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Quick Facts

Medium Of Instructions	Mode Of Learning	Mode Of Delivery
English	Self Study	Video and Text Based

Course Overview

The Crystals, Symmetry and Tensors certification course is a 12-week programme. The course is elective and is designed for the undergraduate and postgraduate. The certification programme covers a comprehensive curriculum that includes geometrical crystallography, reciprocal lattice, the concept of symmetry, rotation axes, and symmetry-based classification of lattices.

The students interested in solid-state science and engineering will benefit from this certification course. Apart from them, the UG and PG students of Physics, Chemistry, Metallurgy, Materials Science, Mechanical Engineering, and Chemical Engineering will find this course beneficial. The Crystals, Symmetry and Tensors certification by NPTEL provides a comprehensive understanding of the subject to excel in the field.

Also Read: Online Metallurgical Engineering Courses & Certifications

The Highlights

Video Course
12 Weeks Duration
Completion Certification

Courses and Certificate Fees

Certificate Availability	Certificate Providing Authority
yes	IIT Delhi

Eligibility Criteria

Certification Qualifying Details

The candidates must pass the written examination by registering for the exam on the NPTEL official website to get a certificate.

What you will learn

The students will learn from the fundamentals to advanced concepts of point, space groups symmetry, vector and tensor applications in crystallography. After completing the Crystals, Symmetry and Tensors certification syllabus, they will gain a deep understanding of the definition, properties of mathematical groups, stereographic projection and matrix representation of symmetry operations.

Upon completion of the Crystals, Symmetry and Tensors training, the students will be able to calculate the useful elastic properties such as modulus, Poisson ratio and others using tensor methods. With the leading industry experts support students will gain hands-on experience to apply the learned concepts and methods in real-world projects.

Who it is for

This Crystals, Symmetry and Tensors certification course is designed for aspiring students to enhance their skills and knowledge in the field. This course is also beneficial for:

Admission Details

To join the Crystals, Symmetry and Tensors classes, follow the steps mentioned below:

Step 1: Browse the link mentioned below:

https://nptel.ac.in/courses/113102108

Step 2: Log in with a Google account or create a new account and log in.

Step 3: Fill out the form with the required information, submit it and start the course.

The Syllabus

Geometrical crystallography: crystals, lattice and motif, lattice points and translation vectors, unit cells: primitive and non-primitive
Miller indices of planes and directions.

Reciprocal lattice, use of reciprocal lattice in crystallographic calculations, angle between planes, angle between a plane and a direction, d-spacing of planes, volume of a crystal
Structure and metric matrices.

Concept of Symmetry
Symmetry operations
Proper and Improper operations. Point and Space operations. Rotation axes
Roto-reflection and Roto-inversion axes. Mirror and glide planes
Inversion centre. Screw axes

Definition and properties of mathematical groups
Subgroups. Cosets. Lagrange’s theorem

Stereographic projection and matrix representation of symmetry operations.

Symmetry based Classification of lattices: 7 crystal systems and 14 Bravais lattices
17 plane groups

Symmetry based classification of crystal 32 Crystal classes and 230 space group
Possible proper rotation axes for crystals
Possible combination of pure rotation axes: Euler’s construction

Development of 32 point groups

Space groups and International Tables

Cartesian tensors: definition, rank, representation quadric
Magnitude of a property in a given direction.

Second-rank tensor properties
Electrical and thermal conductivity, thermal expansion coefficient

Elasticity and fourth rank tensors
Elastic stiffness and compliance
Calculation of useful elastic properties such as modulus, Poisson ratio etc using tensor methods

Evaluation process

Opting for the exam is optional, for students who desire to receive a certificate must write the exam after the completion of the course. The passing marks for this course are a minimum of 25% in assignments and 75% in the written exam, with a total of 100 marks.