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Properties of quantum materials are tuned by pressure, magnetic field & doping. Dilute semiconductor perovskite STO exhibits unconventional superconductivity over a wide range of carrier densities 10¹⁹-10²¹cm⁻³, Fermi level traverses a number of vibrational modes & it maintains gap to T_c ratio of BCS weak-coupling limit, despite being in anti-adiabatic regime. At lowest SC-densities, lone remaining adiabatic phonon van Hove singularity is anomalously soft transverse-optic mode associated to ferroelectric instability. Recent works suggest emergence of multiferroic (magnetic & ferroelectric) quantum critical behavior, interplay between ferroelectricity vs SC and SC mediated by odd-parity ferroelectric modes. Presence of soft phonons & their possible role as scattering centers raised suspicion that T² resistivity is not due to e-e scattering. LT RBS- ICh is used to probe displacive phase transition & lattice distortion. It provides direct evidence of incoherent lattice fluctuations as function of temp across AFD at T_a=105 K. JT effect occur for degenerate filled & empty molecular orbitals. Critical channeling angle Ψ_c & ratio of minima of angular RBS-lCh spectral yield χ_min for Sr & Ti sublattices determine JT lattice distortion in transition element (Cr & Fe) implanted STO. JT effect at Cr⁵⁺ & Fe⁴⁺ centers in STO lattice are investigated by RBS- ICh. Valence mismatch between substituent & host plays key role. Similar values of Ψ_1/2 for Sr sublattice indicates no displacement of Sr. Impurity hardly causes displacements of Sr ions but causes displacement of Ti ions from ideal lattice sites. Cr & Fe impurities predominantly leads to distortion of Ti sublattice, infers Cr/Fe is actually located at Ti positions but not in interstitial. Temp dependence of Thermal vibrational amplitudes (ρ) of Sr & Ti also displacements of Ti⁴⁺ are calculated based on Linhard's continuum model. FWHM is strongly affected by incoherent atomic displacements. Change in ρ value indicating a dynamic or static displacement of Sr & Ti atoms. With Temp ρ changes across AFD, infers different lattice constants. Local microstructure & atomic distortions studied with HR-TEM (FIB prepared), XPS, GID-XRD & Raman Scattering. Implanted STO shows a minor tetragonal phase corresponds to lattice expansion along c-axis & it's not randomly oriented.