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Unit cell definition using parallelepiped with lengths a, b, c and angles between the sides given by α, β, γ [1]. A lattice constant or lattice parameter is one of the physical dimensions and angles that determine the geometry of the unit cells in a crystal lattice, and is proportional to the distance between atoms in the crystal.
The molar volume of gases around STP and at atmospheric pressure can be calculated with an accuracy that is usually sufficient by using the ideal gas law. The molar volume of any ideal gas may be calculated at various standard reference conditions as shown below: V m = 8.3145 × 273.15 / 101.325 = 22.414 dm 3 /mol at 0 °C and 101.325 kPa
A primitive cell is a unit cell that contains exactly one lattice point. For unit cells generally, lattice points that are shared by n cells are counted as 1 / n of the lattice points contained in each of those cells; so for example a primitive unit cell in three dimensions which has lattice points only at its eight vertices is considered to contain 1 / 8 of each of them. [3]
Until 1982, STP was defined as a temperature of 273.15 K (0 °C, 32 °F) and an absolute pressure of 101.325 kPa (1 atm). Since 1982, STP is defined as a temperature of 273.15 K (0 °C, 32 °F) and an absolute pressure of 100 kPa (1 bar). Conversions between each volume flow metric are calculated using the following formulas: Prior to 1982,
Using the number density as a function of spatial coordinates, the total number of objects N in the entire volume V can be calculated as = (,,), where dV = dx dy dz is a volume element. If each object possesses the same mass m 0 , the total mass m of all the objects in the volume V can be expressed as m = ∭ V m 0 n ( x , y , z ) d V ...
In this case, the unit is the centimeter cubed per gram (cm 3 /g or cm 3 ·g −1). To convert m 3 /kg to cm 3 /g, multiply by 1000; conversely, multiply by 0.001. Specific volume is inversely proportional to density. If the density of a substance doubles, its specific volume, as expressed in the same base units, is cut in half.
The unit cell is defined as the smallest repeating unit having the full symmetry of the crystal structure. [2] The geometry of the unit cell is defined as a parallelepiped, providing six lattice parameters taken as the lengths of the cell edges (a, b, c) and the angles between them (α, β, γ). The positions of particles inside the unit cell ...
where N particle is the number of particles in the unit cell, V particle is the volume of each particle, and V unit cell is the volume occupied by the unit cell. It can be proven mathematically that for one-component structures, the most dense arrangement of atoms has an APF of about 0.74 (see Kepler conjecture ), obtained by the close-packed ...