Bcc Fcc Primitive Cubic Unit Cell - Definition, Structure, Types, FAQs

Edited By Team Careers360 | Updated on Jul 02, 2025 04:26 PM IST

The arrangement of atoms inside the material influences its properties. Like gold is very soft, malleable, and ductile, iron is tough and strong, while aluminium is light in weight. The difference in the properties is only because of the arrangement of atoms inside their unit cells. The unit cell is the smallest repetitive unit of the crystal lattice or a crystal structure. The 3D arrangement of atoms, molecules, or ions inside the given crystal is called a crystal lattice. There are three main types of unit cells: Simple cubic cell, Body-centered cubic unit cell, and Face-centred cubic unit cell. The unit structure of iron is BCC, which is why it’s strong, while the unit structure of Gold and aluminium is FCC, making them soft and malleable.

This Story also Contains

FCC structure
BCC structure
1. Primitive Cubic Unit Cell
2. Body-centered Unit Cell (BCC)
3. Face-centered unit Cell (FCC)
Definition of Unit Cell
What is Lattice?

Bcc Fcc Primitive Cubic Unit Cell - Definition, Structure, Types, FAQs

FCC structure

FCC (face-centered cubic): Atoms are usually arranged at the corners and even at the center of the surface of each given cell. Atoms are considered to affect the diagonals of the face. 4 atoms in a single unit cell. Atoms are arranged in the corners of the cube, and another atom is in the center of the cube.

BCC structure

The BCC unit cell has a total number of two atoms, one in the center and one in the eight from the corners. In the FCC system, there are also eight atoms in the corners of a cell cell with one atom centered on each surface. The atom on the surface is shared with a nearby cell.

What is an FCC structure and a BCC structure?

The most direct difference between FCC crystals and BCC is in the atomic systems. The cubic structure in the center of the face has an atom in all 8 positions, and in the center of all 6 faces. The body-centered cubic structure has atoms in all eight corner positions, and one is in the center of the cube.

Primitive meaning

1. Relating to, identifying, or preserving a first-degree character in the development of the appearance or history of a particular object.

2. Very basic or non-technical in terms of comfort, ease of use, or efficiency.

"Camp accommodation was old."

Types of Unit Cell

Multiple unit cells together form a crystal lattice. Physical particles such as atoms, and molecules also exist. Each lattice point remains such particles.

1. First Cubic Cell

2. Body-centered Body Unit Cell

3.A cell unit in the center of the face

1. Primitive Cubic Unit Cell

In the first cell of the cubic unit, atoms are found only in the corners. Every atom in a corner is shared between cells in eight adjacent units. There are four unit cells in the same layer as 4 in the upper (or lower) layer. Thus, a single unit of cell has only 1 / 8th of an atom. Each subdivision in each of the following figures represents the particle center in that particular position and not its size. This building is known as the open-air building.

Atoms in the first phase of the simple cubic unit cell are found only in the corners

All the atoms in the corner are divided between the cells of the eight adjacent units

Four unit cells exist in the same layer

One unit cell is in the upper / lower layer

Thus, a single cell unit has only 18 atoms

Each subdivision in each of the following figures represents the particle center in that particular position and not its size

In each cell of the cubic unit, there are 8 atoms in the corners. Therefore, the total number of atoms in a single cell is

8 × 1/8 = 1 atom.

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2. Body-centered Unit Cell (BCC)

The BCC unit cell has atoms in each corner of the cube and the atom in the center of the structure. According to this structure, the atom in the center of the body entirely belongs to the cell unit in which it is located. In the BCC unit cell, every corner has atoms. There is one atom in the center of the building. At the bottom of the drawing is an open structure.

According to this, the atom of the structure in the physical organs is entirely the cell of the unit in which it is located.

Number of atoms in a BCC cell:

Therefore, in the BCC cell, we have:

8 x 1/8 corners with each atom = 8 × 1/8 = 1 atom

1 physical center atom = 1 × 1 = 1 atom

Hence, here the total number of atoms that are present per cell unit = 2 atoms.

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3. Face-centered unit Cell (FCC)

The FCC unit cell contains atoms in all corners of the crystal lattice and in the center of each cube surface. An atomic surface atom is divided between cells in two adjacent units, and only 1/2 of each atom is in each cell.

In the FCC unit cell, atoms are present in all corners of the crystal lattice

Also, there is an atom at the center of the whole surface of the cake

This atomic center is divided between cells in two adjacent units

Only about 12 atoms are part of a cell

Number of atoms in an FCC cell

a) 8 x 1/8 corners with each atom = 8 × 1/8 = 1 atom

b) Six surface atoms × 1/2 atom per unit of cell = 3 atoms

Therefore, the total number of atoms in a cell = 4 atoms

Therefore, in the cellic unit centered on the surface, we have:

8 x 1/8 corners with each atom = 8 × 1/8 = 1 atom

Six atoms centered on the surface × 1/2 atom per unit of cell = 3 atoms

Therefore, the total number of atoms in a cell = 4.

Definition of Unit Cell

The smallest group of atoms has the same number of crystals, and where the entire lattice can be formed by three dimensions is called the Cell Unit. Crystalline Solids exhibit a normal and repetitive pattern of existing particles.

Representation of the three-dimensional design of the particles present in the crystal, in which each particle is presented as a point in space known as a crystal lattice.

What is Lattice?

A lattice is a three-dimensional structure, a series of periodic points, on which a crystal is formed. In 1850, M. A. Bravais showed that similar points can be arranged geographically to produce 14 types of standard patterns. These 14 space fragments are known as Bravais lattices.

The crystal lattice of solidity can be defined according to its unit cell. A crystal lattice is made up of a very large number of unit cells, where every lattice point resides in a single particle. A unit cell can be seen as a three-dimensional structure consisting of one or more atoms.

We can see the volume of this cell unit in terms of cell unit size. For example, if we have a single edge cell “a”, the unit cell volume can be given as “a³”. The unit size of a cell is given as a measure of the size and volume of the cell. The unit size of a cell is equal to the product of the number of atoms in the cell and the size of each atom in the unit cell.

Quantity of cell unit = number of atoms per cell unit × size of each atom = z × m

Where, z = number of atoms in a cell,

m = Mass for each atomic mass

Atomic mass can be given with the help of Avogadro number and molar mass as:

MNA

Where, M = molar mass

NA number = Avogadro

Cell unit volume, V = a³

=> Multiple cell unit = maximum cell unit unit cell

=> Cell unit quantity = mV = z × ma³ = z × Ma³ × NA

Therefore, with the knowledge of the number of atoms in the unit cell, the marginal length and the molar size can determine the cell density of the unit.

A general description of the cell unit size of the various cases is found below:

1. The first cell unit: In the cell of the first unit, the number of atoms in a unit is equal to one. Therefore, the size is given by:

Maximum cell unit = 1 × Ma³ × NA

2. Cells centered in a cubic unit: In a cell-centered cubic unit cell, the number of atoms in a cell is equal to two. Therefore, the size is given by:

Maximum cell unit = 2 × Ma³ × NA

3. Cube-centered cubic unit cell: In a cell-centered cubic unit cell, the number of atoms in a unit cell is equal to four. Therefore, the size of the cell unit is given as:

Maximum cell unit = 4 × Ma³ × NA

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Frequently Asked Questions (FAQs)

1. What is a primitive unit cell?

A primitive unit cell is the smallest repeating unit of a crystal lattice that can be used to construct the entire lattice through translation. It contains one or more atoms and reflects the symmetry and structure of the crystal.

2. What are BCC and FCC structures?

BCC and FCC are two types of crystal structures found in metals and other materials. BCC has atoms positioned at the corners of a cube with one atom at the center, while FCC has atoms at each corner and the centers of each face of the cube.

3. How many atoms are there in a BCC unit cell?

A BCC unit cell effectively contains 2 atoms. There are 8 atoms located at the corners (contributing 1/8 each) and 1 atom in the center, totaling 2 atoms when added together.

4. How many atoms are there in an FCC unit cell?

An FCC unit cell contains 4 atoms. It has 8 corners (contributing 1/8 each) and 6 face-centered atoms (contributing 1/2 each), which totals to 4 atoms.

5. What is the packing efficiency of BCC and FCC?

The packing efficiency of BCC is about 68%, while FCC boasts a higher packing efficiency of around 74%. Packing efficiency calculates the volume occupied by the atoms relative to the total volume of the unit cell.

6. What is the coordination number of atoms in a primitive cubic unit cell?

The coordination number in a primitive cubic unit cell is 6. Each atom is surrounded by six nearest neighbors, one along each of the three axes in both positive and negative directions.

7. How many atoms are effectively contained within one primitive cubic unit cell?

One primitive cubic unit cell effectively contains 1 atom. Although there are 8 atoms at the corners, each is shared by 8 adjacent unit cells, so 1/8 of each atom belongs to a single unit cell (8 × 1/8 = 1).

8. What is the packing efficiency of a primitive cubic structure?

The packing efficiency of a primitive cubic structure is about 52.4%. This means that only 52.4% of the total volume is occupied by atoms, making it the least efficiently packed of the three cubic structures.

9. What is the relationship between atomic radius (r) and edge length (a) in a primitive cubic unit cell?

In a primitive cubic unit cell, the edge length (a) is equal to twice the atomic radius (r). This can be expressed as a = 2r, as the atoms at opposite corners of the cube just touch each other along the edge.

10. What is the difference between a primitive unit cell and a conventional unit cell?

A primitive unit cell is the smallest possible unit cell that can be used to construct the entire lattice through translation. A conventional unit cell, while not always the smallest, is chosen for its symmetry and ease of visualization. For example, the conventional unit cell for a face-centered cubic structure is larger than its primitive unit cell but better illustrates the crystal's symmetry.

11. How many atoms are effectively contained within one BCC unit cell?

A BCC unit cell effectively contains 2 atoms. It has 8 corner atoms (each shared by 8 unit cells, contributing 1 atom) and 1 center atom (fully contained within the cell).

12. Why are primitive cubic structures relatively rare in nature?

Primitive cubic structures are rare because they have the lowest packing efficiency (52.4%) among cubic structures. This inefficient use of space makes them less stable and energetically unfavorable compared to more efficiently packed structures like BCC or FCC.

13. How does pressure affect the unit cell parameters of a crystal?

Increasing pressure generally causes a decrease in unit cell parameters as atoms are forced closer together. This compression can lead to phase transitions, where the crystal adopts a more compact structure with a different unit cell. The degree of compression can vary in different directions for non-cubic crystals, leading to anisotropic behavior.

14. What is the significance of symmetry operations in describing unit cells?

Symmetry operations (such as rotations, reflections, and inversions) that leave the crystal structure unchanged are crucial in categorizing and understanding crystal structures. They define the crystal system and space group of the material, which in turn determine many of its physical properties.

15. What is the relationship between unit cell structure and the mechanical properties of a material?

The unit cell structure greatly influences mechanical properties. For example, the slip systems (planes along which deformation occurs) are determined by the unit cell geometry. FCC structures typically have more slip systems than HCP, making FCC metals generally more ductile. The strength of interatomic bonds within the unit cell also affects properties like hardness and elastic modulus.

16. How does the coordination number change from primitive cubic to BCC to FCC structures?

The coordination number increases from primitive cubic (6) to BCC (8) to FCC (12). This reflects the increasing number of nearest neighbors in each structure.

17. Why is the FCC structure more common in metals than the primitive cubic structure?

The FCC structure is more common in metals because it has a higher packing efficiency (74%) compared to primitive cubic (52.4%). This allows for more atoms to be packed into a given volume, resulting in a more stable and energetically favorable arrangement.

18. How does the packing efficiency of FCC compare to BCC and primitive cubic structures?

FCC has the highest packing efficiency at 74%, followed by BCC at 68%, and primitive cubic at 52.4%. This means FCC structures can accommodate more atoms in a given volume, making them more common in nature.

19. How many octahedral voids are present in one FCC unit cell?

There are 4 octahedral voids in one FCC unit cell. These are located at the center of the unit cell and at the center of each edge.

20. How does a primitive cubic unit cell differ from body-centered cubic (BCC) and face-centered cubic (FCC) unit cells?

A primitive cubic unit cell has atoms only at the corners of the cube. BCC has an additional atom at the center of the cube, while FCC has atoms at the center of each face in addition to the corner atoms.

21. How does polymorphism relate to different unit cell structures of the same substance?

Polymorphism occurs when a substance can exist in multiple crystal structures. Each polymorph has a different arrangement of atoms or molecules, resulting in different unit cell structures. This can lead to variations in properties such as solubility, melting point, and stability, despite having the same chemical composition.

22. How does the concept of unit cells help in understanding alloys and solid solutions?

Unit cells provide a framework for understanding how different atoms can be incorporated into a crystal structure. In substitutional alloys, atoms of one element replace some atoms of another in the unit cell. In interstitial solid solutions, smaller atoms fit into the voids (interstitial sites) of the host structure's unit cell. This concept helps explain the properties and behavior of alloys and solid solutions.

23. What is the significance of the atomic packing factor (APF) in crystal structures?

The atomic packing factor (APF) represents the fraction of volume in a unit cell that is occupied by atoms. It's a measure of how efficiently space is used in the crystal structure. A higher APF generally indicates a more stable structure and influences properties like density and melting point.

24. How does the presence of vacancies or defects affect the ideal unit cell structure?

Vacancies or defects disrupt the perfect periodicity of the crystal structure. They can cause local distortions in the lattice, affecting properties like electrical conductivity, mechanical strength, and diffusion rates. While unit cells describe the ideal structure, real crystals often contain these imperfections.

25. What is the relationship between unit cell volume and density in a crystal?

The density of a crystal is directly related to its unit cell volume and the mass of atoms within it. It can be calculated by dividing the total mass of atoms in the unit cell by the unit cell volume. This relationship allows for the determination of crystal density from X-ray diffraction data.

26. What is a unit cell in crystalline solids?

A unit cell is the smallest repeating structural unit of a crystal lattice. It represents the basic arrangement of atoms, ions, or molecules that, when repeated in three dimensions, forms the entire crystal structure.

27. What is meant by the term "lattice parameters" in crystallography?

Lattice parameters are the dimensions and angles that define the unit cell of a crystal structure. For cubic structures, this is typically just the length of one side of the cube (a). For other structures, it may include multiple lengths (a, b, c) and angles (α, β, γ).

28. How does the concept of unit cells relate to X-ray diffraction in crystallography?

Unit cells are fundamental to X-ray diffraction analysis. The repeating pattern of unit cells in a crystal creates a regular array of scattering centers for X-rays. The diffraction pattern produced depends on the arrangement and spacing of atoms within the unit cell, allowing researchers to determine the crystal structure.

29. How does the concept of unit cells help in understanding the properties of materials?

Unit cells provide insight into a material's properties by revealing its atomic arrangement. This arrangement influences characteristics such as density, melting point, conductivity, and mechanical properties. Understanding the unit cell structure helps predict and explain these macroscopic properties.

30. How does the concept of unit cells apply to non-cubic crystal systems?

While cubic systems have equal edge lengths and 90° angles, non-cubic systems can have different edge lengths and/or angles. The unit cell concept still applies, but these cells may be described by more parameters. For example, a hexagonal close-packed (HCP) structure uses a hexagonal prism as its unit cell.

31. What is meant by the term "close-packed structure"?

A close-packed structure refers to an arrangement of atoms or particles that maximizes the packing efficiency. In such structures, atoms are arranged to occupy the maximum possible space. FCC is an example of a close-packed structure.

32. What is an interstitial site in a crystal structure?

An interstitial site is a void or empty space between atoms in a crystal structure. These sites can sometimes accommodate smaller atoms or ions, leading to interstitial solid solutions. The size and number of interstitial sites depend on the type of unit cell.

33. How does the number of nearest neighbors (coordination number) affect the stability of a crystal structure?

Generally, a higher coordination number leads to greater stability in crystal structures. This is because more nearest neighbors allow for stronger overall bonding and better distribution of forces within the crystal.

34. How does temperature affect the size of a unit cell?

Generally, as temperature increases, the size of the unit cell increases due to thermal expansion. This is because higher temperatures cause atoms to vibrate more, increasing their average separation and thus the overall dimensions of the unit cell.

35. What is the relationship between the number of atoms per unit cell and the type of cubic structure (primitive, BCC, FCC)?

The number of atoms per unit cell increases from primitive cubic (1 atom) to BCC (2 atoms) to FCC (4 atoms). This reflects the increasing complexity and packing efficiency of these structures.

36. What is the difference between a lattice point and an atom in a unit cell?

A lattice point is a mathematical point in space that defines the repeating pattern of the crystal structure. An atom is the physical particle occupying a position in the crystal. In some cases, atoms may be located at lattice points, but not all lattice points are necessarily occupied by atoms.

37. What is Bravais lattice and how does it relate to unit cells?

A Bravais lattice is an infinite array of discrete points with an arrangement and orientation that appears the same from any point of the array. There are 14 unique Bravais lattices in three dimensions, each describing a distinct crystal structure. Unit cells are the building blocks that, when repeated, form these lattices.

38. How does the concept of unit cells apply to molecular crystals?

In molecular crystals, the unit cell contains whole molecules rather than individual atoms. The arrangement of these molecules within the unit cell determines properties like crystal shape, melting point, and solubility. Intermolecular forces (like hydrogen bonding or van der Waals forces) play a crucial role in stabilizing these structures.

39. How does the unit cell structure influence the electronic properties of materials?

The unit cell structure determines the arrangement of atoms and their electron orbitals, which directly influences the electronic band structure of the material. This affects properties like electrical conductivity, optical behavior, and magnetism. For instance, the difference between conductors, semiconductors, and insulators can often be explained by their unit cell structures and resulting electron configurations.

40. What is the relationship between unit cell structure and thermal conductivity in crystals?

The unit cell structure affects how heat is transmitted through a crystal. In metals, where thermal conductivity is primarily due to free electrons, the structure influences electron mobility. In non-metals, where heat is conducted through lattice vibrations (phonons), the regularity and strength of bonds in the unit cell structure determine how efficiently these vibrations can propagate.

41. What is the significance of the c/a ratio in hexagonal close-packed (HCP) structures?

The c/a ratio in HCP structures is the ratio of the height of the unit cell (c) to the length of its hexagonal base (a). For an ideal HCP structure, this ratio is 1.633. Deviations from this ideal value can affect properties like ductility and slip systems in metals with HCP structures.

42. How do the sizes of tetrahedral and octahedral voids compare in an FCC structure?

In an FCC structure, octahedral voids are larger than tetrahedral voids. The radius of an octahedral void is 0.414 times the radius of the sphere (atom), while the radius of a tetrahedral void is 0.225 times the radius of the sphere.

43. How does the concept of unit cells help in understanding phase transitions in materials?

Phase transitions often involve changes in the unit cell structure. For example, a material might transition from one crystal structure to another as temperature or pressure changes. Understanding these transitions in terms of unit cell transformations helps explain changes in material properties and behavior during phase changes.

44. What is the significance of Wyckoff positions in describing atomic arrangements within unit cells?

Wyckoff positions describe the symmetry-equivalent positions that atoms can occupy within a unit cell. They are crucial for fully specifying crystal structures, especially in more complex systems. Knowing the Wyckoff positions helps in understanding the symmetry of the crystal and in calculating properties like X-ray diffraction patterns.

45. How does the unit cell structure relate to the concept of anisotropy in materials?

Anisotropy, the variation of physical properties with direction, is often a direct result of the unit cell structure. Non-cubic crystals, in particular, tend to exhibit anisotropic behavior because their unit cells are not symmetrical in all directions. This can lead to direction-dependent properties like thermal expansion, electrical conductivity, and mechanical strength.

46. What is the relationship between unit cell structure and the formation of twinning in crystals?

Twinning occurs when two or more crystals share some of the same crystal lattice points in a symmetrical manner. The unit cell structure determines the possible twinning modes by defining the symmetry elements and potential twinning planes. Understanding the unit cell helps predict and explain the occurrence and nature of twinning in different materials.

47. How does the concept of unit cells apply to quasicrystals?

Quasicrystals challenge the traditional concept of unit cells as they lack periodicity while maintaining long-range order. Instead of a repeating unit cell, quasicrystals are described using higher-dimensional models projected onto three-dimensional space. This concept expands our understanding of possible atomic arrangements beyond conventional crystalline structures.

48. What is the significance of the reciprocal lattice in relation to the real-space lattice of unit cells?

The reciprocal lattice is a mathematical construct that is inversely related to the real-space lattice of unit cells. It is crucial in understanding X-ray diffraction patterns and in describing the propagation of waves in crystals. Each point in the reciprocal lattice corresponds to a set of planes in the real-space lattice, facilitating the analysis of crystal structures.

49. How does the unit cell structure influence the optical properties of crystals?

The unit cell structure determines how light interacts with the crystal. It affects properties like refractive index, birefringence, and optical activity. In anisotropic crystals, the variation in atomic spacing in different directions within the unit cell leads to direction-dependent optical properties.

50. What is the relationship between unit cell structure and the phenomenon of piezoelectricity?

Piezoelectricity, the generation of electric charge in response to applied mechanical stress, is directly related to the symmetry of the unit cell. It occurs in crystals that lack a center of symmetry in their unit cell structure. Understanding the unit cell helps in predicting which materials will exhibit piezoelectric properties and in designing new piezoelectric materials.

51. How does the concept of unit cells help in understanding and predicting crystal growth patterns?

The unit cell structure influences crystal growth by determining the energetically favorable directions and planes for atom or molecule addition. This affects the overall shape (habit) of macroscopic crystals. Understanding the unit cell can help predict growth rates in different crystallographic directions and explain phenomena like dendritic growth or faceting.

52. What is the significance of Bernal holes in relation to unit cell structures?

Bernal holes are interstitial voids found in certain close-packed structures, particularly in liquids and amorphous solids. While not directly related to the periodic unit cells of crystals, understanding these holes helps bridge the gap between crystalline and non-crystalline structures, providing insights into the atomic arrangements in materials that lack long-range order.

53. How does the unit cell structure influence the magnetic properties of materials?

The unit cell structure determines the arrangement of magnetic moments in a material. In ferromagnetic materials, for example, the alignment of spins within and between unit cells leads to net magnetization. The symmetry of the unit cell also influences magnetic anisotropy, which is important in applications like data storage.

54. What is the relationship between unit cell structure and the phenomenon of superconductivity?

The unit cell structure plays a crucial role in superconductivity, particularly in high-temperature superconductors. Features like layered structures, specific atomic arrangements, and the presence of certain elements in defined positions within the unit cell can promote