Models of a Face Centered Cubic Structure

Description

Potassium hexachloromanganate, K2MnCl6, crystallizes in an interesting yet simple face centered cubic structure related to the fluorite structure - calcium fluorite. The K ion and the octahedral MnCl6 ion occupy, respectively, the F ion and Ca ion positions of the fluorite structure. There are 4 K2MnCl6 units in the cell. The MnCl6 ions are at the corners and centers of the faces of the unit cell. They are surrounded by 8 K ions at the corners of a smaller cube. If the potassium atoms are considered alone they form a simple cubic structure with a cell length half that of the K2MnCl6 cell. This smaller cell is centered at the center of the larger cell. Eight of the smaller cells exist for each of the larger cells, each smaller cell has 8 potassium atoms at its vertices. If we count these with multiplicity 1/8. since each vertex is shared by 8 small cells, we see that there is one potassium atom per smaller cell, making the required 8 potassium atoms in the larger cell. If the smaller cells are considered to be a "checker board" of red and black cells; the red cells are empty except for the potassium ions at the vertices and each black cell has 8 potassium ions at the vertices surrounding an MnCl6 ion. The models are meant as an aid in understanding these structures. "Manganese_fcc.stl" shows the manganese atoms at their face centered positions in the unit cell. "Manganese_inverse_fcc.stl" shows that an eighth of a manganese atom is at each corner of the unit cell and that the six half manganese atoms at the cell faces add 3 additional manganese atoms. "Manganese_potassium.stl" shows the unit cell containing 4 manganese atoms at face centered cubic positions and 8 potassium atoms in the smaller unit cell. It also describes the well known fluorite structure. "K2MnCl6_model.stl" shows a single MnCl6 group surrounded by 8 potassium atoms.

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