Centrosymmetricity of unit cell or the pattern.?

[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.

 

[DrDu]

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.

 

[A Dhingra]

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.

 

[DrDu]

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

 

[LudusRex]

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.