8.3 Phase Transformations 287 (25.7 J/g).This is because of the stronger intermolecular attractions in carbon dioxide compared to nitrogen. A phase transition that does not involve a latent heat is known as a second- order phase transition or a continuous phase transition.The glass transition is an example of such a transition.The glass transition involves no latent heat because there is no difference in heat content between the initial state(the amorphous solid state)and the final state(the softened state).The transition between ferromagnetic and paramagnetic states is another example of a second-order phase transition. The latent heat associated with a first-order phase transition provides a mech- anism for the storage of thermal energy.For example,energy is stored during melting(when the ambient temperature is above the melting temperature)and released during freezing(when the ambient temperature is below the freezing temperature).A material with a melting temperature that is near room tempera- ture and placed outdoors can be used to store energy during the day(when the outside temperature is above room temperature)and release energy during the night(when the outside temperature is below room temperature).Such a material is known as a phase-change material(abbreviated to PCM;note that this should not be confused with phase-change memory,which has the same abbreviation). Wax is an example of a phase-change material. Due to the difference in kinetics between the melting and freezing transitions, the melting temperature and the freezing temperature may not be equal.Freezing changes a liquid to a crystalline solid,the formation of which requires the ordering of atoms,ions or molecules.The ordering process can be hastened if freezing is allowed to occur on a crystalline solid surface,which serves as a seed for crystallization.Hence,the freezing of a liquid is facilitated by the presence of seed crystals(called nuclei)around which the liquid freezes.Thus,in the absence of nuclei,a liquid can remain a liquid (called a supercooled liquid)below the equilibrium freezing temperature(the freezing temperature in the case of infinitely slow cooling,which provides plenty of time for freezing to take place,and where kinetics do not affect the outcome).For example,droplets of supercooled water in the clouds may change to ice upon being hit by the wings of a passing airplane. The ice formed on the wings can cause problems with lift.Freezing rain is also supercooled water droplets,which become ice upon hitting a solid surface. The supercooling ATis defined as AT melting temperature-freezing temperature. (8.21) When the supercooling is positive,the freezing temperature is below the melting temperature.This is usually due to the sluggishness of the freezing.When the su- percooling is negative,the freezing temperature is above the melting temperature. Negative supercooling occurs,but it is not well understood. 8.3.2 Shape Memory Effect The shape memory effect (Sect.3.6.3)involves a phase transformation (called a martensitic transformation)that changes the material from the austenite phase
8.3 Phase Transformations 287 (25.7J/g). This is because of the stronger intermolecular attractions in carbon dioxide compared to nitrogen. A phase transition that does not involve a latent heat is known as a secondorder phase transition or a continuous phase transition. The glass transition is an example of such a transition. The glass transition involves no latent heat because there is no difference in heat content between the initial state (the amorphous solid state) and the final state (the softened state). The transition between ferromagnetic and paramagnetic states is another example of a second-order phase transition. The latent heat associated with a first-order phase transition provides a mechanism for the storage of thermal energy. For example, energy is stored during melting (when the ambient temperature is above the melting temperature) and released during freezing (when the ambient temperature is below the freezing temperature). A material with a melting temperature that is near room temperature and placed outdoors can be used to store energy during the day (when the outside temperature is above room temperature) and release energy during the night (when the outside temperature is below room temperature). Such a material is known as a phase-change material (abbreviated to PCM; note that this should not be confused with phase-change memory, which has the same abbreviation). Wax is an example of a phase-change material. Due to the difference in kinetics between the melting and freezing transitions, the melting temperature and the freezing temperature may not be equal. Freezing changes a liquid to a crystalline solid, the formation of which requires the ordering of atoms, ions or molecules. The ordering process can be hastened if freezing is allowed to occur on a crystalline solid surface, which serves as a seed for crystallization. Hence, the freezing of a liquid is facilitated by the presence of seed crystals (called nuclei) around which the liquid freezes. Thus, in the absence of nuclei, a liquid can remain a liquid (called a supercooled liquid) below the equilibrium freezing temperature (the freezing temperature in the case of infinitely slow cooling, which provides plenty of time for freezing to take place, and where kinetics do not affect the outcome). For example, droplets of supercooled water in the clouds may change to ice upon being hit by the wings of a passing airplane. The ice formed on the wings can cause problems with lift. Freezing rain is also supercooled water droplets, which become ice upon hitting a solid surface. The supercooling ΔTis defined as ΔT = melting temperature − freezing temperature . (8.21) When the supercooling is positive, the freezing temperature is below the melting temperature. This is usually due to the sluggishness of the freezing. When the supercooling is negative, the freezing temperature is above the melting temperature. Negative supercooling occurs, but it is not well understood. 8.3.2 Shape Memory Effect The shape memory effect (Sect. 3.6.3) involves a phase transformation (called a martensitic transformation) that changes the material from the austenite phase
288 8 Thermal Properties (cubic)to the martensite phase(typically tetragonal).Due to the change in crystal structure,the martensitic transformation is accompanied by twinning,meaning that the martensite that forms from the austenite is heavily twinned,as illustrated in Figs.8.4 and 8.5. Twin boundary Twin boundary Twin boundary b Figure 8.4.a Austenite,b austenite(cross-hatched region)coexisting with martensite(dotted region),which is twinned. The change in lattice parameters upon changing from austenite to martensite is exaggerated in(b)for the sake of darity a 6 Figure 8.5.Typical crystal structures of a shape memory alloy in the form of an AB compound,with A atoms shown by solid cirdles and B atoms shown by open circles.a Austenite,b twinned martensite,with the twin boundary being the horizontal plane Twin Twin boundary Figure 8.6.The formation of a twin
288 8 Thermal Properties (cubic) to the martensite phase (typically tetragonal). Due to the change in crystal structure, the martensitic transformation is accompanied by twinning, meaning that the martensite that forms from the austenite is heavily twinned, as illustrated in Figs. 8.4 and 8.5. Figure 8.4. a Austenite, b austenite (cross-hatched region) coexisting with martensite (dotted region), which is twinned. The change in lattice parameters upon changing from austenite to martensite is exaggerated in (b) for the sake of clarity a b Figure 8.5. Typical crystal structures of a shape memory alloy in the form of an AB compound, with A atoms shown bysolid circles and B atoms shown by open circles. a Austenite, b twinned martensite, with the twin boundary being the horizontal plane Figure 8.6. The formation of a twin
8.3 Phase Transformations 289 Twinning refers to the existence of a mirror plane in a material such that the parts of the material adjacent to the mirror plane are mirror images in terms of the positions of the atoms in them,as illustrated in Fig.8.6,which shows two mirror planes(each of which is called a twin boundary).The region between the two twin boundaries is called the twin,and it differs in structure from the regions outside the twin.The arrows in Fig.8.6 show the movements of the atoms during the twin formation.The atom movement means deformation (i.e.,strain). The martensite phase is special in that it is highly twinned,thus allowing it to undergo reversible strain that is beyond the elastic limit.This phenomenon is known as pseudoplasticity or superplasticity.If the strain is restrained,stress is provided.Thus,the shape memory effect can be used to provide strain and/or stress;i.e.,it serves as an actuator.Upon the subsequent return from the martensite phase to the austenite phase (i.e.,the reverse of the martensitic transformation), the original shape (i.e.,nearly zero strain)returns. Figure 3.33a shows pseudoplastic behavior.It involves the use of stress to induce the change from the austenite phase to the martensite phase.Applications include orthodontal braces,bone plates,eyeglass frames,medical tools,cellular phone antennae,and bra underwiring.In case of an orthodontal brace,the brace is installed in a patient in the state corresponding to the upper(loading)plateau in Fig.3.33a.The lower (unloading)plateau then allows the stress to be maintained at a roughly constant value as the strain is gradually decreased (i.e.,as the teeth are gradually pulled together by the brace).It is important for the stress to be maintained during the course of this dental treatment.Similarly,for a bone plate that is used to fasten pieces of broken bones,it is important for the stress to be maintained as the fracture gradually heals. The martensitic transformation can be induced by cooling instead of the appli- cation of stress.After cooling,the martensite phase is deformed to a new shape. The deformation is easy due to the twinned structure of the martensite.Subsequent heating returns the martensite phase to the austenite phase.This change in phase means a return to the shape associated with the original austenite. 0000000 8888888 0000000 o0ooooo 0900000 Austenite Cool Heat 。g0 0000000 00 0000090 0090000 Deform 0000900 Martensite Martensite (twinned) (deformed) Figure 8.7.The shape memory effect that involves cooling from austenite to form martensite,deformation of the martensite,and then heating to change the martensite back to austenite.The retum to the austenite phase brings a retum to the shape of the austenite (i.e.,the shape prior to the deformation)
8.3 Phase Transformations 289 Twinning refers to the existence of a mirror plane in a material such that the parts of the material adjacent to the mirror plane are mirror images in terms of the positions of the atoms in them, as illustrated in Fig. 8.6, which shows two mirror planes (each of which is called a twin boundary). The region between the two twin boundaries is called the twin, and it differs in structure from the regions outside the twin. The arrows in Fig. 8.6 show the movements of the atoms during the twin formation. The atom movement means deformation (i.e., strain). The martensite phase is special in that it is highly twinned, thus allowing it to undergo reversible strain that is beyond the elastic limit. This phenomenon is known as pseudoplasticity or superplasticity. If the strain is restrained, stress is provided. Thus, the shape memory effect can be used to provide strain and/or stress; i.e., it serves as an actuator. Upon the subsequent return from the martensite phase to the austenite phase (i.e., the reverse of the martensitic transformation), the original shape (i.e., nearly zero strain) returns. Figure 3.33a shows pseudoplastic behavior. It involves the use of stress to induce the change from the austenite phase to the martensite phase. Applications include orthodontal braces, bone plates, eyeglass frames, medical tools, cellular phone antennae, and bra underwiring. In case of an orthodontal brace, the brace is installed in a patient in the state corresponding to the upper (loading) plateau in Fig. 3.33a. The lower (unloading) plateau then allows the stress to be maintained at a roughly constant value as the strain is gradually decreased (i.e., as the teeth are gradually pulled together by the brace). It is important for the stress to be maintained during the course of this dental treatment. Similarly, for a bone plate that is used to fasten pieces of broken bones, it is important for the stress to be maintained as the fracture gradually heals. The martensitic transformation can be induced by cooling instead of the application of stress. After cooling, the martensite phase is deformed to a new shape. The deformation is easy due to the twinned structure of the martensite. Subsequent heating returns the martensite phase to the austenite phase. This change in phase means a return to the shape associated with the original austenite. Figure 8.7. The shape memory effect that involves cooling from austenite to form martensite, deformation of the martensite, and then heating to change the martensite back to austenite. The return to the austenite phase brings a return to the shape of the austenite (i.e., the shape prior to the deformation)
290 8 Thermal Properties Heat Strain→ Figure8.8.The stress-strain curve during the deformation of a shape memory alloy in the form of martensite(belowA). Heating subsequent to the deformation returns the strain to zero (ie.,the original shape) The shape memory effect is illustrated in Fig.8.7,which shows that austenite(the initial phase)transforms to a martensite upon cooling,which is heavily twinned. The martensite is then mechanically deformed to a particular shape.After this,the deformed martensite is heated so that it transforms back to austenite.The reverse transformation is accompanied by a return to the original shape of the austenite (i.e.,the shape prior to the deformation).This effect is further illustrated in Fig.8.8, where the starting point is martensite.The loading part of the stress-strain curve shows the deformation of the martensite.After subsequent unloading,heat is applied to change the martensite back to austenite.This change of phase results in the restoration of the shape of the austenite;i.e.,the state prior to deformation(or strain 0). As shown in Fig.8.9,the temperature at which the transformation from austenite to martensite begins upon cooling is denoted Ms.The temperature at which the martensitic transformation is completed upon cooling is denoted Mf.Obviously, Mr is below M.The temperature at which the transformation from martensite to austenite begins upon heating is denoted As.The temperature at which the transformation from martensite to austenite finishes upon heating is denoted Af. Again,obviously Af is above As.Due to hysteresis,Ms tends to be less than As, though it is usually close to As. Figure 8.8 is the behavior belowAs,since it describes the deformation of the martensite.If the stress after unloading is continued into the negative regime without heating,ferroelasticity(Fig.3.33b)results,provided that there are two states of twinning that allow the positive stress plateau and the negative stress plateau. The values of these four temperatures defined in Fig.8.9 depend on the stress, as illustrated in Fig.8.10.Due to the dependence on the stress,at a fixed tempera- ture austenite changes to martensite upon increasing the stress.The pseudoplastic behavior shown in Fig.3.33a is based on this stress-induced martensitic trans- formation;it occurs at temperatures above Af,so that applying stress causes the change from austenite to martensite
290 8 Thermal Properties Strain Heat Stress Figure 8.8. The stress–strain curve during the deformation of a shape memory alloy in the form of martensite (below As). Heating subsequent to the deformation returns the strain to zero (i.e., the original shape) The shape memory effect is illustrated in Fig. 8.7, which shows that austenite (the initial phase) transforms to a martensite upon cooling, which is heavily twinned. The martensite is then mechanically deformed to a particular shape. After this, the deformed martensite is heated so that it transforms back to austenite. The reverse transformation is accompanied by a return to the original shape of the austenite (i.e., the shape prior to the deformation). This effect is further illustrated in Fig. 8.8, where the starting point is martensite. The loading part of the stress–strain curve shows the deformation of the martensite. After subsequent unloading, heat is applied to change the martensite back to austenite. This change of phase results in the restoration of the shape of the austenite; i.e., the state prior to deformation (or strain = 0). As shown in Fig. 8.9, the temperature at which the transformation from austenite to martensite begins upon cooling is denoted Ms. The temperature at which the martensitic transformation is completed upon cooling is denoted Mf. Obviously, Mf is below Ms. The temperature at which the transformation from martensite to austenite begins upon heating is denoted As. The temperature at which the transformation from martensite to austenite finishes upon heating is denoted Af. Again, obviously Af is above As. Due to hysteresis, Ms tends to be less than As, though it is usually close to As. Figure 8.8 is the behavior belowAs, since it describes the deformation of the martensite. If the stress after unloading is continued into the negative regime without heating, ferroelasticity (Fig. 3.33b) results, provided that there are two states of twinning that allow the positive stress plateau and the negative stress plateau. The values of these four temperatures defined in Fig. 8.9 depend on the stress, as illustrated in Fig. 8.10. Due to the dependence on the stress, at a fixed temperature austenite changes to martensite upon increasing the stress. The pseudoplastic behavior shown in Fig. 3.33a is based on this stress-induced martensitic transformation; it occurs at temperatures above Af, so that applying stress causes the change from austenite to martensite
8.3 Phase Transformations 291 The values of these four temperatures defined in Fig.8.9 may shift upon repeated use of the shape memory effect.This shift is known as functional fatigue and is due to microstructural changes upon multiple cycles of the effect. The various manifestations of the shape memory effect are illustrated in Fig.8.11. These manifestations depend on the temperature.The effect in Fig.8.1la is the same as that in Fig.8.8 and occurs at temperatures below As,with the deformation shown in the stress-strain curve being that of martensite.The effect shown in Fig.8.11b occurs at temperatures above Af(ie.,when the phase is austenite prior to deformation)and relates to pseudoelasticity;it is the same as the effect shown in Fig.3.33a,except that,for the sake of simplicity,it does not show any degree of strain irreversibility after unloading.The effect in Fig.8.11c occurs at temperatures between As and Ar and shows characteristics that are intermediate between those shown in Fig.8.1la and b.In this intermediate temperature range,austenite and martensite coexist,with the martensite portion undergoing the effect shown in Fig.8.11a and the austenite portion undergoing the effect depicted in Fig.8.11b. The shape memory effect shown in Fig.8.8 (i.e,Fig.8.1la)is valuable for numerous applications.Examples of its application are self-expandable cardiovas- cular stents,blood clot filters,engines,actuators,flaps that change the direction of air flow depending on the temperature(for air conditioners and aircraft),and couplings.Some of these applications are described below.However,applications to robotics have problems due to energy inefficiency,slow response,and large hysteresis. A stent is used to reinforce weak vein walls and to widen narrow veins.It can be introduced in a chilled deformed shape;i.e.,a scaffold with a relatively small diameter.During deployment,the stent travels through the arteries.After deployment,due to the warmth from the body,the stent expands to the appropriate diameter with sufficient force to open the vessel lumen and reinstate blood flow. Such a stent replaces similar stainless steel stents that are expanded with a little balloon. M Heating Cooling M Temperature Figure 8.9.Decrease in the martensite fraction during heating,and the increase in this fraction during subsequent cooling
8.3 Phase Transformations 291 The values of these four temperatures defined in Fig. 8.9 may shift upon repeated use of the shape memory effect. This shift is known as functional fatigue and is due to microstructural changes upon multiple cycles of the effect. ThevariousmanifestationsoftheshapememoryeffectareillustratedinFig.8.11. These manifestations depend on the temperature. The effect in Fig. 8.11a is the same as that in Fig. 8.8 and occurs at temperatures below As, with the deformation shown in the stress–strain curve being that of martensite. The effect shown in Fig. 8.11b occurs at temperatures above Af (i.e., when the phase is austenite prior to deformation) and relates to pseudoelasticity; it is the same as the effect shown in Fig. 3.33a, except that, for the sake of simplicity, it does not show any degree of strain irreversibility after unloading. The effect in Fig. 8.11c occurs at temperatures between As and Af and shows characteristics that are intermediate between those shown in Fig. 8.11a and b. In this intermediate temperature range, austenite and martensite coexist, with the martensite portion undergoing the effect shown in Fig. 8.11a and the austenite portion undergoing the effect depicted in Fig. 8.11b. The shape memory effect shown in Fig. 8.8 (i.e., Fig. 8.11a) is valuable for numerous applications. Examples of its application are self-expandable cardiovascular stents, blood clot filters, engines, actuators, flaps that change the direction of air flow depending on the temperature (for air conditioners and aircraft), and couplings. Some of these applications are described below. However, applications to robotics have problems due to energy inefficiency, slow response, and large hysteresis. A stent is used to reinforce weak vein walls and to widen narrow veins. It can be introduced in a chilled deformed shape; i.e., a scaffold with a relatively small diameter. During deployment, the stent travels through the arteries. After deployment, due to the warmth from the body, the stent expands to the appropriate diameter with sufficient force to open the vessel lumen and reinstate blood flow. Such a stent replaces similar stainless steel stents that are expanded with a little balloon. Martensite fraction Temperature Heating O 1 Mf Ms As Af Cooling Figure 8.9. Decrease in the martensite fraction during heating, and the increase in this fraction during subsequent cooling