Bravais Lattice - Types, Crystal Structures and FAQs

Edited By Team Careers360 | Updated on Jul 02, 2025 04:51 PM IST

In the year of 1850 scientist name Auguste Bravias discovered about bravais lattice. Bravais lattice generally refers with the different type of arrangement of atoms in a crystal in three dimensional which is generally abbreviated as 3-D geometry. Bravais lattice generally referred to the arrangement of atoms in any crystal in its three dimensional structure and there are 14 known arrangement of bravais lattices are present by now.

Before moving to bravais lattice the first thing we have to know about is unit cell which can be defined as the smallest group of those atoms which are symmetrically aligned and those are repeating repeatedly in an array which further form the entire crystal i.e. in easy manner we can say unit cell is the repeating unit form the whole crystal.

There are a number of methods which easily describe bravias lattice the most common and easiest way to describe what is bravais lattice; Bravias lattice definition can be defined as an arrangement of different points in an array and orientation of these points look exactly same from any point or we can say that lattice points which are of indistinguishable in nature.

Bravais lattice is said to or we can say refer to be one of the 14 different types of unit cells through which a crystal structure is made up of where crystal structure can be defined as any structure which is composed up of atoms or in which atoms are arranged in a definite order while a crystal lattice is made up of points. Bravais lattice is named after the scientist who discovered this, A French scientist named Auguste Bravais.

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Bravais Lattice Types

There are basically 14 bravias lattice out of these type of lattice 5 bravais lattice are grouped together in four crystal lattices out of which every crystal lattice is divided into two categories known by the name primitive and centered crystal lattice and these 5 bravais lattice are combined into 4 crystal lattice which can be defined as follows:

1. Monoclinic crystal lattice: In this type of crystal lattice bravais lattice in present in the primitive category and have oblique type structure.

2. Orthorhombic crystal lattice: In this 2 bravais lattice are present in both primitive as well as centered crystal lattice in the form of rectangular and centered rectangular crystal lattice.

3. Tetragonal crystal lattice: In this type of bravais lattice is present in primitive group as square. These can also be present as face centred tetragonal.

4. Hexagonal crystal lattice: In this bravais lattice is present in the form of hexagon in primitive type.

7 lattices are present in three dimensional geometry which can be discussed as follows:

1. Cubic lattice: In this type of crystal lattice the following relationships between unit cells like the letter a, b and c which describe the dimensions of unit cell and letter represented by denotes the corresponding angle and the relation can be shown as follows:

a = b = c and

In this cubic lattice three possible types of lattices are there which can be known by the name Simple cubic cell or primitive unit cell, Body centered cubic cell and face centered cubic unit cell.

The main cubic lattice example for cubic structure is polonium, for body centered cubic iron is the one and for face centered cubic is copper.

2. Orthorhombic lattice: These are of orthorhombic structure and relation between edge lengths and angles can be derived as:

and

In this type four possible structures can be seen which are named as simple cubic, base centered cubic unit cell, body centered cubic unit cell and face centered cubic unit cell.

The main example of orthorhombic crystal lattice are: For orthorhombic crystal lattice the main example is Rhombic sulfur, base centered orthorhombic structure can be seen in case of magnesium sulfate hexahydrate, potassium nitrate is said to be the example of body-centered orthorhombic while the barium sulfate is the known example for face-centered orthorhombic.

3. Tetragonal systems: In this type of crystal lattice the relation can be discussed as follows:

and

There are only two types of tetragonal unit cell which can be known by the name simple tetragonal cell and body centered tetragonal cells.

Examples of tetragonal bravais lattice are stannic oxide and titanium dioxide for simple tetragonal and body centered tetragonal respectively.

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4. Monoclinic systems: Bravais lattice which shows monoclinic system can be have the relations of edge length and angles can be shown as follows:

and

Two main possible structures shown by monoclinic structures are primitive and base centered monoclinic unit cells and for these two the main examples are monoclinic sulfur in case of primitive monoclinic system while for base centered monoclinic sodium sulfate decahydrate is the known example.

5. Triclinic system: In this type of system only one bravais lattice is known which is called primitive cell and the relation between edge lengths and the angles of this cell can be shown as follows:

and

Triclinic unit cell are known in the form of potassium dichromate.

6. Rhombohedral system: This type also contain only one type of bravias lattice which can be known by the name rhombohedric primitive unit cell or rhombohedral unit cell in which the relations of edge length and angle can be shown as:

a = b = c and .

The main examples of simple rhombohedric unit cell are calcite and sodium nitrate.

Also, students can refer,

7. Hexagonal system: This hexagonal system also contain only one type of lattice cell known by the name simple hexagonal cell and the relation of edge lengths and angles can be represented as:

and

The main examples of simple hexagonal unit cells are zinc oxide and beryllium oxide. Other arrangement of this bravias lattices can be shown in four dimensional geometry abbreviated as 4-D geometry. In this 64 types of bravais lattice out of which 23 are known as primitive one and most bravais lattices are of the type i.e. 41 are known by the centred lattice whereas ten bravais lattices are split into enantiomorphic pairs. From all this discussion we can notice that 14 possible bravais lattices are varies from each other with the relationship between edge length and angles as for every arrangement the relation is different. It is also an important thing which suggest that bravias lattice is not exactly equal to crystal lattice in each case. Bravias lattice table can be shown as:

Hexagonal system

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Frequently Asked Questions (FAQs)

1. Which type of crystals contains more than one bravais lattice?

There are 14 types of bravias lattice out of which 4 contain more than one crystal lattice which can be named as cubic lattice, orthorhombic lattice, tetragonal systems and monoclinic systems.

2. Define unit cell.

In an easy manner we can describe unit cell as the shortest or smallest cell which by repeating itself many times to form a whole crystal lattice.

3. Bravais lattice is discovered by whom?

Bravias lattice was discovered in the year of 1951 by the scientist named Auguste Bravias who was a French scientist and also the name bravias lattice is originated from the name of its discoverer.

4. Give the example of orthorhombic unit cell.

5. a = b = c is true for which cubic cell?

This relation is true for cubic lattice and rhombohedral system.

6. What is a Bravais lattice?

A Bravais lattice is a mathematical concept used to describe the periodic arrangement of atoms or molecules in a crystal structure. It represents an infinite array of discrete points with an arrangement and orientation that appears exactly the same, from whichever of the points the array is viewed.

7. How many types of Bravais lattices exist in three-dimensional space?

There are 14 types of Bravais lattices in three-dimensional space. These 14 lattices are divided among seven crystal systems: triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic.

8. What determines the type of Bravais lattice a crystal will form?

The type of Bravais lattice a crystal forms is determined by the nature of the atoms or molecules in the crystal, their bonding characteristics, and the conditions under which the crystal forms (such as temperature and pressure). The arrangement that minimizes the overall energy of the system is typically favored.

9. How does the concept of symmetry relate to Bravais lattices?

Symmetry is crucial in defining Bravais lattices. Each lattice type has specific symmetry operations (such as rotations, reflections, and translations) that leave the lattice unchanged. The symmetry of a lattice determines its crystal system and influences its physical properties.

10. What is the difference between a unit cell and a Bravais lattice?

A unit cell is the smallest repeating unit of a crystal structure that shows the full symmetry of the crystal lattice. A Bravais lattice, on the other hand, is an infinite array of discrete points with an arrangement and orientation that appears exactly the same from any of these points. The unit cell is essentially a building block of the Bravais lattice.

11. What is meant by the term "close-packed structure" in crystallography?

A close-packed structure refers to an arrangement of atoms or molecules in a crystal where they are packed together as tightly as possible. The two most common close-packed structures are hexagonal close-packed (HCP) and face-centered cubic (FCC). These structures maximize the packing efficiency, with atoms occupying 74% of the available space.

12. What is the relationship between crystal structure and physical properties of materials?

The crystal structure, determined by the Bravais lattice and atomic arrangement, significantly influences a material's physical properties. It affects properties such as density, melting point, electrical and thermal conductivity, mechanical strength, and optical characteristics. For example, the ductility of metals is often related to their ability to slip along close-packed planes, which depends on the crystal structure.

13. What is the importance of Miller indices in describing crystal planes and directions?

Miller indices are a system of notation used to describe planes and directions in Bravais lattices and crystal structures. They provide a standardized way to identify specific crystal planes and directions, which is crucial for understanding crystal growth, cleavage, and various physical properties. Miller indices are also essential in analyzing X-ray diffraction patterns and predicting crystal behavior.

14. What is the significance of coordination number in crystal structures?

Coordination number refers to the number of nearest neighbors an atom has in a crystal structure. It's determined by the Bravais lattice type and atomic packing. For instance, in a simple cubic lattice, the coordination number is 6, while in FCC and HCP, it's 12. The coordination number influences properties like melting point, hardness, and chemical reactivity of the material.

15. What is the significance of the reciprocal lattice in crystallography?

The reciprocal lattice is a mathematical construct derived from the real space Bravais lattice. It's crucial in understanding X-ray diffraction patterns and in calculations involving wave-like properties of crystals. Each point in the reciprocal lattice corresponds to a set of planes in the real lattice. The reciprocal lattice simplifies the mathematical description of diffraction phenomena and is essential in techniques like electron and neutron diffraction.

16. How do Bravais lattices influence the phenomenon of epitaxial growth in thin films?

Epitaxial growth, where a crystalline film grows on a crystalline substrate, is heavily influenced by the Bravais lattices of both materials. The compatibility between the lattices of the film and substrate determines the quality and properties of the grown film. Lattice mismatch can lead to strain and defects in the film. Understanding these lattice relationships is crucial in semiconductor technology, where epitaxial growth is used to create high-quality thin films for electronic and optoelectronic devices.

17. How do Bravais lattices relate to the concept of Peierls distortion in one-dimensional metals?

Peierls distortion, a phenomenon in one-dimensional metals where the lattice distorts to open up a band gap, is intimately related to the periodicity of the Bravais lattice. The distortion changes the periodicity of the lattice, affecting the electronic band structure. While Bravais lattices typically describe three-dimensional structures, understanding them is crucial for grasping how changes in lattice periodicity can dramatically alter electronic properties, as seen in the Peierls distortion.

18. How do Bravais lattices influence the formation and properties of quasicrystals?

Quasicrystals challenge the traditional concept of Bravais lattices as they possess long-range order but lack periodicity. While they don't fit into the 14 Bravais lattices, understanding Bravais lattices is crucial for appreciating the unique nature of quasicrystals. Quasicrystals

19. Can you explain the concept of primitive and non-primitive unit cells?

A primitive unit cell contains exactly one lattice point, which may be distributed among the corners of the cell. A non-primitive unit cell contains additional lattice points, either on the faces or within the cell, and thus represents more than one lattice point. Non-primitive cells are often used because they better demonstrate the overall symmetry of the crystal structure.

20. What is the significance of the body-centered cubic (BCC) structure?

The body-centered cubic (BCC) structure is a common and important crystal structure where atoms are located at each corner of the cubic unit cell and one atom at the center of the cube. It's significant because many important metals, such as iron at room temperature, crystallize in this structure. BCC structures often have high strength and ductility.

21. How does the face-centered cubic (FCC) structure differ from BCC?

In a face-centered cubic (FCC) structure, atoms are located at each corner of the cubic unit cell and at the center of each face of the cube. Compared to BCC, FCC has a higher packing efficiency (74% vs 68% for BCC) and is common in metals like copper, aluminum, and gold. FCC structures typically have good ductility and malleability.

22. How do Bravais lattices relate to X-ray diffraction patterns?

Bravais lattices are crucial in interpreting X-ray diffraction patterns. The regular, repeating structure of a Bravais lattice causes X-rays to diffract in specific directions, creating a characteristic pattern. This pattern can be used to determine the crystal structure, including the type of Bravais lattice, unit cell dimensions, and atomic positions within the unit cell.

23. What is the hexagonal close-packed (HCP) structure and how does it differ from FCC?

The hexagonal close-packed (HCP) structure is a close-packed crystal structure where atoms are arranged in hexagonal layers stacked on top of each other. While both HCP and FCC have the same packing efficiency (74%), they differ in their stacking sequence. FCC has an ABCABC... stacking pattern, while HCP has an ABAB... pattern. Some metals like magnesium and zinc prefer the HCP structure.

24. How do lattice parameters describe a crystal structure?

Lattice parameters describe the size and shape of the unit cell in a crystal structure. They include the lengths of the unit cell edges (a, b, c) and the angles between them (α, β, γ). These parameters fully define the unit cell and, by extension, the entire crystal structure. They are essential for calculating properties like density and identifying the specific Bravais lattice type.

25. How does polymorphism relate to Bravais lattices?

Polymorphism is the ability of a solid material to exist in more than one crystal structure. Different polymorphs of the same substance can have different Bravais lattices. For example, carbon can exist as diamond (FCC lattice) or graphite (hexagonal lattice). The different structures result in vastly different properties, despite having the same chemical composition.

26. How do interstitial sites in crystal structures relate to Bravais lattices?

Interstitial sites are empty spaces between atoms in a crystal structure. The size and number of these sites depend on the specific Bravais lattice and atomic packing. For example, BCC structures have larger interstitial sites than FCC structures. Understanding interstitial sites is crucial for predicting and explaining phenomena like interstitial diffusion, alloying, and the behavior of impurities in crystals.

27. How do crystal defects relate to the ideal Bravais lattice concept?

Crystal defects are deviations from the perfect, repeating pattern of a Bravais lattice. While Bravais lattices describe ideal, defect-free crystals, real crystals always contain defects. These defects, such as vacancies, interstitials, or dislocations, can significantly affect the material's properties. Understanding the ideal Bravais lattice helps in identifying and characterizing these defects and their effects on material behavior.

28. What is the difference between a crystal system and a Bravais lattice?

A crystal system is a category of crystal structures classified by the relationships between their unit cell edges and angles. There are seven crystal systems. A Bravais lattice, on the other hand, is a specific arrangement of lattice points that fills all of space. There are 14 Bravais lattices distributed among the seven crystal systems. Multiple Bravais lattices can exist within a single crystal system.

29. How does temperature affect crystal structure and Bravais lattice type?

Temperature can significantly impact crystal structure and potentially change the Bravais lattice type. As temperature increases, atoms vibrate more, which can lead to phase transitions where the crystal adopts a different structure and Bravais lattice. For example, iron changes from BCC to FCC as it's heated, a transition crucial in steel processing. Understanding these temperature-dependent changes is vital in materials science and engineering.

30. What is the relationship between atomic radius and Bravais lattice selection?

The atomic radius plays a crucial role in determining which Bravais lattice a material will adopt. The ratio of atomic radii in a compound often dictates the most stable crystal structure. For instance, in ionic compounds, the ratio of cation to anion radii influences whether the structure will be rock salt (NaCl), cesium chloride (CsCl), or another type. This relationship is key to predicting and understanding crystal structures in materials science.

31. How do Bravais lattices relate to the concept of crystal anisotropy?

Bravais lattices are fundamental to understanding crystal anisotropy, which is the variation of physical properties with direction in a material. The symmetry of a Bravais lattice determines the degree and nature of anisotropy in a crystal. For example, cubic lattices tend to have more isotropic properties, while hexagonal or tetragonal lattices often exhibit significant anisotropy in properties like thermal expansion, electrical conductivity, and mechanical strength.

32. How do Bravais lattices influence the formation of twinning in crystals?

Twinning is a crystal growth phenomenon where two separate crystals share some of the same crystal lattice points in a symmetrical manner. The type of Bravais lattice influences the possible twinning modes and their frequency. For example, FCC metals often exhibit twinning along {111} planes. Understanding the relationship between Bravais lattices and twinning is important in metallurgy and materials processing, as twinning can significantly affect material properties.

33. What is the Wigner-Seitz cell and how does it relate to Bravais lattices?

The Wigner-Seitz cell is a particular kind of primitive cell in a Bravais lattice. It's constructed by drawing perpendicular bisector planes between a lattice point and all its nearest neighbors. The resulting polyhedron is the Wigner-Seitz cell. This cell is important in solid-state physics for understanding electronic band structures and phonon dispersion. It provides a way to visualize the symmetry of the lattice and is particularly useful in studying properties that depend on the lattice symmetry.

34. How do Bravais lattices influence the concept of Brillouin zones in solid-state physics?

Brillouin zones are the Wigner-Seitz cells of the reciprocal lattice. The shape and symmetry of Brillouin zones are directly determined by the Bravais lattice of the crystal. These zones are crucial in understanding the electronic and vibrational properties of solids. They provide a framework for describing electron and phonon states in crystals and are fundamental to concepts like band structure and wave propagation in periodic media.

35. What is the role of point groups in classifying Bravais lattices?

Point groups describe the symmetry operations (rotations, reflections, inversions) that leave a point in the lattice unchanged. They are crucial in classifying Bravais lattices and determining crystal systems. Each Bravais lattice belongs to a specific point group, which defines its symmetry properties. Understanding point groups is essential for predicting and explaining various physical properties of crystals, including their optical, electrical, and mechanical behaviors.

36. How do Bravais lattices relate to the concept of crystal morphology?

Crystal morphology, or the external shape of crystals, is closely related to the underlying Bravais lattice. The symmetry of the Bravais lattice often manifests in the macroscopic shape of the crystal. For instance, cubic crystals often grow as cubes or octahedra, while hexagonal crystals may form prisms or pyramids. The growth rates of different crystal faces, influenced by the lattice structure, determine the final morphology. This relationship is crucial in fields like mineralogy and materials science.

37. What is the significance of the packing fraction in different Bravais lattices?

The packing fraction is the proportion of space occupied by atoms in a crystal structure. It varies among different Bravais lattices and is a key factor in determining many physical properties. For example, FCC and HCP structures have the highest packing fraction (0.74), while simple cubic has the lowest (0.52) among common structures. Higher packing fractions generally correlate with higher densities and often influence properties like melting point, hardness, and conductivity.

38. How do Bravais lattices influence the formation and propagation of dislocations in crystals?

Dislocations, which are line defects in crystal structures, are significantly influenced by the Bravais lattice. The lattice type determines the possible slip systems along which dislocations can move. For instance, FCC metals typically have more available slip systems than HCP metals, contributing to their generally higher ductility. The energy required to create and move dislocations, which affects material strength and plasticity, is also dependent on the specific Bravais lattice structure.

39. What is the relationship between Bravais lattices and the formation of solid solutions?

Bravais lattices play a crucial role in the formation of solid solutions. The compatibility of different elements in forming a solid solution depends largely on their atomic sizes and the type of crystal structure (Bravais lattice) they prefer. Elements with similar atomic sizes and the same preferred crystal structure are more likely to form extensive solid solutions. This concept is fundamental in alloy design and understanding phase diagrams in materials science.

40. What is the significance of the Bravais lattice in determining the Curie temperature of ferromagnetic materials?

The Bravais lattice structure significantly influences the Curie temperature of ferromagnetic materials. The Curie temperature, above which a material loses its ferromagnetic properties, depends on the strength of magnetic interactions between atoms. These interactions are determined by the distances and arrangements of atoms in the lattice. For instance, body-centered cubic (BCC) iron has a higher Curie temperature than face-centered cubic (FCC) nickel, partly due to differences in their lattice structures affecting magnetic coupling.

41. What is the role of Bravais lattices in understanding martensitic transformations?

Martensitic transformations, which are diffusionless phase transformations in solids, involve a change from one Bravais lattice to another. For example, the transformation of austenite (FCC) to martensite (body-centered tetragonal) in steel. The relationship between the parent and product lattices determines the crystallographic theory of martensite formation, including the shape change and orientation relationships. This understanding is crucial in materials processing, especially in the heat treatment of steels and shape memory alloys.