I would like to determine the effect of the chemical composition of the alloy and annealing temperature on lattice misfit between M23C6 and matrix, i.e. ferrite or austenite. Exemplary lattice parameters for these phases are 10.6533, 2.8803 and 3.60609 for M23C6, ferrite and austenite, respectively. Currently, I use the following equation δ=2(aM23C6 -3aM)/(aM23C6 + 3aM), where aM23C6 and aM are the lattice constants of the M23C6 and α or γ matrix. The lattice parameter of the matrix was multiplied by a factor of three for the corresponding structural comparison. This equation gives me following misfits: M23C6/ferrite - 20.9 % and M23C6/austenite -1.5%. Is the equation used by me is appropriate to determine the misfit? Result for M23C6/austenite seems to be appropriate when compared to literature data, but what do you think about the M23C6/ferrite misfit value?
Article The crystallography of M23C6 carbides in a martensitic 9% Cr...
This may help :)
Thank you Grzegorz. According to the equation, found in this paper, i.e. δ=(dM23C6 - dM)/dM for (110)ferrite//(333) M23C6 and (111)austenite//(333) M23C6 orientation, the lattice misfits in my case are 0.66 % and -1.53 %, respectively. Between ferrite and M23C6 is typical Kurdjumov-Sachs crystallographic orientation relationship (P.R. Howell, J. V. Bee, R.W.K. Honeycombe, The crystallography of the austenite-ferrite / carbide transformation in Fe-Cr-C alloys, Metall. Trans. A. 10A (1979) 1213–1222). This results seems to be more appropriate. Now I understand my error during previous calculations. The δ=2(aM23C6 -3aM)/(aM23C6 + 3aM) equation is valid only for M23C6/austenite misfit calculation because of (111)austenite//(333) M23C6 crystalographic relationship.
Yes, usually if there is crystallographic orientation relationship it likes smallest misfit due to minimum energy on such phase boundary. So for austenite it is cube to cube orientation relationship but for ferrite K-S is most probable I guess.
There is nice software where you can put 2 lattices and find most probable crystallographic orientation relationship (plane) with calculated misfit and even visualise it.
Gu, X.-F., Furuhara, T. & Zhang, W.-Z., (2016). J. Appl. Cryst. 49, 1099 –1106.
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