The analysis of physical and chemical characteristics of materials (composite or not) via the determination of change in the effective atomic number (Zeff) can be performed by measuring the relation between the intensities of γ-rays under coherent (Rayleigh) and inelastic (Compton) scattering. The creation of methods for no-contact, non destructive control of Zeff and density ρ of localized areas of the material samples will allow the clarification of the physical and mathematical models of degradation of the composite materials under conditions of high temperatures. For the determination of Zeff, it is necessary to use detectors with high energy resolution, due to the need to distinguish between spectrum lines of coherent and incoherent scattering of γ-rays. Using a solid state Ge(Li) detector, we developed a method for the determination of the effective atomic number, Zeff. This number was determined experimentally for several materials, including Textolite, which has been exposed to high temperature.