The granular structure of sands and other geomaterials makes them amongst the most difficult engineering materials to model. In this paper a recently developed thermomechanical procedure is used to derive constitutive models for sands undergoing triaxial deformations. The well-known geomechanical state parameter is given a new significance and is taken as the fundamental thermomechanical state parameter. The logarithm of the specific volume is shown to be the plastic volume strain, and its relationship to the logarithm of the effective pressure is shown to be fractal. In addition the shear-induced volume strains, characteristic of granular materials, are introduced via a workless constraint, and the resulting deformation is seen to exhibit ‘induced anisotropy' automatically. The associated reaction stress tensor is shown to be identical with the extant fabric tensor. The plastic flow rule is shown to be necessarily non-associated. Comparison with experimental data is made, together with some discussion of the model's relation to the predictions of distinct element simulations.

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The phase stability of transition metal oxides and the thermodynamic equilibrium of their reductionoxidation reactions were previously reported to be size-dependent [1]. As the metal oxide's dimension decreases to the nanoscale, the free energies for redox reactions and phase stability temperatures alter drastically for most compounds, including iron oxides [1]. Navrotsky and colleagues [1] have calculated phase diagrams for nanoscale Fe-O system using calorimetric surface energy data and thermodynamic property values of the bulk systems. It was predicted that g-Fe2O3 nanoparticles smaller than 100 nm undergo reduction to Fe3O4 with increasing temperature, before transforming directly to metallic Fe, hence bypassing the formation of the FeO phase.Bonifacio and colleagues have recently carried out in-situ heating experiments to study the sintering behavior of iron oxide nanochains [2]. g-Fe2O3 nanoparticles with diameters around 40-50 nm were assembled into 1-dimensional chains using a H2/air diffusion flame inside a magnetic field [3]. The assembled chains were subsequently utilized for in-situ TEM heating experiments using the Protochips Aduro sample holder. The oxidation states of Fe during in-situ heating were probed by electron energyloss spectroscopy (EELS) measurement. The L3/L2 intensity ratios of the Fe L2,3 ionization edges were determined from spectra acquired at different temperatures [2]. It was found that consolidation of iron oxide nanochains is accommodated by the stepwise reduction of g-Fe2O3 at room temperature to metallic iron above 900 °C.In this study, in-situ selected area electron diffraction (SAED) heating experiments were carried out for g-Fe2O3 nanoparticles with an aberration corrected JEOL JEM 2100F/Cs scanning transmission electron microscope. Images and diffraction patterns were acquired in TEM mode under parallel illumination using a Gatan Rio16 camera. Figure 1(a) shows a bright field TEM image recorded at room temperature that displays nanoparticle chains with lengths around 600 to 800 nm. Figure 1(b) shows the same nanochains at 800°C. SAED patterns and bright field TEM images were collected at various temperatures. After holding times of 10 min, no more changes of the diffraction patterns were detected, which suggests completion of any phase transformations. Diffraction patterns recorded at each temperature were subsequently indexed for phase identification. The SAED patterns of the chain-like g-Fe2O3 nanoparticles under room temperature and 800 °C are shown in Figure 2(a) and 2(b), respectively.

Anisotropic growth of nanostructures from individual nickel nanoparticles was observed during in situ heating experiments in an environmental scanning electron microscope (ESEM) at 800 • C under water vapor atmosphere. The morphology of nanostructures exhibited one directional growth with rates ranging below 1.8 nm/s. Energy dispersive X-ray spectroscopy and selected area electron diffraction confirmed NiO stoichiometry of the growing nanostructures. Variations of the oxygen partial pressure during ex situ annealing and in situ ESEM heating experiments elucidate that anisotropic NiO growth is energetically favored in areas where the local surface energy density is relatively high. Growth of NiO nanostructures was absent in dry air and dry nitrogen environments and required the presence of water vapor. The results of this study suggest that the manipulation of surface energy prior to exposure to water vapor at elevated temperatures can prevent unwanted oxide nanostructure growth.

Increasing surface-to-volume ratios for nanoscale materials may cause metal(II)oxides phases to be thermodynamically unstable compared to their bulk counterparts. For instance, previous studies have found FeO to be unstable for nanoparticles with dimensions below 100 nm. In this study insitu TEM was used to gradually reduce nanoparticles and nanochains of Fe 2 O 3. Electron energy-loss spectroscopy and selected area diffraction at different temperatures not only confirm earlier predictions, but also reveal the unexpected stabilization of the FeO phase for nanochains with a minimal critical length. Hence, dimensionally constrained phases were stabilized on length-scales that were previously considered unattainable. IMPACT STATEMENT This study provides direct experimental evidence for the previously unanticipated stabilization of metal(II)oxides with dimensions well below 100 nm, which has exciting potential for catalyst technologies and next generation memory devices.