I would calculate the lattice mismatch of a and a' as

2*|(a-a')|/(a+a')

which ist the difference per mean value. Don't know any other definition. The resulting numbers are slightly different from those you gave.

Rudolf Feile according to your formula value of a is 11.54 and value of c is 0.1079 ,which are totally different from the calculated lattice mismatch that is given in question. 

Thanks Vassilis saltas

but according to formulas given in that links ,i cannot find the lattice mismatch ma InN and GaN

According to the numbers you posted, you can get the number given in the attachment.

In your answer you presented one percentage value and on decimal value, you may not argue with that different representations. 'Totally different'  is not the proper description for the comparision for 10% deviations from literature values.

To define a mismatch between two numbers depends on the basis for the comparision. You can define the differences relative to the first number or the second number or the mean value of both numbers (as I did). It is not a question of formula you apply but a question of definition of the basis for your calculation. If you mention your definition (by words or by formula as I did) everything is clear.

For the numbers you gave the results you may find in the attachment are the only numbers for a mismatch you can get. According to Vasilis Saltas reference you may see that there is more information necessary if you want to get more precise numbers for the behaviour of your material: temperature of preparation of the epitxial film and the corresponding lattice constants, temperature where you want to calculate the mismatch (for that you have also to consider the thermal expansion of the materials), and even more parameters.

You can only get a proper answer for a proper question.

Best regards.

please find the attachment and calculate the desired mismatch.

Are both screen shots from the same article?

If yes, then please ask one of the authors, how they got the numbers for the mismatch.

If no, then please ask the authors of the second screen shot about the lattice parameters used for their calculation, and how they received the numbers for the mismatch.

Sorry, I cannot present you a better answer, the calculations based on my simple definition for describing mismatch you find on my pdf sent wih my last answer.

lattice mismatch of GaN and InN depends on the chosen parameters a and c. If you take these parameters from: 

Vurgaftman, I., & Meyer, J. N. (2003). Band parameters for nitrogen-containing semiconductors. Journal of Applied Physics, 94(6), 3675-3696. 

doi: http://dx.doi.org/10.1063/1.1600519

ie:  a= 0.3189 nm  &     c= 0.5185 nm   for GaN

       a=0.3545 nm   &     c= 0.5703 nm   for InN

then, ep=100*(ab-aw)/aw   (%)

for InN on GaN:    

a:        ep = 100*(3.189-3.545)/3.545  = -10.042%       (10.042 % absolute value)

c:        ep = 100*(5.185-5.703)/5.703  = -9.0829%       (9.0829 % absolute value)

Well done literature search for the appropriate lattice constants!

Thus my definition for the mismatch was correct.

To be mathematically right I would calculate:

a:   ep = (3.189-3.545)/3.545  = -0.10042 = -10.042%

c:   ep = (5.185-5.703)/5.703  = 0.090829 = -9.0829%

(% = 1/100 per definition)