CRYSTAL LATTICE AND UNIT CELL

7activestudio

27 May 201403:03

Summary

TLDRThe video script delves into the fascinating world of crystal lattices, explaining their three-dimensional cubic arrangement as points in space. It introduces the concept of unit cells, which are the building blocks of crystals, and distinguishes between primitive and centered unit cells. The script further explores the seven crystal systems and 14 Bravais lattices, highlighting the importance of unit cell parameters and angles in understanding crystal structures.

Takeaways

🔬 Crystal lattices are three-dimensional arrangements of particles in space.
🌐 There are 14 different three-dimensional lattices known as Bravais lattices, named after French mathematician Auguste Bravais.
📏 Unit cells are the basic building blocks of crystals, with parameters a, b, c for edges and alpha, beta, gamma for angles between them.
🏠 Unit cells can be of two types: Primitive (particles only at corners) and Centered (particles also at other positions).
🔶 Primitive unit cells have particles only at the corners.
🔵 Centered unit cells have particles at additional positions besides the corners and are further divided into three types: body-centered, face-centered, and end-centered.
🔵 Body-centered unit cells have a particle at the center of the body in addition to the corners.
🔵 Face-centered unit cells have particles at the centers of all six faces plus the corners.
🔵 End-centered unit cells have particles at the centers of any two opposite faces along with the corners.
🌐 There are seven crystal systems that classify crystal forms based on symmetry and crystallographic parameters a, b, c, and angles alpha, beta, gamma.
📊 Crystal systems are further divided into 32 classes based on symmetry.

Q & A

What is a crystal lattice?
-A crystal lattice is a three-dimensional arrangement of particles as points in space, which forms the basis of a crystal's structure.
Who was Bravais?
-Bravais was a French mathematician who identified 14 different three-dimensional lattices that are possible in crystals.
What are the unit cell parameters?
-The unit cell parameters are 'a', 'b', and 'c', which are the lengths of the edges of the unit cell, and 'alpha', 'beta', and 'gamma', which are the angles between them.
What is a unit cell?
-A unit cell is the smallest part of a crystal lattice that, when repeated, generates the entire crystal structure.
What are the two types of unit cells?
-There are two types of unit cells: Primitive, where particles are only at the corners, and Centered, where particles are at additional positions along with corners.
What is a Primitive unit cell?
-A Primitive unit cell is one where the constituent particles are present only at the corners.
What are the three types of Centered unit cells?
-The three types of Centered unit cells are Body-centered, Face-centered, and End-centered.
Define a Body-centered unit cell.
-A Body-centered unit cell is one where a particle is present at the body center along with the particles at the corners.
What is a Face-centered unit cell?
-A Face-centered unit cell is one where particles are present at the centers of all six faces along with the particles at the corners.
Explain an End-centered unit cell.
-An End-centered unit cell is one where particles are present at the centers of any two opposite faces along with the particles at the corners.
What are crystal systems?
-Crystal systems are the classification of crystal forms based on symmetry, which are divided into seven categories depending on the crystallographic parameters a, b, c, and alpha, beta, gamma.
How many crystal systems are there?
-There are seven crystal systems.
How many classes are there in the classification of crystal systems?
-There are 32 classes in the classification of crystal systems based on symmetry.

Outlines

00:00

🔬 Crystal Lattices and Unit Cells

This paragraph introduces the concept of crystal lattices, which are three-dimensional arrangements of particles as points in space. It explains that there are 14 different three-dimensional lattices known as Bravais lattices, named after the French mathematician Auguste Bravais. The paragraph further discusses the unit cell, which is the smallest part of a crystal lattice that can be repeated to generate the entire crystal structure. It mentions that unit cells can be of two types: Primitive, where particles are only at the corners, and Centered, which includes particles at other positions besides the corners. Centered unit cells are further divided into three types: body-centered, face-centered, and end-centered, each defined by the presence of particles at specific locations within the unit cell.

Mindmap

Keywords

💡Crystal Lattice

A crystal lattice is a three-dimensional arrangement of particles as points in space, which forms the basis of a crystal's structure. It is the repeating pattern of atoms, ions, or molecules that defines the crystal's symmetry and shape. In the video, crystal lattices are described as the fundamental structure of crystals, with the unit cell being a simple part of this lattice that repeats itself to generate the entire crystal.

💡Unit Cell

The unit cell is the smallest repeating unit in a crystal lattice that, when replicated in three dimensions, generates the entire crystal structure. It is a fundamental concept in crystallography and is used to describe the symmetry and geometry of a crystal. In the script, unit cells are categorized into primitive and centered types, which are further subdivided into body-centered, face-centered, and end-centered.

💡Bravais Lattices

Bravais lattices are the 14 different three-dimensional lattices that are possible in a crystal structure. They are named after the French mathematician Auguste Bravais, who studied and classified them. These lattices are the basis for understanding the symmetry of crystals and are a central concept in the video's discussion of crystal structures.

💡Unit Cell Parameters

The unit cell parameters a, b, and c refer to the lengths of the edges of the unit cell, while alpha, beta, and gamma are the angles between these edges. These parameters are crucial in defining the geometry of the unit cell and, by extension, the crystal structure. They are used in the video to describe how the unit cells are arranged in space.

💡Primitive Unit Cell

A primitive unit cell is one where the constituent particles are present only at the corners of the cell. This is a fundamental type of unit cell described in the video, and it is the simplest form where particles are not repeated within the cell itself, only at the vertices.

💡Centered Unit Cell

A centered unit cell is characterized by the presence of constituent particles not only at the corners but also at other positions within the cell. This type of unit cell is more complex than the primitive one and is further divided into body-centered, face-centered, and end-centered unit cells, as explained in the script.

💡Body-Centered Unit Cell

A body-centered unit cell is a specific type of centered unit cell where a particle is present at the center of the cell in addition to the particles at the corners. This configuration is mentioned in the video as one of the ways a unit cell can be centered, affecting the crystal's symmetry and packing efficiency.

💡Face-Centered Unit Cell

In a face-centered unit cell, particles are located at the centers of all the faces of the cell as well as at the corners. This arrangement is highlighted in the video as it is one of the types of centered unit cells, and it is significant for understanding how atoms can be densely packed in certain crystal structures.

💡End-Centered Unit Cell

An end-centered unit cell is defined by particles being present at the centers of any two opposite faces of the cell, along with the corners. This type of unit cell is less common than body-centered or face-centered ones but is still important for understanding certain crystal structures, as discussed in the video.

💡Crystal Systems

Crystal systems are classifications of crystal forms based on their symmetry and geometric properties. There are seven crystal systems, and they are fundamental to the study of crystallography. The video mentions that these systems are based on the crystallographic parameters a, b, c, and the angles alpha, beta, and gamma, which define the symmetry and shape of the unit cells.

💡Symmetry

Symmetry in the context of crystals refers to the repeating patterns and arrangements of atoms that can be identically superimposed by certain transformations, such as rotations, reflections, or translations. The video emphasizes the importance of symmetry in classifying crystals into different systems and lattices, which is crucial for understanding their physical properties.

Highlights

Crystal lattices are three-dimensional arrangements of particles as points in space.

There are 14 different three-dimensional lattices possible, known as Bravais lattices.

Bravais lattices are named after the French mathematician Auguste Bravais.

Unit cell parameters include a, b, c for edges and alpha, beta, gamma for angles between them.

A unit cell is the smallest part of a crystal lattice that repeats itself to generate the crystal.

Unit cells are of two types: Primitive and Centered.

Primitive unit cells have particles only at the corners.

Centered unit cells have particles at additional positions besides the corners.

Centered unit cells are further divided into body-centered, face-centered, and end-centered.

A body-centered unit cell has a particle at the center of the body in addition to the corners.

A face-centered unit cell has particles at the centers of all six faces.

An end-centered unit cell has particles at the centers of any two opposite faces.

There are seven crystal systems based on symmetry and crystallographic parameters.

Crystal systems are classified into 32 classes based on symmetry.

Crystallographic parameters a, b, c, and alpha, beta, gamma determine the crystal system.

The symmetry of a crystal system is crucial for its classification.

Understanding crystal systems is essential for material science and crystallography.

The arrangement of particles in a crystal lattice affects its physical properties.