Atomic models of non-stoichiometric layered diborides M$_{1-x}$B$_2$ (M   = Mg, Al, Zr and Nb) from first principles
  Two atomic models of non-stoichiometric metal diborides M$_{1-x}$B$_2$ are now assumed: (i) the presence of cation vacancies and (ii) the presence of 'super-stoichiometric' boron which is placed in cation vacancy site. We have performed first principle total energy calculations using the VASP-PAW method with the generalized gradient approximation (GGA) for the exchange-correlation potential in a perspective to reveal the trends of M$_{1-x}$B$_2$ possible stable atomic configurations depending on the type of M cations (M = Mg, Al, Zr or Nb) and the type of the defects (metal vacancies versus metal vacancies occupied by 'super-stoichiometric' boron in forms of single atoms, dimers B$_2$ or trimers B$_3$). Besides we have estimated the stability of these non-stoichiometric states (on the example of magnesium-boron system) as depending on the possible synthetic routes, namely via solid state reaction method, as well as in reactions between solid boron and Mg vapor; and between these reagents in gaseous phase. We demonstrate that the non-stoichiometric states such as B$_2$ and B$_3$ placed in metal sites may be stabilized, while the occupation of vacancy sites by single boron atoms is the most unfavorable. 
I.R.Shein, A.L. Ivanovskii