The Temperature Factor of the Size Parameters of Nanoparticles

Between the nano and the macro states there is a size boundary whose existence is explained within the framework of the Debye model of behaviour of phonons in crystals. If the particle size is such that a phonon with a wavelength greater than the Debye wavelength is unable to propagate, then the substance acquires different properties from the bulk properties, as only high-frequency excitations can exist within it. The particle size and temperature affect the intensity and profiles of the X-ray reflexes. On the basis of a combined examination of the Sherrer formula and the Debye-Waller factor, a method is proposed for estimating the temperature factor in the size of crystalline nanoparticles. An examination is made of the influence of temperature on the change in nanoparticle size. With account taken of the Debye-Waller factor, the possibility is shown of estimating the size of a nanoparticle on the basis of the change in energy state owing to dispersion. Grinding of the particle (increase in the coefficient of dispersion) results in a change in the effective temperature, the magnitude of which must be taken into account when assessing the parameters of nanoparticles.