An important aspect of any engineering design is the material to be used. The time-honoured method of designing a material has been through experiments, which may be quite time-consuming and costly. However, with the tremendous progress over the past two decades in the theory of electronic-structure, coupled with the availability of fast computers, it has become possible to calculate and predict the properties of a wide range of materials accurately. This along with powerful simulation techniques has made it possible to design materials theoretically. Such an approach to designing materials of desired properties cuts down the time and cost of experimenting significantly. Further, many a time an engineering design may require parameters which are either not available or are very difficult to obtain experimentally. In such cases, theoretical estimate of these parameters is the only available option. Thus, we feel that an introduction to the theory of material design must be an integral part of the training of modern engineers, particularly those in the fields of Electrical Engineering, Material Science and Metallurgical Engineering. With this in mind, we propose the following interdisciplinary course that combines the physical principles and the computational techniques to give the students a general perspective of how the properties of materials are obtained and how one can manipulate them. Our aim in the course is that, after having gone through it a student should feel that he understands the basic scientific principles and the related computational aspects reasonably well to tackle the calculations involved in obtaining properties of different kinds of materials.
Schrodinger Equation: Review of basics of quantum-mechanics (2); Introduction to Many-electron problem, Example of helium, exchange; Idea of mean field, Hartree and Density functional theory ( 5);
Schrodinger equation for solids: Jellium model of metals (Homogeneous-electron gas); calculations for metal surfaces properties such as the work function and surface energies (surface tension); Jellium model of metallic clusters (5); Bloch's theorem, Kronig-Penny model; Bands, Pseudopotentials (4)
Semiclassical dynamics: DC conductivity; Effective mass and holes; Bloch Oscillations etc. (3)
Semiconductors: Introduction; Some devices (3); Band-gap engineering: Quantum wells and superlattices (3); Nanotechnology -Quantum dots and wires (1)
Dynamics of atoms: Classical Molecular Dynamics (2); Bom-Oppenheimer approximation, Hellman-Feynman theorem (I); Carr-Perrinello method (3); Assembling atoms to make clusters (2);
Superconductivity: Introduction to superconductivity (2); High Tc superconductivity (I); Some applications (I);
Introduction to Polymers, optical materials, superionic conductors etc. (2)
Since this course is really a combination of many topics and has a broad scope, there is no single book that can be used as the text-book for the course. We therefore intend to write our own extensive notes and distribute them to the students.