Detailed knowledge of solids circulation, bubble motion, and frequencies of porosity oscillations is needed for a better understanding of tube erosion in fluidized bed combustors. A predictive two-phase flow model was derived starting with the Boltzmann equation for velocity distribution of particles. The model is a generalization of the Navier-Stokes equations of the type proposed by R. Jackson, except that the solids viscosities and stresses are computed by simultaneously solving a fluctuating energy equation for the particulate phase. The model predictions agree with time-averaged and instantaneous porosities measured in two-dimensional fluidized beds. Observed flow patterns and bubbles were also predicted.

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Traditional metallic alloys are mixtures of elements where the atoms of minority species tend to distribute randomly if they are below their solubility limit, or lead to the formation of secondary phases if they are above it. Recently, the concept of medium/high entropy alloys (MEA/HEA) has expanded this view, as these materials are single-phase solid solutions of generally equiatomic mixtures of metallic elements that have been shown to display enhanced mechanical properties. However, the question has remained as to how random these solid solutions actually are, with the influence of chemical short-range order (SRO) suggested in computational simulations but not seen experimentally. Here we report the first direct observation of SRO in the CrCoNi MEA using high resolution and energy-filtered transmission electron microscopy. Increasing amounts of SRO give rise to both higher stacking fault energy and hardness. These discoveries suggest that the degree of chemical ordering at the nanometer scale can be tailored through thermomechanical processing, providing a new avenue for tuning the mechanical properties of MEA/HEAs.

In a 3D model mimicking realistic Cu 64 Zr 36 metallic glass, we uncovered a direct link between the quasi-localized low-frequency vibrational modes and the local atomic packing structure. We also demonstrate that quasi-localized soft modes correlate strongly with fertile sites for shear transformations: geometrically unfavored motifs constitute the most flexible local environments that encourage soft modes and high propensity for shear transformations, whereas local configurations preferred in this alloy, i.e., the full icosahedra (around Cu) and Z16 Kasper polyhedra (around Zr), contribute the least.liquid-like regions | heterogeneity | structure-property relationship | uncommon motifs | shear transformation zones M etallic glasses (MGs) have an inherently inhomogeneous internal structure, with a wide spectrum of atomic-packing heterogeneities (1-4). As a result, an a priori identification of structural defects that carry atomic rearrangements (strains) under imposed stimuli such as temperature and externally applied stresses has always been a major challenge (3-6). In several quasi-2D or 3D models of amorphous solids (such as jammed packings of soft spheres interacting via repulsive potentials or colloidal particles), low-frequency vibrational normal modes have been characterized, and it has recently been demonstrated that some of these modes are quasilocalized (7)(8)(9)(10)(11)(12)(13)(14). A population of "soft spots" has been identified among them in terms of their low-energy barriers for local rearrangements (13,14), correlating also with properties in supercooled liquids such as dynamic heterogeneity (15-17). However, it is not certain where the soft spots are in realistic MGs (18), in terms of an explicit correlation with local atomic packing and topological arrangements (18)(19)(20). In particular, there is a pressing need to determine whether it is possible to identify shear transformation zones, i.e., the local defects that carry inelastic deformation (21,22). Accomplishing this would permit the characterization of MG microstructure in a way that directly ties atomic configuration with mechanical response beyond the elastic regime. We will show here that there is indeed a correlation between soft modes and atoms that undergo shear transformations, and both have their structural signature in specific atomic packing environments defined in terms of coordination polyhedra (3). Fig. 1 displays the vibrational density of states (V-DOS), D(ω), calculated from the eigen-frequencies obtained by normal mode analysis of the Cu 64 Zr 36 MG prepared with a cooling rate of 10 9 K/s (Methods). The main peak stays around 14 meV and becomes only slightly narrower (or wider) when the cooling rate used to prepare the MG is slower (or faster), as seen in Fig. S1; the glasses cooled at slower rates exhibit fewer low-frequency (or low-energy) vibrational modes. The blue portion in Fig. 1 indicates the 1% lowest-frequency normal modes, which will be summed over in our calculations of the participation fraction, P i , in s...