# Centrosymmetricity of unit cell or the pattern.?

• A Dhingra
In summary, the concept of center of symmetry applies to both unit cells and patterns or systems of specific unit cells. While all Bravais lattices are inversion symmetric, real crystals rarely exhibit this symmetry. The presence or absence of inversion symmetry in an elementary cell is important for bulk properties, such as ferroelectricity. The overall symmetry of a crystal structure is determined by the symmetry of its elementary cell, such as a cube formed by cubic unit cells or a cuboid formed by tetragonal unit cells. The shape of the elementary unit cell, such as being tetragonal, does not necessarily determine its inversion symmetry.
A Dhingra
hello
i got to ask if the center of symmetry is specific to a unit cell or a pattern or system of specific unit cell? I mean is Cubic (Bravis Lattice) is Centro symmetric or the structures formed by it. As an example, Tetragonal unit cell appears centro-symmetric but forming structures like Tetragonal Scalenohedral crystal lattice makes it non centrosymmetric as shown in the link:
http://www.uwgb.edu/dutchs/symmetry/tetraguc.htm

Any help is appreciated.

First you have to be careful with definitions. A Bravais lattice is an idealization for an infinite crystal. All these lattices are inversion symmetric.
On the other hand, hardly any real crystal is inversion symmetric and obviously this can matter quite trivially, e.g. when two faces related by inversion have different size.
Whether or not an elementary cell is inversion symmetric is of most importance for bulk properties like optical activity or the x-ray diffraction pattern.

But, without any such mention, it is said that ferroelectric effect is not evident in Centro-symmetric crystal.
I am just repeating what you have said to be sure i get it.
When we describe properties of any crystal's unit cell we presume that the crystal is infinite, though in real, this is not so.
One more thing, if the (ideal) crystal structure is, let's say, a cube formed by cubic unit cells, then is the structure as a whole Centro-symmetric? And what about a cuboid formed using tetragonal unit cell? Also is it true that the elementary unit cell tetragonal in shape has inversion symmetry or not.

Yes, ferroelectricity is a typical bulk property, whence it depends on the symmetry of the elementary cell.

The concept of centrosymmetry is specific to individual unit cells, as each unit cell can have its own unique arrangement of atoms. The overall pattern or system is determined by the arrangement of these unit cells. In the example provided, the Tetragonal Scalenohedral crystal lattice is non-centrosymmetric because of the specific arrangement of unit cells within the larger structure. The overall centrosymmetry of a pattern or system is determined by the individual centrosymmetry of each unit cell within it. This concept is important in understanding the symmetry and properties of various crystals and materials.

## What is centrosymmetricity?

Centrosymmetricity refers to the property of a unit cell or pattern being symmetrical with respect to a central point or axis. This means that when a line is drawn from the center of the structure to any point on its surface, the same arrangement of atoms or molecules is found on either side of the line.

## How is the centrosymmetricity of a unit cell determined?

The centrosymmetricity of a unit cell can be determined by analyzing its crystallographic symmetry operations, such as rotations, reflections, and inversions. If the unit cell possesses a center of symmetry, it is considered to be centrosymmetric.

## What are the implications of a centrosymmetric unit cell or pattern?

A centrosymmetric unit cell or pattern has several implications, such as having a net electric dipole moment of zero, meaning it is non-polar. This property also affects the physical properties of the material, such as its optical and magnetic properties.

## Can a unit cell or pattern be centrosymmetric in one direction and not in another?

Yes, it is possible for a unit cell or pattern to be centrosymmetric in one direction and not in another. This is known as polar centrosymmetry and occurs when the symmetry of the unit cell is broken along a specific direction, resulting in a net dipole moment in that direction.

## Why is the centrosymmetricity of a unit cell or pattern important in crystallography?

The centrosymmetricity of a unit cell or pattern is important in crystallography because it helps to determine the crystal system and space group of a crystal. It also affects the diffraction patterns observed in X-ray crystallography and can provide valuable information about the physical and chemical properties of a material.

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