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We show the reconciliation of the strain ( ε )-, pressure ( P )-, and layer-number ( N )-dependence of the phonon frequency and photon energy shifts for MX 2 in terms of stimulated bond relaxation, with quantification of the coefficients of bond length and energy relaxation, the bond nature index, force constant, and cohesive energy density. We found that (i) atomic under-coordination shortens and stiffens the M–X bond, which widens the bandgap; (ii) the directional strain governs phonon-frequency splitting and narrowing; and (iii) homogenous mechanical compression induces the opposite effect of stretching. [ABSTRACT FROM AUTHOR]

Highlights: [•] Bond order (z), length (d), and strength (E) determine the Raman shift, Δω. [•] Heating (T) and bond order (z) variation vary the d, E, and Δω. [•] Raman shift of nanocrystals results from the bond relaxation in the skin region. [•] Δω(T) results in the atomic cohesive energy and Debye temperature. [•] Δω(z) leads to the bond nature index and the reference ω from which the Δω proceeds. [Copyright &y& Elsevier]