High resolution neutron scattering measurements on a single crystal of ${\mathrm{SrCu}}_{2-x}{\mathrm{Mg}}_x({\mathrm{BO}}_3{)}_2$ with $x\sim 0.05$ reveal the presence of new spin excitations within the gap of this quasi-two-dimensional, singlet ground state system. The application of a magnetic field induces Zeeman-split states associated with $S=1/2$ unpaired spins which are antiferromagnetically correlated with the bulk singlet. Substantial broadening of both the one- and two-triplet excitations in the doped single crystal is observed, as compared with pure ${\mathrm{SrCu}}_2({\mathrm{BO}}_3{)}_2$. Theoretical calculations using a variational algorithm and a single quenched magnetic vacancy on an infinite lattice are shown to qualitatively account for these effects.

Crystal plasticity finite element models have been extensively used to simulate various aspects of polycrystalline deformations. A common weakness of practically all models lies in a relatively large number of constitutive modeling parameters that, in principle, would require dedicated measurements on proper length scales in order to perform reliable model calibration. It is important to realize that the obtained data at different scales should be properly accounted for in the models. In this work, a two-scale calibration procedure is proposed to identify (conventional) crystal plasticity model parameters on a grain scale from tensile test experiments performed on both single crystals and polycrystals. The need for proper adjustment of the polycrystalline tensile data is emphasized and demonstrated by subtracting the length scale effect, originating due to grain boundary strengthening, following the Hall–Petch relation. A small but representative volume element model of the microstructure is identified for fast and reliable identification of modeling parameters. Finally, a simple hardening model upgrade is proposed to incorporate the grain size effects in conventional crystal plasticity. The calibration strategy is demonstrated on tensile test measurements on 316L austenitic stainless steel obtained from the literature.