Towards a universal ansatz for heat-induced emission peak shifts: insights from M ₂ SiO ₄ :Eu ²⁺ (M = Sr, Ba, Ca) phosphors

Abstract Heat-induced emission peak shift (HIEPS), encompassing both redshift and blueshift, remains mechanistically unresolved in phosphor materials. Using state-of-the-art first-principles calculations of M 2 SiO 4 :Eu 2+ (M = Sr, Ba, Ca), we reveal that conventional thermal expansion theory cannot adequately explain these phenomena. Instead, our frozen phonon analysis identifies local electron–phonon coupling as the dominant mechanism, where anisotropic thermal vibrations selectively distort the asymmetric Eu-5d potential well that arises from the dopant’s coordination environment. This distortion manifests through the temperature-sensitive <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Δ</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>−</mml:mo> <mml:mi>d</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> parameter governing the 5d → 4f transition energy, directly controlling spectral shifts. Our findings establish a universal framework for HIEPS in rare-earth phosphors and enable a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Δ</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>−</mml:mo> <mml:mi>d</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> -guided strategy for designing thermally stable phosphors.