Habit plane

The orientational relationships between the martensite and austenite lattice which we observe are partially in accordance with experimental results In experiments a Nishiyama-Wasserman relationship is found for those systems which we have simulated. We think that the additional rotation of the (lll)f< c planes in the simulations is an effect of boundary conditions. Experimentally bcc and fee structure coexist and the plane of contact, the habit plane, is undistorted. In our simulations we have no coexistence of these structures. But the periodic boundary conditions play a similar role like the habit plane in the real crystals. Under these considerations the fact that we find the same invariant direction as it is observed experimentally shows, that our calculations simulate the same transition process as it takes place in experiments. The same is true for the inhomogeneous shear system which we see in our simulations. 

In dynamic ETEM studies, to determine the nature of the high temperature CS defects formed due to the anion loss of catalysts at the operating temperature, the important g b criteria for analysing dislocation displacement vectors are used as outlined in chapter 2. (HRTEM lattice images under careful conditions may also be used.) They show that the defects are invisible in the = 002 reflection suggesting that b is normal to the dislocation line. Further sample tilting in the ETEM to analyse their habit plane suggests the displacement vector b = di aj2, b/1, 0) and the defects are in the (120) planes (as determined in vacuum studies by Bursill (1969) and in dynamic catalysis smdies by Gai (1981)). In simulations of CS defect contrast, surface relaxation effects and isotropic elasticity theory of dislocations (Friedel 1964) are incorporated (Gai 1981). 

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. 

Diffusionless transformations have been sometimes called military , in contrast to the more civilian diffusion controlled transformations. Considering their technical relevance, the crystallographic theory of martensite transformation has been worked out in much detail, and particularly for the habit plane selection of the given 0-0 lattice structural change. The reader is referred to the corresponding metallurgical literature (D.A. Porter, K.E. Easterling (1990) D.S. Liebermann (1970) C.M. Wayman (1983)]. 

Wayman describes in detail how the tensor formalism can be used to solve the crystallographic problem [5]. A simple graphical demonstration, in two dimensions, of how an invariant line (habit plane) can be produced by the deformations B, S, and R is given in Exercise 24.6. 

The input data for the model consist of the description of the lattice deformation and the choice of the slip system in the lattice-invariant shear. The model has successfully predicted the observed geometrical features of many martensitic transformations. The observed and calculated habit planes generally have high indices that result from the condition that they be macroscopically invariant. 

Because of the four-fold symmetry of the [001] pole figures in Figs. 24.6-24.9, additional symmetry-related invariant planes can be produced. Also, further work shows that additional invariant planes can be obtained if a lattice-invariant shear corresponding to a = 7.3° rather than a = 11.6° (see Fig. 24.8) is employed [5]. Multiple habit planes are a common feature of martensitic transformations. 

In many cases, the martensite phase is internally twinned and is composed of two types of thin twin-related lamellae, as illustrated in Fig. 24.10. In such cases, the lattice-invariant shear is accomplished by twinning rather than by slip as has been assumed until now (see Fig. 24.106). The critical amount of shear required to produce the invariant habit plane is then obtained by adjusting the relative thicknesses of the two types of twin-related lamellae shown in Fig. 24.106. 

The crystallographic model for martensite described above is primarily due to Wechsler et al. [1], A similar model, employing a different formalism but leading to essentially equivalent results, has also been published by Bowles and MacKen-zie [2-4]. In both models, a search is made for an invariant (or near-invariant) plane which is then proposed as the habit plane, since the selection of this plane... 

---