Quantifying rigidity for thermally stable Cr³⁺ phosphors

Near-infrared (NIR) phosphors with high thermal stability are significant for NIR light-emitting diodes (LEDs). For a decade, Debye temperature has been a successful indicator of structural rigidity and thermal stability for phosphors, but some exceptions exist due to its dependence on atomic mass. Inspired by the Debye temperature model that relates the elastic properties of solids, our density functional theory calculations revealed that the Vickers hardness of Cr³⁺-doped NIR phosphors was negatively correlated with Stokes shifts (Pearson's R = -0.81) and positively correlated with thermal stabilities (Pearson's R = 0.85) within a set of 13 distinct material types. Highlighting the predictive power of Vickers hardness, two new NIR phosphors were investigated: KMg(PO₃)₃:Cr³⁺ showed low thermal stability, correlating with its lower Vickers hardness, in contrast to the high thermal stability and correspondingly higher Vickers hardness of La₂MgSnO₆:Cr³⁺. Vickers hardness can be used to screen potential hosts for Cr³⁺-doped NIR phosphors with high thermal stabilities, due to the advantages of the predictable feature by density functional theory calculation and low independence on atomic mass.