The atomic packing factor for the BCC unit cell will be Which shows that the atoms in the BCC unit cell touch each other across the cubic diagonal. The relationship between a and R is obtained from the above figure. The volume of the BCC unit cell is V unit cell = a 3 Since there are two atoms per BCC unit cell, the volume of atoms in the unit cell of radius R is We know the Formula for Atomic Packing Factor (APF) for the BCC StructureĪPF = volume of atoms in BCC unit cell /volume of BCC unit cell Example Problem to Calculate Atomic Packing Factor (APF) for the BCC StructureĬalculate the atomic packing factor (APF) for the BCC unit cell, assuming the atoms to be hard spheres Let us solve an example problem to calculate the Atomic Packing Factor (APF) for the BCC unit cell. Using this equation, the APF for the BCC unit cell can be calculated. If the atoms in the BCC unit cell are considered to be spherical, an atomic packing factor (APF) can be calculated by using the following equationĪPF = volume of atoms in unit cell /volume of the unit cell *Calculated from lattice constants by using Eqn, R = √3 a/4. The following table shows the lattice constants and atomic radii of selected metals that have the BCC crystal structure at room temperature (20☌) Metal Lattice Constant a (nm) Atomic Radius R* (nm) Chromium 0.289 0.125 Iron 0.287 0.124 Molybdenum 0.315 0.136 Potassium 0.533 0.231 Sodium 0.429 0.186 Tantalum 0.33 0.143 Tungsten 0.316 0.137 Vanadium 0.304 0.132 Table 1: Selected metals that have the BCC crystal structure at room temperature (20☌) and their lattice constants and atomic radii The lattice constant of the Iron with BCC structure at 20☌ is 0.287 nm. Therefore, considering that three significant digits should be used in all calculations, the answer will be Thus, if a is the length of the cube edge, then The extremely small size of the unit cells of crystalline metals that are shown below should be emphasized.īCC unit cell showing the relationship between the lattice constant a and the atomic radius R. Thus, the densely packed structures are in lower and more stable energy arrangements. Most metals crystallize in these dense-packed structures because energy is released as the atoms come closer together and bond more tightly with each other. The HCP structure is a denser modification of the simple hexagonal crystal structure. A unit cell is a building block of the Crystal structure. 👉 Crystal Structure: the particular repeating arrangement of atoms throughout a crystal. 👉 Unit Cell: is the smallest replicating portion of a crystal lattice 👉 Crystal Lattice/space Lattice: is an atomic arrangement of the constituent atoms or ions or molecules to the points of intersection of a network of lines in three dimensions space. 👉 Crystal: is a solid composed of atoms, ions, or molecules arranged in a pattern that is repetitive in three dimensions.
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