  Physisorbed Kr layers on TiO$_{2}$(110) surfaces were investigated by means
of nuclear resonant scattering (NRS) of synchrotron radiation at Kr thicknesses
ranging from multilayer to monolayer. The NRS intensity was measured as a
function of the Kr exposure, from which the NRS signal corresponding to
monolayer was estimated as 0.23 cps. The time spectra measured at various
thicknesses showed a monotonous decay without any quantum beat features. The
recoiless fraction $f$ evaluated from the analysis of the time spectrum
revealed a substantial reduction upon temperature rise from 19 to 25 K. As its
origin, an order-disorder phase transition of the monolayer Kr is proposed.
