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The plane of a face-centered cubic lattice is a hexagonal grid. Attempting to create a base-centered cubic lattice (i.e., putting an extra lattice point in the center of each horizontal face) results in a simple tetragonal Bravais lattice. Coordination number (CN) is the number of nearest neighbors of a central atom in the structure. [1]
For a face-centered cubic unit cell, the number of atoms is four. A line can be drawn from the top corner of a cube diagonally to the bottom corner on the same side of the cube, which is equal to 4r. Using geometry, and the side length, a can be related to r as: =.
This is calculated by assuming that all the atoms are identical spheres, with a radius large enough that each sphere abuts on the next. The atomic packing factor is the proportion of space filled by these spheres which can be worked out by calculating the total volume of the spheres and dividing by the volume of the cell as follows:
By Euler's theorem in geometry on the distance between the circumcenter and incenter of a triangle, two concentric circles (with that distance being zero) are the circumcircle and incircle of a triangle if and only if the radius of one is twice the radius of the other, in which case the triangle is equilateral. [5]: p. 198
In another example, iron transforms from a body-centered cubic (bcc) structure called ferrite to a face-centered cubic (fcc) structure called austenite when it is heated. [14] The fcc structure is a close-packed structure unlike the bcc structure; thus the volume of the iron decreases when this transformation occurs.
A centered cube number is a centered figurate number that counts the points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points, with i 2 points on the square faces of the i th layer.
Arithmetic mean of the equirectangular projection and the Aitoff projection. Standard world projection for the NGS since 1998. 1904 Van der Grinten: Pseudoconic Compromise Alphons J. van der Grinten: Boundary is a circle. All parallels and meridians are circular arcs. Usually clipped near 80°N/S. Standard world projection of the NGS in 1922 ...
The Body centered cubic structure (BCC). It is not a close packed structure. In this each metal atom is at the centre of a cube with 8 nearest neighbors, however the 6 atoms at the centres of the adjacent cubes are only approximately 15% further away so the coordination number can therefore be considered to be 14 when these are on one 4 fold ...