths were apparently limited by "internal boundary scattering" to length scales of 10 - 100 micrometers.
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.
Electronic structure
The influence of
thermalA thermal column is a column of rising air in the lower altitudes of the Earth's atmosphere. Thermals are created by the uneven heating of the Earth's surface from solar radiation, and are an example of convection. The sun warms the ground, which in turn warms the air directly above it...
phononIn physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...
s and their interaction with
electronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
ic structure is a topic which was appropriately introduced in a discussion of the
resistanceThe electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
of liquid metals.
Lindemann's theory of melting is referenced, and it is suggested that the drop in
conductivityElectrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...
in going from the
crystalA crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
line to the liquid state is due to the increased
scatteringScattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
of conduction electrons as a result of the increased
amplitudeAmplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
of atomic
vibrationVibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.Vibration is occasionally "desirable"...
. Such theories of localization have been applied to transport in metallic glasses, where the
mean free pathIn physics, the mean free path is the average distance covered by a moving particle between successive impacts which modify its direction or energy or other particle properties.-Derivation:...
of the electrons is very small (on the order of the interatomic spacing).
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 bondMetallic bonding is the electrostatic attractive forces between the delocalized electrons, called conduction electrons, gathered in an "electron sea", and the positively charged metal ions...
.
Other work indicates that the
mobilityMobility may refer to:* Mobility * "Mobiliy" , a song by Moby* Mobility * Mobility , the ability of military units or weapon systems to move to an objective-See also:* Academic mobility* Apprentices mobility...
of localized
electronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
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 models 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
solidSolid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...
s.
Thus, if the electrical conductivity is low, the
mean free pathIn physics, the mean free path is the average distance covered by a moving particle between successive impacts which modify its direction or energy or other particle properties.-Derivation:...
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
disorderDisorder may refer to :* Chaos, unpredictability and in the metaphysical sense, it is the opposite of law and order* Civil disorder, one or more forms of disturbance caused by a group of people...
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.
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.
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
polymorphicPolymorphism in materials science is the ability of a solid material to exist in more than one form or crystal structure. Polymorphism can potentially be found in any crystalline material including polymers, minerals, and metals, and is related to allotropy, which refers to chemical elements...
forms and a high degree of bonding
anisotropyAnisotropy is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions. It can be defined as a difference, when measured along different axes, in a material's physical or mechanical properties An example of anisotropy is the light...
. Crystallization becomes more unlikely as bonding anisotropy is increased from isotropic metallic to anisotropic metallic to covalent bonding, thus suggesting a relationship between the group number in the
periodic tableThe periodic table of the chemical elements is a tabular display of the 118 known chemical elements organized by selected properties of their atomic structures. Elements are presented by increasing atomic number, the number of protons in an atom's atomic nucleus...
and the glass forming ability in
elementalAn elemental is a mythological being first appearing in the alchemical works of Paracelsus in the 16th century. Traditionally, there are four types:*gnomes, earth elementals*undines , water elementals*sylphs, air elementals...
solidSolid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...
s.
Further reading
- Handbooks
- Handbook of Glass Data ( Elsevier, 1993 )
- Engineered Materials Handbook ( ASM International, 2005 )
External links