# #11 Energy Generated When Crystal Regularity Is Broken: Stacking Fault Energy

Viewed : 632 times,  2019-07-09 11:59:08
Crystal is a microstructure in which atoms are arranged in a highly orderly pattern. Thus, the atomic arrangement shows the crystal planes stacked in a certain pattern. [1]

Atom arrangement patterns are the same, but arranged atom locations may be different depending on the plane. If the atoms on each plane are expressed as an alphabet, in the case of FCC 111 direction, the normal stacking can be described as ABCABC. In the case of HCP, it can be as ABAB. This may be the most stable structure of the crystal (perfect stacking). However, if some of the crystal is moved, the boundary surface where the crystal arrangement regularity is broken is created, and structural instability may occur. [2]

This distortion is called a stacking fault. The energy generated by the stacking fault is called stacking fault energy (SFE). Stacking fault is classified according to the distortion occurring method. If distortion occurs because a material is partially removed, this case is called intrinsic stacking fault. If a material is added, it is called extrinsic stacking fault. The stacking fault energy can be used to determine the thermodynamic stability of a crystal structure or to find out the deformation behavior. [3]

Stacking fault energy can be calculated as follows:[4]

To calculate the stacking fault energy with DFT, intentionally make a stacking fault in the calculation model, and calculate the energy of the stacking faulted structure. At the time, you should be careful when performing the relax calculation to the stacking faulted model, as it may converge to the perfect stacking structure.

Thus, take the following steps for the calculation:

1. Model a perfect stacking structure, and get the energy with the perfect stacking structure.
2. Import the optimized perfect stacking structure, and select a part of the structure. Select the Move menu to move it to model the stacking fault structure, and get the energy with the stacking fault structure.
3. Calculate SFE by using the energy obtained. If necessary, get the energies of multiple structures to draw a graph.

For the Aluminum (111) structure, according to the calculation result of the intrinsic stacking fault energy, SFE is about 129 mJ/m2. When drawing an energy graph of displacement, you can see the following generalized planar fault energy (GPFE) curve.

👉 Check the calculation results

According to the graph, it is found that stacking fault energy, an additional energy, is generated when stacking fault occurs, where a part of the crystal is moved, and with the arrangement change ABCABC to ABCBCA. As it is a graph that describes the energy changed depending on displacement, it can be used as a kind of activation energy graph, and it can be interpreted that at least 129 mJ/m2 energy is needed to break the arrangement of the crystal.

Furthermore, the stacking fault energy is largely affected by the element composition of the alloy. [5] Thus, it is possible that plotting a graph according to the composition ratio instead of plotting a graph of displacement describes the SFE change depending on the composition ratio of alloy.

[1] Hosford, W. F. (2010). Mechanical behavior of materials. Cambridge university press.
[2] Smallman, R. E., & Bishop, R. J. (1999). Modern physical metallurgy and materials engineering. elsevier.
[3] Gavriljuk, V. G., & Berns, H. (2013). High nitrogen steels: structure, properties, manufacture, applications. Springer Science & Business Media.
[4] Zhao, D., Løvvik, O. M., Marthinsen, K., & Li, Y. (2016). Impurity effect of Mg on the generalized planar fault energy of Al. Journal of materials science, 51(14), 6552-6568.
[5] Thornton, P. R., Mitchell, T.E., Hirsch, P.B., (1962). The dependence of cross-slip on stacking fault energy in face centered cubic metals and alloys. Philosophical Magazine, 7, (80), 1349-1369.

Materials Square