What are shape memory alloys used for?

2 shape memory alloys

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1 2 Shape memory alloys Shape memory alloys belong to the class of so-called smart materials. This is understood to mean materials that show an active reaction to a signal. Shape memory alloys change their shape when you change the temperature and can achieve very large deformations in the process. Another example of such materials are piezoelectrics, which are the subject of the next chapter. Shape memory alloys can change their shape in response to a signal. 2.1 Phenomenology The special properties of shape memory alloys can best be illustrated by a few experiments with these alloys. We start with an ordinary metal alloy, which has no shape memory properties, as a reference experiment: If you take a paper clip in your hand, it is no major problem to deform it and, for example, bend it into a long straight wire. This deformation is plastic, i.e. irreversible. Apart from a certain solidification in the plastically deformed areas, there is nothing in the elongated wire that would remind of the original shape. The exact properties of such a deformation can be recorded in a stress-strain diagram. As is customary in factory mechanics, the mechanical tension is applied against the elongation. (In factory mechanics, the stress is denoted as force per area, the elongation as a change in length in relation to the initial length. Details can be found, for example, in [52].) A typical (not to scale) stress-strain diagram is plotted in Figure 2.1 a: At first, stress and strain behave linearly (area I), whereby the curve has a steep slope. This slope is the material's modulus of elasticity. At a certain value of the stress (flow stress) the curve kinks, so that the stress now increases more slowly as the elongation increases (area II). Plastic deformation takes place in this area. When the load is relieved, the material follows the elastic straight line again, which must now be shifted in parallel so that a finite stretch remains even with zero stress (area III). This is the plastic stretch. As we shall see in a moment, the influence of temperature is important for many shape memory sects. In order to be able to draw this eect, a temperature axis must be added to the stress-strain diagram. If there is no voltage during the temperature increase (thermal stresses due to uneven heating should be neglected here), the event must be drawn in the expansion-temperature plane. The mechanical behavior is described with stress-strain curves. Metals deform plastically (irreversibly) even with small elongations. M. Bäker, functional materials, DOI / _2, Springer Fachmedien Wiesbaden 2014

2 30 2 Shape memory alloys a: Common metal b: One-way eect c: Two-way eect d: Superelasticity Figure 2.1: Schematic stress-strain-temperature curves for common metals and different shape memory alloys. Detailed explanation in the text. (Modified from [12].) Some shape memory alloys take on their old shape again after plastic deformation when the temperature rises (one-way effect). In the case of an ordinary metal, the elongation increases with temperature and decreases again when it cools down (area IV), regardless of whether the material has been plastically deformed or not. Next we'll use a shape memory alloy paper clip. Just like with ordinary paper clips, it is not a problem to first deform them elastically (area I) and then plastically (area II). The stress-strain curve looks a little different (Figure 2.1 b) as it has a plateau for this material, but this seems to be the only difference. The material also reacts in the usual way to relief (area III). If the temperature of the deformed material is increased, for example by placing it in hot water, it initially expands thermally (area IV). If the temperature exceeds a certain value, the material remembers its original shape and deforms back into its original shape without any further application of force (area V). When it cools down to room temperature, the thermal expansion also decreases again (area VI). This is the shape memory sect that gives this class of materials its name. This eect is called a one-way eect because the material has a memory when it is heated, but not

3 2.2 Crystal structure and phase transitions 31 on cooling. This terminology suggests that there is also a two-way eect. No voltage is applied to the material, only the temperature is increased, see Figure 2.1 c. Initially, the material deforms due to thermal expansion (area I), but when a certain temperature is exceeded, the expansion changes significantly (area II). If the temperature is increased further, the material deforms again due to thermal expansion. If the material is cooled instead, part of the thermal expansion is reduced (area III), but when the temperature falls below a certain level, the material changes its shape again and assumes its original shape (area IV). A paper clip that has been pretreated accordingly deforms when the temperature is increased, but deforms back again when the temperature is lowered again. A similar effect can of course also be achieved with a bimetal strip, in which two metals with different coefficients of thermal expansion are glued to one another. In contrast to the shape memory alloys, the deformation there is approximately linear with temperature, so that correspondingly high temperatures are necessary to achieve large deformations. This is different with the shape memory alloys, here a large deformation takes place in a relatively narrow temperature range. In addition, shape memory alloys can be adjusted to very complex shape changes, which is not easily possible with bimetals. As a final eect, we consider the so-called superelasticity (Figure 2.1 d): For this, too, we use a suitably prepared paper clip. At first it deforms elastically like an ordinary metal (area I). If a certain tension is exceeded, the curve kinks sharply and shows a plateau (area II), so that the elongation increases sharply with almost constant tension. If the material is relieved (area III), the curve initially runs parallel to the elastic straight line, but then bends back to a plateau (area IV). When the load is completely removed, the material returns to its original shape. Since the deformation goes back immediately after the load is removed, the material behaves elastically. In contrast to a normal metal, elastic deformations of around 10% can be achieved, where normal metals would be plastically deformed. With the two-way eect, the alloy has one shape at low temperature and another at high temperature. Super elastic shape memory alloys can withstand very large elastic strains. 2.2 Crystal structure and phase transitions Crystal structures The shape memory materials considered here are metallic alloys. 1 Like (almost) all metals, they are characterized by the fact that they are arranged in a crystalline structure in which the atoms have a long-range order 1 There are also polymer materials with shape memory properties; however, these should not be dealt with here. Shape memory alloys are crystalline metals.

4 32 2 shape memory alloys a: triclinic b: rhombohedral c: hexagonal single base-centered d: monoclinic single body-centered e: tetragonal single base-centered body-centered face-centered f: orthorhombic simple body-centered face-centered g: cubic Figure 2.2: Unit cells of the 14 possible crystal types (from [52]) The unit cell: the building block of the crystal There are 14 different types of crystal lattices. to sit. We already got to know this principle of the crystalline structure in the last chapter. The shape memory effect is caused by a change in the crystal structure; in order to understand it, we therefore have to take a closer look at what crystal structures there can be. A crystal structure can be denoted as a structure that can be built up by periodically repeating a building block called a unit cell. We consider here the simplest case of a crystal made up of a single type of atom. If all atoms within the crystal are identical in terms of their position relative to the surrounding atoms, there are only 14 different possible arrangements, which are called Bravais lattices and are shown in Figure 2.2. The so-called lattice constants of a crystal lattice are dened as the lengths of the edges of the unit cell.

5 2.2 Crystal structure and phase transitions 33 Often the term unit cell is used instead of unit cell. These two terms differ slightly: A unit cell is any cell from which the entire crystal can be built up through periodic repetition, a unit cell is the smallest possible unit cell. For example, a checkerboard pattern can be built up by periodically repeating squares from four fields (two black, two white). Such a square is therefore a unit cell. However, it is not a unit cell, because the checkerboard pattern can also be generated by periodically repeating a black and a white field. In the previous chapter we dealt with crystals that are made up of long chain molecules. In this case there are of course a lot more possibilities of arrangement, because the elementary units from which the crystal is composed have a structure and are therefore no longer perfectly symmetrical. Such lattices are called lattices with a basis The Boltzmann law and the entropy p i = 1 Z e Ei / k BT. (2.1) Here, Z is a normalization factor that ensures that the overall probability of viewing the system in any state is equal to one. k B is the Boltzmann constant, which has a value of 1, J / K. The 2 The term Boltzmann's law is not used uniformly; Often this also means the Stefan-Boltzmann law from section. In this book, equation (2.1) is always understood as Boltzmann's law. One might be tempted to simply call this equation the Boltzmann equation, but this term is reserved for another equation from statistical mechanics. At low temperatures, atoms arrange themselves favorably in terms of energy. Boltzmann's law is one of the most important laws in physics. The type of crystal that forms in a particular material depends on the bonding relationships between the atoms of the crystal. At low temperatures, the atoms arrange themselves in such a way that their energy is minimized; but at higher temperatures this is no longer necessarily the case. The reason for this is the so-called Boltzmann law, named after Ludwig Eduard Boltzmann (). 2 To explain this, let us consider a system in thermal equilibrium. The system is in contact with a heat bath at a certain temperature T and has had enough time to exchange heat with it, so that the system itself is also at temperature T. We assume that the system can exist in different states Z 1, Z 2, Z 3, ..., to which the energies E 1, E 2, E 3, ... belong. Each of these states fully describes all components of the system. In a gas this means that in a state Z i the locations and velocities of all atoms or molecules of the gas are exactly specified. Such a precisely specified state is also referred to as a micro-state. Boltzmann's law states that the probability p i of viewing the system in a state Z i is given by Boltzmann's law: A state is improbable if its energy is high.

6 34 2 Shape memory alloys Boltzmann constant and Boltzmann factor. Boltzmann's constant is a kind of conversion factor that relates a temperature to an energy. The exponential term e Ei / k BT is often referred to as the Boltzmann factor. The normalization factor Z is also called the partition function. The following applies: Z = X i e E i / k B T. (2.2) Low temperatures: States of low energy are strongly preferred. Typical size of a thermal fluctuation: k BT. At high temperatures, systems are usually not in their basic state. This is due to the entropy. Using Boltzmann's law, we see that a system always assumes the most energetically favorable state at zero temperature, while other states of higher energy become more and more probable with increasing temperature. At a temperature of infinity all states are finally equally probable. An important consequence of Boltzmann's law is that the energy of a system at a temperature T is subject to random fluctuations, which are called thermal fluctuations. According to Boltzmann's law, a typical size of such a fluctuation is about E = k B T. One can clearly imagine that the system withdraws energy from the heat bath or transfers energy to the heat bath. In a gas that settles in a container at a certain temperature, the atoms can, for example, absorb or release energy when they collide with the container wall. In this presentation of Boltzmann's law, we have assumed that the states of the system are countable. From the later chapters we know that this is the case, for example, for atoms that have discrete energy levels. In many cases, however, the states of a system cannot be counted. An example of this is a free particle that moves with a velocity v and whose energy is given by E = mv 2/2. Since every real number is a possible speed value, the number of possible states is uncountably infinite. An exact speed value then always has the probability zero. In this case, the probability must be replaced by the probability density, which we can denote in this case with p (v) and which is dened in such a way that the probability that particles travel at a speed in an interval of width dv around the value v to be viewed, is given by p (v) dv. The Boltzmann law then has the form p (v) exp (E (v) / k BT). We have already observed the tendency of systems to preferentially adopt low-energy states in the previous chapter, but we have also seen that other structures are possible at higher temperatures. However, we did not explain there why a structure that minimizes the energy does not always appear, even at any high temperatures. Boltzmann's law seems to require this, because the state of lowest energy always has the highest probability. The reason for this is entropy. In addition to their tendency to minimize their energy, systems at a certain temperature also have the second tendency to maximize their entropy. To understand this in more detail,

7 2.2 Crystal structure and phase transitions 35 we must first clarify what the entropy is. As we shall see, it is closely related to the Boltzmann law. The entropy creates a connection between the microscopic arrangement of the atoms of a system and the macroscopically observed quantities. As an example, consider an ideal gas in which the atoms do not interact with each other. From a macroscopic point of view, such a gas can be fully described in terms of pressure, temperature and volume. We know that the gas atoms are in constant motion within the gas, but we cannot measure the details of this motion with macroscopic experiments. The entropy of a system is a measure of how many possibilities there are to reach a certain macroscopic state (or macrostate for short) through the arrangement of the individual atoms (i.e. through different microstates). The fact that the gas tends to maximize its entropy means that it prefers to adopt states that can be achieved in as many different ways as possible by arranging the atoms. Entropy is also often referred to as a measure of the disorder of a system. After what has just been said, we can easily understand this: The arrangement of the atoms in a gas would certainly be most ordered if all the atoms in a small area of ​​the container were arranged regularly, but the rest of the container were empty. The number of possibilities to achieve such an arrangement is, of course, much smaller than the number of possibilities to achieve an even distribution of the atoms, in which there are approximately the same number of atoms in each area of ​​the container. A similar phenomenon can also be observed in everyday life when using a desk: there is essentially only one arrangement in which a desk is perfectly tidy (although this arrangement may be different for different people), but very many untidy arrangements. If you take a book off your desk and then put it back again without taking the order into account, it is very unlikely that the book will end up in exactly the right place again. Over time, therefore, the disorder of the desk increases.Despite this notion, the concept of disorder is of course problematic because it is subjective. Exercise 2.1: Consider a container filled with N interaction-free gas atoms in thermal equilibrium and neglect all external forces. Divide the container into M areas of equal size. What is the probability that one of the areas is empty? As an example, estimate how likely it is that in the room in which you are currently living, a certain volume of the size 1 mm 3 is not occupied by any atom. Note: At room temperature and normal pressure, one mole of a gas takes up a volume of 24.47 l. Using Boltzmann's law, we can easily understand why entropy ensures that systems move at higher temperatures. Entropy is a measure of how many microstates there are for a macrostate. Entropy and disorder.

8 36 2 Shape memory alloys Figure 2.3: The probability of an excited state can be higher than that of the ground state if there are more micro-states for the excited state. In the example, the system is in the ground state with 20% probability and in each of the excited states with 10% probability. The total probability of the excited state is then 80%. Why systems are usually not in the ground state at elevated temperatures. The equation for entropy. mostly not ending in the ground state: We consider a system that can assume N + 1 different states, one of which is the ground state with energy E 0, while the other N states all have the same higher energy E 1> E 0. According to Boltzmann's law, the ground state is more likely by a factor of exp ((E 0 E 1) / k BT) than any of the other states, but if there are many more of these other states, the probability that the system to be viewed in the basic state, but still become extremely small. Figure 2.3 illustrates this with a simple example. Exercise 2.2: Calculate how large the value N must be in the system with two states, so that at a certain temperature the probability of finding the system in an excited state is greater than the probability of the ground state. This consideration can be generalized and can then be used to quantitatively denate the entropy. This is done using the famous equation S = k ln W, (2.3) which was established by Ludwig Boltzmann and (as S = k. Log W) was carved on his tombstone. W is the number of possibilities to reach the respective macrostate through different microstates. So far we have spoken of tendencies of a system, namely on the one hand its tendency to minimize its energy and on the other hand its tendency to maximize its entropy. We can also quantify this microscopically, as we have just seen. However, it is often desirable to restrict oneself to macroscopic quantities when considering systems. For this we consider the internal energy U of a system and its

9 2.2 Crystal structure and phase transitions 37 Entropy S. 3 We denote a new quantity, the so-called free energy F as F = UT S. (2.4) The higher the temperature T des, the more the entropy enters into the free energy System is. For a system in thermal equilibrium with the environment, the free energy is minimized. At low temperatures the entropy only makes a small contribution to the free energy, at higher temperatures its contribution becomes larger and larger, so that it finally dominates the system behavior. Exercise 2.3: Show that the same result follows for exercise 2.2 if one calculates macroscopically with the help of free energy. Use equation 2.3 to calculate entropy. When using the free energy as a minimization criterion, it was assumed that we are looking at a system with a fixed volume. Real systems are usually not with a fixed volume, but at a certain pressure, and can expand against the external pressure, where work is done, or contract, where energy is gained. In this case, it is not the free energy that is minimized, but the so-called free enthalpy G, which is dened as G = F + pv. Where p is the pressure and V is the volume of the system. This additional term plays a role in shape memory alloys, see Exercise 2.4. If, on the other hand, the system is closed off from the environment, its energy is constant, since energy conservation applies to a closed system. In this case the entropy of the system is maximized, i.e. That is, the system assumes the atomic arrangement of the greatest possible entropy, which is compatible with the given energy value. Free energy measures the interplay between energy and entropy. In thermal equilibrium, the free energy is minimal are. At lower temperatures, the free energy can then first be reduced by the formation of the liquid crystalline mesophase, whereby the entropy is reduced by the orientation of the molecules, but is still greater than in the crystalline state due to the mobility of the molecules. This is why this occurs only at even lower temperatures. Figure 2.4 shows a simplified representation of the free energy of a material with a solid, a liquid crystalline and a liquid phase. Phase transitions occur because the high-temperature phase has a higher entropy and therefore dominates at high temperatures. 3 More precisely, entropy, entropy degeneracy, can also be measured experimentally without the need for atomic considerations, see e.g. B. [13, 50].

10 38 2 Shape memory alloys Free energy, solid liquid crystalline Temperature liquid Figure 2.4: Free energy of a liquid crystal as a function of temperature. The free energy of each phase is F ph = U ph T S ph. In the illustration it was assumed that the internal energy and the entropy do not depend on the temperature. The solid phase has the lowest internal energy, the liquid phase the largest. Conversely, the entropy of the liquid phase is greater than that of the liquid crystalline and solid phase, so that the free energy is minimal depending on the temperature in different phases. Shape memory alloys undergo a phase transition in the solid state. Martensitic phase transitions are diusionless. They are also available at low temperatures. And what does all of this have to do with shape memory alloys? Shape memory alloys are characterized by the fact that they carry out a phase transition in the solid state. They have a certain crystal structure at low temperatures, but a different one at higher temperatures. Among the usual materials, one knows such transformations from iron, which, depending on the temperature, can be present as α-, γ- or δ-iron, or from tin, which converts from gray to white tin at 13 C, which leads to disintegration from objects made of tin (so-called tin plague). The conversion from metallic, white tin above 13 C to gray, non-metallic tin below this temperature generally takes place very slowly. Historically, however, it is held responsible for two significant events: On the one hand, Napoleon Bonaparte's () Russian campaign in 1812 is said to have failed because the buttons on the uniform jackets were made of pewter and melted in the cold Russian winter [34]. One hundred years later, during Robert Scott's South Pole expedition (), the expedition lost its kerosene supplies because the canisters used were soldered with tin so that the kerosene could eventually escape. However, both cases are not clearly proven. For most phase transitions it is necessary that atoms diuse through the crystal lattice, i.e. cover distances of more than one lattice constant length. Such phase transitions, such as the phase transition in tin, therefore take place very slowly at low temperatures. Shape memory alloys, on the other hand, carry out phase transitions without diusion, in which the paths that the individual atoms have to cover are short. Therefore, such conversions can also take place at low temperatures, at which normal phase transitions take a very long time due to the slow dissolution

11 2.2 Crystal structure and phase transitions 39 a: Unit cell austenite phase b: Unit cell martensite phase c: Conversion of austenite to martensite I d: Conversion of austenite to martensite II Fig. 2.5: Crystal structure of nitinol. The two unit cells of the austenite and martensite phase as well as the position of a tetragonal cell within the austenite phase, which becomes a martensitic unit cell during the phase transition, are shown. The in part d. The solid plane is the base plane of the Martensite cell: Titanium atoms are shown in black or green, depending on their position in the cell, nickel atoms in red. would last. Such transformations are also called martensitic (according to Adolf Martens,), and the corresponding low-temperature phase is called martensite. Technically used shape memory alloys usually consist of a combination of nickel and titanium, which is why they are also referred to as nitinol. (NOL stands for the Naval Ordnance Laboratory, where these alloys were discovered.) In this connection, the high-temperature phase is a body-centered cubic phase in which titanium and nickel atoms each lie on regular single-cubic sublattices, see Figure 2.5 a. This structure is called the cesium chloride structure (CsCl structure) or the B2 structure. In analogy to steel, this phase is called the austenite phase, but it is identified with the letter β. The low-temperature phase, known as the martensite or α-phase, has a relatively complex monoclinic structure called the B19 'structure (Figure 2.5 b). In order to understand how the phase transition can take place without the atoms having to swap places (i.e. diuse), we consider four unit cells of the austenite lattice, see Figure 2.5 c. The dashed line shows that the arrangement within these cells is very similar to the arrangement in the martensite phase; the cell is simply oriented differently (Figure 2.5 d). A slight shift in the atoms can therefore turn the austenite phase into the martensite phase. The orientation of the new and the old crystal lattice to one another is determined. The special thing about the martensite phase is that it can exist in different orientations. In two dimensions these can be referred to as α + and α. There are 24 different orientation options in three dimensions. In contrast to most metals, plastic deformation within the α-phase does not occur through dislocation movement, but rather in an important shape memory alloy is the nickel-titanium alloy nitinol. Nitinol has a high temperature phase (austenite) and a low temperature phase (martensite).

12 40 2 shape memory alloys K 2 K '2 K 2 K' 2 twin a 1 a2 undeformed area twin K 1 a 1 a2 undeformed area K 1 undeformed area K 1 a 1 a 2 a 1 a 2 a: representation of a twin b: deformation through a twin belt Figure 2.6: Deformation through the formation of twins. The atoms above the twin plane K 1 shear off at the ratio a 1: a 2 used by the angle (K 2, K 2) = 37. The orientation of the lattice rotates by a significantly larger value of α = 71. Shear angles in real crystals are usually significantly smaller. Plastic deformation in a metal can result from the formation of a twin band. At the same time, two parallel, opposite twin planes are formed, so that the upper part of the crystal is displaced. (From [52].) The martensite phase can flip between different orientations. This happens with plastic deformation. Essentially through twinning. This can be thought of as folding over individual α-areas into the opposite orientation, for example α + α. Figure 2.6 illustrates this process using a two-dimensional example. If one cools a shape memory alloy from the austenitic to the martensitic phase, different orientations of the α-phase are initially formed. Due to plastic deformation, some of these α-phase components are reoriented through the formation of twins. If the temperature is increased again, the original austenite phase is formed again. Since the different orientations of the α-phase all belong to the same austenite phase, a deformation applied at low temperatures is restored. This process is illustrated in Figure 2.7. This already explains the creation of the shape memory sect. In the following section, the individual eects will be discussed in more detail before we turn to the applications. Exercise 2.4: We have seen that a martensitic phase transition is necessary for the shape memory eect. However, not every alloy with such a transition is suitable as a shape memory alloy. Think about the reasons for this.

13 2.3 Explanation of the shape memory effects 41 a: Austenite phase (high temp.) B: Martensite phase (low temp.) C: Load: Turning the martensite phase d: Load: Turning the martensite phase e: Relief: Structure is retained f: Heating up: Austenite phase is formed Figure 2.7: One-way eect. When the martensite phase is loaded, individual areas of the grid fold over. Austenite forms again when it is heated up. Detailed explanation in the text. 2.3 Explanation of the shape memory eect We already explained the one-way eect at the end of the previous section. The stress-strain diagram from Figure 2.1 should be discussed again here. After cooling, the material is in the α-phase. If it is plastically deformed (area II), the plastic deformation does not come about through dislocation movement, but through folding over within the α-structure, i.e. through the formation of twins. There is therefore no consolidation, but the stress level remains the same. This happens until all α-areas have been folded over, in which this is energetically more favorable than the dislocation movement. If one deforms even further, dislocations are finally also moved; However, this area should be avoided in applications as it leads to irreversible components in the deformation. If the system is warmed up again, all α-regions form β-regions again, all of which have the same orientation as before cooling. The material therefore takes on its original shape again. Next, let's look at the superelasticity, see Figure 2.8. The material is initially in the austenitic phase, but only just above the transition temperature. If a voltage is applied to the material, plastic deformation within the austenite phase would have a certain one-way effect: flipping over at low temperature One-way effect: reverse transformation at high temperature.

14 42 2 Shape memory alloys a: Austenite phase b: Load: Fold over in martensite phase c: Load: Fold over in martensite phase d: Load: Fold over in martensite phase e: Relieve: Fold over in austenite phase Figure 2.8: Superelasticity. In the event of a mechanical load, the austenite phase forms the martensite phase, which is oriented towards the load. If the load is removed, austenite will form again. Detailed explanation in the text. Super elasticity: tension turns austenite into martensite. Need energy. It can now be energetically more favorable to form suitably oriented martensite areas instead of plastic deformation in the austenite phase if the increase in internal energy during deformation in the austenite phase is greater than the free energy of the martensite phase. Stress-induced martensite then forms. Here, too, the voltage remains practically constant during the forming process (area II). If the load is removed again, the free energy of the austenite is lower again and the austenite phase is formed again. There is a certain delay in the reconversion (area III) so that the voltage level is somewhat lower (area IV). The two-way effect must obviously be based on the fact that when the austenite cools down, a martensite phase arises which is macroscopically deformed compared to the austenite phase. But how is that supposed to work? From an energetic point of view, it should always be best to form the martensite phase in such a way that it arises from the austenite phase without changing its shape. In fact, this eect is based on a trick that can first be explained with a substitute model [12]. We are constructing a strip of shape memory metal that takes on a straight shape in the austenite phase, the

15 2.3 Explanation of the shape memory eects 43 a: Austenite phase: spring force is not sufficient for deformation. b: Martensite phase: the favorable phase is preferentially formed during cooling. Figure 2.9: Extrinsic two-way eect. When cooling from the austenite phase, martensite of one orientation is preferentially formed because of the applied stress. the strip has memorized. We clamp this strip at one end and attach a spring to the other end, which tries to bend the strip, but whose force is not sufficient to deform the austenite, see Figure 2.9.If one cools down below the transition temperature, the martensite phase would normally form in such a way that the macroscopic shape does not change (Fig. 2.7 a and 2.7 b). Because of the applied external tension, it is energetically more favorable if the martensite phase has a preferred orientation. It is usually the case that martensite areas with any orientation arise initially, but that favorably oriented regions grow faster than unfavorably oriented ones. This uneven growth of the different orientations then leads to a macroscopic deformation, whereby the spring contracts. If the system is heated up again, the austenite phase forms again and assumes its original shape. In doing so, it exerts a corresponding force on the spring. This eect is also known as an extrinsic two-way eect (Latin extrinsecus, outside). The secret of the two-way effect is based on the use of tension to influence the formation of the martensite phase. These stresses can also be present within the material as internal stresses that can be generated, for example, by dislocation movement or by cooling. In this case, the eect is intrinsic (Latin intrinsecus, within). In order to introduce such intrinsic stresses into the material, it has to be trained: This can be done, for example, by repeated plastic deformation. A load is applied that brings the material into the desired shape, then the load is removed and the material is heated up (using the one-way effect) and then cooled down again. If such a cycle is repeated about ten to twenty times, the dislocations formed during plastic deformation create a two-way effect: stresses control the martensite shape. For the two-way eect you have to train the material to create tension.

16 44 2 Shape Memory Alloys Free Energy Cooling Martensite Heating Austenite Temperature Percentage Austenite Cooling Heating Temperature Image Hysteresis in the transformation of austenite into martensite. As in Figure 2.4 it is assumed that the internal energy and the entropy themselves do not depend on the temperature. More detailed explanation in the text. internal stress field, which then controls the formation of the martensite phase. With the two-way effect, the phase transition takes place during cooling at a lower temperature than during heating. This eect is comparable to the undercooling of water: If you cool pure water very slowly below freezing point, it can remain liquid below a temperature of 0 C because ice crystals can only form on crystallization nuclei. This is similar for shape memory alloys. Directly at the point of the phase transition, the free energy of the two phases is the same, see picture The conversion from one phase to the other would therefore take a very long time at this temperature. If the temperature is lowered further, the driving force for the phase transition increases. If a shape memory alloy is cooled from the austenite phase, the transformation into the martensite phase usually only begins below the actual phase transition temperature. If you then heat up again, the transition temperature is higher than the actual phase transition temperature, because the driving force for this process is initially zero. So there is a hysteresis, see picture The width of the hysteresis in the often used alloy Nitinol is around 50 C [46]. There is a similar delay in the stress-induced transformation in a superelastic material. Therefore, the level of tension on the plateau is lower when the load is released than when the load is applied. If this delay is large enough, it can also happen that the deformation is no longer reversible, but remains as plastic deformation. In this case you first have to use the

17 2.4 Applications 45 Figure 2.11: Stent for expanding veins. The stent folds inside a catheter and expands when the catheter is withdrawn in the vein. At the ends of the stent there are tantalum platelets that have a good X-ray contrast. Increase temperature to form austenite again. This is another way of realizing the one-way eect. Finally, the question still remains to be clarified, how the desired shape for the one-way eect or the superelasticity is imprinted on the material. If the material has a memory, how is this memory set in the beginning? For this purpose, the material is mechanically brought into the desired final shape at a sufficiently high temperature (in the case of nitinol in the range of 500 C). It is now in the austenitic phase. Creep processes ensure that the internal stresses that arise during deformation are reduced and that the material retains the desired shape [26]. As a result, the forced shape is now imprinted and is retained when it cools down. The shape is imprinted during a heat treatment. 2.4 Applications The main area of ​​application for shape memory alloys is currently medical technology. In minimally invasive surgery, in which the intrusion into the body should be kept as small as possible, super-elastic guide wires are inserted into the body, for example to guide diagnostic devices. The use of super-elastic wires has the advantage that, on the one hand, they have a high degree of rigidity, but on the other hand, they do not tend to kink, so that they can be guided more easily and removed again. Another important application are so-called stents, which are used to expand veins that are threatened with collapse, see picture These are small, tubular woven metal wires that are strongly compressed in a super-elastic state and inserted into a catheter. The catheter is then withdrawn within the vein and the tube unfolds, exerting even pressure on the vein walls. A special functional material is often used in these stents: The tips of the stent can be provided with small plates made of tantalum. Tantalum is a good absorber for X-rays and thus facilitates the precise positioning of the stent within the body. Super-elastic alloys are also advantageous in dental technology. There they are used as tension wires in tooth brackets. The advantage here lies in applications in medical technology. Shape memory alloy stents keep blood vessels open.

18 46 2 Shape memory alloys Figure 2.12: Lock breaking in response to a signal (frangibolt). A cylinder made of a shape memory alloy is heated by the supply of electricity and can break a screw at a notch. Such closures are used, for example, in space travel to blow off parts or unfold solar sails. (Courtesy of TiNi Aerospace, Inc.) Super-elastic braces and glasses take advantage of the tension plateau. Surgical staples compress bones together. How do you blow a cap? Actuators with shape memory. Problem: The eect is used up. that large elastic strains are possible and that, when the tooth follows the pull of the wire, the tension remains constant because of the plateau in the tension-strain curve. Such clasps therefore have to be retightened less often. Eyeglass frames with super-elastic temples made of shape memory alloys can withstand large deformations reversibly and can therefore withstand extreme loads [63]. The one-way eect is used for surgical staples in bone healing: a staple can be attached to two bones to be joined. If it warms up to body temperature, it deforms and thus presses the two pieces of bone together. One application in space travel are locking mechanisms that break in response to a signal. A screw is provided with a notch and then enclosed in a cylinder made of a shape memory alloy that was compressed in the martensitic phase. If you introduce electricity, the cylinder heats up and expands, so that the screw breaks. 4 The two-way eect has so far been used very little in practice. A two-way actuator 5 with external tension (i.e. a restoring spring) was used to open and close a valve on a thermostat. Other conceivable applications are actuators in microtechnology, for example for moving read heads in hard drives, robotic grippers or active endoscopes. A problem with the application of the one and two-way eect is that these eects cannot be repeated as often as desired. With every phase transition within the material, defects form at the interfaces between the phases. These shift the transition temperature so that it can be shifted by more than 20 C after a few thousand cycles. Attempts are therefore being made to develop alloys that do not have this effect [46]. 4 In principle, a similar eect could also be achieved simply by thermal expansion. The forces achieved here are, however, relatively small, so that large changes in temperature would be necessary. 5 An actuator converts a signal into a mechanical movement.

19 2.5 Key Concepts 47 A disadvantage of components made of shape memory alloys is that switching is usually relatively slow, as it takes place via a change in temperature. Particularly in the case of large components, the thermal capacity of the components requires correspondingly long heating times. The advantage of these alloys is that complex changes in shape with large deformations and large forces can also be implemented. In the next chapter we will get to know another class of material that behaves in exactly the opposite way: Here, deformation paths are small, but switching can take place very quickly. 2.5 Key concepts Disadvantage of shape memory alloys: Temperature changes require long switching times. Advantage: large changes in shape are possible. ˆ Crystalline solids can exist in different crystal structures. These are described by their unit cell. ˆ Systems in contact with a heat bath at temperature T reach thermal equilibrium. In this equilibrium, the probability of a microstate Z i can be given by the Boltzmann law p i = 1 Z e Ei / k BT. ˆ In a system at temperature T the energy fluctuates due to thermal fluctuations by amounts in the order of magnitude of k B T. ˆ The entropy in a closed system is determined by the number of possible microstates for a certain macrostate. In thermal equilibrium, the most likely macrostate is therefore the one with the highest entropy. ˆ In a system in thermal equilibrium (with a fixed volume at a fixed temperature) the free energy is minimized. ˆ Phase transitions occur because different phases can have a different temperature dependence of the free energy. In order to minimize the free energy, a system can therefore switch between different phases when the temperature changes. ˆ At high temperatures there is a system in the phase with the highest entropy, at low temperatures in the phase with the lowest energy.

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