Journal of Materials Science

, Volume 48, Issue 21, pp 7642–7651 | Cite as

Trends in formation energies and elastic moduli of ternary and quaternary transition metal nitrides

  • V. Petrman
  • J. Houska


The paper deals with characteristics of a wide range of ternary and quaternary metal nitrides (M = Ti, Zr, Hf, V, Nb or Ta) of various compositions obtained by ab initio calculations. We focus on the formation energies (E form), bulk moduli (B), shear moduli (G) and a difference of B and G from the weighted average of B and G of binary metal nitrides (∆B and ∆G). We show numerous monotonous dependencies, and identify exceptions to them. For elastic moduli of M1M2N we find that ∆B decreases (down to −19 GPa) and ∆G increases (up to 20 GPa) with increasing difference between atomic radii of M1 and M2. In parallel, low ∆B and high ∆G correspond to high E form and |E form|, respectively. E form of M1M2N increases with increasing difference between atomic radii and electronegativities of M1 and M2. The lowest E form values were observed for Ta-containing compositions, and the difference between E form of TaM1M2N and M1M2N is more significant for lower atomic radius and higher electronegativity of M1 and M2. Overall, we present trends which allow one to use fundamental arguments (such as atomic radii and electronegativities) to understand and predict which compositions form (nano)composites, which compositions form (stable) solid solutions, and which materials exhibit enhanced elastic moduli. The phenomena shown can be tested experimentally, and examined for even wider range of materials.


Nitrides Formation Energy Elastic Modulo Atomic Radius Metal Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported in part by the Grant Agency of the Czech Republic GACR under Project No. P108/12/0393, and by the European Regional Development Fund under Project “NTIS—New Technologies for Information Society”, European Centre of Excellence, CZ.1.05/1.1.00/02.0090. Computational resources were provided by Metacentrum Czech Republic.


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Physics and NTIS - European Centre of ExcellenceUniversity of West BohemiaPlzenCzech Republic

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