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Lattice Arrangements of Solids

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Lattice arrangements are representations of atoms in a three dimensional structure very often repeated over and over again with exactly the same symmetry.

Lattices are 3d spacial representation of atoms in a regular arrangement that are repeated over and over again in a large 3d structure.


We consider lattices as Bravais lattices. These lattices are based on their rotational symmetry, when you rotate the unit cell will it look exactly the same as it was. Each of these lattices has a distinct arrangement of atoms in its unit and also angles between its lengths. Auguste Bravais, a mathematician identified 14 different lattices that can exist in nature and identified their dimensions. He identified that each lattice has lengths identified letters a, b, and c. If two sides are equal, such as in a tetragonal lattice, then the lengths of the two lattice parameters are designated a and c, with b omitted. The angles are designated by the Greek letters α, β, and γ.

Cubic systems

As well as the crystal system being in the shape of a cube as seen above we can designate the layout of a lattice according to the different layout of the atoms.


Primitive cubic

Is much like the cubic system in the 7 crystal systems seen above. each corner of the unit is the position of an atom in the relative lattice.


Body Centered cubic

Much like the cubic structure contains 8 points in each corner and sides and angles of equal magnitude. Expect it also contains a lattice point in the centre of the cubic body.


An example of a body centered cubic structure for Caesium Chloride containing a Caesium ion (shown in red) with the white atoms representing the placement of the chloride ions



Face centered cubic

Again like the cubic structure contains 8 corners the location of 8 atomic points but also on each of the face an atom contained centrally.


An example of the face centered cubic structure is Magnesium Oxide as can be seen in the image the oxygen and magnesium atoms occupy the faces and corners of the crystal unit.

Terms in section
Unit cell

A unit cell is a single unit of atoms that have the same overall symmetry and can be used to build up a total crystal lattice with the repetition of these units

Lattices

A lattice is a term given to an ordered arrangement of points in a 3D shape creating a regular arrangement of atoms and ions

Bravais lattice

A bravais lattice is the name given to the distinct shapes of lattices based on a mathematical system of vectors in directions

Rotational symmetry

Rotational symmetry is a property of a shape when it looks the same after it has been rotated or turned

Auguste Bravais

August Bravais was a French physician who used crystallography to analyse the arrangement of atoms in crystal lattices

Regular arrangement

Regular arrangement describes the ordered layout of atoms in the same space of a lattice with high orders of symmetry

Length relationships

The length relationship is the measured lengths of the sides of unit cells in a crystal lattice

Angles

Angles are the measured angle between the atoms in a crystal structure

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