Bessemer Memorial Lecture The dimensions of steel

H. K. D. H. Bhadeshia*

There are important aspects of steel hexagonal close–packed (h.c.p., e) and allotropes of iron which may or may not which are hidden from ordinary view cubic–close packed (c.c.p., c–austenite). exist in reality. Fig. 1 shows a favourite and largely from the users of steels. The last structure is more commonly graph which captures the essence of They nevertheless determine the referred to as face–centred cubic but the method.4 It shows the cohesive macroscopic behaviour. One example is c.c.p. is preferred since it emphasises energy at 0 K of the postulated crystal that the magnetic properties of close–packing. It is possible that other structures of iron, as a function of the austenite determine that it has a larger crystal structures are present in bulk density. Of all the test structures, h.c.p. thermal expansion coefficient than form at the very high pressures and iron is found to show the highest ferrite, whereas intuition would suggest temperatures in the core of the Earth.1 cohesion and therefore should otherwise given that austenite has a For example, the double hexagonal represent the most stable form. This greater density. This and other aspects close–packed structure in which the result contradicts experience, because of the physical and descriptive stacking sequence of close–packed b.c.c. iron occurs naturally at low dimensions of steel are described in this planes is …ABAC…, repeated every temperatures and ambient pressure. paper. four layers, in contrast to …ABAB… for The discrepancy arises because the h.c.p. and …ABC… for c.c.p.. This calculations in this case neglect peculiar structure occurs in the rare magnetic effects – it is ferromagnetism 2 Some of the resources that Bessemer earth elements Am, La, Nd and Pr. which stabilises b.c.c. iron over the had to conjure in order to experiment There is some evidence from diamond h.c.p. form. There are of course on the making of steel came from his anvil experiments of the existence of calculations which account for secret method for manufacturing fine d.h.c.p. iron at high pressures and magnetism and predict the correct 3 5 particles of brass, used in ‘gold’–paint. temperatures. However, the ground state. Small metallic particles are still a topic pressures achieved there are The diamond form of iron (Fig. 1) 23 of research and speculation, but the apparently only a third of the .350 GPa would have a density of only 5 g cm general notion of understanding how at the earth’s core, in which case which compares with about . 23 tangible objects behave when their calculations suggest that the solid iron 7 8gcm for ordinary iron. internal or external dimensions are at the core should be in the h.c.p. Unfortunately, the calculations show manipulated is a fascinating subject. structure under equilibrium. That solid that the difference in energy between Iron is in this context especially core of e–iron would truly correspond to the diamond and b.c.c. forms is so interesting given the superposition that the ‘bulk form’ emphasised earlier, with large that it is improbable that the is possible of magnetic, atomic and dimensions measured in kilometres! b.c.c. R diamond transformation other entities in a rich variety of ways Quantum mechanics can be used to can be induced, for example, by that yield an equally diverse range of examine the possibility of other alloying. properties and phenomena. I hope in this paper to describe this subject, taking liberties with the term dimension. Whilst the meaning of external dimensions is obvious, an internal dimension refers either to the scale over which a defined periodicity is maintained, or to some fractional dimension associated with the roughness of internal features such as interfaces.

Allotropes of iron in three and two dimensions Only three crystalline allotropes of iron are readily available in bulk form, the body–centred cubic (b.c.c., a–ferrite),

University of Cambridge, Materials Science and Metallurgy, U.K; Graduate Institute of Ferrous 1 Plot of cohesive energy versus the normalised volume per atom for a vari- Technology, Postech, Korea ety of trial crystal–structures of iron. Hexagonal–P and Cubic–P are primi- *www.msm.cam.ac.uk/phase–trans tive structures4

ß 2007 Institute of Materials, Minerals and Mining Published by Maney on behalf of the Institute 194 DOI 10.1179/174328107X174753 Ironmaking and Steelmaking 2007 VOL 34 NO 3 NEWS AND VIEWS

There are two further allotropes austenitic stainless steels cannot be which have been created in the form of used with vengeance in the thin films with some fascinating construction of efficient steam outcomes. Face–centred tetragonal turbines.17–19 The much higher thermal iron can be prepared by coherently expansivity of the austenite when depositing iron as a thin film on a {1 0 0} compared with ferrite gives rise to plane of a substrate such as copper, thermal fatigue. The higher creep with which the iron has a mismatch. strength of the austenite cannot The position of atoms in the first therefore be exploited so we are stuck deposited layer in this case replicates with steam temperatures of about that of the substrate. A few 620uC unless other much more monolayers can be forced into expensive materials are used in place coherency in the plane of the substrate of steel. with a corresponding distortion normal 2 Variety of dipole alignments in Two–dimensional magnets to the substrate. This gives the deposit materials containing atoms with a face–centred tetragonal structure unspin–paired electrons There are two special magnetic effects which in the absence of any mismatch associated with thin films of iron. would be face–centred cubic.6,7 low temperatures by coherent Firstly, the magnetic moment per atom 13,14 . Eventually, as the film thickens during precipitation in copper. becomes very large (3 1 mB) when . the deposition process to beyond about The antiferromagnetic state of compared with bulk iron (2 2 mB). ten monolayers (on copper), the austenite is more dense than the Secondly, there exists a large structure relaxes to the low–energy ferromagnetic state. If pure iron is perpendicular magnetic–anisotropy in b.c.c. form, a process accompanied by coherently deposited as a thin film on a ultrathin epitaxial films of iron. the formation of dislocation defects hot–copper substrate, then it remains The increase in the magnetic which accommodate the misfit with austenitic but is ferromagnetic at the moment per atom is due to the smaller the substrate. deposition temperature because of the coordination number for atoms in a thin Growing iron on a misfitting {1 1 1} larger lattice parameter it is forced to film. The atoms of the substrate used surface of a face–centred cubic adopt.15 This can also be done at to produce the thin film do not substrate similarly causes a distortion ambient temperature by expanding the contribute to the coordination number along the surface normal, giving lattice parameter of copper with gold in because there is a lack of hybridisation trigonal iron.8 We shall see in the next solid solution.16 between the electronic states of the 20,21 section that these thin films have The effects of the strange magnetic iron layer and the substrate. The d–bands in bulk ferromagnets are much unusual magnetic properties. properties of austenite are routinely broader than they would be for a single observed in steel metallurgy and atom because of hybridisation between Small magnets of austenite engineering. Because the low–density atoms. In reducing the number of ferromagnetic austenite is promoted Commercially available ferrite–meters nearest neighbours, the hybridisation over the high–density monitor the magnetism in steel is reduced so the bands become antiferromagnetic austenite as the samples and thereby indicate the ‘atomic–like’. This squashing of the temperature is increased, the thermal quantity of ferrite in the microstructure. d–bands increases the density of states expansion coefficient of austenite is This assumes that any austenite gives a at the Fermi level, and resolves the much greater than that of ferrite. This null response. majority spin–up band from the of course is a major reason why But austenite in fact has fascinating minority spin–down band. A magnetic properties – from a pragmatic low–coordination atom therefore has point of view, the austenite coexists as Table 1 Transformation temperatures more electrons in its majority spin–up and thermodynamic data for pure two magnetic phases in a single 10–12 band, and so has a higher moment per crystalline phase.9 The magnetic phases iron at ambient pressure. The atom. An isolated atom has the highest transformation temperatures are correspond to two different states of consistent with the International moment and the bulk material the electron spin separated by a small Practical Temperature Scale, which lowest. Reducing the coordination energy gap. The ground state was in 1968 modified by raising the makes the material less bulk–like and corresponds to antiferromagnetic designated melting point of more single–atom–like. a austenite with a small magnetic palladium by 2 K. T c is the Curie The magnetic anisotropy seen in thin moment per atom and a Ne´el temperature for the transition films is a general feature found even in between the ferromagnetic and temperature in the range 55–80 K. In bulk iron where it is more readily paramagnetic states of ferrite. The contrast the state excited at high approximate Curie and Ne´el magnetised along the n100m axis than temperatures has a huge moment of temperatures for the two states of along the n111m axis of the b.c.c. . 2 8 Bohr magnetons (mB) per atom and a austenite are also stated form. Anisotropy is caused by the Curie temperature of about 1800 K. The coupling of the directions of the spin T, C T,K nature of the spin alignments in various u magnetic moments and orbital magnetic states is illustrated in Fig. 2. aRc 911.5 1184.65 magnetic moments. For a thin film of It is curious that the Ne´el cRa 1394.0 1667.15 iron, the net effect is often such that it temperature of austenite can be cRL 1527.0 1800.15 causes the spins to align in a direction measured given that it is unstable in aRL 1538.0 1811.15 normal to its plane. Thus, thin layers of a . . pure iron below 911.5 C, Table 1. It T c 769 0 1042 15 iron separated by intervening layers of u c turns out that minute particles of pure T c 1800 chalcogenides have been found to be T c 55–80 iron can be retained as austenite to very N highly anisotropic with the internal field

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perpendicular to the plane.22 Such arises because of an interaction of the well–defined for objects which are materials show a large change in Fe 3d and substrate 4d band electrons. rough, because they depend on the resistance as the magnetic field is The interaction can induce weak resolution of the measuring technique. changed and may have applications as magnetic moments in the adjacent The surface area of a brick is a function improved detectors in recording substrate atoms (Au, Ag, Pd) which of the method used to measure the devices. normally are not magnetic. area; the brick is said to be a rough The details of this spin alignment The degree of magnetic anisotropy object. normal to the plane of the film can only varies with the thickness of the iron The way in which the measured be accessed via precise calculations of film. For austenite ‘clamped’ to the property varies with resolution is the band structure along different (1 0 0) plane of copper, the anisotropy expressed using a single number crystallographic directions. However, changes as a function of the number of known as a fractal dimension.30 For

Van Vleck proposed a model which monolayers deposited, becoming example, the amount of ab/c interfacial gives some intuitive feel for the maximum at 5 layer thick film. This is area per unit volume SV can be written problem. Quantum mechanics shows related to the fact that the f.c.c. iron ~ DT ÀD that the spin direction and spin orbit films expand normal to the surface with SV S0e (1) the strain reaching a maximum value of energy are coupled. Thus, as the spin where S0 is the surface–to–volume direction changes, the spin orbit energy 6% at 5 layer thick films. This ratio of a smooth object of topological phenomenon is attributed to subtle changes and so the electron dimension DT and D is the details of the electronic band structure wavefunction must redistribute in order corresponding fractal dimension of a which is critically dependent on the to change the spin direction. This rough object. For a smooth object, strain.25 change in the wavefunction changes DT5D and hence SV5S0. the electron overlap between nearest The fractal dimension of bainite neighbour atoms, which alters Fractional dimensions when treated as a three–dimensional electrostatic interactions. The energy of An aspect of the bainite reaction in object has been estimated to be the system becomes a function of the . . steels is that it occurs by a stepwise approximately 3 6–3 7, determined by direction of the electron spin with mechanism in which a platelet of ferrite making measurements over a large respect to the crystalline lattice. Hence, 25 grows to a limited size, even though range of spatial resolutions, 10 – magnetocrystalline anisotropy which 29 32 there is no impingement with obstacles 10 m. Modelling a bainite sheaf as reflects the symmetry of the crystalline such as austenite grain boundaries. The a fractal in which self–similarity lattice. In bulk iron this is cubic whereas transformation then propagates by the propagates over an infinite range of in a monolayer it must be uniaxial and nucleation and growth of another unit, observations gives a fractal dimension hence the spins rotate out of plane. the collection of units being known as a of 4. A true fractal character, which There is a further consequence of the sheaf.26 indefinitely repeats itself at ever finer fact that the magnetisation tends to be The units within an individual bainite resolutions, is not physically normal to the film of iron.23 Bulk sheaf are contiguous, as shown by the reasonable. The sheaf in reality samples of iron generally contain a tracing in Fig. 3a, made using an actual contains much less detail and magnetic–domain structure to 32 transmission electron microscope roughness when examined with care. minimise the overall energy. But image of a bainite sheaf.27–29 It follows The bainite sheaf cannot therefore be domain formation is opposed by the that the topology of the austenite regarded as consisting of many exchange energy which acts to make generations of ever finer sub-units, but (c)/bainitic–ferrite (ab) interface is far the magnetic moment of each atom from smooth. at the same time is not a smooth object line up with the moments of its A smooth object is one whose with a fixed surface area independent neighbouring atoms. Consequently, properties do not change with of magnification. Fig. 4 shows how the sufficiently small particles tend to have resolution, for example, the perimeter ab/c interfacial area area per unit a single domain structure. This applies of a perfect circle. Measures such as volume varies with the measurement to thin films as well. Thus, thin films of perimeter and surface area are not resolution, together with a curve cobalt with in–plane magnetisation are assuming an ideal fractal. The single–domain whereas iron films interfacial area increases at higher where the magnetisation in normal to the film plane contain a domain structure. Reducing the thickness of an iron film has no influence on its domain structure. When ultra–thin layers of iron are deposited on slightly mismatching substrates, the spins mostly tend to align along the normal to the film. This is confirmed both experimentally20,24 and using total energy calculations 3 (a) Represents a tracing from a which show that the spin–alignment is transmission electron micrograph in–plane for a free–standing monolayer of a bainite sheaf.31 The tracing of iron, but perpendicular when a was then electronically reduced in 4 Comparison of measured variation

monolayer of iron is deposited on a magnification and used to gener- in the amount of ab/c interfacial 21 monolayer of Au, Ag or Pd. The ate the larger sheaf illustrated in area per unit volume (SV) versus difference with free–standing iron (b) that calculated for an ideal fractal

196 Ironmaking and Steelmaking 2007 VOL 34 NO 3 NEWS AND VIEWS

resolutions but not as rapidly as would Table 2 TI,Vc, sY and sUTS stand be the case for a true fractal. for isothermal transformation tem- What then are the consequences of perature, the volume fraction of retained austenite, the 0.2% proof this roughness? The answer depends and ultimate tensile strengths on the property of interest. In a respectively49 thermodynamic context it is important s , s , Elongation, to measure SV at a resolution Y UTS consistent with the spacing of TI, uCVc GPa GPa % dislocations in the interface. The 200 0.17 1.41 2.26 7.6 product of SV and the interfacial energy 300 0.21 1.40 1.93 9.4 per unit area then gives the amount of 400 0.37 1.25 1.727.5 energy stored in the material in the . . . . . form of boundaries, energy which has 5Fe-098C-1 46Si-1 89Mn-0 26Mo-1 26Cr- . when forced to shear failed to deform to be supplied to create the boundaries 0 09V wt-%, transformed at 200uC by ordinary mechanisms and instead in the first instance.33 This quantity is a for 5 days. Transmission electron 41,42,44 underwent displacive transformation to measure of the internal dimension of micrograph austenite at room temperature as a the steel, since the grain size defined ¯ deformation is plastically way of accommodating the applied as a mean lineal intercept L is inversely 40 34 accommodated in the adjacent stress. related to SV as 2/L¯ 5SV. 27,35 On the other hand, when considering austenite adjacent. The resulting The motivation for ever finer grain a phenomenon such as fracture, it is dislocation debris renders the interface sizes comes from a desire for stronger immobile, and hence the sub–unit materials. Work–hardening must appropriate to measure SV using a much coarser resolution in the region of mechanism of sheaf growth. This therefore be introduced into micrometers, reflecting the dimensions mechanism is quantitatively nanostructured materials to avoid 36 of the plastic zone associated with predicted. plastic instabilities and hence enable typical cracks. From a physical point–of–view, it is the exploitation of strength. This has Also indicated on Fig 4 are expected and observed that there been achieved in a wonderful steel by phenomena linked with specific should exist only two generations, introducing retained austenite between resolutions. Chemical attack, for leading to a bimodal distribution of plates of bainite, each of which is 37 example using an etchant or a corrosive sub–unit sizes. The largest generation thinner than a typical carbon 41–47 medium, is sensitive to defect density represents the platelets which have nanotube, Fig. 5. Notice that and the fluids concerned interact both formed to the point where their growth although the thickness of the plates is at a molecular level and at a level where is stifled by mechanical of the order of 20–40 nm, their length is 27,36 capillarity effects become important. stabilization. The much smaller much longer. Nevertheless, the mean For studying chemical reactivity, it platelets are the sub–operational slip distance through a plate is about twice the thickness, so in spite of the would be necessary to measure SV at embryos which have yet to make it into 37 least at a resolution of 1027 m. the rapid growth stage. anisotropy of shape, this can, from a In contrast, dislocations have a line strength point of view, be classified as a nanostructured metal. The mixture of tension and long range strain fields. Mixed internal dimensions Therefore the roughness in the large and small dimensions is an interface is only relevant at coarser A high density of internal surfaces is advantage over equiaxed grains in resolutions and it is appropriate to not always good for a steel. This is giving a much greater amount of because the boundaries either act as surface per unit volume within the measure grain size (related to SV) using 48 resolutions in the micrometre range. sinks for dislocations or there is bulk. When considering structures which insufficient room for dislocation In this microstructure, the austenite have evolved over geological or multiplication mechanisms to operate. transforms into martensite under the astronomical time scales (for example As a consequence there is no influence of applied stress and this the meteorites), it is likely that the grain mechanism for work hardening and results in work hardening, with large boundaries have smoothed in order to nanostructured materials therefore and almost completely uniform plastic minimise energy and have evolved into suffer from plastic instability soon after strain Fig. 6, details listed in Table 2. 38,39 huge grain sizes. In this case a yielding. Indeed, in one What then determines the fracture experiment, a nanostructured ferrite strain? representative measurement of SV can be made at a much coarser scale. Causes of interface roughness The question arises, why is the fractal dimension of bainite different from its topological dimension? The answer is found again in the structure of the interface which is glissile. A glissile interface contains glide dislocations whose motion is impeded by any obstacle which leads to work– hardening of the austenite. Because 6 Fe–0.79C–1.56Si–1.98Mn–0.24Mo–1.01Cr–1.51Co–1.01Al wt %. True and engi- bainite forms at temperatures where neering stress–strain curves. (a) Bainite generated by transformation at the austenite is weak, it shape 200uC. (b) Bainite generated by transformation at 300uC. Data from Ref. 49

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threshold when freely overlapping anisotropic grains to boost the total objects (general ellipsoids) are placed in amount of interfaces per unit volume. a matrix.52 Since the austenite is Steel therefore leads in the context of subdivided roughly into the form of bulk nanostructured materials for plates by the bainite, it can be structural applications, whether these represented by oblate ellipsoids with an are metallic or otherwise. aspect ratio r of between about 1/10 and 1/100. The percolation threshold is References then found to be p .1.27r, i.e., c 1. D. Alfe, M. J. Gillan, L. Vocadlo, 0.127>p >0.0127. This is consistent c J. Brodholt, and G. D. Price: ‘The ab with the observation that tensile failure initio simulation of the earth’s occurs when V .0.1. 7 Calculated variation in the fraction c core’, Philos. Trans. R. 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