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Mixing
Published in Ko Higashitani, Hisao Makino, Shuji Matsusaka, Powder Technology Handbook, 2019
Ideal homogenous mixture is defined as the state that there is no spatial gradient of the objective material concentration in the mixture. The samples taken out at any potion indicate the same concentration, regardless of the sample size. This mixing state and the mixture are referred to as the perfect (ordered) mixing2 as shown in Figure 5.8.1. In the normal mixing process, it is impossible to achieve the perfect mixing state. Homogeneous mixture3 in the normal mixing process is defined as a statistically perfect mixture, meaning that the probability of finding the objective material is all the same in any places in the mixture. This mixture is referred to as a random mixture. In order to understand the degree of mixing, it is important to use a statistical method.
Mixing and Packing of Powders
Published in Mohamed N. Rahaman, Ceramic Processing, 2017
Several terms are used in the literature to describe the particle arrangements possible for a mixture of two or more components. Here, we shall simplify them to just three: ordered, random, and partially ordered mixtures. An ordered mixture is one in which the particles are arranged in a regular repeating pattern, such as a lattice structure with a unit cell. This is the most perfect mixture, but it cannot be achieved in practice. Generally, the aim is to produce a random mixture, defined as a mixture in which the probability of finding a particle of any component is the same at all positions in the mixture and is equal to the proportion of that component in the mixture as a whole. For particles that do not have a tendency to segregate, this is the best quality of mixture that can be achieved. A partially ordered mixture is one in which at least one component is ordered in its distribution, such as a coating of fine particles on the surfaces of larger particles. Figure 6.1 gives schematic examples of the three types of mixtures.
Granulation, Mixing, and Packing of Particles
Published in Mohamed N. Rahaman, Ceramic Processing, 2017
Mixing of particulate solids is a key step in ceramic processing and in many other processing operations [1,8–10]. Several terms are used in the literature to describe the different possible arrangements of the particles in a mixture of two or more components. Here, we shall simplify them to just three: ordered, random, and partially ordered mixtures (Figure 9.6). An ordered mixture is one in which the particles are arranged in a regular repeating pattern, such as a lattice structure with a unit cell. This is the most perfect mixture, but it cannot be achieved in practice. Generally, the aim is to produce a random mixture, defined as a mixture in which the probability of finding a particle of any component is the same at all positions in the mixture and is equal to the proportion of that component in the mixture as a whole. For particles that do not have a tendency to segregate, this is the best quality of mixing that can be achieved. A partially ordered mixture is one in which at least one component is ordered in its distribution, such as a coating of fine particles on the surface of larger particles.
LaFeO3 films on SiO2 for supported-Pt catalysts
Published in International Journal of Green Energy, 2022
Tianyu Cao, Ohhun Kwon, John M. Vohs, Raymond J. Gorte
It is not surprising that ultrathin films formed by La2O3 and Fe2O3 on SiO2 would be amorphous on the XRD length scale. As-deposited films would be expected to form a random mixture, with crystallization occurring only upon heating to higher temperatures. Because SiO2 is amorphous, there is no underlying structure to facilitate that crystallization process. It is perhaps more surprising that the mixed oxides form large perovskite crystallites already at a much lower temperature of 873 K in MgAl2O4 (Onn et al. 2015). The fact that the support plays such an important role in forming crystallites suggests that the support “seeds” formation of the crystalline film via some kind of “heterogeneous nucleation” step (Bretos et al. 2018). The nanoscale seeds at the interface between the support and its overlayer may reduce the energy barrier for crystallization by promoting nucleation at a specific surface site.
Developing a space-filling mixture experiment design when the components are subject to linear and nonlinear constraints
Published in Quality Engineering, 2019
Greg F. Piepel, Bryan A. Stanfill, Scott K. Cooley, Bradley Jones, Jared O. Kroll, John D. Vienna
To accommodate the NMCCs in the nepheline HLW glass example discussed previously, Step 1 of the FFF algorithm was modified as now described. Outside of JMP®, 50,000 random mixtures satisfying the SCCs, LMCCs, and NMCCs were generated. This involved iteratively generating a random mixture in the constrained region specified by the SCCs (in Table 1). The formulas for generating such random mixtures are presented in the appendix of Borkowski and Piepel (2009), based on some work by Fang and Yang (2000). Then, the random mixture was retained if it satisfied the LMCCs (in Eq. [5]) and the NMCCs (in Eqs. [6] to [11]). This iterative process was continued until 50,000 random points (over the constrained mixture region specified by the SCCs, LMCCs, and NMCCs) were obtained. Because a design of 20 HLW glasses was desired (discussed in the next section), generating N = 50,000 random points was expected to easily satisfy the Lekivetz and Jones (2015) preferred recommendation of at least 100 random points per cluster.
First-principles calculation of mechanical properties of simulated debris Zr x U1− x O2
Published in Journal of Nuclear Science and Technology, 2019
Mitsuhiro Itakura, Hiroki Nakamura, Toru Kitagaki, Takanori Hoshino, Masahiko Machida
For most of the calculations, we use [200][020][002] calculation cell of fluorite structure which contains 32 U/Zr atoms and 64 O atoms. For the calculation of fracture surface, we use cell, which contains 48 U/Zr atoms and 96 O atoms. The random mixture of U and Zr is prepared using the special quasi-random structures (SQS) [6], using ATAT software [7]. We employ SQS structures in which two-body and three-body correlation of nearby atoms (up to the fourth neighbor) is as close to the ideally random case as possible, among a huge number of random structures generated by Monte Carlo sampling.