text: Understanding the mechanical properties of Heusler compounds is paramount for temperature-sensitive applications (e.g. thermoelectrics) for which some sub-classes of Heusler compounds are used. However, experimental studies are rarely encountered in literature. In fact, the commercialization of these compounds is limited by the materials ability to undergo intense, repetitive thermal cycling and resist cracking from vibrations. An appropriate measure for crack resistance is the materials toughness, which typically scales inversely with another important mechanical property: the mechanical strength. In this section, we highlight existing experimental and computational studies on the mechanical properties of Heusler alloys. Note that the mechanical properties of such a compositionally-diverse class of materials is expectedly dependent on the chemical composition of the alloys themselves, and therefore trends in mechanical properties are difficult to identify without a case-by-case study.
  The elastic modulus values of half-Heusler alloys range from 83 to 207 GPa, whereas the bulk modulus spans a tighter range from 100 GPa in HfNiSn to 130 GPa in TiCoSb. A collection of various density functional theory (DFT) calculations show that half-Heusler compounds are predicted to have a lower elastic, shear, and bulk modulus than in quaternary-, full-, and inverse-Hausler alloys. DFT also predicts a decrease in elastic modulus with temperature in NiXAl (X=Sc, Ti, V), as well as an increase in stiffness with pressure. The decrease in modulus with respect to temperature is also observed in TiNiSn, ZrNiSn, and HfNiSn, where ZrNiSn has the highest modulus and Hf has the lowest. This phenomenon can be explained by the fact that the elastic modulus decreases with increasing interatomic separation: as temperature increases, the atomic vibrations also increase, resulting in a larger equilibrium interatomic separation.
  The mechanical strength is also rarely studied in Heusler compounds. One study has shown that, in off-stoichiometric NiMnIn, the material reaches a peak strength of 475 MPa at 773 K, which drastically reduces to below 200 MPa at 973 K. In another study, a polycrystalline Heusler alloy composed of the Ni-Mn-Sn ternary composition space was found to possess a peak compressive strength of about 2000 MPa with plastic deformation up to 5%. However, the addition of Indium to the Ni-Mn-Sn ternary alloy not only increases the porosity of the samples, but it also reduces the compressive strength to 500 MPa. It is unclear from the study what percentage of the porosity increase from the indium addition reduces the strength. Note that this is opposite to the outcome expected from solid solution strengthening, where adding indium to the ternary system slows dislocation movement through dislocation-solute interaction and subsequently increases the material's strength.
  The fracture toughness can also be tuned with composition modifications. For example, the average toughness of Ti(Zr, Hf)NiSn ranges from 1.86 MPa m to 2.16 MPa m, increasing with Zr/Hf content. The preparation of samples may affect the measured fracture toughness however, as elaborated by O’Connor et al. In their study, samples of TiHfCoIrSbSn were prepared using three different methods: a high-temperature solid state reaction, high-energy ball milling, and a combination of both. The study found higher fracture toughness in samples prepared without a high-energy ball milling step of 2.7 MPa m to 4.1 MPa m, as opposed to samples that were prepared with ball milling of 2.2 MPa m to 3.0 MPa m. Fracture toughness is sensitive to inclusions and existing cracks in the material, so it is as expected dependent on the sample preparation.