How can I determine stacking fault energy of a high manganese austenitic steel from TEM images and XRD pattern?
try to use XRD analysis method (peak shift method) to calculate SFE of the materials..if it has high Mn or Ni means fully austenitic than you can also use thermodynamic model to calculate SFE...These two methods are quite reliable as compared to other methods..if you have austenitic stainless steel than use theoritical equation for SFE Calculation ....
If you are able to observe pairs of partial dislocations separated by stacking fault ribbons, it may be possible to estimate the stacking fault energy by measuring the partial dislocation spacing. I believe this method is explained in the TEM 'bible' by Williams and Carter.
The separation width between partial dislocations can be used to calculate the associated stacking fault energy. From the measured values PSo (by TEM) of the image peak separation, values for the partial separation PS are deduced by applying the corrections introduced by Cockayne et al., Phil. Mag. 24 (1971) 1383. The stacking fault energy SFE is calculated based on isotropic and anisotropic elasticity theories; in the former case, the equation that describes the equality between SFE and the repulsive elastic force between partials with a separation PS can be used (see J.P. Hirth and J. Lothe, Theory of dislocations, McGraw-Hill Publ. Co., New York 1967, p. 298); in the latter SFE can be calculated by using PS as the input for the DISDI subroutine (J. Douin, Thèse, Université de Poitiers, 1987).
See our paper
P.N.B. Anongba and S.G. Steinemann, Dislocations and Plasticity in 113 CoSi2 Single Crystals between Room Temperature and 1173 K, Phys. Stat. Sol. (a) 140 (1993) 391
for SFE determination using partial separation.
I am not sure if the topic is still relevant. As Volker told, yes, measuring the radius of dislocation node can be used to measure the SFE. But one has to be very lucky to observe dislocation nodes in TWIP steel. I have not seen many papers. Rather, more useful should be to observe the dissociated dislocation pairs with weak beam (dark field) i.e. g-3g, g-4g or g-5g. More the weaker the beam, the higher is the resolution. But it is an experienced TEM personnels job. Then, as you said, you are concerned with TWIP steels, these are low SFE steels and the width of SFs vary dramatically. It invariably will lead to poor statistics.
Regarding X-ray method, yes there are some approaches as well, like the Schramm & Reed approach, then the method that considers the effect of dislocations on SFs to estimate SFE and finally also the approach on SFE estimation from X-ray elastic constants. If you need further information, let me know.
I am happy to say that the paper " Dislocations and Plasticity in 113 CoSi2 Single Crystals between Room Temperature and 1173 K, Phys. Stat. Sol. (a) 140 (1993) 391" is now available; see our contributions in ResearchGate.
try to use XRD analysis method (peak shift method) to calculate SFE of the materials..if it has high Mn or Ni means fully austenitic than you can also use thermodynamic model to calculate SFE...These two methods are quite reliable as compared to other methods..if you have austenitic stainless steel than use theoritical equation for SFE Calculation ....
One way of determining the SFE is by measuring the distance between the partial dislocations using transmission electron microscopy (TEM).
Using the structural characteristic of a stacking fault, Olson and Cohen12 suggested a formulation for SFE, as
γsf = 2ρΔGhcp-fcc + 2σ.
where ΔGhcp-fcc is the free energy difference between the hcp and fcc structures, ρ is the surface atomic number density of the (111) layer, and σ is the fcc/hcp interfacial free energy. The factor of 2 reflects the two interfaces between the fcc structure and stacking fault. The variation in σ with composition, temperature, and volume is often neglected for the same kind of materials13.
It is a first principle in physics that the response of a material in equilibrium to external perturbation appears to be the second order of the variation of the physical parameter. By employing this fact, we expand the total energy of a given material near equilibrium as a function of volume V. It is straightforward to obtain the energy difference of the hcp and fcc structures
Eh(V)−Ef(V)≈{Eh(V0)−Ef(V0)}+Bh(V0−V1V1)(V−V0).
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