Anomalous lattice stiffening in tungsten tetraboride solid solutions with manganese under compression

Tungsten tetraboride (WB₄)-based solid solutions represent one of the most promising superhard metal candidates; however, their underlying hardening mechanisms have not yet been fully understood. Here, we explore the lattice compressibility of WB₄ binary solid solutions with different manganese (Mn) concentrations using high-pressure x-ray diffraction (XRD) up to 52 GPa. Under initial compression, the lattices of low and high Mn-doped WB₄ alloys (i.e. W_0.96Mn_0.04B₄ and W_0.84Mn_0.16B₄) are shown to be more and less compressible than pure WB₄, respectively. Then, a c-axis softening is found to occur above 39 GPa in WB₄, consistent with previous results. However, an anomalous sudden a-axis stiffening is revealed at ~36 GPa in W_0.96Mn_0.04B₄, along with suppression of c-axis softening observed in WB₄. Furthermore, upon Mn addition, a simultaneous stiffening of a- and c-axes is demonstrated in W_0.84Mn_0.16B₄ at ~37 GPa. Speculation on the possible relationship between this anomalous stiffening and the combined effects of valence-electron concentration (VEC) and atomic size mismatch is also included to understand the origin of the nearly identical hardness enhancement in those two solid solutions compared to WB₄. Our findings emphasize the importance of accurate bonding and structure manipulation via solute atoms to best optimize the hardness of WB₄ solid solutions.