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Crystalline Structure of Metals
Published in Zainul Huda, Metallurgy for Physicists and Engineers, 2020
In general, there are three important crystal-structure properties: (a) number of atoms per unit cell, (b) coordination number (CN), and (c) atomic packing factor. The CN is defined as the number of atoms touching any given atom in the crystal lattice. The fraction of volume occupied by atoms (as solid spheres) in a unit cell is called the atomic packing factor (APF). Numerically, APF=NaVaVucwhere Na is the number of atoms per unit cell, Va is the volume of an atom, and Vuc is the volume of the unit cell.
The Structure of Solids
Published in Joseph Datsko, Materials Selection for Design and Manufacturing, 2020
The FCC structure is referred to as a dense or closely packed structure. A quantitative measure of how efficiently the atoms are packed in a structure is the atomic packing factor (APF) which is the ratio of the volume of the atoms in a cell to the total volume of the unit cell. The volume of a sphere is 1.333π r3 The volume of an FCC unit cell is a3, or, from Eq. (2–1), 22.64r3.
Electronic structure, thermodynamic properties and metallic behaviours of hydrogen
Published in Molecular Physics, 2021
Mahdi Kheirmand, Neda Heydari, Seyed Mohammad Azami
In this section, electronic structure of the metallic hydrogen chain is discussed and several theromodynamic and electrochemical properties of these systems are considered. Since there is no experimental evidence for one-dimensional hydrogen chain, to compare our results with experimental and other theoretical works on bulk metallic hydrogen, this model is extended to three-dimensional cubic systems including simple (cP), BCC, and FCC cubic systems. In this respect, one can assume that interatomic distances in the one-dimensional chain are close to that of three-dimensional structure, and this assumption will be verified via comparison of results with reported values for three-dimensional structures. Figure 1 displays the employed cubic models, where a and d stand for the average interatomic distance and cube side length, respectively. Therefore, the number of atoms in each side would be and Equations (1) and (2) can be applied for estimation of average density and pressure in bulk state, respectively. where and stand for average density, pressure, total mass, volume of the cube, hydrogen atom’s mass and force on the single hydrogen atom located on sides, respectively. Atomic packing factor (η) is a fraction that represents the ratio of the volume of the particle constituting a crystal relative to the total volume of the crystal structure as equation for one-component crystal shown below: where Nparticle is the number of atom in crystal structure, Vparticle is the volume of any atom and Vunite cell is the volume of the crystal.