Having formulas at hand is one thing, but making use of them in a sensible way is another thing. Look at your specific situation and identify the material that has the role of being the reference. Then, in the calculation of lattice mismatch, use the IN-PLANE lattice constant a of this material to obtain the relative deviation from it by the other material (with an IN-PLANE lattice constant b) in the following way:

strain in % = 100 * (b – a) / a.

Obviously, a positive (negative) strain value means that the other material has a larger (smaller) IN-PLANE lattice constant than the reference material.

(Edited on January 25th, 2018: I added "IN-PLANE" in case the materials have more than just one lattice constant.)

If their are similar materials you can take one material as reference and then you divide difference in lattice pr. of the two by the referance lattice constant and multiply by 100 

usually lattice matching is required in heterostructures, especially when we have to do with graduated refractive index and/or gap tuning! As for formulae Net is full of papers.

hope you success!

Having formulas at hand is one thing, but making use of them in a sensible way is another thing. Look at your specific situation and identify the material that has the role of being the reference. Then, in the calculation of lattice mismatch, use the IN-PLANE lattice constant a of this material to obtain the relative deviation from it by the other material (with an IN-PLANE lattice constant b) in the following way:

strain in % = 100 * (b – a) / a.

Obviously, a positive (negative) strain value means that the other material has a larger (smaller) IN-PLANE lattice constant than the reference material.

(Edited on January 25th, 2018: I added "IN-PLANE" in case the materials have more than just one lattice constant.)

yeah! it's up to what we're going to do, i mean it depends of the applications.

is there any book that explains about lattice mismatch and formula to calculate lattice mismatch? I apologize for asking about this case because I am new in this field and want to learn it. then, I also want to calculate lattice mismatch between graphene/Ru(0001)

please get first the experimental values of both lattice parameters the apply the rule above.

"is there any book that explains about lattice mismatch and formula to calculate lattice mismatch? I apologize for asking about this case because I am new in this field and want to learn it." -- Haven't you read my previous answer? Why do you ask about books? What more do you need to know, specifically?

Kindly, see for more details the attached file below.

Thank you very much, Prof Jan-Martin Wagner and Prof Boualem Merabet for suggestions. I'm sorry for my late reply. I want to understand more about the lattice mismatch. the meaning of a compressive (+) or tensile (-) stress in the overlayer

"the meaning of a compressive (+) or tensile (-) stress in the overlayer" -- Well, stress is another thing: The lattice mismatch is just the relative difference between the in-plane lattice constants, giving either a positive or a negative strain value specified in % (as I have explained above). Stress, on the other hand, is a measure for force per square area; it is related to the strain via the elastic constants of the material. Positive strain means tensile stress, and negative strain means compressive stress.

Thank you very much for your help and attention, Prof. I understand right now, this is very helpful for me

how we find lattice mismatch of between two 2D materials?

The lattice mismatch is always the relative difference between the in-plane lattice constants, even if you deal with two 2D materials. So, what is your specific problem here? Of course in this case the lattice mismatch might depend crucially on the relative orientation of the two 2D materials, and it can be different in different directions. Thus, such a case can lead to a bunch of mismatch values. However, which of these data are really relevant depends on the specific situation and the specific question you are interested in.

Respected Jan-Martin Wagner thanks for a genius reply. Actualy I want to model an interface between borophene and boron nitride both have hexagonal structure ... I want to calculated lattice mismatch according to formula , and also

I want to understand how this could affect the stability of the structure in real.

need your worthy attention

thanks

So, what is the fully relaxed B--N bond length in boron nitride, and what is "the" (if existent; there are different types of borophene) fully relaxed B--B bond length in borophene?

sir sorry for late reply ..the B-N bond length is 1.45 angstorm and B-B length is 1.61 angstorm.

So the bond length difference is 0.16 angstrom, which is about 10% of the B--B bond length and about 11% of the B--N bond length. These percentages are the relevant lattice mismatch values.

respected sir ! if there are two 2D materials for example one is (A) 2D material having lattice constants of a=10.04 and b=8.70 and second is (B) 2D material having lattice constants a= 9.69 and b=8.61 after the prepartion supercell .then what is total lattice mismatch of A material with B material?

https://www.researchgate.net/post/How_to_calculate_lattice_mismatch_in_thin_film[accessed Aug 21, 2016].

Hello everyone, I am glad to have found this thread, I see mostly that this is a discussion about lattice mismatch between 2-D materials/ thin-films, but, I would like to know if there is a way to figure out the lattice mismatch between any binary or tertiary core-shell quantum dots by using their lattice constants or any other parameters, are there any good formulas or textbooks that can help shed light in this area ? If so, I would like any input I can get!

Thank you!

you can take the difference between lattice parameters of the respective unit cell( for cubic structure ) and divide them with the average of the two lattice parameters and multiply the value by 100 to get the misfit percentage