A predictive computational approach has been developed and implemented to evaluate the bulk modulus ( B ) and single-crystal hardness ( H V ) of ZrB 2 -based solid solutions containing substitutional Mo and/or C impurities. By employing first-principles studies of isolated atomic clusters as representative structural fragments, this method provides a cost-effective alternative to expensive trial-and-error experimental synthesis of complex ultra-high-temperature ceramics (UHTCs). The validity of the model is confirmed by its high predictive accuracy, showing close agreement with experimental benchmarks for the matrix and related doped systems. For the first time, a quantitative assessment of the synergistic effect of Mo and C co-doping on the intrinsic mechanical properties of the ZrB2 crystal lattice is presented. The results reveal that a significant enhancement in bulk modulus (11–13 %) and hardness (16–17 %) is achieved at a total impurity concentration of approximately 15–17 at.%. These findings establish the intrinsic mechanical limits of the doped lattice, providing a theoretical baseline for the design and development of UHTCs where Mo and C are used for activated sintering. • Studied (Zr,Mo)(B,C)2 solid solutions are energetically stable and favorable. • Cluster cohesive energy is a key descriptor for predicting bulk modulus and hardness. • Max increments in B (13%) and Hv (17%) occur at 15–17 at.% of impurities. • The cluster ab initio approach shows high agreement with available experimental data. • The model enables UHTC design by bypassing costly trial-and-error synthesis.
Rozhenko et al. (Fri,) studied this question.