Alpha-U has been observed to undergo the following sequence of transformations at T 0 < 43K (lower limit of stability of the structure) a transition involving modes for which q CDW = < q x , q y , q z >; ortho.: Cmcm T 0 = 43K > mono.: C2/m11 (q x , q y , q z) T 1 = 37K > mono.: P211 (1/2, q y , q z). The phonon dispersion was measured by neutron inelastic scattering in the range (200, 43K) of existence of the high-temperature orthorhombic phase and in the range of the phase transformations at 43, 37 and 22K. Soft branches were associated with the normal-to-incommen-surate transitions in Brillouin zone: (201). The main component of the displacement pattern is consistent with the symmetry for a Σ 4 phonon mode. The static displacements associated with the displacive transition are produced by low-frequency and damped phonons at positions q s [(q x , q y , q z)] which on approaching the second-order phase transition (T 0) soften more than those with q c = [1/2, 0, 0], but not totally. Increasing the energy resolution by using cold neutrons on the three axis spectrometer IN14 near (101), we have seen in the range T-T 0 = 7K a small deviation from the linear law of Curie. The experimental phonon softening [1] which is accompanied by large changes in cell parameters at T 0 , is dependent on q y (T), q z (T) contrary to predictions of the Yamada theory. At T 0 = 43 K the modulation wave vector of the incommensurate low-temperature condensing soft mode is q min = [0.497 (1), 0.13 (1), 0.21 (1)] (q CDW. The electronic instability which causes Kohn anomaly also triggers the displacive (Peierls) transition. Relaxors are special class of ferroelectrics that exhibit a broad, diffuse phase transition over a temperature range and a strong frequency dependence of the dielectric constant as a function of temperature. Near room temperature they exhibit very high dielectric permittivity, electrostrictive and electrooptical coefficients , which determine relaxors as multi-functional materials, with a wide range of technological applications, including non-volatile memory devices. The global, average structure of relaxors, detectable by diffraction methods, remains pseudo-cubic even at liquid helium temperatures, whereas their nanoscale structure is rather complex. Near the Curie range and under zero-field conditions the ferroic clusters are sized only a few unit-cell parameters and they create and annihilate within 10-5-10-6 s. Thus, because of its length-and timescale sensitivity, inelastic light scattering is vital for gaining structural information. The mechanism of paraelectric-to-relaxor ferroelectric phase transition is still not clarified. To better understand the local structural phenomena occurring in relaxors we have applied Raman scattering and X-ray diffraction on single crystals of stoichiometric PbSc 0.5 Ta 0.5 O 3 (PST), solid solutions of type PbSc 0.5 Ta .5 O 3-PbSc 0.5 Nb .5 O 3 and PbSc 0.5 Ta .5 O 3-PbSnO 3 , A-site mixed (Pb 1-x A'' x)Sc 0.5 Ta 0.5 O 3 (A'' = Ba,), as well as Ru-doped PbSc 0.5 Ta 0.5 O 3. The ...