Materials Science and Engineering

**Syllabus Not Found**

## Short Course Description

Elective course: Physical properties of crystals

First semester, 2019 - 2020

Lecturer: Dr Semyon Gorfman

Language:English

The goal of this course:

To become familiar with the physical properties of crystalline materials, their description and applications.

Prerequisites: All the basic courses in mathematics and physics. Introduction to crystallography and structure analysis.

Format of the course:

3 hours per week of lecture (including some examples exercises, solved in the classroom). You will get homework assignments to be submitted individually.

Grading and exam:

The final grade will be calculated from the exam (80 %) and the solved homework (20%). However, many additional extra-tasks will be available throughout the course and there will be opportunity to collect sufficient number of points during the semester.

Tentative topics:

Part I. Mathematical Introduction

Introduction: Definition of materials properties. Physical properties of crystals.

Operations with tensors: The use of tensors for the description of materials properties. Transformation of coordinate systems and tensor components.

Symmetry: Definition of symmetry, symmetry operations, mathematical representation of symmetry operations. The role of symmetry of the structures for materials properties. Neumann principle.

Symmetry and physical properties of crystals: Symmetry of crystals. Bravais types of lattices, crystal systems and point symmetry groups.

Part II. Physical properties of materials

Electrocaloric and dielectric properties of crystals: Heat capacity, pyroelectric effect, electrocaloric effect and dielectric susceptibility. Polar and non-polar crystals. Applications.

Strain and stress tensors: Description of materials deformation and external forces by second rank tensors. Tensile and shear strains / stresses.

Elastocaloric properties of crystals: Thermal expansion and piezocaloric effect. Thermodynamics of elastocaloric properties and their relation to crystal symmetry. Negative thermal expansion coefficients. Preparation of cuts for zero thermal expansion.

Piezoelectric properties crystals: Direct and converse piezoelectric effects. Voigt notations. Crystal symmetry and piezoelectric effect. Representation surfaces.

Piezoelectric ceramics and applications of piezoelectric effect: Preparation, symmetry and properties of piezoelectric ceramics. Applications of piezoelectric materials.

Elastic properties of crystals: elastic stiffness and elastic compliance. Voigt notations for elastic coefficients. Bulk compressibility, Young modulus and Poisson ratio.

Propagation of elastic waves through crystalline materials: Mathematical description of elastic waves. Calculation of sound velocities and measurement of elastic coefficients.

Part III (Optional). Advanced physical properties of materials

Optical properties of crystals: Propagation of light through crystalline solids. Optical birefringence. Optical indicatrix. Optical birefringence and crystal symmetry. Applications.

Second Harmonic Generation (SHG): Definition of the property and SHG-tensors. Voigt notations. Crystal symmetry and SHG. Applications

Exotic physical properties of crystalline materials: Quadratic electrostriction, flexoelectric effect.

Recommended literature:

[1]. J.F. Nye. Physical properties of crystals and their representations by tensors and matrices. Oxford University Press. 1985.

[2]. Robert E Newnham. Properties of Materials : Anisotropy, Symmetry, Structure. Oxford University Press. 2005.

[2]. International Tables for Crystallography, Volume D. International Union of Crystallography, 2016.

Full syllabus is to be published

**Final Exam**

Students may be required to submit additional assignments

Full requirements as stated in full syllabus

**Introd' to Mathematics 1**(05811117)

**+**

**Calculus 1b for Mec' & Ma**(05091646)

**+**

**Physics (1)**(05091826)

**+**

**Physics (2)**(05091829)

**+**

**Introduc' Mathematics 2**(05811118)