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The particular half-Heusler compounds of interest as thermoelectric materials (space group ) are the semiconducting ternary compounds with a general formula XYZ where X is a more electropositive transition metal (such as Ti or Zr), Y is a less electropositive transition metal (such Ni or Co), and Z is heavy main group element (such as Sn or Sb).
For the constant energy white point, it was required that x = y = z = 1/3. By virtue of the definition of chromaticity and the requirement of positive values of x and y, it can be seen that the gamut of all colors will lie inside the triangle [1, 0], [0, 0], [0, 1]. It was required that the gamut fill this space practically completely.
The XYZ file format is a chemical file format. There is no formal standard and several variations exist, but a typical XYZ format specifies the molecule geometry by giving the number of atoms with Cartesian coordinates that will be read on the first line, a comment on the second, and the lines of atomic coordinates in the following lines. [ 1 ]
While the intention behind CIELAB was to create a space that was more perceptually uniform than CIEXYZ using only a simple formula, [3] CIELAB is known to lack perceptual uniformity, particularly in the area of blue hues. [4] The lightness value, L* in CIELAB is calculated using the cube root of the relative luminance with an offset near black.
It is useful as a theoretical reference; an illuminant that gives equal weight to all wavelengths. It also has equal CIE XYZ tristimulus values, thus its chromaticity coordinates are (x,y)=(1/3,1/3). This is by design; the XYZ color matching functions are normalized such that their integrals over the visible spectrum are the same. [1]
The old coordinates (x, y, z) of a point Q are related to its new coordinates (x′, y′, z′) by [14] [′ ′ ′] = [ ] []. Generalizing to any finite number of dimensions, a rotation matrix A {\displaystyle A} is an orthogonal matrix that differs from the identity matrix in at most four elements.
The physics convention.Spherical coordinates (r, θ, φ) as commonly used: (ISO 80000-2:2019): radial distance r (slant distance to origin), polar angle θ (angle with respect to positive polar axis), and azimuthal angle φ (angle of rotation from the initial meridian plane).
Let (x, y, z) be the standard Cartesian coordinates, and (ρ, θ, φ) the spherical coordinates, with θ the angle measured away from the +Z axis (as , see conventions in spherical coordinates). As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range ...