Calculating 2D Dispersion Relation with Different Atom Types

yasef
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I have derived 2D dispersion relation which has the same atoms. But I also need to calculate this 2D dispersion relation with two different atoms. One atom is located at the center and the other type of atoms surrounds this atom. But I am not sure how ı should calculate it because only difference with the first system is force constant. I should need different perspectives or some calculatıons about it.
 
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Sorry, this doesn't answer your question, but poses another. Could you please help me with the 2D proof? Maybe send it as an attached file to mosquisofly@gmail.com or post it here. Sorry once more and thank you.
 

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