[Pw_forum] questions on lattice dynamical principle

[luch001]

Dear all:
 
I have read the paper titled ¡°Theory of systematic absence of NaCl-type (¦Â-Sn-type) high pressure phases in covalent (ionic) semiconductors¡± (Phys Rev Lett. 82, 767, 1999). The phonon behaviors are dominated by the competition between the attractive electrostatic Madelung energy ¨CZ2/R (where Z is the excess charge within the atomic sphere) and the repulsive short-range energy.I can not understand well the formula of the force constant given in the last part of page 769. I thought to present the formula here. Unfortunately, I can not add it in my email text. I am very sorry for that. 
 
How does it come from? Does it apply to all the systems or just apply to some specific system?  The values of A and ¦Ë are determined by what factors? 
 
The authors claimed that the transverse acoustic mode at X point lowers the repulsive energy and raises the Madelung energy, but why?
 
I have pondered hardly and consulted with others. But I have reached no conclusion.
Any reply will be appreciated!
 
With all my best regards!
 
                                                      Yours sincerely
                                                       Jingyun Zhang
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