Influence of defects on the critical behaviour at the \boldmath{105} K   structural phase transition of SrTiO$_3$: II. The sharp component
  The depth dependence of the crystallographic parameters mosaicity, lattice parameter variation and integrated reflectivity and of the critical scattering above the 105 K structural phase transition of SrTiO$_3$ have been studied in five different single crystals by means of high resolution triple-crystal diffractometry using 100-120 keV synchrotron radiation. Depth-dependent impedance measurements indicate that the presence of oxygen vacancies is not responsible for the two-length scale phenomenon. It is found that the sharp component occurs only in surface near regions of highly perfect single crystals and is coupled to an exponential inrease of the crystallographic quantities. The second length scale is absent at a surface where the strain fields are able to relax by a macroscopic bending of the lattice planes. The sharp component is also strongly suppressed in crystals of relatively large mosaicity. The combination of long range strain fields in highly perfect samples and the vicinity of the surface seem to be necessary conditions for the observation of the sharp component. The critical exponents for the second length scale are in satisfying agreement with scaling laws if the intensity of the critical scattering is assumed to be proportional to the square of the Lorentzian susceptibility and not, as usual in the current convention, to a Lorentzian-squared susceptibility. The critical exponents of the broad component are independent of the appearance of the sharp component. 
H. H\"unnefeld, T. Niem\"oller, J. R. Schneider, U. R\"utt, S.   Rodewald, J. Fleig and G. Shirane