• Engineering and Architecture
  • Management and Business Administration
  • Medicine and Allied Sciences
  • Law
  • Animation and Design
  • Media, Mass Communication and Journalism
  • Finance & Accounts
  • Computer Application and IT
  • Pharmacy
  • Hospitality and Tourism
  • Competition
  • School
  • Study Abroad
  • Arts, Commerce & Sciences
  • Learn
  • Online Courses and Certifications
Crystal Lattices and Unit Cells - Difference, Parameters, Properties, FAQs

Crystal Lattices and Unit Cells - Difference, Parameters, Properties, FAQs

Team Careers360Updated on 02 Jul 2025, 04:50 PM IST

The crystal lattice and the unit cell are the three-dimensional, repeating patterns of the atomic, ionic, or molecular positions of atoms in a crystal. Such a structured pattern extends and gives an orderly structure to the material. The Unit Cell is the smallest building block of the crystal lattice that can be repeated in space to form the entire lattice.

In the article, we cover the topic of crystal lattice which is the sub-topic of the chapter on Solid states. it is important for board exams JEE Mains Exam, NEET Exam, and other entrance exams.

Crystal Lattices and Unit Cells

A portion of the three-dimensional crystal lattice and its unit cell as shown in Fig below:

3D Cube

In the three-dimensional crystal structure, a unit cell is characterized by:
(i) its dimensions along the three edges a, b, and c. These edges may or may not be mutually perpendicular.
(ii) angles between the edges, α (between b and c), β (between a and c), and γ (between a and b). Thus, a unit cell is characterized by six parameters a, b, c, α, β, and γ.
These parameters of a typical unit cell are shown in Fig given below:

Angles in 3D cube

Related Topics link,

Primitive and Centred Unit Cells

Primitive Unit Cells
When constituent particles are present only on the corner positions of a unit Cell, it is called as primitive unit cell.

Centered Unit Cells
When a unit cell contains one or more constituent particles present at positions other than corners in addition to those at corners, it is called a centered unit cell. Centered unit cells are of three types:

  • Body-centered Unit Cells: Such a unit cell contains one constituent particle (atom, molecule, or ion) at its body center besides the ones that are at its corners.
  • Face-centered Unit Cells: Such a unit cell contains one constituent particle present at the center of each face, besides the ones that are at its corners.
  • End-centered Unit Cells: In such a unit cell, one constituent particle is present at the center of any two opposite faces besides the ones present at its corners.
NEET Highest Scoring Chapters & Topics
This ebook serves as a valuable study guide for NEET exams, specifically designed to assist students in light of recent changes and the removal of certain topics from the NEET exam.
Download EBook

Inspection of a wide variety of crystals leads to the conclusion that all can be regarded as conforming to one of the seven regular figures. These basic regular figures are called seven-crystal systems.

Types of lattice

Seven Primitive Unit Cells and Their Possible Variations as Centred Unit Cells

Crystal system

Bravias latticesInterceptsInterfacial angleExamples
CubicPrimitive, face-centered, body-centered = 3 a = b = c⍺ = β = ? = 90o

Ag, Au, Hg, Pb, diamond, NaCl, ZnS

OrthorhombicPrimitive, face-centered, body-centered, end centered = 4a ≠ b ≠ c⍺ = β = ? = 90o

K2SO4,KNO2, BaSO4, Rhombic Sulphur

TetragonalPrimitive, body-centred = 2a = b ≠ c⍺ = β = ? = 90o

TiO2, SnO2, CaSO4, White Tin

MonoclinicPrimitive, end centered = 2a ≠ b ≠ c

⍺ = ? = 90

β ≠ 90o

CaSO4.2H2O

TriclinicPrimitive = 1a ≠ b ≠ c⍺ ≠ β ≠ ? ≠ 90o

CuSO4.5H2O, K2Cr2O7, H3BO3

HexagonalPrimitive = 1a = b ≠ c⍺ = β = 90o ? = 120o

Zn, Mg, Cd, SiO2, Graphite, ZnO

RhombohedralPrimitive = 1a = b = c⍺ = β = ? ≠ 90o

Bi, As, Sb, CaCO3, HgS

Total = 14


Unit Cells of 14 Types of Bravais Lattices

Types of Bravais Lattice

Types of Bravais Lattice
Crystal Lattice

Any crystal lattice is made up of a very large number of unit cells and every lattice point is occupied by one constituent particle (atom, molecule or ion).

Primitive Cubic Unit Cell

The primitive cubic unit cell has atoms only at its corner. Each atom at a corner is shared between eight adjacent unit cells as shown in Fig. given below:

3D Cube
four unit cells in the same layer and four unit cells in the upper (or lower) layer. Therefore, only 1/8th of an atom (or molecule or ion) actually belongs to a particular unit cell. In Fig. given below, a primitive cubic unit cell has been depicted in three different ways. Each small sphere in this figure represents only the center of the particle occupying that position and not its actual size. Such structures are called open structures.
Lattice points
The arrangement of particles is easier to follow in open structures as shown in the figure given below depicts a space-filling representation of the unit cell with actual particle size
Voids
The figure given below shows the actual portions of different atoms present in a cubic unit cell. In all, since each cubic unit cell has 8 atoms on its corners, the total number of atoms in one unit cell 8x(1/8) = 1 atom.
Unit Cell

Body Centred Cubic Unit Cell

A body-centred cubic (bcc) unit cell has an atom at each of its corners and also one atom at its body center. The figure given below depicts (a) open structure (b) space-filling model and (c) the unit cell with portions of atoms actually belonging to it. It can be seen that the atom at the body centre wholly belongs to the unit cell in which it is present.
Number of atoms in unit cell

Thus in a body-centered cubic (bcc) unit cell:

  • 8 corners x 1/8 per corner atom = 8 x 1/8 = 1 atom
  • 1 body centre atom = 1 x 1 = 1 atom
    Thus, total number of atoms per unit cell = 2 atoms

Face Centred Cubic Unit Cell

A face-centered cubic (fcc) unit cell contains atoms at all the corners and at the center of all the faces of the cube. It can be seen in the figure given below, that each atom located at the face-centre is shared between two adjacent unit cells and only ½ of each atom belongs to a unit cell.

unit cell

The fig. given below depicts (a) an open structure (b) a space-filling model and (c) the unit cell with portions of atoms actually belonging to it.
Types of unit cell
Thus, in a face-centred cubic (fcc) unit cell:

  • 8 corners atoms x 1/8 atom per unit cell = 8 x 1/8 = 1 atom
  • 6 face-centred atoms x 1/2 atom per unit cell = 6 x 1/2 = 3 atoms
    Thus, total number of atoms per unit cell = 4 atoms

Also read -

Some Solved Examples

Example 1
Question: The smallest repeating pattern which when repeated in 3-D results in the crystal of substance is called:
1) Space lattice
2) Crystal lattice
3) (correct) Unit cell
4) Bravais lattice

Solution: The unit cell is the smallest repeating unit in the crystal which has all the properties of a crystal. Hence, the answer is the option (3).

Example 2
Question: The most unsymmetrical crystal system is:
1) Cubic
2) Hexagonal
3) (correct) Triclinic
4) Orthorhombic

Solution: The triclinic crystal system has the parameters a neq b neq c and alpha neq beta neq gamma neq900 . Hence, the answer is the option (3).

Example 3
Question: The crystal system of a compound with unit cell dimensions a=0.387,nm,b=0.387,nm,c=0.504,nmandgamma=1200 is:
1) (correct) Hexagonal
2) Cubic
3) Rhombohedral
4) Orthorhombic

Solution: For hexagonal systems, the conditions are a = b neq c and alpha=beta=900,gamma=1200 . Thus, the answer is the option (1).

Example 4
Question: For which of the given crystal families does the following relation hold? a not equal b not equal c and alpha=gamma=900,betaneq900
1) (correct) Monoclinic
2) Triclinic
3) Orthorhombic
4) Hexagonal

Solution: The given relation corresponds to the monoclinic crystal system. Hence, the answer is the option (1).

Example 5
Question: The crystal system characterized by a = b = c and alpha=beta=gamma=900 is:
1) Cubic
2) Tetragonal
3) (correct) Orthorhombic
4) Rhombohedral

Solution: The cubic crystal system has equal edge lengths and all angles equal to 900. Therefore, the answer is the option (1).

NCERT Chemistry Notes:

Frequently Asked Questions (FAQs)

Q: How do crystal lattices influence the behavior of materials at extreme conditions (high pressure, temperature)?
A:
Under extreme conditions, crystal lattices can undergo phase transitions, structural transformations, or even amorphization. The initial crystal structure influences how the material responds to these conditions, affecting properties like compressibility, melting behavior, and phase stability at high pressures or temperatures.
Q: What is the significance of Vegard's law in understanding solid solutions?
A:
Vegard's law states that there is often a linear relationship between the crystal lattice parameter of an alloy and the concentration of its constituent elements. This helps in predicting and analyzing the composition of solid solutions based on X-ray diffraction data.
Q: How do crystal lattices influence the behavior of materials under irradiation?
A:
Crystal lattices affect how materials respond to radiation damage. The lattice structure influences the formation and migration of point defects, dislocation loops, and other radiation-induced defects, which in turn affect the material's dimensional stability and mechanical properties under irradiation.
Q: What is the role of crystal lattices in determining the cleavage planes of minerals?
A:
Cleavage planes in minerals are determined by the weakest bonds in the crystal lattice. The arrangement of atoms and the nature of bonding in different crystallographic directions influence where the crystal is most likely to split when stress is applied.
Q: How do crystal lattices affect the thermal expansion behavior of materials?
A:
The crystal lattice structure influences thermal expansion through factors like bond strength, atomic packing, and anharmonicity of lattice vibrations. Anisotropic crystal structures often exhibit different thermal expansion coefficients along different crystallographic directions.
Q: How do crystal lattices influence the formation and stability of grain boundaries?
A:
Crystal lattices determine the possible orientations of grain boundaries and their energies. The mismatch between adjacent crystal orientations affects grain boundary structure, mobility, and properties, influencing phenomena like grain growth, recrystallization, and material strength.
Q: What is the relationship between crystal structure and superconductivity?
A:
Crystal structure plays a crucial role in superconductivity by influencing electron-phonon interactions and the formation of Cooper pairs. Certain crystal structures, like layered perovskites, are particularly conducive to high-temperature superconductivity.
Q: How do crystal lattices affect the formation and properties of intermetallic compounds?
A:
Crystal lattices in intermetallic compounds often have specific stoichiometries and ordered arrangements of different metal atoms. These structures can lead to unique properties like high hardness, thermal stability, and interesting magnetic or electronic characteristics.
Q: What is the significance of the concept of reciprocal lattice in crystallography?
A:
The reciprocal lattice is a mathematical construct that represents the Fourier transform of the real crystal lattice. It is crucial for understanding X-ray diffraction patterns, electron and neutron scattering, and for describing the electronic band structure of solids.
Q: How do crystal lattices influence the formation and properties of semiconductor devices?
A:
Crystal lattices in semiconductors determine the band structure, carrier mobility, and dopant incorporation. The lattice structure influences how impurities are incorporated, how charge carriers move, and how various semiconductor junctions and interfaces behave.
Articles
Previous
Next