Bain transformation

We have mentioned above the tendency of atoms to preserve their coordination in solid state processes. This suggests that the diffusionless transformation tries to preserve close-packed planes and close-packed directions in both the parent and the martensite structure. For the example of the Bain-transformation this then means that 111) -> 011). (J = martensite) and <111> -. Obviously, the main question in this context is how to conduct the transformation (= advancement of the p/P boundary) and ensure that on a macroscopic scale the growth (habit) plane is undistorted (invariant). In addition, once nucleation has occurred, the observed high transformation velocity (nearly sound velocity) has to be explained. Isothermal martensitic transformations may well need a long time before significant volume fractions of P are transformed into / . This does not contradict the high interface velocity, but merely stresses the sluggish nucleation kinetics. The interface velocity is essentially temperature-independent since no thermal activation is necessary. 

The fcc-bct conversion, known as the Bain transformation, is a diffusionless process. That is, unlike the previous high-temperature conversions we saw earlier e.g., austenite to ferrite), martensite can form at temperatures significantly below room... 

We found that without any exception in all of our simulations Bain s lattice correspondence actually applies, i.e. one set of (110) planes of the bcc structure corresponds to a set of fee (111) planes, while the bcc [001] direction lying in these planes is transformed into the [110] direction of the fee phase. Moreover, these directions are exactly parallel to each other. This would correspond to a Nishiyama-Wassermann orientational relationship if the (110) and (111) planes would also be parallel to each other. But this is not the case. These planes are rotated around [001] by an angle between 0 and 9 during the transformation. This angle differs between the simulations in a non-systematic way. 

Najafbadi and Yip (18) have investigated the stress-strain relationship in iron under uniaxial loading by means of a MC simulation in the isostress isothermal ensemble. At finite temperatures, a reversible b.c.c. to f.c.c. transformation occurs with hysteresis. They found that the transformation takes place by the Bain mechanism and is accompanied by sudden and uniform changes in local strain. The critical values of stress required to transform from the b.c.c. to the f.c.c. structure or vice versa are lower than those obtained from static calculations. Parrinello and Rahman (14) investigated the behavior of a single crystal of Ni under uniform uniaxial compressive and tensile loads and found that for uniaxial tensile loads less than a critical value, the f.c.c. Ni crystal expanded along the axis of stress reversibly. 

Busch, L. and Bain, C. (2004) New Improved The transformation of the global agrifood system. Rural Sociology 69 (3) 321-346. 

Dav] Davenport, E.S., Bain, E.C., Transformation of Austenite at Constant Subcritical Temperatures , Transactions Amer. Inst, of Mining and Met. Eng. Iron and Steel Div, 117. (1930) [1932Takl] Takei, T., On flie Ferromagnetic Carbides in Molybdenum Steels , Kinzoku no Kenkyu, 9, 97-124 (1932) (Phase Diagram, Experimental, 5)... 

This visualisation of the diffusion-less transformation according to Bain is not totally correct. X-ray diffraction experiments have shown that, in reality, the (111) planes of the face-centred cubic lattice become the... 

We consider two simple transformation paths connecting cubic structures. They are the bcc-fcc transformation path via tetragonal deformation corresponding to extension along the [001] axis (the usual Bain s path) and the trigonal deformation path that corresponds to uniaxial deformation along the [111] axis (Figs. 1 and 2). 

Craievich et ah have shown that some energy extrema on constant-volume transformation paths are dictated by the symmetry. Namely, most of the structures encountered along the transformation paths between some higher-symmetry structures, say between bcc and fee at the Bain s path, have a symmetry that is lower than cubic. At those points of the transformation path where the symmetry of the structure is higher, the... 

A great scientific and atomistic step was taken by Bain (1 ) when he proposed a rather simple, albeit elegant, scheme for f.c.c. austenite to transform into b.c.t. martensite (Figure 1). The Bain distortion relates corresponding unit cells in the two structures and speciHes the upsetting strain, by means of which martensite is formed. This picture is too simple in itself but has remained an integral part of the more sophisticated theories that have ensued. 

The basic PTMC presented above and the notion of an internally modulated martensite phase applies to all known martensitic transformations. The idea of a shape change and lattice (Bain) correspondence is also universal. We may, therefore, conclude that martensitic transformations are shear-like (displacive) in nature, involving cooperative atomic movements. There will, accordingly, by predictable interactions with mechanical stresses, as will be seen later. 

Bainite forms isothermally as an intermediate transformation product above but below the temperature of eutectoid decomposition in ferrous alloys. This product is a mixture of ferrite and carbide, which is distinctly different from pearlite (a eutectoid product), and is termed bainite in honor of E. C. Bain who first observed such microstructures in collaboration with Davenport (Davenport and Bain, 1930). Bainite also forms during continuous cooling. Bainite transformations occur not only in ferrous alloys but also in non-ferrous... 

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