|
The lattice constant, or lattice parameter, refers to the physical dimension of unit cells in a crystal lattice. Lattices in three dimensions generally have three lattice constants, referred to as ''a'', ''b'', and ''c''. However, in the special case of cubic crystal structures, all of the constants are equal and we only refer to ''a''. Similarly, in crystal structures, the ''a'' and ''b'' constants are equal, and we only refer to the ''a'' and ''c'' constants. A group of lattice constants could be referred to as lattice parameters. However, the full set of lattice parameters consist of the three lattice constants and the three angles between them. For example, the lattice constant for diamond is ''a'' = 3.57 Å at 300 K. The structure is equilateral although its actual shape cannot be determined from only the lattice constant. Furthermore, in real applications, typically the average lattice constant is given. Near the crystal's surface, lattice constant is affected by the surface reconstruction that results in a deviation from its mean value. This deviation is especially important in nano-crystals since surface to nano-crystal core ratio is large.〔Mudar A. Abdulsattar, Solid State Sci. 13, 843 (2011).〕 As lattice constants have the dimension of length, their SI unit is the meter. Lattice constants are typically on the order of several angstroms (i.e. tenths of a nano-metre). Lattice constants can be determined using techniques such as X-ray diffraction or with an atomic force microscope. Lattice constant of a crystal can be used as a natural length standard of nanometer range. In epitaxial growth, the lattice constant is a measure of the structural compatibility between different materials. Lattice constant matching is important for the growth of thin layers of materials on other materials; when the constants differ, strains are introduced into the layer, which prevents epitaxial growth of thicker layers without defects. == Volume == The volume of the unit cell can be calculated from the lattice constant lengths and angles. If the unit cell sides are represented as vectors, then the volume is the dot product of one vector with the cross product of the other two vectors. The volume is represented by the letter ''V''. For the general unit cell For monoclinic lattices with α = 90°, γ = 90°, this simplifies to For orthorhombic, tetragonal and cubic lattices with β = 90° as well, then 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lattice constant」の詳細全文を読む スポンサード リンク
|