Evidence for phase transition in the incoherent lattice fluctuations, lattice distortion and local microstructure of pure and implanted SrTiO$_{\mathrm{3}}$

Low temp Rutherford Backscattering Spectrometry-Axial Ion Channeling used to probe displacive structural phase transition (PT) {\&} Jahn-Teller (JT) lattice distortion in perovskite SrTiO$_{\mathrm{3}}$. It provides direct evidence of incoherent lattice fluctuations as function of temp across non-ferroelectric (FE) 2$^{\mathrm{nd}}$ order antiferrodistortive cubic to body-centered tetragonal structural PT at Curie-Weiss T$_{\mathrm{0}}=$105 K, caused by antiphase tilting of TiO$_{\mathrm{6}}$ octahedra by minimizing Gibbs free energy,~opens bandgap {\&} weakens FE instability by reducing cross gap hybridization. Defects in semiconducting SrTiO$_{\mathrm{3\thinspace }}$narrows large band gap {\&} raises Fermi level into conduction band {\&} ensures conductivity. JT effect occur for degenerate filled {\&} empty molecular orbitals. Critical channeling angle $\psi_{\mathrm{c\thinspace }}${\&} ratio of minima of angular RBS-ICh spectral yield $\chi_{\mathrm{min}}$ for Sr {\&} Ti sublattices determine JT lattice distortion in transition element (Fe, Cr etc.) implanted SrTiO$_{\mathrm{3}}$. Similar $\psi_{\mathrm{1/2}}$ values for Sr sublattice indicates no displacement of Sr. Distortion of Ti sublattice infers implanted Fe {\&} Cr is actually located in Ti positions but not in interstitial positions. Temp dependence of Thermal vibrational amplitudes of Sr {\&} Ti also displacements of Ti$^{\mathrm{4+}}$ are calculated based on Linhard's continuum model. Implanted SrTiO$_{\mathrm{3}}$ shows a minor tetragonal phase corresponds to lattice expansion along c-axis {\&} it's not randomly oriented. Local microstructure {\&} atomic distortions studied with HR-TEM (FIB prepared), XPS, GID-XRD {\&} Raman Scattering.