The results of sputtering coefficient measurements of pure metals, alloys, amorphous alloys, semiconductors and Highly Oriented Pyrolytic Graphite under swift heavy ion irradiation are presented. The possible mechanisms of strong sputtering of materials with high level of defect concentration are discussed. The three dimensional thermal spike model ("hot ion track") with the temperature dependence of thermo-dynamical parameters (specific capacity and thermal conductivity) in the case of one layer mono- and polycrystals and also for multi-layers systems (materials) is formulated. The results of numerical analysis of introduced system of spatial differential equations for the calculation of lattice and electron subsystem temperatures around and along the swift heavy ion trajectory versus the time t and coordinates: radial - r and longitudinal - z with taking into account of possible phase transitions such as melting and evaporation are presented. The discussions of obtained results are made.

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