Kinetics of structural change: III – displacive transformations 81 Fig. 8.5. The diffusive f.c.c. → b.c.c. transformation in iron: the time–temperature–transformation (TTT) diagram, or “C-curve”. The 1% and 99% curves represent, for all practical purposes, the start and end of the transformation. Semi-schematic only. Fig. 8.6. If we quench f.c.c. iron from 914°C to room temperature at a rate of about 10 5 °C s −1 we expect to prevent the diffusive f.c.c. → b.c.c. transformation from taking place. In reality, below 550°C the iron will transform to b.c.c. by a displacive transformation instead. 82 Engineering Materials 2 Fig. 8.7. The displacive f.c.c. → b.c.c. transformation in iron. B.c.c. lenses nucleate at f.c.c. grain boundaries and grow almost instantaneously. The lenses stop growing when they hit the next grain boundary. Note that, when a new phase in any material is produced by a displacive transformation it is always referred to as “martensite”. Displacive transformations are often called “martensitic” transformations as a result. Table 8.2 Characteristics of transformations Displacive (also called diffusionless, shear, or martensitic) Atoms move over distances խ interatomic spacing. Atoms move by making and breaking interatomic bonds and by minor “shuffling”. Atoms move one after another in precise sequence (“military” transformation). Speed of transformation ≈ velocity of lattice vibrations through crystal (essentially independent of temperature); transformation can occur at temperatures as low as 4 K. Extent of transformation (volume transformed) depends on temperature only. Composition cannot change (because atoms have no time to diffuse, they stay where they are). Always specific crystallographic relationship between martensite and parent lattice. Diffusive Atoms move over distances of 1 to 10 6 interatomic spacings. Atoms move by thermally activated diffusion from site to site. Atoms hop randomly from site to site (although more hop “forwards” than “backwards”) (“civilian” transformation). Speed of transformation depends strongly on temperature; transformation does not occur below 0.3 T m to 0.4 T m . Extent of transformation depends on time as well as temperature. Diffusion allows compositions of individual phases to change in alloyed systems. Sometimes have crystallographic relationships between phases. Kinetics of structural change: III – displacive transformations 83 grains at speeds approaching the speed of sound in iron (Fig. 8.7). In the “switch zone” atomic bonds are broken and remade in such a way that the structure “switches” from f.c.c. to b.c.c This is very similar to the breaking and remaking of bonds that goes on when a dislocation moves through a crystal. In fact there are strong parallels between displacive transformations and plastic deformation. Both happen almost instantaneously at speeds that are limited by the propagation of lattice vibrations through the crystal. Both happen at low as well as at high temperatures. And both happen by the precisely sequenced switching of one atom after another. As Table 8.2 shows, most characteristics of displacive transformations are quite different from those of diffusive transformations. Details of martensite formation As Fig. 8.8 shows, the martensite lenses are coherent with the parent lattice. Figure 8.9 shows how the b.c.c. lattice is produced by atomic movements of the f.c.c. atoms in the “switch zone”. As we have already said, at ≈ 550°C martensite lenses form and grow almost instantaneously. As the lenses grow the lattice planes distort (see Fig. 8.8) and some of the driving force for the f.c.c. → b.c.c. transformation is removed as strain energy. Fewer lenses nucleate and grow, and eventually the transformation stops. In other words, provided we keep the temperature constant, the displacive transforma- tion is self-stabilising (see Fig. 8.10). To get more martensite we must cool the iron down to a lower temperature (which gives more driving force). Even at this lower temperature, the displacive transformation will stop when the extra driving force has been used up in straining the lattice. In fact, to get 100% martensite, we have to cool the iron down to ≈ 350°C (Fig. 8.10). Fig. 8.8. Martensites are always coherent with the parent lattice. They grow as thin lenses on preferred planes and in preferred directions in order to cause the least distortion of the lattice. The crystallographic relationships shown here are for pure iron. 84 Engineering Materials 2 Fig. 8.9. (a) The unit cells of f.c.c. and b.c.c. iron. (b) Two adjacent f.c.c. cells make a distorted b.c.c. cell. If this is subjected to the “Bain strain” it becomes an undistorted b.c.c. cell. This atomic “switching” involves the least shuffling of atoms. As it stands the new lattice is not coherent with the old one. But we can get coherency by rotating the b.c.c. lattice planes as well (Fig. 8.8). Fig. 8.10. The displacive f.c.c. → b.c.c. transformation in iron: the volume of martensite produced is a function of temperature only, and does not depend on time. Note that the temperature at which martensite starts to form is labelled M s (martensite start); the temperature at which the martensite transformation finishes is labelled M F (martensite finish). Kinetics of structural change: III – displacive transformations 85 The martensite transformation in steels To make martensite in pure iron it has to be cooled very fast: at about 10 5 °C s −1 . Metals can only be cooled at such large rates if they are in the form of thin foils. How, then, can martensite be made in sizeable pieces of 0.8% carbon steel? As we saw in the “Teaching Yourself Phase Diagrams” course, a 0.8% carbon steel is a “eutectoid” steel: when it is cooled relatively slowly it transforms by diffusion into pearlite (the eutectoid mixture of α + Fe 3 C). The eutectoid reaction can only start when the steel has been cooled below 723°C. The nose of the C-curve occurs at ≈ 525°C (Fig. 8.11), about 175°C lower than the nose temperature of perhaps 700°C for pure iron (Fig. 8.5). Diffusion is much slower at 525°C than it is at 700°C. As a result, a cooling rate of ≈ 200°C s −1 misses the nose of the 1% curve and produces martensite. Pure iron martensite has a lattice which is identical to that of ordinary b.c.c. iron. But the displacive and diffusive transformations produce different large-scale structures: myriad tiny lenses of martensite instead of large equiaxed grains of b.c.c. iron. Now, fine-grained materials are harder than coarse-grained ones because grain boundaries get in the way of dislocations (see Chapter 2). For this reason pure iron martensite is about twice as hard as ordinary b.c.c. iron. The grain size argument cannot, however, be applied to the 0.8% carbon steel because pearlite not only has a very fine grain size but also contains a large volume fraction of the hard iron carbide phase. Yet 0.8% carbon martensite is five times harder than pearlite. The explanation lies with the 0.8% carbon. Above 723°C the carbon dissolves in the f.c.c. iron to form a random solid solution. The carbon atoms are about 40% smaller in diameter than the iron atoms, and they are able to squeeze into the space between the iron atoms to form an intersti- tial solution. When the steel is quenched, the iron atoms transform displacively to martensite. It all happens so fast that the carbon atoms are frozen in place and remain Fig. 8.11. The TTT diagram for a 0.8% carbon (eutectoid) steel. We will miss the nose of the 1% curve if we quench the steel at ≈ 200°C s −1 . Note that if the steel is quenched into cold water not all the g will transform to martensite. The steel will contain some “retained” g which can only be turned into martensite if the steel is cooled below the M F temperature of −50°C. 86 Engineering Materials 2 * This may seem a strange result – after all, only 68% of the volume of the b.c.c. unit cell is taken up by atoms, whereas the figure is 74% for f.c.c. Even so, the largest holes in b.c.c. (diameter 0.0722 nm) are smaller than those in f.c.c. (diameter 0.104 nm). Fig. 8.12. The structure of 0.8% carbon martensite. During the transformation, the carbon atoms put themselves into the interstitial sites shown. To make room for them the lattice stretches along one cube direction (and contracts slightly along the other two). This produces what is called a face-centred tetragonal unit cell. Note that only a small proportion of the labelled sites actually contain a carbon atom. in their original positions. Under normal conditions b.c.c. iron can only dissolve 0.035% carbon.* The martensite is thus grossly oversaturated with carbon and something must give. Figure 8.12 shows what happens. The carbon atoms make room for themselves by stretching the lattice along one of the cube directions to make a body-centred tetragonal unit cell. Dislocations find it very difficult to move through such a highly strained structure, and the martensite is very hard as a result. A martensite miscellany Martensite transformations are not limited just to metals. Some ceramics, like zirconia, have them; and even the obscure system of (argon + 40 atom% nitrogen) forms martensite when it is cooled below 30 K. Helical protein crystals in some bacteria undergo a martensitic transformation and the shape change helps the bacteria to bur- row into the skins of animals and people! The martensite transformation in steel is associated with a volume change which can be made visible by a simple demonstration. Take a 100 mm length of fine piano wire and run it horizontally between two supports. Hang a light weight in the middle and allow a small amount of slack so that the string is not quite straight. Then connect the ends of the string to a variable low-voltage d.c. source. Rack up the voltage until the wire glows bright red. The wire will sag quite a bit as it expands from room temperature to 800°C. Then cut the power. The wire will cool rapidly and as the γ contracts the wire will move upwards. Below M s the γ will transform almost instantane- ously to martensite. The wire will move sharply downwards (because the martensite occupies a bigger volume than the γ ). It can be seen to “shiver” as the shear waves run through the wire, and if you listen very hard you can hear a faint “pinging” sound as Kinetics of structural change: III – displacive transformations 87 Fig. 8.13. Displacive transformations are geometrically reversible. well. Down at room temperature you should be able to snap the wire easily, showing that you have indeed made brittle martensite. One of the unique features of martensite transformations is that they are structurally reversible. This means that if we displacively transform martensite back to the high- temperature phase each atom in the martensite will go back to its original position in the high-temperature lattice (see Fig. 8.13). In fact, small heat engines have been made to work using this principle – as the alloy is cycled between high and low temper- atures, the structure cycles between the high-temperature phase and martensite and the alternating shape change makes the mechanism move back and forth. A range of so-called “memory” alloys has been developed which apply this principle to devices ranging from self-closing rivets to self-erecting antennae for spacecraft. This allows of strange psychokinetic jokes: a bent (but straightened out) tea spoon made of memory- steel, inserted into a cup of hot tea, spontaneously distorts (remembering its earlier bent shape), thereby embarrassing guests and affording its owner the kind of pleasure that only practical jokers can comprehend. Further reading D. A. Porter and K. E. Easterling, Phase Transformations in Metals and Alloys, 2nd edition, Chapman and Hall, 1992. R. W. K. Honeycombe and H. K. D. H. Bhadeshia, Steels: Microstructure and Properties, 2nd edition, Arnold, 1995. K. J. Pascoe, An Introduction to the Properties of Engineering Materials, Van Nostrand Reinhold, 1978. R. E. Reed-Hill, Physical Metallurgy Principles, Van Nostrand Reinhold, 1964. 88 Engineering Materials 2 Problems 8.1 Compare and contrast the main features of (a) diffusive transformations, (b) displacive transformations. 8.2 Describe the structure of 0.8% carbon martensite (a) at the nm-scale level, (b) at the µm-scale level. Why is 0.8% carbon martensite approximately five times harder than pearlite? 8.3 Sketch the time-temperature-transformation (TTT) diagram for a plain carbon steel of eutectoid composition which exhibits the following features: (i) At 650°C, transformation of the austenite (fcc phase) is 1% complete after 10 seconds and is 99% complete after 100 seconds. (ii) The fastest rate of transformation occurs at 550°C. At this temperature, trans- formation of the austenite is 1% complete after 1 second and is 99% complete after 10 seconds. (iii) At 360°C, transformation of the austenite is 1% complete after 10 seconds and is 99% complete after 300 seconds. (iv) The martensite start temperature is 240°C. 90% of the austenite has trans- formed to martensite at 100°C. The martensite finish temperature is 50°C. Explain briefly the shape of the lines drawn on the TTT diagram. Case studies in phase transformations 89 Chapter 9 Case studies in phase transformations Introduction We now apply the thermodynamic and kinetic theory of Chapters 5–8 to four prob- lems: making rain; getting fine-grained castings; growing crystals for semiconductors; and making amorphous metals. Making rain Often, during periods of drought, there is enough moisture in the atmosphere to give clouds, but rain does not fall. The frustration of seeing the clouds but not getting any rain has stimulated all manner of black magic: successful rainmakers have been highly honoured members of society since society existed. But it is only recently that rain-making has acquired some scientific basis. The problem is one of heterogeneous nucleation. A cloud is cloudy because it is a suspension of vast numbers of minute, spherical water droplets. The droplets are too small and light to fall under gravity; and they are stable, that is to say they do not coarsen and become large enough to fall.* Rain falls when (surprisingly) the droplets freeze to ice. If a droplet freezes it be- comes a stable ice nucleus which then grows by attracting water vapour from the surrounding droplets. The ice particle quickly grows to a size at which gravity can pull it down, and it falls. On cold days it falls as hail or snow; but in warmer weather it remelts in the warmer air near the ground and falls as rain. The difficult stage in making rain is getting the ice to nucleate in the first place. If the water droplets are clean then they will not contain any heterogeneous nucleation catalysts. Ice can then only form if the cloud is cooled to the homogeneous nucleation temperature, and that is a very low temperature (−40°C; see Example 7.1). Clouds rarely get this cold. So the ice must nucleate on something, heterogeneously. Industrial pollution will do: the smoke of a steel works contains so much dirt that the rainfall downwind of it is significantly increased (Fig. 9.1). But building a steelworks to produce rain is unneces- sarily extravagant. There are cheaper ways. * We saw in Chapter 5 that there is a driving force tending to make dispersions of precipitates in alloys coarsen; and we would expect a dispersion of droplets in water vapour to do the same. Water droplets in clouds, however, carry electrostatic charges; and this gives a different result for the driving force. 90 Engineering Materials 2 Fig. 9.1. Rain falls when the water droplets in clouds turn to ice. This can only happen if the clouds are below 0°C to begin with. If the droplets are clean, ice can form only in the unlikely event that the clouds cool down to the homogeneous nucleation temperature of −40°C. When dust particles are present they can catalyse nucleation at temperatures quite close to 0°C. This is why there is often heavy rainfall downwind of factory chimneys. The crystal structure of ice is hexagonal, with lattice constants of a = 0.452 nm and c = 0.736 nm. The inorganic compound silver iodide also has a hexagonal struc- ture, with lattice constants (a = 0.458 nm, c = 0.749 nm) that are almost identical to those of ice. So if you put a crystal of silver iodide into supercooled water, it is almost as good as putting in a crystal of ice: more ice can grow on it easily, at a low under- cooling (Fig. 9.2). Fig. 9.2. The excellent crystallographic matching between silver iodide and ice makes silver iodide a very potent nucleating agent for ice crystals. When clouds at sub-zero temperatures are seeded with AgI dust, spectacular rainfall occurs. [...]... strengthening is not dominant The light alloys 103 Fig 10.2 Semi-schematic TTT diagram for the precipitation of Mg5Al8 from the Al–5.5 wt % Mg solid solution Table 10.3 Yield strengths of 5000 series (Al–Mg) alloys Alloy wt% Mg sy(MPa) (annealed condition) 5005 5050 5052 545 4 5083 545 6 0.8 1.5 2.5 2.7 4. 5 5.1 40 55 90 5 4 120 6 supersaturated 145 4 160 7 as it is in the 5000 series Turning to the other light... E1/3/r* sy /r* Creep temperature (°C) 2.7 1.7 4. 5 (7.9) 71 45 120 (210) 25–600 70–270 170–1280 (220–1600) 26 25 27 27 3.1 4. 0 2 .4 1.8 1.5 2.1 1.1 0.75 9–220 41 –160 38–280 28–200 150–250 150–250 40 0–600 (40 0–600) * See Chapter 25 and Fig 25.7 for more information about these groupings are also corrosion resistant (with titanium exceptionally so); they are non-toxic; and titanium has good creep properties... Yttrium Barium Scandium Aluminium Strontium Caesium Beryllium Magnesium Calcium Rubidium Sodium Potassium Lithium Density (Mg m−3) Tm (°C) 4. 50 4. 47 3.50 2.99 2.70 2.60 1.87 1.85 1. 74 1. 54 1.53 0.97 0.86 0.53 1667 1510 729 1538 660 770 28.5 1287 649 839 39 5 4 98 6 63 4 181 7 Comments High Tm – excellent creep resistance Good strength and ductility; scarce Scarce Reactive in air/water Creeps/melts; very... series aluminium alloys, which contain about 4% copper The Al–Cu phase diagram tells us that, between 500°C and 580°C, the 4% Cu alloy is single phase: the Cu dissolves in the Al to give the random substitutional solid 1 04 Engineering Materials 2 Fig 10.3 The aluminium end of the Al–Cu phase diagram Fig 10 .4 Room temperature microstructures in the Al + 4 wt% Cu alloy (a) Produced by slow cooling from... fail to get the peak value of yield strength Table 10 .4 Yield strengths of heat-treatable alloys Alloy series Typical composition (wt%) sy(MPa) Slowly cooled 2000 6000 7000 Al + 4 Cu + Mg, Si, Mn Al + 0.5 Mg 0.5 Si Al + 6 Zn + Mg, Cu, Mn 130 85 300 Quenched and aged 46 5 210 570 Work hardening Commercially pure aluminium (1000 series) and the non-heat-treatable aluminium alloys (3000 and 5000 series) are... striking faces of high-tech golf clubs! Further reading F Franks, Biophysics and Biochemistry at Low Temperatures, Cambridge University Press, 1985 G J Davies, Solidification and Casting, Applied Science Publishers, 1973 D A Porter and K E Easterling, Phase Transformations in Metals and Alloys, 2nd edition, Chapman and Hall, 1992 M C Flemings, Solidification Processing, McGraw-Hill, 19 74 Case studies in... easy to produce amorphous polymers and glasses, but difficult to produce amorphous metals? 100 Engineering Materials 2 Chapter 10 The light alloys Introduction No fewer than 14 pure metals have densities 4. 5 Mg m−3 (see Table 10.1) Of these, titanium, aluminium and magnesium are in common use as structural materials Beryllium is difficult to work and is toxic, but it is used in moderate quantities for... freeze and die A mutant of the organism has been produced which lacks the ability to nucleate ice (the so-called “ice-minus” mutant) American bio-engineers have proposed that the ice-minus organism should be released into the wild, in the hope that it will displace the natural organism and solve the frost-damage problem; but environmentalists have threatened law suits if this goes ahead Interestingly, ice... are, however, many non-structural applications for the light metals Liquid sodium is used in large quantities for cooling nuclear reactors and in small amounts for cooling the valves of high-performance i.c engines (it conducts heat 143 times better than water but is less dense, boils at 883°C, and is safe as long as it is kept in a sealed system.) Beryllium is used in windows for X-ray tubes Magnesium... crystals grow competitively until 92 Engineering Materials 2 Fig 9.3 A simple laboratory set-up for observing the casting process directly The mould volume measures about 50 × 50 × 6 mm The walls are cooled by putting the bottom of the block into a dish of liquid nitrogen The windows are kept free of frost by squirting them with alcohol from a wash bottle every 5 minutes Fig 9 .4 Chill crystals nucleate with . 50°C and adding ammonium chloride crystals until the solution just becomes saturated. The solution is then warmed up to 75°C and poured into the cold mould. When the solution touches the cold metal. outside and the inside of the casting. The second problem is one of grain size. As we mentioned in Chapter 8, fine-grained materials are harder than coarse-grained ones. Indeed, the yield strength. and die. A mutant of the organism has been produced which lacks the ability to nucleate ice (the so-called “ice-minus” mutant). American bio-engineers have proposed that the ice-minus organism