ELASTIC PROPERTIES OF NANOMATERIALS THROUGH THE INFLUENCE OF GRAIN SIZE ON STRUCTURAL PHASE TRANSITIONS

The physical properties of large crystals are generally more or less independent of grain size. In the standard understanding of nanocrystals, changes in bulk physical properties become evident when the volume of material influenced by the grain surfaces becomes greater than the volume of material within a grain. Chemical and thermodynamic properties of nanomaterials have been investigated extensively on this basis but elastic properties are much more difficult to determine, as the available experimental methods typically require samples which are substantially greater than the size at which the crossover to nano properties might occur. It is well known that structural phase transitions are highly sensitive to elastic behaviour, however, and this link can be exploited by investigating the influence of grain size to get at the influence on elasticity indirectly. An example of this is the alpha-beta phase transition in quartz (McKnight et al. J. Phys. Cond. Matt. 20, 075229, 2009), which has been followed in natural samples with grain sizes of 100-300 microns (quartzite) down to ~50 nm (agate) using Resonant Ultrasound Spectroscopy (RUS). Landau theory shows that suppression of spontaneous strain at grain/grain interfaces renormalizes the fourth order coefficient so that a first order transition tends towards second order character and the transition temperature is reduced. In the case of quartz, the crossover towards nano properties must occur at grain sizes of less than 50 nm. This approach has now been extended to powder samples in a “test-of-concept” experiment on magnetite. Magnetite powders with grain sizes of ~7, 1.7 and 0.3 microns have been pressed into dense pellets using a matrix of KBr. These pellets were then sawn up into parallelepipeds for measurement of elastic properties of the bulk sample. RUS spectra collected between room temperature and 50 K clearly show softening of the shear modulus at the Verwey transition. The transition temperature reduces with decreasing grain size (~121 K at 7 microns, ~117 K at 0.3 microns and the degree of elastic softening also diminishes. In principle this approach could be applied to pellets with different KBr/particle mixtures to determine absolute values of shear and bulk moduli of nanocrystals which do not undergo phase transitions.