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The unit cell


Since the crystal lattice is made up of a regular arrangement which repeats in three dimensions, we can save ourselves a great deal of work by considering the simple repeating unit rather than the entire crystal lattice. The basic repeating unit is known as the unit cell. Crystalline solids often have flat, well-defined faces that make definite angles with their neighbors and break cleanly when struck. These faces lie along well-defined directions in the unit cell.

The unit cell is the smallest, most symmetrical repeating unit that, when translated in three dimensions, will generate the entire crystal lattice.


It is possible to have a number of different choices for the unit cell. By convention, the unit cell that reflects the highest symmetry of the lattice is the one that is chosen. A unit cell may be thought of as being like a brick which is used to build a building (a crystal). Many bricks are stacked together to create the entire structure. Because the unit cell must translate in three dimensions, there are certain geometrical constraints placed upon its shape. The main criterion is that the opposite faces of the unit cell must be parallel. Because of this restriction there are only six parameters that we need to define in order to define the shape of the unit cell. These include three edge lengths a, b, and c and three angles α size 12{α} {} , β size 12{β} {} and γ size 12{γ} {} . Once these are defined all other distances and angles in the unit cell are set. As a result of symmetry, some of these angles and edge lengths may be the same. There are only seven different shapes for unit cells possible. These are given in the chart below.

Unit Cell Type Restrictions on Unit Cell Parameters Highest Type of Symmetry Element Required
Triclinic a is not equal to b is not equal to c; α size 12{α} {} is not equal to β size 12{β} {} is not equal to γ size 12{γ} {} . no symmetry is required, an inversioncenter may be present
Monoclinic a is not equal to b is not equal to c α size 12{α} {} = γ size 12{γ} {}  90 ° size 12{"90"°} {} β size 12{β} {} is not equal to 90 ° size 12{"90"°} {} . highest symmetry element allowed is aC2 axis or a mirror plane
Orthorhombic a is not equal to b is not equal to c α size 12{α} {} = β size 12{β} {} = γ size 12{γ} {}  90 ° size 12{"90"°} {} has three mutually perpendicularmirror planes and/or C2 axes
Tetragonal a =b is not equal to c α size 12{α} {} = β size 12{β} {} = γ size 12{γ} {}  90 ° size 12{"90"°} {} has one C4 axis
Cubic a =b =c α size 12{α} {} = β size 12{β} {} = γ size 12{γ} {}  90 ° size 12{"90"°} {} has C3 and C4 axes
Hexagonal, Trigonal a =b is not equal to c α size 12{α} {} = β size 12{β} {} = 90 ° size 12{"90"°} {}  γ size 12{γ} {}  120 ° size 12{"120"°} {} C6 axis (hexagonal); C3 axis (trigonal)
Rhombohedral* a =b =c α size 12{α} {} = β size 12{β} {} = γ size 12{γ} {} is not equal to 90 ° size 12{"90"°} {} C3 axis (trigonal) 

*There is some discussion about whether the rhombohedral unit cell is a different group or is really a subset of the trigonal/hexagonal types of unit cell.


You will be asked to count the number of atoms in each unit cell in order to determine the stoichiometry (atom-to-atom ratio) or empirical formula of the compound. However, it is important to remember that solid state structures are extended, that is, they extend out in all directions such that the atoms that lie on the corners, faces, or edges of a unit cell will be shared with other unit cells, and therefore will only contribute a fraction of that boundary atom. As you build crystal lattices in these exercises you will note that eight unit cells come together at a corner. Thus, an atom which lies exactly at the corner of a unit cell will be shared by eight unit cells which means that only⅛of the atom contributes to the stoichiometry of any particular unit cell. Likewise, if an atom is on an edge, only¼of the atom will be in a unit cell because four unit cells share an edge. An atom on a face will only contribute½to each unit cell since the face is shared between two unit cells.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Honors chemistry lab fall. OpenStax CNX. Nov 15, 2007 Download for free at http://cnx.org/content/col10456/1.16
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