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Introduction:
Shown in the image is a cubic crystal structure called
the Perovskite crystal structure
Overview:
All solids are aggregates of atoms. Based on the way
the atoms are arranged, most solids can be classified
as crystalline or amorphous (glass). In crystalline
materials, the atoms constituting the solid are
arranged in a periodic manner, whereas in glass they
are in "arranged" in a random manner such
as in liquids. The structure shown in the figure is
that of a mineral called Perovskite. A typical example
of the Perovskite structure pictured is barium titanate
(BaTiO3). 8 Ba atoms (orange ones) "sit"
at the cube corners, 1 Titanium atom (the black one)
"sits" in the centre of the cube and 6 oxygen
atoms (the rest) "sit" at the centre of the
faces. Note that an actual crystal of bigger dimensions
is built up by stacking up such cubes of much smaller
dimension of the order of 5Å. Each atom at the
cube corner is shared by eight other cubes, while the
atoms at the center of the cube face are shared by two
cubes. Hence, only 1/8 of each Ba atom and ½
of each oxygen atom actually belong to the cube shown,
resulting in the formula above. There are 230 possible
periodic arrangements that can fill space and these
were deduced by mathematicians even before it was actually
proven to be so experimentally by x-ray diffraction
in the early part of the twentieth century.
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