Coexistence of ordered and disordered vacancies in tungsten diboride with a broken hexagonal symmetry

As an important member of transition-metal borides, tungsten diboride (i.e., ${\mathrm{WB}}_{2+x}$) contains complex atomic vacancies with the originally assigned hexagonal symmetries, exhibiting many fascinating properties such as superconductivity and superior hardness. However, due to the difficulties in exploring atomic vacancies of transition-metal borides, the actual structure and composition of ${\mathrm{WB}}_{2+x}$ have been long-standing unsettled issues, which have impeded in-depth understanding of its structural stability and origins of such extraordinary properties. Here, we report a systematic investigation of the crystal structure of high-pressure synthesized ${\mathrm{WB}}_{2+x}$ samples by combination of state-of-the-art diffraction techniques and microstructural observations, leading to the discovery of an unusual coexistence of both the ordered and disordered atomic vacancies in ${\mathrm{WB}}_{2+x}$ with a broken hexagonal symmetry that can be well described by a dual-phase model involving hP12-${\mathrm{W}}_{0.70}{\mathrm{B}}_{1.73}$ and P1-${\mathrm{W}}_{0.75}{\mathrm{B}}_{1.64}$. Superposition of thin sample layers with disordered vacancies along the [001] or [110] direction is revealed to produce ordered vacancies, rationalizing the observed size-dependent symmetry breaking. These findings not only provide solid foundations for studying the phase stability and properties of this boride but also give powerful insights into how the intricate atomic vacancies can influence crystal structures of transition-metal borides.