8 Thermal Properties This chapter considers composites for thermal applications,including the basic principles related to the thermal behavior of materials.The applications include thermal conduction,heat dissipation,thermal insulation,heat retention,heat stor- age,rewritable optical discs,and shape-memory actuation. 8.1 Thermal Expansion Upon heating,the length of a solid typically increases.Upon cooling,its length typically decreases.This phenomenon is known as thermal expansion. The coefficient of thermal expansion(CTE,also abbreviated to a)is defined as a=(1/Lo)(△L/△T), (8.1) where Lo is the original length and L is the length at temperature T.In other words, a is the fractional change in length per unit change in temperature(i.e.,strain per unit change in temperature).Equation 8.1 can be rewritten as △L/L。=AT. (8.2) Thermal expansion is reversible,so thermal contraction occurs upon cooling,and the extent of thermal contraction is also governed by a. The change in dimensions that occurs upon changing the temperature may be undesirable when the dimensional change results in thermal stress;i.e.,internal stress associated with the fact that the dimensions are not the same as those the component should have when it is not constrained.An example concerns a joint between two components that exhibit different thermal expansion coefficients. The joint is created at a given temperature.Subsequent to the bonding,the joint is heated or cooled.Upon heating or cooling,the bonding constrains the dimensions of both components,thus causing both components to be unable to attain the dimensions that they would do if they were not bonded.When the thermal stress is too high,deformation such as warpage may occur.Debonding can even occur. If thermal cycling occurs,the thermal stress is cycled,thus resulting in thermal fatigue when the number of thermal cycles is sufficiently high. Thermal expansion can be advantageously used to obtain a tight fit between two components.For example,a pipe(preferably one with a rather high coefficient of 277
8 Thermal Properties This chapter considers composites for thermal applications, including the basic principles related to the thermal behavior of materials. The applications include thermal conduction, heat dissipation, thermal insulation, heat retention, heat storage, rewritable optical discs, and shape-memory actuation. 8.1 Thermal Expansion Upon heating, the length of a solid typically increases. Upon cooling, its length typically decreases. This phenomenon is known as thermal expansion. The coefficient of thermal expansion (CTE, also abbreviated to α) is defined as α = (1/Lo)(ΔL/ΔT) , (8.1) where Lo is the original length and L is the length at temperature T. In other words, α is the fractional change in length per unit change in temperature (i.e., strain per unit change in temperature). Equation 8.1 can be rewritten as ΔL/Lo = αΔT . (8.2) Thermal expansion is reversible, so thermal contraction occurs upon cooling, and the extent of thermal contraction is also governed by α. The change in dimensions that occurs upon changing the temperature may be undesirable when the dimensional change results in thermal stress; i.e., internal stress associated with the fact that the dimensions are not the same as those the component should have when it is not constrained. An example concerns a joint between two components that exhibit different thermal expansion coefficients. The joint is created at a given temperature. Subsequent to the bonding, the joint is heated or cooled. Upon heating or cooling, the bonding constrains the dimensions of both components, thus causing both components to be unable to attain the dimensions that they would do if they were not bonded. When the thermal stress is too high, deformation such as warpage may occur. Debonding can even occur. If thermal cycling occurs, the thermal stress is cycled, thus resulting in thermal fatigue when the number of thermal cycles is sufficiently high. Thermal expansion can be advantageously used to obtain a tight fit between two components. For example, a pipe (preferably one with a rather high coefficient of 277
278 8 Thermal Properties thermal expansion)is cooled and then,in the cold state,inserted into a larger pipe. Upon subsequent warming of the inner pipe,thermal expansion causes a tight fit between the two pipes. The energy associated with a bond depends on the bond distance(i.e.,the bond length),as shown in Fig.8.1a.The energy is lowest at the equilibrium bond dis- tance.The curve of energy vs.bond distance takes the shape of a trough that is asymmetric.The higher the temperature,the higher is the energy,and the aver- age bond distance(the midpoint of the horizontal line cutting across the energy trough)increases.Thermal expansion stems from the increasing amplitude of thermal vibrations with increasing temperature and the greater ease of outward vibration (bond lengthening)than inward vibration(bond shortening),reflecting the asymmetry in the energy versus bond length curve.This asymmetry causes the distance QR to be greater than the distance QP in Fig.8.1b,so that the outward vi- bration travels a greater distance than the inward vibration at a given temperature. The depth of the energy trough below the energy of zero is the bond energy.At the energy minimum,the bond length is the equilibrium value.A weaker bond has a lower bond energy and corresponds to greater asymmetry in the energy trough. Greater asymmetry means a higher value of the CTE.Hence,weaker bonding tends to give a higher CTE. Table 8.1 shows that the CTE tends to be high for polymers,medium for metals, and low for ceramics.This reflects the weak intermolecular bonding in polymers, Average bond distance Bond distance Equilibrium bond length Energy →Bond length %0 Weak bonding Bond Strong bonding P R energy ← b Inward Outward Figure 8.1.Dependence of the energy between two atoms on the distance between the atoms.a The average bond distance,which occurs at the midpoint of the horizontal line across the energy trough at a given energy,increases with increasing energy.b Comparison of a solid with strong bonding and one with weak bonding.The equilibrium bond length occurs at the minimum energy
278 8 Thermal Properties thermal expansion) is cooled and then, in the cold state, inserted into a larger pipe. Upon subsequent warming of the inner pipe, thermal expansion causes a tight fit between the two pipes. The energy associated with a bond depends on the bond distance (i.e., the bond length), as shown in Fig. 8.1a. The energy is lowest at the equilibrium bond distance. The curve of energy vs. bond distance takes the shape of a trough that is asymmetric. The higher the temperature, the higher is the energy, and the average bond distance (the midpoint of the horizontal line cutting across the energy trough) increases. Thermal expansion stems from the increasing amplitude of thermal vibrations with increasing temperature and the greater ease of outward vibration (bond lengthening) than inward vibration (bond shortening), reflecting the asymmetry in the energy versus bond length curve. This asymmetry causes the distance QR to be greater than the distance QP in Fig. 8.1b, so that the outward vibration travels a greater distance than the inward vibration at a given temperature. The depth of the energy trough below the energy of zero is the bond energy. At the energy minimum, the bond length is the equilibrium value. A weaker bond has a lower bond energy and corresponds to greater asymmetry in the energy trough. Greater asymmetry means a higher value of the CTE. Hence, weaker bonding tends to give a higher CTE. Table 8.1 shows that the CTE tends to be high for polymers, medium for metals, and low for ceramics. This reflects the weak intermolecular bonding in polymers, a b O Energy Bond energy Inward Bond length Outward Equilibrium bond length P Q R Weak bonding Strong bonding Energy Bond distance Average bond distance Figure 8.1. Dependence of the energy between two atoms on the distance between the atoms. a The average bond distance, which occurs at the midpoint of the horizontal line across the energy trough at a given energy, increases with increasing energy. b Comparison of a solid with strong bonding and one with weak bonding. The equilibrium bond length occurs at the minimum energy
8.1 Thermal Expansion 279 Table 8.1.Coefficients of thermal expansion(CTEs)of various materials at 20C Material CTE(10-6/K Rubber 77 Polyvinyl chloride* 52 Leadb 29 Magnesiumb 26 Aluminum 23 Brassb 19 Silverb 18 Stainless steelb 17.3 Copperb 17 Goldb 14 Nickelb 13 Steelb 11.0-13.0 Ironb 11.1 Carbon steelb 10.8 Platinum 9 Tungstenb 4.5 Invar (Fe-Ni36)b 1.2 Concrete 12 Glass 8.5 Gallium arsenide 5.8 Indium phosphide 4.6 Glass,borosilicate 3.3 Quartz(fused) 0.59 Silicon 3 Diamond a Polymer;b metal;ceramic the moderately strong metallic bonding in metals,and the strong ionic/covalent bonding in ceramics.Silicon and diamond are not ceramics,but their CTE values are low because they are covalent network solids.Because stronger bonding tends to give a higher melting temperature,a lower CTE tends to correlate with a higher melting temperature.This is why tungsten,with a very high melting temperature of 3,410C,has a low CTE of 4.5 x 10-6/K.In contrast,magnesium,with a low melting temperature of 660C,has a high CTE of 23.Invar(Fe-Ni36)has an excep- tionally low CTE among metals because of its magnetic character(due to the iron part of the alloy)and the effect of the magnetic moment on the volume.Among ceramics,quartz has a particularly low CTE due to its three-dimensional network of covalent/ionic bonding.Glass has a higher CTE than quartz due to its lower degree of networking. The CTE of a composite can be calculated from those of its components.When the components are placed in series,as illustrated in Fig.8.2a,the change in length ALc of the composite is given by the sum of the changes in the lengths of the components: △Lc=△L1+△L2, (8.3)
8.1 Thermal Expansion 279 Table 8.1. Coefficients of thermal expansion (CTEs) of various materials at 20°C Material CTE (10−6/K) Rubbera 77 Polyvinyl chloridea 52 Leadb 29 Magnesiumb 26 Aluminumb 23 Brassb 19 Silverb 18 Stainless steelb 17.3 Copperb 17 Goldb 14 Nickelb 13 Steelb 11.0–13.0 Ironb 11.1 Carbon steelb 10.8 Platinumb 9 Tungstenb 4.5 Invar (Fe-Ni36)b 1.2 Concretec 12 Glassc 8.5 Gallium arsenidec 5.8 Indium phosphidec 4.6 Glass, borosilicatec 3.3 Quartz (fused)c 0.59 Silicon 3 Diamond 1 a Polymer; b metal; c ceramic the moderately strong metallic bonding in metals, and the strong ionic/covalent bonding in ceramics. Silicon and diamond are not ceramics, but their CTE values are low because they are covalent network solids. Because stronger bonding tends to give a higher melting temperature, a lower CTE tends to correlate with a higher melting temperature. This is why tungsten, with a very high melting temperature of 3,410°C, has a low CTE of 4.5 × 10−6/K. In contrast, magnesium, with a low melting temperature of 660°C, has a high CTE of 23. Invar (Fe-Ni36) has an exceptionally low CTE among metals because of its magnetic character (due to the iron part of the alloy) and the effect of the magnetic moment on the volume. Among ceramics, quartz has a particularly low CTE due to its three-dimensional network of covalent/ionic bonding. Glass has a higher CTE than quartz due to its lower degree of networking. The CTE of a composite can be calculated from those of its components. When the components are placed in series, as illustrated in Fig. 8.2a, the change in length ΔLc of the composite is given by the sum of the changes in the lengths of the components: ΔLc = ΔL1 + ΔL2 , (8.3)
280 8 Thermal Properties where ALI and AL2 are the changes in the lengths of the components.Only two components are shown in the summation in Eq.8.3 for the sake of simplicity. Dividing by the original length Lco of the composite gives △Lc/Lco=△L1/Lco+△L2/Lco=h△L1/L1o+V2△L2/L2o, (8.4) where Lio and L2o are,respectively,the original lengths of component 1(all of the strips of component I together)and component 2(all the strips of component 2 to- gether),and v and v2 are the volume fractions of components I and 2,respectively. In Eq.8.4,the relations L1o VILco (8.5) and L20 V2Lco (8.6) have been used.Using Eq.8.2,Eq.8.4 becomes cc△T=V1x1△T+y2a2△T, (8.7) where ac is the CTE of the composite and a and az are the CTEs of components 1 and 2,respectively.Division by AT gives ac via1+v2a2. (8.8) Equation 8.8 is the rule of mixtures expression for the CTE of the composite in the case of the series configuration shown in Fig.8.2a. For the parallel configuration of Fig.8.2b,when the component strips are per- fectly bonded to one another,the two components are constrained so that their lengths are the same at any temperature.This constraint causes each component 2 2 2 2 b Figure 8.2.Calculation ofthe CTE ofa composite with two components,labeled 1 and 2.a Series configuration,b parallel configuration
280 8 Thermal Properties where ΔL1 and ΔL2 are the changes in the lengths of the components. Only two components are shown in the summation in Eq. 8.3 for the sake of simplicity. Dividing by the original length Lco of the composite gives ΔLc/Lco = ΔL1/Lco + ΔL2/Lco = v1ΔL1/L1o + v2ΔL2/L2o , (8.4) where L1o and L2o are, respectively, the original lengths of component 1 (all of the strips of component 1 together) and component 2 (all the strips of component 2 together), and v1 and v2 are the volume fractions of components 1 and 2, respectively. In Eq. 8.4, the relations L1o = v1Lco , (8.5) and L2o = v2Lco (8.6) have been used. Using Eq. 8.2, Eq. 8.4 becomes αcΔT = v1α1ΔT + v2α2ΔT , (8.7) where αc is the CTE of the composite and α1 and α2 are the CTEs of components 1 and 2, respectively. Division by ΔT gives αc = v1α1 + v2α2 . (8.8) Equation 8.8 is the rule of mixtures expression for the CTE of the composite in the case of the series configuration shown in Fig. 8.2a. For the parallel configuration of Fig. 8.2b, when the component strips are perfectly bonded to one another, the two components are constrained so that their lengths are the same at any temperature. This constraint causes each component Figure 8.2. Calculation of the CTE of a composite with two components, labeled 1 and 2. a Series configuration, b parallel configuration
8.1 Thermal Expansion 281 to be unable to change its length by the amount dictated by its CTE(Eq.8.2). As a result,each component experiences a thermal stress.The component that expands more than the amount indicated by its CTE experiences thermal stress that is tensile,whereas the component that expands less than the amount indicated by its CTE experiences thermal stress that is compressive.The thermal stress is equal to the thermal force divided by the cross-sectional area.In the absence of an applied force, F1+F2=0, (8.9) where F and Fare the thermal forces in component I(all of the strips of com- ponent I together)and component 2(all of the strips of component 2 together), respectively.Hence, F1=-F2. (8.10) Since force is the product of stress and cross-sectional area,Eq.8.10 can be written U1VIA U2V2A, (8.11) where U and U2 are the stresses in components 1 and 2,respectively,and A is the area of the overall composite.Dividing by A gives U1=U22. (8.12) Using Eq.8.2,the strain in component 1 is given by (ac-)AT and the strain in component 2 is given by(ac-a2)AT.Since stress is the product of the strain and the modulus,Eq.7.12 becomes (ae-a1)△TM1h=-(ae-a2)△TM22, (8.13) where M and M2 are the elastic moduli of components 1 and 2,respectively. Dividing Eq.8.13 by AT gives (ac-a1)M1v1 =-(ac-a2)M2v2. (8.14) Rearrangement gives ac=(a1M1V1+c2M2V2)/(M11+M2V2). (8.15) Equation 8.15 is the rule of mixtures expression for the CTE of a composite in the parallel configuration. In the case that M M2,Eq.8.15 becomes xc=(1M+c22)/(v1+v2)=a1+a22, (8.16) since 1+V2=1. (8.17)
8.1 Thermal Expansion 281 to be unable to change its length by the amount dictated by its CTE (Eq. 8.2). As a result, each component experiences a thermal stress. The component that expands more than the amount indicated by its CTE experiences thermal stress that is tensile, whereas the component that expands less than the amount indicated by its CTE experiences thermal stress that is compressive. The thermal stress is equal to the thermal force divided by the cross-sectional area. In the absence of an applied force, F1 + F2 = 0 , (8.9) where F1 and F2are the thermal forces in component 1 (all of the strips of component 1 together) and component 2 (all of the strips of component 2 together), respectively. Hence, F1 = −F2 . (8.10) Since force is the product of stress and cross-sectional area, Eq. 8.10 can be written as U1v1A = U2v2A , (8.11) where U1 and U2 are the stresses in components 1 and 2, respectively, and A is the area of the overall composite. Dividing by A gives U1v1 = U2v2 . (8.12) Using Eq. 8.2, the strain in component 1 is given by (αc − α1)ΔT and the strain in component 2 is given by (αc − α2)ΔT. Since stress is the product of the strain and the modulus, Eq. 7.12 becomes (αc − α1)ΔTM1v1 = −(αc − α2)ΔTM2v2 , (8.13) where M1 and M2 are the elastic moduli of components 1 and 2, respectively. Dividing Eq. 8.13 by ΔT gives (αc − α1)M1v1 = −(αc − α2)M2v2 . (8.14) Rearrangement gives αc = (α1M1v1 + α2M2v2)/(M1v1 + M2v2) . (8.15) Equation 8.15 is the rule of mixtures expression for the CTE of a composite in the parallel configuration. In the case that M1 = M2, Eq. 8.15 becomes αc = (α1v1 + α2v2)/(v1 + v2) = α1v1 + α2v2 , (8.16) since v1 + v2 = 1 . (8.17)
282 8 Thermal Properties If there are three components instead of two components in the composite,Eq.8.9 becomes F1+F2+F3=0, (8.18) and Eq.8.17 becomes V1+V2+3=1, (8.19) but the method of deriving the rule of mixtures expression is the same. 8.2 Specific Heat The heat capacity of a material is defined as the heat energy required to increase the temperature of the entire material by 1C.The units of specific heat are commonly JK-1.The specific heat(also known as the specific heat capacity)is defined as the heat energy required to increase the temperature of a unit mass of the material by 1C.The units of specific heat are commonly JgK-1.Hence,the specific heat is the heat capacity divided by the mass of the material.However,this distinction between heat capacity and specific heat is not strictly followed by many authors. The specific heat of a composite can be calculated from those of the components of the composite.Consider that the composite has a component 1 of specific heat c and mass fraction fi,and a component 2 of specific heat c2 and mass fraction f2. Let M be the total mass of the composite.Hence,the mass of component l is fiM, and the mass of component 2 is f2M.The heat absorbed per K rise in temperature is cifiM for component 1,and is c2f2M for component 2. The specific heat ce of the composite is the total heat absorbed per C rise in temperature divided by the total mass.Hence, cc (cifiM+c2fM)/M=cif +c2f2. (8.20) Equation 8.20 implies that the specific heat of the composite is the weighted av- erage of the specific heats of the components,where the weighting factors are the mass fractions of the components.This equation is a manifestation of the rule of mixtures.Note that the derivation of this equation does not require any particular distribution of the two components. Kinetic energy is stored in a material through the vibrations of the crystal lattice and molecules and the rotations of molecules.Each way of vibrating or rotating is said to be a degree of freedom.Heat is needed to increase the temperature of a material because the kinetic energy per degree of freedom needs to increase as the temperature increases.The more degrees of freedom,the greater the specific heat of the material.Figure 8.3 shows the various vibrational modes in graphite. For solids,the specific heat refers to that at a constant pressure(abbreviated cp), unless noted otherwise.This is because the pressure is usually fixed when using solid materials
282 8 Thermal Properties If there are three components instead of two components in the composite, Eq. 8.9 becomes F1 + F2 + F3 = 0 , (8.18) and Eq. 8.17 becomes v1 + v2 + v3 = 1 , (8.19) but the method of deriving the rule of mixtures expression is the same. 8.2 Specific Heat The heat capacity of a material is defined as the heat energy required to increase the temperature of the entire material by 1°C. The units of specific heat are commonly JK−1. The specific heat (also known as the specific heat capacity) is defined as the heat energy required to increase the temperature of a unit mass of the material by 1°C. The units of specific heat are commonly Jg−1 K−1. Hence, the specific heat is the heat capacity divided by the mass of the material. However, this distinction between heat capacity and specific heat is not strictly followed by many authors. The specific heat of a composite can be calculated from those of the components of the composite. Consider that the composite has a component 1 of specific heat c1 and mass fraction f1, and a component 2 of specific heat c2 and mass fraction f2. Let M be the total mass of the composite. Hence, the mass of component 1 is f1M, and the mass of component 2 is f2M. The heat absorbed per K rise in temperature is c1f1M for component 1, and is c2f2M for component 2. The specific heat cc of the composite is the total heat absorbed per °C rise in temperature divided by the total mass. Hence, cc = (c1f1M + c2f2M)/M = c1f1 + c2f2 . (8.20) Equation 8.20 implies that the specific heat of the composite is the weighted average of the specific heats of the components, where the weighting factors are the mass fractions of the components. This equation is a manifestation of the rule of mixtures. Note that the derivation of this equation does not require any particular distribution of the two components. Kinetic energy is stored in a material through the vibrations of the crystal lattice and molecules and the rotations of molecules. Each way of vibrating or rotating is said to be a degree of freedom. Heat is needed to increase the temperature of a material because the kinetic energy per degree of freedom needs to increase as the temperature increases. The more degrees of freedom, the greater the specific heat of the material. Figure 8.3 shows the various vibrational modes in graphite. For solids, the specific heat refers to that at a constant pressure (abbreviated cp), unless noted otherwise. This is because the pressure is usually fixed when using solid materials
8.2 Specific Heat 283 Raman active active Silent Figure 8.3.Various modes of vibration in graphite Table 8.2.Specific heat values(p)of various materials Material p (g-IK-1) Water(25C) 4.1813 Ice(-10C) 2.050 Paraffin wax 2.5 Magnesium 1.02 Aluminum 0.897 Graphite 0.710 Diamond 0.5091 Glass 0.84 Silica(fused) 0.703 Table 8.2 shows a comparison of the cp values for various materials.cp is higher for water than ice.This is because there are more degrees of freedom for vibra- tions/rotations in the liquid,which has a disordered structure,than in the ordered structure of ice.cp of paraffin wax is higher than that ofice,due to the disordered structure of solid wax,which is a molecular solid.Magnesium has a higher cp than aluminum(which is next to magnesium in the periodic table of the elements),be- cause it has a hexagonal crystal structure.In contrast,aluminum has a cubic(fcc) crystal structure.A hexagonal structure is less symmetrical than a cubic structure, resulting in more modes of lattice vibration.Similarly,graphite (hexagonal)has a higher cp than diamond(cubic),even though graphite and diamond are both 100%carbon.Glass has a higher cp than fused silica due to the lower degree of
8.2 Specific Heat 283 Figure 8.3. Various modes of vibration in graphite Table 8.2. Specific heat values (cp) of various materials Material cp (Jg−1 K−1) Water (25°C) 4.1813 Ice (−10°C) 2.050 Paraffin wax 2.5 Magnesium 1.02 Aluminum 0.897 Graphite 0.710 Diamond 0.5091 Glass 0.84 Silica (fused) 0.703 Table 8.2 shows a comparison of the cp values for various materials. cp is higher for water than ice. This is because there are more degrees of freedom for vibrations/rotations in the liquid, which has a disordered structure, than in the ordered structure of ice. cp of paraffin wax is higher than that of ice, due to the disordered structure of solid wax, which is a molecular solid. Magnesium has a higher cp than aluminum (which is next to magnesium in the periodic table of the elements), because it has a hexagonal crystal structure. In contrast, aluminum has a cubic (fcc) crystal structure. A hexagonal structure is less symmetrical than a cubic structure, resulting in more modes of lattice vibration. Similarly, graphite (hexagonal) has a higher cp than diamond (cubic), even though graphite and diamond are both 100% carbon. Glass has a higher cp than fused silica due to the lower degree of
284 8 Thermal Properties three-dimensional networking in glass,meaning that there are more degrees of freedom for vibrations. A material with a high specific heat may be used for thermal energy storage.An increase in temperature causes the storage of energy(which is the energy needed to raise the temperature of the material),while a decrease in temperature causes the release of this stored energy.A building should be designed to have a high heat capacity(known as the thermal mass in this context,so as to be distinguished from the specific heat)so that the temperature of the building does not change readily as the outdoor temperature changes.Thus,building materials ofhigh specific heat are valuable.They include gypsum(1.09,Jg-K-1),asphalt(0.92,Jg-K-),concrete (0.88,Jg-K-)and brick (0.84,Jg-K). 8.3 Phase Transformations 8.3.1 Scientific Basis A phase is a physically homogeneous region of matter.Different phases differ in structure.For example,ice and liquid water are different phases due to their dif- ferent structures.A phase transformation,also known as a phase transition,refers to the change in phase upon changing the temperature/pressure.For example,the melting of ice to form liquid water is a phase transition.A phase transition is usually reversible.Indeed,liquid water freezes upon cooling. The melting temperature limits the applicable temperature range of a solid mate- rial.However,below the melting temperature,there can be other limits.In the case of a solid that is at least partially amorphous(i.e.,not completely crystalline)and an application in which high stiffness is required,the glass transition temperature (Ts)is a temperature limit.Upon heating,a solid that is at least partially amorphous softens(i.e.,the modulus reduces)at Tg,because the amorphous part in it softens. The softening at Te is due to the movements of the constituent molecules,ions or atoms above Tg.Below Tg,there is not enough thermal energy for such movements to occur.This phase transition is reversible.Upon cooling,the modulus increases at Tg because the molecules,ions or atoms cannot move below Tg.Tg is below the melting temperature. Amorphous materials(also known as glassy materials and noncrystalline ma- terials)are commonly polymers and ceramics.Metals can be amorphous,but they are usually 100%crystalline.To make an amorphous metal it is necessary to cool the liquid metal at an extremely fast cooling rate so that there is insufficient time for the atoms to order and form a crystalline phase.On the other hand,polymers and ceramics involve ionic/covalent units that are much larger than atoms,and the ordering of these units to form a crystalline phase is relatively difficult.As a re- sult,polymers and ceramics are commonly partially amorphous,if not completely amorphous
284 8 Thermal Properties three-dimensional networking in glass, meaning that there are more degrees of freedom for vibrations. A material with a high specific heat may be used for thermal energy storage. An increase in temperature causes the storage of energy (which is the energy needed to raise the temperature of the material), while a decrease in temperature causes the release of this stored energy. A building should be designed to have a high heat capacity (known as the thermal mass in this context, so as to be distinguished from the specific heat) so that the temperature of the building does not change readily as the outdoor temperature changes. Thus, building materials of high specific heat are valuable. They include gypsum (1.09, Jg−1 K−1), asphalt (0.92, Jg−1 K−1), concrete (0.88, Jg−1 K−1) and brick (0.84, Jg−1 K−1). 8.3 Phase Transformations 8.3.1 Scientific Basis A phase is a physically homogeneous region of matter. Different phases differ in structure. For example, ice and liquid water are different phases due to their different structures. A phase transformation, also known as a phase transition, refers to the change in phase upon changing the temperature/pressure. For example, the melting of ice to form liquid water is a phase transition. A phase transition is usually reversible. Indeed, liquid water freezes upon cooling. The melting temperature limits the applicable temperature range of a solid material. However, below the melting temperature, there can be other limits. In the case of a solid that is at least partially amorphous (i.e., not completely crystalline) and an application in which high stiffness is required, the glass transition temperature (Tg) is a temperature limit. Upon heating, a solid that is at least partially amorphous softens (i.e., the modulus reduces) at Tg, because the amorphous part in it softens. The softening at Tg is due to the movements of the constituent molecules, ions or atoms above Tg. Below Tg, there is not enough thermal energy for such movements to occur. This phase transition is reversible. Upon cooling, the modulus increases at Tg because the molecules, ions or atoms cannot move below Tg. Tg is below the melting temperature. Amorphous materials (also known as glassy materials and noncrystalline materials) are commonly polymers and ceramics. Metals can be amorphous, but they are usually 100% crystalline. To make an amorphous metal it is necessary to cool the liquid metal at an extremely fast cooling rate so that there is insufficient time for the atoms to order and form a crystalline phase. On the other hand, polymers and ceramics involve ionic/covalent units that are much larger than atoms, and the ordering of these units to form a crystalline phase is relatively difficult. As a result, polymers and ceramics are commonly partially amorphous, if not completely amorphous
8.3 Phase Transformations 285 Table 8.3.Glass transition temperatures of various materials Material Ts(C) Polyethylene (low-density) -105 Polypropylene(atactic) -20 Polypropylene(isotactic) 0 Polyvinyl chloride 81 Polystyrene 95 Chalcogenide AsGeSeTeb 245 Soda lime glassb 520-600 Fused quartzb 1,175 apolymer;bceramic Although the glass transition and melting are distinct phase transitions,both involve the movements of atoms,ions or molecules in the solid.These movements are more extensive during melting than during the glass transition.Therefore, a material that has a high melting temperature tends to have a high Tg. Table 8.3 lists the Tg values of various polymers and ceramics.The Tg values are higher for ceramics than for polymers.This is consistent with the higher melting temperatures of ceramics. Among the polymers,polyethylene has a very low Te because of an absence of functional groups that cause intermolecular interactions,and an absence of bulky side groups.The bulky side groups as well as the intermolecular interactions hinder the sliding of molecules relative to one another.Polyvinyl chloride has a higher Tg because of the chloride functional group in its structure,which promotes intermolecular interactions.Polystyrene has an even higher Tg because of its bulky benzeneside group.Isotactic polypropylene(with the-CH3 side groupsof different mers on the same side of the polymer molecular chain)has a higher Te than atactic polypropylene(with the-CH,side groups of different mers positioned randomly on both sides of the polymer molecular chain)because the former is associated with more order and hence better packing of the molecular chains relative to one another.The better packing hinders the sliding of molecules relative to one another,thus causing a higher Tg. Isotactic polypropylene is a commonly used thermoplastic polymer.The addi- tion of rubber to it results in a composite that is tough and flexible.Polypropylene- polyethylene copolymers(with two types of mer in the same molecule)are attrac- tive because the presence of the polyethylene component increases the low tem- perature impact.A shortcoming of polypropylene is its tendency to degrade upon exposure to ultraviolet(UV)radiation.In order to increase the UV resistance, carbon black can be added as a filler that absorbs the UV radiation. Among ceramics,fused quartz has a higher Tg than soda lime glass.This is consistent with the higher melting temperature of fused quartz. A chalcogenide is a compound with at least one chalcogen ion(sulfur,selenium or tellurium:all elements in Group IV of the periodic table)and atleast one element that is more electropositive.For example,AsGeSeTe is a chalcogenide that has Se
8.3 Phase Transformations 285 Table 8.3. Glass transition temperaturesTg of various materials Material Tg (°C) Polyethylene (low-density)a −105 Polypropylene (atactic)a −20 Polypropylene (isotactic)a 0 Polyvinyl chloridea 81 Polystyrenea 95 Chalcogenide AsGeSeTeb 245 Soda lime glassb 520–600 Fused quartzb 1,175 aPolymer; b ceramic Although the glass transition and melting are distinct phase transitions, both involve the movements of atoms, ions or molecules in the solid. These movements are more extensive during melting than during the glass transition. Therefore, a material that has a high melting temperature tends to have a high Tg. Table 8.3 lists the Tg values of various polymers and ceramics. The Tg values are higher for ceramics than for polymers. This is consistent with the higher melting temperatures of ceramics. Among the polymers, polyethylene has a very low Tg because of an absence of functional groups that cause intermolecular interactions, and an absence of bulky sidegroups.Thebulky sidegroupsaswellastheintermolecular interactionshinder the sliding of molecules relative to one another. Polyvinyl chloride has a higher Tg because of the chloride functional group in its structure, which promotes intermolecular interactions. Polystyrene has an even higher Tg because of its bulky benzenesidegroup.Isotacticpolypropylene(withthe–CH3 sidegroupsofdifferent mers on the same side of the polymer molecular chain) has a higher Tg than atactic polypropylene (with the –CH3 side groups of different mers positioned randomly on both sides of the polymer molecular chain) because the former is associated with more order and hence better packing of the molecular chains relative to one another. The better packing hinders the sliding of molecules relative to one another, thus causing a higher Tg. Isotactic polypropylene is a commonly used thermoplastic polymer. The addition of rubber to it results in a composite that is tough and flexible. Polypropylene– polyethylene copolymers (with two types of mer in the same molecule) are attractive because the presence of the polyethylene component increases the low temperature impact. A shortcoming of polypropylene is its tendency to degrade upon exposure to ultraviolet (UV) radiation. In order to increase the UV resistance, carbon black can be added as a filler that absorbs the UV radiation. Among ceramics, fused quartz has a higher Tg than soda lime glass. This is consistent with the higher melting temperature of fused quartz. A chalcogenide is a compound with at least one chalcogen ion (sulfur, selenium or tellurium: all elements in Group IV of the periodic table) and at least one element that is more electropositive. For example, AsGeSeTe is a chalcogenide that has Se
286 8 Thermal Properties and Te as chalcogens and As and Ge as electropositive elements.Another example is AgInSbTe,where Te is the chalcogen and Ag,In and Sb are the electropositive elements. The Ta values of chalcogenides make these materials suitable for use in phase-change memory (abbreviated PCM,PRAM,PCRAM,chalcogenide RAM or C-RAM),which is a non-volatile computer memory that functions by switch- ing between crystalline and amorphous states upon heating.Heating can change an amorphous material to a crystalline material because the amorphous state is a metastable state (a state that is not the lowest energy state,though it is not unstable),whereas the crystalline state is the thermodynamically stable state(the state with the lowest energy).On the other hand,the change of a crystalline state to an amorphous state requires melting and then rapid cooling.The cooling must be quick enough to avoid the formation of the crystalline state from the melt. AgInSbTe is commonly used for rewritable optical discs(CDs).The writing pro- cess involves switching from the crystalline state to the amorphous state,which has low reflectivity,thereby storing the information optically.This involves(i)initially erasing the disc by switching the surface to the crystalline state through long,low- intensity laser irradiation(avoiding melting),(ii)heating the spot with short(less than 10ns)high-intensity laser pulses to achieve local melting,and (iii)rapidly cooling the molten spot to transform it to the amorphous state. A phase transition is known as a first-order phase transition if it involves the absorption or release oflatent heat during the transition.The units oflatent heat are joules(J).Latent heat is also known as the heat oftransformation.The specificlatent heat(often loosely called the latent heat)is the latent heat per unit mass,so its units are J/g.During the transformation,the temperature stays constant as the latent heat is absorbed or released.For example,latent heat of fusion is absorbed during melting and latent heat of solidification is released during freezing.A process that absorbs latent heat is said to be endothermic,while a process that evolves latent heat is said to be exothermic.All spontaneous reactions are exothermic. The latent heat is due to the difference in heat content (also known as the enthalpy)between the initial and final states of the phase transition.The heat content is higher for the liquid state than for the solid state because the atoms,ions or molecules are slightly more separated in the liquid state than in the solid state, and energy is needed to cause this separation.The greater the energy required to cause the separation,the higher the latent heat of fusion.For the same material, the latent heat of vaporization is much higher than that of fusion.For example,the specific latent heat of fusion of lead is 24.5 J/g,whereas the specific latent heat of vaporization of lead is 871 J/g.This difference is due to the much greater change in the degree of separation required for a liquid to boil (i.e.,to change from liquid to vapor,where the vapor has a much lower density than the liquid)than that required for a solid to melt (i.e.,to change from solid to liquid;in other words, the density difference between the solid and the liquid is small compared to the density difference between the liquid and the vapor).Latent heat is absorbed when a solid melts and latent heat is released when a solid freezes.The specific latent heat of fusion of carbon dioxide is high (184J/g),whereas it is low for nitrogen
286 8 Thermal Properties and Te as chalcogens and As and Ge as electropositive elements. Another example is AgInSbTe, where Te is the chalcogen and Ag, In and Sb are the electropositive elements. The Tg values of chalcogenides make these materials suitable for use in phase-change memory (abbreviated PCM, PRAM, PCRAM, chalcogenide RAM or C-RAM), which is a non-volatile computer memory that functions by switching between crystalline and amorphous states upon heating. Heating can change an amorphous material to a crystalline material because the amorphous state is a metastable state (a state that is not the lowest energy state, though it is not unstable), whereas the crystalline state is the thermodynamically stable state (the state with the lowest energy). On the other hand, the change of a crystalline state to an amorphous state requires melting and then rapid cooling. The cooling must be quick enough to avoid the formation of the crystalline state from the melt. AgInSbTe is commonly used for rewritable optical discs (CDs). The writing process involves switching from the crystalline state to the amorphous state, which has low reflectivity, thereby storing the information optically. This involves (i) initially erasing the disc by switching the surface to the crystalline state through long, lowintensity laser irradiation (avoiding melting), (ii) heating the spot with short (less than 10ns) high-intensity laser pulses to achieve local melting, and (iii) rapidly cooling the molten spot to transform it to the amorphous state. A phase transition is known as a first-order phase transition if it involves the absorption or release of latent heat during the transition. The units of latent heat are joules(J).Latentheatisalsoknownastheheatoftransformation.Thespecificlatent heat (often loosely called the latent heat) is the latent heat per unit mass, so its units are J/g. During the transformation, the temperature stays constant as the latent heat is absorbed or released. For example, latent heat of fusion is absorbed during melting and latent heat of solidification is released during freezing. A process that absorbs latent heat is said to be endothermic, while a process that evolves latent heat is said to be exothermic. All spontaneous reactions are exothermic. The latent heat is due to the difference in heat content (also known as the enthalpy) between the initial and final states of the phase transition. The heat content is higher for the liquid state than for the solid state because the atoms, ions or molecules are slightly more separated in the liquid state than in the solid state, and energy is needed to cause this separation. The greater the energy required to cause the separation, the higher the latent heat of fusion. For the same material, the latent heat of vaporization is much higher than that of fusion. For example, the specific latent heat of fusion of lead is 24.5J/g, whereas the specific latent heat of vaporization of lead is 871J/g. This difference is due to the much greater change in the degree of separation required for a liquid to boil (i.e., to change from liquid to vapor, where the vapor has a much lower density than the liquid) than that required for a solid to melt (i.e., to change from solid to liquid; in other words, the density difference between the solid and the liquid is small compared to the density difference between the liquid and the vapor). Latent heat is absorbed when a solid melts and latent heat is released when a solid freezes. The specific latent heat of fusion of carbon dioxide is high (184J/g), whereas it is low for nitrogen
