Syllabus
Unit 1
Learning Objectives:
In the unit-1, students will learn to
Relate the crystal structure to symmetry and explain the crystallographic planes & directions of different crystal systems
Explain the nature of defects in the crystals
Discuss the solid solutions and the binary phase diagrams
Crystal Structure: Periodic array of atoms, fundamental types of lattices, index system for crystal planes. Crystal structure data. Crystal symmetry – point and space groups. Quasi crystals. Non-ideal Crystal Structures.
Crystal Defects: Lattice Vaccancies, Frenkel and Schottky defects, Colour centers, Dislocations: Slip and plastic deformation, Shear strength of single crystals, Edge dislocationn, Screw dislocation, Stress field around an edge dislocation, Surface defects.
Alloys: Substitutional solid solutions, Hume – Rothery rules, binary phase diagrams, lever rule.
Unit 2
Learning Objectives:
In the unit-2, students will learn the
Correspondence between real and reciprocal space
Diffracting planes and determination of diffraction intensity, structure of different
crystalline materials
Different Experimental techniques used in X-ray diffractions
Diffraction of waves and reciprocal lattice: Diffraction of waves by crystals, Reciprocal lattice and Brillouin zone, Laue Condition, Bragg’s law, scattered wave amplitude, Friedel’s law, Anomalous scattering, Atomic and geometric structure factors, systematic absences, Fourier analysis of basis, Ewald construction, Experimental methods.
Unit 3
Learning Objectives:
In the unit-3, students will learn
The concept of phonons and how the dispersion relationship appears for different lattices.
Phonon contribution to the solid’s specific heat capacity
Lattice Vibrations and Thermal Properties: Vibrations of crystals with monatomic basis-two atoms per primitive basis. Quantization of Elastic Waves, phonon momentum, inelastic scattering by phonons. Phonon heat capacity: Einstein and Debye models of phonon specific heat, anharmonic crystal interactions, Thermal Conductivity.
Unit 4
In the unit-3, students will learn
The Fermi Dirac distribution and Free electron gas in three dimensions
Electrical and Thermal conductivity of metals, Temperature dependent resistivity
The elementary band theory of solids and Fermi surfaces
Free Electron Fermi Gas: Energy levels in one dimension, effect of temperature on Fermi-Dirac distribution, free electron gas in three dimensions. Heat capacity of electron gas. Electrical conductivity and Ohm’s law, motion in magnetic fields, thermal conductivity of metals. Temperature dependent conductivity in metals- Matthiessen’s rule, Nordheim rule.
Energy Bands: Bloch Functions, Kronig-Penney model. Methods of Calculation of Energy bands: Nearly free electron model, Reduced zone-periodic zone schemes, Tight Binding method.
Fermi Surfaces: Construction of Fermi surfaces, electron orbits, hole orbits, and open orbits. Experimental methods in Fermi surface studies.
Unit 5
In the unit-5, students will learn
The different types of polarizations
Dielectric constant and polarizability
Ferroelectric Crystals, Phase Transitions and Piezoelectricity
Dielectrics: Maxwell’s equations, Macroscopic electric field, Depolarization field, Local electric field at an atom, Lorentz field, Dielectric constant and polarizability- Clausius-Mossotti relation, Electronic polarizability, classical theory of Electronic polarizability, Ferroelectric crystals, Displacive Transitions – Landau Theory of Phase Transitions anti-ferroelectricity and piezoelectricity.
Objectives & Outcomes
Prerequisites: Basic knowledge of calculus, classical mechanics, electricity and magnetism, statistical mechanics and quantum mechanics.
Course Objectives
To develop a clear perception of the crystal classes and symmetries and to understand the relationship between the real and reciprocal space
To create the knowledge on the concepts of X-ray diffractions and diffraction patterns in solids
To study the basics of the optical and acoustic phonons in crystals
To give clear understanding on the basic concepts of energy bands in solids
To learn the different polarization mechanisms in dielectrics
Course Outcomes
Upon completion of the course, students will be able to
CO1. Classify the crystal system based on symmetry and explain the nature of imperfections in the solids
CO2. Explain the diffraction conditions in crystals and compute the conditions for allowed and forbidden reflections in crystals
CO3. Understand the concept of phonons in mono and diatomic lattice and explain phonon’s heat capacity of solids
CO4: Familiar with the free-electron theory of metals, Fermi surfaces and basic concepts of the band theory of solids
CO5. Acquire knowledge on different types of polarization in dielectrics and describe the ferroelectricity and piezoelectricity in solids.
Skills: Problem solving skills as well as computational skills of the students in analyzing the properties of solid-state materials will be improved through assignments, quizzes, and presentations.
CO-PO Mapping
|
PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PSO1 |
PSO2 |
PSO3 |
| CO1 |
3 |
3 |
2 |
|
|
3 |
2 |
|
| CO2 |
3 |
3 |
2 |
1 |
|
3 |
3 |
|
| CO3 |
3 |
3 |
2 |
|
|
3 |
1 |
|
| CO4 |
3 |
3 |
2 |
|
|
3 |
2 |
|
| CO5 |
3 |
3 |
2 |
|
|
3 |
2 |
|
Text Book & Reference
Text Book
Charles Kittel, Introduction to Solid State Physics, Eighth Edition, Wiley, 2016.
Reference
- Wahab M A., Solid State Physics, Narosa Publishing House Pvt. Ltd. – New Delhi, 2015.
- Ali Omar, Elementary Solid State Physics, Pearson India; Revised edition, 2007.
- M Vijaya, Rangarajan G, Materials Science, McGraw Hill Education, 2004.
- Azaroff Leonid V., Introduction to Solids, McGraw-Hill Education, 2017.
- S. O. Kasap, Principles of Electronic Materials and Devices Fourth Edition, McGraw-Hill Education, 2021.
Evaluation Pattern
CO-PO Mapping
| Assessment |
Internal |
External Semester |
| Periodical 1 (P1) |
15 |
|
| Periodical 2 (P2) |
15 |
|
| *Continuous Assessment (CA) |
20 |
|
| End Semester |
|
50 |
*CA – Can be Quizzes, Assignments, Projects, and Reports.
Justification for CO-PO Mapping
| Mapping |
Justification |
Affinity level |
| CO1-PO1 |
CO1 is related to acquiring thorough knowledge on the Bravais lattices, symmetry, and defects in crystals. CO1improves the fundamentals of crystal physics in students. Since PO1 is related inculcate strong science (physics) fundamentals, CO1 has been mapped with PO1 with maximum affinity of 3. |
3 |
| CO1-PO2 |
PO2 is about developing the analytical skills and critical thinking among students. In CO1 the fundamental crystallographic problems and problems related to defects will be solved. Hence the affinity level is given maximum for CO1 when mapped with PO2. |
3 |
| CO1-PO3 |
Understanding the mentioned concepts of CO1 will primarily intend to solve crystallographic planes, symmetry determination and phases in alloys. PO3 is to expose students to solve complex problems which enhance the existing scientific knowledge. Since complex problems is not dealt in CO1, the affinity with PO3 is given as medium level |
2 |
| CO1-PSO1 |
PSO1 is related to develop curiosity and inquisitiveness among students to look at fundamental problems. As CO1 matches highly with PSO1 it is given maximum affinity level |
3 |
| CO1-PSO2 |
PSO2 is to impart analytical and experimental skills so that students are equipped to take up independent research. In CO1, the analysis of crystallographic directions, planes of solids, defects and phase formation in alloys are covered which partly provide the platform for analytical skills to do independent research among students, hence it is mapped with medium level affinity |
2 |
| CO2-PO1 |
CO2 improves the fundamental physics of diffractions. Since PO1 is related to the knowledge in fundamental sciences, CO2 is given maximum affinity of 3 when mapped with PO1. |
3 |
| CO2-PO2 |
Problems corresponds related to structure factors, reciprocal lattice etc. (CO2) will be solved by students which improves the analytical skills and critical thinking as mentioned in PO2. So, the CO2- PO2 mapping is given an affinity level of 3. |
3 |
| CO2-PO3 |
In CO2, students will primarily solve problems related to structural identification from the x-ray diffractions in solids with high symmetry. PO3 is to expose students to solve complex problems which enhance the existing scientific knowledge. Since, complex structural solving (with low symmetry structures) is not dealt in CO2, the affinity with PO3 is given as medium level |
2 |
| CO2-PO4 |
Students get exposed to basic analysis XRD patterns of specific solid samples, since only basic research parameters in diffractions are gained it is given a minimum affinity |
1 |
| CO2-PSO1 |
In CO2, as the learners will develop curiosity in solving the diffraction patterns of solids which highly matches with the described PSO1, it is mapped with a maximum affinity level of 3 |
3 |
| CO2-PSO2 |
As students develop the analytical skills of determining the crystal structure in solids which equips them to do independent research. Hence, a high affinity level of 3 is given in the mapping of CO2-PSO2. |
3 |
| CO3-PO1 |
CO3 develops knowledge of phonon dispersion in lattice and thermal conductivity of solids. Since PO1 is related to acquiring strong knowledge in basic science, CO2 is given maximum affinity of 3 when mapped with PO1. |
3 |
| CO3-PO2 |
In CO3, Students develop analytical skills of finding solutions to the problems corresponds to the specific heat of different materials. PO2 is related to developing the analytical skills involving fundamentals of basic sciences. So, the CO2- PO2 mapping is given an affinity level of 3. |
3 |
| CO3-PO3 |
Learners’ gain knowledge of determining the phonon modes and their dispersion in solids (CO3), which will develop them to undertake and solve problems in spectroscopic analysis and hence the mapping of CO3 is given a medium affinity of 2 with PO3. |
2 |
| CO3-PSO1 |
In CO3, students develop interest of determining specific heat capacity of solids and so the mapping of CO3 with PSO1 is given a high affinity level |
3 |
| CO3-PSO2 |
In CO3, students develop basic knowledge of phonon dispersion in solids which is the fundamental of Raman spectroscopy. It will lay the platform for them to take up independent research analysis in spectroscopy. The mapping with PSO2 is given a minimum affinity as CO3 covers the fundamentals alone. |
1 |
| CO4-PO1 |
Students learn the fundamentals of electrical conductivity in CO4 which highly matches with PO1. The mapping of CO4-PO1 is given a maximum affinity level |
3 |
| CO4-PO2 |
Students develop problem solving skills related to constructing Fermi surfaces, electrical conductivity in metals etc. Hence, the mapping of CO4 with PO2 is given a maximum affinity of 3. |
3 |
| CO4-PO3 |
In CO4, learners develop fundamental understanding of energy levels in bandstructure and finding solutions to the Fermi surface of metals which maps with PO3 with medium affinity level |
2 |
| CO4-PSO1 |
In CO4, Students gain problem solving curiosity with respect to the Fermi surfaces, electrical conductivity in metals etc. Hence, the mapping of CO4 with PSO1 is given a maximum affinity of 3. |
3 |
| CO4-PSO2 |
Gaining knowledge of the formation of energy bands, Fermi surfaces and electrical conductivity gives students fundamental platform to understand materials research. The affinity with PSO2 is given a medium level. |
2 |
| CO5-PO1 |
In CO5, students get benefited the learning of dielectrics, ferroelectrics and piezoelectrics which matches well with PO1 and hence it is assigned maximum affinity. |
3 |
| CO5-PO2 |
Students develop analytical thinking and problem solving with respect to polarizations in solids, phase transitions etc. (CO5) and so it is given maximum affinity with PO2. |
3 |
| CO5-PO3 |
In CO5, learners gain the fundamentals of different dielectric constants which prepares them to analysis the complex problems in dielectric measurements of various materials and thus it is mapped with PO3 with a medium affinity level. |
2 |
| CO5-PSO1 |
In CO5, students enrich their scientific knowledge on how the different polarizations happens in solids and so it is assigned a maximum affinity with PSO1. |
3 |
| CO5-PSO2 |
In CO5, students develop the analysis of different dielectric constants which prepares them to do research experiments of impedance spectroscopy, hence it may be mapped with PSO2 with a medium affinity |
2 |
