1. INTRODUCTORY REMARKS
2. SOLIDIFICATION OF EUTECTIC MIXTURES
3. SOME PROPERTIES OF METALS
4. SOME PROPERTIES OF ICE
5. SOME PROPERTIES OF GLASS
6. APPLICATION OF MATERIALS SCIENCE TO CRYONICS

I. INTRODUCTORY REMARKS

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II. SOLIDIFICATION OF EUTECTIC MIXTURES

Mixtures of some metals, such as copper & nickel, are completely soluble in both liquid and solid states for all concentrations of both metals. Copper & nickel have the same crystal structure (FCC) and have nearly the same atomic radii. The solid formed by cooling can have any proportion of copper & nickel. Such completely miscible mixtures of metals are called isomorphous.

Eutectic Phase Diagram of Tin & Lead

By contrast, a mixture of lead (Pb) & tin (Sn) is eutectic because these metals are only partially soluble in each other when in the solid state. Lead & tin have different crystal structures (FCC versus BCT) and lead atoms are much larger. No more than 19.2% by weight of solid tin can dissolve in solid lead and no more than 2.5% of solid lead can dissolve in solid tin. The solid lead-tin alloy thus consists of a mixture of two solid phases, one consisting of a lead-rich solid (alpha, α-phase) that can dissolve in a maximum of 19.2 wt% tin (Sn) at 183ºC (more at higher temperature), and one consisting of a tin-rich (beta, β-phase) that can dissolve in a maximum of 2.5 wt% lead (Pb) at 183ºC (more at higher temperature).

For example, above 260ºC 40 wt%; tin in a tin-lead mixture will be a completely intermixed liquid. The liquidus line separates pure liquid phase from phases which can be mixtures of liquid and solid. The solidus line separates mixtures of liquid and solid from pure solid (pure α-phase or pure β-phase at extremes of concentration). Just below the liquidus line 40 wt% tin in a tin-lead mixture will have some solid α-phase tin-lead (12 wt% tin proeutectic) and the rest a mixture of tin-lead liquid. As temperature drops, the amount of solid α-phase tin-lead in the liquid-solid mixture increases, and the percentage of tin in the α-phase increases until the temperature reaches 183ºC and the mixture becomes completely solid — partially α-phase (19.2 wt% tin) and partially β-phase (97.5 wt% tin) tin-lead mixture, along with some proeutectic solid. A solvus line delineates temperatures below which tin and lead are completely immiscible. Solidification in the alpha proeutectic region consists of layered growth of solid nodules — with each layer containing a higher concentration of tin. This layering of increasing concentrations of tin is called coring. Faster cooling results in reduced coring.

The word eutectic is derived from Greek roots meaning "easily melted". A eutectic mixture has a eutectic composition for which complete liquification occurs at a lower temperature (the eutectic temperature) than for any other composition. For lead & tin the eutectic composition is 61.9 wt% tin and the eutectic temperature is 183ºC — which makes this mixture useful as solder. At 183ºC, compositions of greater than 61.9 wt% tin result in precipitation of a tin-rich solid in the liquid mixture, whereas compositions of less than 61.9 wt% tin result in precipitation of lead-rich solid.

Surprisingly, the principles of eutectics observed with mixtures of metals are much the same when applied to other material mixtures that crystallize, such as glycerol, water and salt — despite the differences between metallic bonding, hydrogen bonding and ionic crystallization. Although a eutectic mixture of salt & water resembles a eutectic mixture of metals in having a eutectic temperature & composition, the solid phases are pure crystals of salt & water rather than composites as with metals — and there is no coring.

Eutectic Phase Diagram of water & NaCl

Eutectic mixtures of salt and water are of critical relevance in cryonics when freezing occurs. The eutectic composition of sodium chloride (NaCl) in water is about 23.3 wt% NaCl and the eutectic temperature is about −21.1ºC. Thus, at concentrations greater than 23.3 wt% NaCl, solid salt will precipitate from salt water at temperatures near and above −21.1ºC. At concentrations less than 23.3 wt% NaCl, some of the water will solidify (freeze) and leave a more highly concentrated salt solution. The latter is what typically occurs with freezing in a cryonics patient (or meat in a freezer) because an isotonic solution of NaCl (ie, as solution that matches the salt concentration of body tissues) is about 0.9%. As solid water precipitates (freezes), the salt concentration in the remaining fluid increases until the eutectic composition of 23.3 wt% NaCl is reached and the final solidification of the eutectic mixture occurs at −21.1ºC. (Freezer temperatures are typically −18ºC to −22ºC).

But unlike the lead-tin eutectic diagram, there is no solidus line on either end for water and NaCl — and there is no concentration of salt solution in which pure NaCl will precipitate. Below the liquidus line on the left there is a mixture of saltwater and pure ice. Ocean water (which is about 3.5 wt% salt, mostly NaCl) has a freezing temperature of −1.91ºC, which is to say at −1.91ºC ice begins to crystallize amidst a slush of increasingly concentrated salty water. In the freezing of water as pure water-ice, the water molecules not only force-away salt ions, but dissolved gasses — which is why gas bubbles are typically seen in ice cubes.

In 1953 the cryobiologist James Lovelock showed how damaging high salt concentrations can be to cells during the freezing process. The first theories of freezing damage were based on Lovelocks's observations. Damage due to cell breakage and hydrolysis by concentrated salt solutions in the −15ºC to −20ºC temperature range can have devastating consequences for the tissues of cryonics patients. Moreover, sodium chloride is not the only salt in human tissue. Calcium chloride has a eutectic composition of 40 wt% and a eutectic temperature of −41ºC — meaning that salt damage and hydrolysis can occur well below −21ºC.

One can speak of the eutectic temperature and composition of a mixture of water, glycerol and NaCl. The eutectic composition is 73% glycerol, 5% NaCl and the eutectic temperature is −64ºC. But eutectic temperature describes freezing temperature under equilibrium conditions. With rapid cooling solidification will occur at lower temperatures.

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III. SOME PROPERTIES OF METALS

Metals solidify as crystals. A pure metal will typically crystallize at a temperature which is lower than the temperature at which it will melt. The difference between melting and minimum solidification temperature is referred to as the maximum undercooling. Maximum undercooling is only 80ºC for lead, but is 330ºC for platinum. The undercooling phenomenon is due to the way pure metals crystallize.

Critical Radius Size

In order to crystallize, atoms of a pure metal must first form a tiny crystalline nucleus. When a solid nucleus forms the atoms in the liquid surrounding it tend to make the nucleus dissolve back into the liquid — a phenomenon related to the surface energy of the nucleus. Fusion into a solid crystal releases heat — heat which can cause adjacent atoms in the nucleus to dissolve. The high fusion energy of platinum contributes significantly to the high solidification temperature and maximum undercooling of that metal.

A large crystal, however, is not so vulnerable to dissolution at the surface. The energy factors favoring dissolution vary in proportion to the nucleus surface area, whereas the energy factors favoring nucleus growth vary in proportion to volume. Surface area varies with the square of the radius, whereas volume varies with the cube of the radius. For each metal and at each temperature there is a critical radius size above which a nucleus will tend grow and below which it will tend to dissolve. As temperature becomes lower, the critical nucleus radius becomes smaller and easier to achieve. (For more information on water nucleation, see Freezing versus Melting Temperature).

Nucleation and Grain Growth

Crystallization of pure metals is described as homogenous nucleation because a pure compound is homogenous. Crystallization may occur with much less undercooling if a higher melting-point metal is added that has similar crystal structure to the original metal, but which is insoluble at the melting temperature of the original metal. Crystal growth around these insoluble nuclei is referred to as heterogenous nucleation.

When a metal solidifies, many crystalline nuclei form and grow simultaneously until the crystals have absorbed all of the remaining liquid atoms. As a result, a block of metal is described as polycrystalline — like a sugar cube composed of many crystal grains (although for a metal the grains are very much smaller). Grain boundaries have surface tension — the same energy that makes water bead into a spherical shape so as to minimize surface area. Fewer crystals mean less total surface energy. For this reason rewarming of a metal results in recrystallization of the smaller grains into larger grains before the melting temperature of the metal is reached.

Predominant Crystal Forms of Pure Metals

The predominant crystal forms for pure metals are described as Face-Centered Cubic (FCC), Body-Centered Cubic (BCC) and Hexagonal Close-Packed (HCP). [Tin has a Body-Centered Tetragonal (BCT) crystal at freezing temperature.] FCC and BCC crystals have cubic unit cells, but HCP unit cells are hexagonal on the plane of the base and have rectangular shapes on the vertical sides. The width of these rectangles (the a-axis size) is less than the height (the c-axis size). Atoms in BCC crystals are surrounded by 8 nearest-neighbor atoms (have coordination number 8), whereas atoms in FCC and HCP crystals have 12 nearest neighbors. Atoms in FCC and HCP crystals are thus more tightly packed than in BCC — are more dense.

Hexagonal Closed-Packed

The crystal structure of a metal has a significant impact on the metal's material properties. Gold and lead are easily plastically deformed because their FCC crystal structure has many slip planes — planes along which displacements can slide. HCP metals such as titanium and cobalt have fewer slip planes and are thus less easily plastically deformed. Iron has a BCC crystal structure at room temperature, but an FCC structure at temperatures closer to 1000ºC (iron melts at 1539ºC).

The ease with which a metal can plastically deform is quantified in metallurgy by ductility, defined as

      fracture length - original length
      ----------------------------------------
                   original length

The conventional concepts of ductile & malleable are both manifestations of metallurgical ductility. The opposite of ductility is brittleness.

Stress-Strain Curve

Other notable material properties of metals are stiffness, yield strength and hardness. Like ductility/brittleness, these properties are all related to the way a metal responds to stress. Stress (force per unit area) can result in strain (deformation). The stress of a person standing on a diving board results in the strain seen in the bending of the board. Deformation can be either elastic or plastic.

For small amounts of stress a metal is completely elastic — stiffness is another term for modulus of elasticity (Young's modulus). Stiffness is due to the resistance to separation between atoms — the interatomic bonding force. Stiffness diminishes with heating and increases with cooling. (The coefficient of thermal expansion — the amount by which length or volume increase with increasing temperature — is similarly a function of interatomic bonding energy.)

For large amounts of applied stress a metal will deform permanently (plastically) rather than elastically return to the original shape. The amount of stress just beyond the threshold of plastic deformation is called yield strength. Yield strength varies inversely with grain size — smaller grains mean greater yield strength.

When a metal plastically deforms, the manner in which it does so is by the formation and propagation of flaws (dislocations) within the crystal grains. Grain boundaries resist crystal propagation of dislocations, which is why smaller grain size increases yield strength. The dislocations themselves resist further dislocation — a phenomenon known as strain hardening. When a blacksmith pounds on a horseshoe, he or she is making the horseshoe harder by increasing the number of dislocations and reducing grain size.

With enough stress a metal will acquire as many dislocations as it can handle without weakening — a level of stress described as ultimate tensile strength. Ultimate tensile strength is directly related to the hardness of the material. (Diamond is the hardest substance.) With further application of stress, the dislocations in the metal merge to form tiny fissures which grow into larger cracks until the metal finally fractures.

In metals, mobile electrons function both to conduct electricity and to conduct heat. At a given temperature the thermal and electrical conductivities are proportional, but raising temperature increases thermal conductivity while decreasing electrical conductivity. These concepts are expressed quantitatively as the Wiedemann-Franz Law (where the constant of proportionality, L, is the Lorenz number and T is temperature):

       thermal conductivity
     -----------------------------  =  LT
     electrical conductivity
      
  

Metals are the best conductors of heat, as can be seen from the following table, where thermal conductivity is expressed as Watts per Kelvin-Meters [W/(K^.m)]. For fibrous or porous material, heat transfer occurs by a combination of conduction, convection and thermal radiation — while being quoted as "effective thermal conductivity".

Note that, for example, the thermal conductivity of perlite is temperature dependent.

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IV. SOME PROPERTIES OF ICE

Water molecule

A water molecule is often visualized as V-shaped 2-dimensional object, with two hydrogens attached to an oxygen at a 104.5º angle. Water molecules can also be visualized as 3-dimensional tetrahedrons — 4-cornered, objects with a triangle on four sides like a pyramid, with the oxygen atom in the middle. Two of the corners are hydrogen atoms and the other two corners are "lone-pairs" of electrons that complete the electron octet of the sp³ hybrid orbitals. A perfect tetrahedron would have 109.5º angles between each pair of corners, but the higher electronegativity of the lone-pairs forces them apart and forces the hydrogen atoms closer together. Most liquids are held together by van der Waals forces between the molecules. But water is primarily held together by hydrogen-bonds — bonds between hydrogens and lone-pairs that are ten times stronger than van der Waals forces, but only a tenth as strong as the covalent bond holding hydrogen to oxygen. Hydrogen bonding accounts for the high heat capacity and high surface tension of water. (At one calorie per gram per degree Celcius, water has over ten times the specific heat capacity of copper.)

In ice, four oxygen atoms form a tetrahedron with hydrogen atoms lying close to the lines between the oxygens. Because water molecules in ice are forced into the 109.5º angles of the tetrahedral crystal structure, they cannot pack as tightly as can liquid water that is slightly warmer. Water has a maximum density at about 4ºC (3.98ºC to be more precise) because at that temperature the flexibility of hydrogen bonds combined with the low molecular mobility allows for the closest packing of the water molecules. As temperature approaches the freezing point, the more rigid tetrahedral arrangement is increasingly forced upon the molecules.

Ice in a lake can only freeze after all of the water in the lake has cooled to at least 4ºC because the heavier water falls to the bottom. Between 4ºC and 0ºC the lighter, colder water stays on the surface where it can be further cooled by cold air to freezing while "floating" on the heavier (most dense) water that is closer to 4ºC. The freezing of water is accompanied by an approximate 9% increase in volume. The fact that the atmospheric pressure forms of ice are less dense than water (0.917 grams/cm³) means that ice stays on the surface of lakes — allowing fish to survive. When ice floats in water 10% of its volume will be above the surface (more if the ice contains air bubbles). Water at 0ºC has 15% of the molecules hydrogen-bonded, whereas ice at 0ºC has nearly 100% of the molecules hydrogen-bonded. Cooling of one gram of water 1ºC requires removal of one calorie of heat, but freezing of one gram of water at 0ºC (no temperature change) requires removal of 80 calories of heat (called the latent heat of fusion because the heat flow is "concealed" by the absence of temperature change). Ocean water freezes at −1.7ºC, with about a fifth of the salt sequestered in pockets between the ice crystals.

The expansion of water upon freezing is what makes water pipes burst in wintertime. Water easily seeps into tiny cracks in rocks, which is why seasonal cycles of freezing and thawing can eventually reduce great boulders to rubble.

Forms of Ice at Varying Temperature and Pressure

There are more solid forms of water than of any other known substance. Below about 2,700 atmospheres of pressure crystalline ice is known as ice I, but above 2,700 atmospheres there are at least 13 other crystal forms (designed by roman numerals II to XIV thus far). Ice I exists in two crystal forms: hexagonal ice (ice Ih) and cubic ice (ice Ic). Cubic ice can be formed by deposition of water vapor onto a solid surface in the temperature range of −140ºC to −120ºC. Below −140ºC the water vapor molecules do not have enough energy to organize themselves into crystals and therefore lie where they land on the surface in an amorphous (vitrified) form. Hexagonal ice nuclei are slightly larger than cubic ice nuclei, which means that cubic ice is lost to hexagonal ice under conditions of crystal growth [JOURNAL OF CRYSTAL GROWTH; Vigier,G; 84:309-315 (1987)]. Hexagonal ice does not transform into a cubic or amorphous form when cooled. Therefore, only hexagonal ice is relevant to the cooling of a cryonics patient at atmospheric pressure. (For more on the forms of ice under pressure, see my essay High Pressure Cryonics.)

The fact that ice has a hexagonal crystal structure might not be surprising in light of the fact that snowflakes are hexagonal. The hexagonal crystal of ice resembles the Hexagonal Close-Packed (HCP) structure of metals such as cobalt, but is much less dense — the coordination number (number of nearest neighbors) is 4 rather than the 12 of HCP. Four oxygen atoms form a tetrahedron in the ice lattice and hydrogen atoms lie close to these tetrahedral lines.

Graphite Crystal	Ice Crystal

Cubic ice has a crystal structure like that of diamond, whereas hexagonal ice is more like graphite. Like hexagonal ice, graphite crystal hexagons form a-axis layers, but the layers are flattened in graphite, allowing them to slip more easily. Both cubic and hexagonal ice have cyclohexane-like rings of oxygen atoms in a "chair" conformation on the basal layer. But cyclohexane-like rings formed between layers has a "boat" conformation for hexagonal ice as distinct from the more symmetric "chair" conformation in cubic ice.

Similar to metals, water freezes by a process of nucleation and nucleus-growth into a polycrystalline material composed of many grains. At cooling rates of a few degrees Celsius per minute, relatively large ice grains are formed which do not result in intracellular mechanical damage in tissues (although salt damage is maximized). At cooling rates higher than 10ºC per minute, osmotic effects lessen, salt damage is reduced, but the small grains formed intracellularly cause mechanical damage. The use of cryoprotectants can reduce both the salt damage and the damage due to intracellular ice.

Although ice has more than twice the thermal conductivity of water, ice is nonetheless a relatively poor conductor of heat (good insulator), which makes it a good building material for igloos.

Like polycrystalline metals, ice deforms by dislocation — preferentially along slip planes. In the temperature range of −3ºC to −40ºC ice is perfectly elastic for a maximum stress of 10 atmospheres applied no faster than 5 atmospheres per second. The rate of pressure application is noteworthy. Although the bonds between layers are stronger in hexagonal ice than they are in graphite, ice can nonetheless deform plastically under sustained pressure by the sliding of layers — like cards in a deck of cards. This kind of deformation by sustained stress maintained over long periods is known as creep — and it partly explains glacier movement. Hexagonal ice ceases to show any plastic properties below -70ºC. Like other brittle materials low temperature ice can show great resistance to stress or impact up to a certain threshold and then shatter — with no intermediate plastic deformation.

Linear Expansion of Ice

Cooling or heating a material can create stresses leading to fracture, ie, thermal shock. Thermal shock resistance typically varies directly with fracture strength & thermal conductivity while it varies inversely with stiffness & thermal expansivity. Vulnerability to thermal shock is higher for materials like ice which have crystals that are not symmetric in all directions (anisotropic) because thermal expansion is dependent upon crystallographic dimensions. For ice, thermal conductivity increases exponentially by about 5 times when cooling from 0ºC to liquid nitrogen temperature, whereas the coefficient of linear expansion decreases linearly to a fifth of the value it has at 0ºC. The combination of these factors should more than compensate for increased stiffness & brittleness with declining temperature. For freezing solid blocks of ice it would seem that the rate of cooling could accelerate with declining temperature with reduced risk of thermal shock. Cryonics patients are not, however, solid blocks of ices — even though the human brain is about 85% water — because water has been replaced by cryoprotectant fluid.

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V. SOME PROPERTIES OF GLASS

The word ceramic derives from the Greek roots for "burnt stuff" — in reference to the hardening of clays upon high-temperature heat-treatment. A more modern definition might refer to solid inorganic, non-metallic compounds which are not polymers — including most glasses. But even metals can form glasses if cooled quickly enough.

Glass Transition (Vitrification)

In molecular terms, glasses are materials that form amorphous rather than crystalline solids upon cooling (ie, materials that vitrify). Although there are many plausible explanations for why materials vitrify rather than crystallize, there is no general rule. In fact, the reason why vitrification occurs may be different for different materials — including a combination of factors such as viscosity, heat of fusion, mixed bonding type, hydrogen-bonding, colligative effects and the effect of cooling rate. For most materials that vitrify, cooling rate is critical — meaning that if cooling rate is too slow the material will crystallize rather than vitrify.

At glass transition temperature (T_g) there is a change in many physical properties (as with freezing), but the changes occur over a temperature range with the formation of a glassy solid rather than the crystal formed at the more precise melting (fusion) temperature (T_m). (For more details on the process of vitrification, see my essays Vitrification in Cryonics and Physical Parameters of Cooling in Cryonics.)

Pure silicon dioxide (silica) will form a crystal if cooled slowly. But silica is extremely viscous — about a half-billion times more viscous at its melting temperature than water at its melting temperature. Such high viscosity is a strong impediment to the formation and growth of crystal nuclei. Silica therefore has a strong tendency to supercool and to vitrify. Upon warming, however, before melting vitreous silica can easily transform into crystalline silica — a process known as devitrification.

(It should be noted that viscosity cannot be the only explanation for vitrification. The viscosity of 60 wt% sucrose solution declines as sucrose concentration is either increased or decreased. A 50-to-60 wt% sucrose solution has the same viscosity as a 60-to-80 wt% sucrose solution, ie, viscosity versus wt% forms an inverted-U curve. Yet a 60-to-80 wt% sucrose solution can vitrify more readily than a 50-to-60 wt% sucrose solution.)

Crystalline and Glassy Silica

The chemical bonding in crystalline silica shows the ordered regularity of a lattice, whereas vitreous silica has more the appearance of a random network. Although the chemical bonding in silica is mainly covalent, it has a character that is somewhat ionic. Materials with mixed bonding type are more viscous and more likely to form random networks than to form regular crystals. The irregularity of the bonding is a partial explanation for the fact that the temperature of vitrification (T_g) is less precise than the temperature of crystallization because when bonding is uniform the temperature at which the bonds will break will be more precise. The fact that nucleation or vitrification is dependent on cooling rate also accounts for the imprecision of T_g. For silica glasses, T_g can vary as much as 100 to 200ºC depending on the cooling rate (vitrification occurs at higher temperatures for faster cooling.) Near T_g the probability of crystal growth and nucleation increases very rapidly, so cooling rate near T_g is particularly critical in determining whether crystallization or vitrification occurs.

Sodium in Silica

Sodium Bridge

The addition of 25% sodium oxide (soda,Na₂O) to silica reduces the viscosity and lowers the melting point from 1,723ºC to 850ºC. Sodium oxide also increases the tendency of silicon dioxide to form networks rather than crystals. Sodium-oxygen bridges may interrupt the regular silicon-oxygen bonding and/or sodium ions may intersperse among the silica molecules to prevent the formation of regular crystals (a colligative effect). But the resulting glass is water-soluble. If calcium oxide (lime, CaO) is added as a stabilizer, the glass becomes water-insoluble. Most glass used for windows and drinking-vessels is soda-lime glass — made from 75% silica, 15% soda and 10% lime (although 1 wt% aluminum oxide is often added as well).

Ice formation is frequently prevented by using compounds having hydroxyl (−OH) groups, such as ethylene glycol (car anti-freeze), propylene glycol (ice cream anti-freeze) or glycerol. Such cryoprotectants probably vitrify by their viscosity as well as by their ability to interrupt the ice lattice by hydrogen-bonding with the water molecules. Glycerol is by far the most viscous of these three cryoprotectants. The high viscosity & larger molecular size of glycerol may have much to do with why it permeates the most slowly into tissues. In cryonics, glycerol has typically been assisted in reducing freezing by the colligative effects of a carrier solution.

THE MERCK INDEX gives pure glycerol a melting point of 17.8ºC, but the profound tendency of glycerol to supercool is described by saying that it "solidifies after prolonged cooling at 0º forming a shiny orthorhombic crystal" — meaning that the freezing point is effectively lower than the melting point. A 30% (weight/weight) mixture of glycerol and water freezes at −9.5ºC whereas an 80% mixture freezes at −20ºC. The eutectic temperature and composition of glycerol is about −46ºC for 67 wt% glycerol. This is of significance because compositions near the eutectic are the easiest to vitrify because the liquid is the least supercooled at T_g (T_g for pure glycerol is about −88ºC). (As mentioned above, a glycerol/water mixture which includes 5% sodium chloride will have a eutectic composition of 73% glycerol and a eutectic temperature of −64ºC.)

Salt solutions can vitrify, and they vitrify best at their eutectic concentrations and temperatures. Nitrates vitrify better than chlorides, and magnesium (Mg²⁺) vitrify better than salts of zinc (Zn²⁺) [THE JOURNAL OF CHEMICAL PHYSICS; Angell,CA; 52(1):1058-1068 (1970)].

Sugar phase diagram	Cryoprotectant phase diagram

Mixtures of sugar and water can solidify either by crystallization or by vitrification. At higher temperatures above a certain sugar concentration, sugar becomes insoluble in water (the solubility curve in the sugar phase diagram), the eutectic temperature (T_e) being the lowest temperature at which a liquid water/sugar mixture can exist in equilibrium — or the highest temperature at which water and sugar can freeze together. But if a sugar-water mixture is cooled rapidly enough (faster than the critical cooling rate), increasing viscosity impedes the ability of the sugar-water mixture to crystallize, and the mixture will vitrify at a glass transition temperature T_g. (Pure water is assumed to vitrify at −135ºC, which would require a cooling rate of 3 million ºC per second.) If cooling occurs slower than at the critical cooling rate, frozen pure water ice may form, leaving a more concentrated unfrozen sugar-water liquid. The more concentrated unfrozen sugar-water liquid will have a new, higher glass transition temperature T_g' [THERMOCHEMICA ACTA; Goff,HD; 399(1-2):43-55 (2003)]. T_g' will be a maximum (T_g'_max) at the highest freeze-concentrated liquid concentration (c_g'_max). For the vitrification solutions used in cryonics, T_g is typically −123ºC and T_g' is about −110ºC. For a poorly perfused cryonics patient that has partial freezing, slow cooling should begin above −110ºC to minimize cracking from thermal stress.

A number of physical properties of glassy materials show a marked change at T_g. The increase in viscosity to 3x10¹⁴ (300 trillion) Poise (the strain point) has dubiously been used as the defining characteristic of T_g. (The strain point is the limit of viscosity beyond which there is no deformation before fracture in response to applied stress.) Heat capacity decreases somewhat linearly above and below T_g, but decreases markedly near T_g. This is important both because it makes T_g easier for scientists to determine by using a Differential Scanning Calorimeter (DSC) and because below T_g the same amount of cooling will result in a significantly greater temperature drop. There is a reduction in specific volume (volume per unit mass) at T_g, but this change is very slight compared to the change in heat capacity.

There is, however, another property that decreases markedly at T_g — the coefficient of thermal expansion. Below T_g, however, the decline in thermal expansivity with temperature for glasses is less than the decline above T_g. Glucose, as a notable example, shows a fourfold decrease in thermal expansivity at its 27ºC glass transition temperature. Glasses typically have lower thermal expansivity than metals, which is why it is easier to remove a metal lid from a glass jar by warming it. (Silica has the lowest coefficient of thermal expansion of any known substance.)

The rapid change of thermal expansivity at T_g and the imprecise temperature of T_g may create stresses within a vitrifying material. The decreasing volume associated with cooling and the fact that the exterior surface cools before the interior means that the liquid interior may try to contract more than the rigid exterior will allow. A vitrified solid will have internal stresses in proportion to the rate of cooling. For most commercial glass this has little consequence, but in optical glass the result can be birefringence (different index of refraction in different directions). To eliminate birefringence, optical glass is typically annealed, ie, heated slowly above the strain point (3x10¹⁴ Poise) to the annealing point (10¹³ Poise) where atomic diffusion is rapid enough to eliminate internal stress, but not so rapid as to result in devitrification. Then the glass is slowly recooled to the strain point and can be cooled more quickly below the strain point. (In metallurgy, annealling can reduced cored structure, reduce internal stress and increase grain size.)

In non-optical glasses used in applications where resistance to cracking is more important than absence of internal stress, compressive stresses are intentionally introduced by a process called tempering. The glass is heated above the strain point and then very rapidly cooled. The compression at the surface resulting from the delayed shrinking of the interior can increase the strength of the glass considerably.

Thermal conductivity for glass is much less than for metal. Thermal conductivity for glass (vitreous silicon dioxide) is one tenth the thermal conductivity of quartz (crystalline silicon dioxide). Non-metallic solids transfer heat by lattice vibrations (phonons: quanta of lattice vibrations), rather than by any net material motion (metals transfer heat by mobile electrons).

In glassy materials thermal conductivity drops as temperature decreases — the opposite to what happens in crystalline materials. This low and declining thermal conductivity could have the unfortunate consequence of creating internal stresses in a vitrified cryonics patient subject to nonuniform cooling (as when the upper surface is being cooled more rapidly than the lower surface). Internal stresses are of concern in glassy materials because glasses cannot plastically deform, despite their high elasticity (low stiffness). (Note the elasticity of fiber optic cables.) A glass subject to stress (internal or external) will elastically deform up to the point of fracture. A glass marble will either bounce or shatter — it will not plastically deform. Unlike polycrystalline materials, a crack in glass travels through a single homogenous phase, unimpeded by grain boundaries. An imperfectly vitrified glass is even more vulnerable to cracking, however, because of the mismatch of expansion coefficients between the glass and the crystal.

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VI. APPLICATION OF MATERIALS SCIENCE TO CRYONICS

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