Condensed Matter Physics Lecture Notes PDF

PHYS 5003 Condensed Matter Physics Lecture 1 Ch. 0. Introduction  Modern technologies from chips to bodies of aircrafts are based on materials science.(Materials science, also commonly known as materials engineering, is an interdisciplinary field applying the properties...

PHYS 5003 Condensed Matter Physics Lecture 1 Ch. 0. Introduction  Modern technologies from chips to bodies of aircrafts are based on materials science.(Materials science, also commonly known as materials engineering, is an interdisciplinary field applying the properties of matter to various areas of science and engineering. It investigates the relationship between the structure of materials at atomic/ molecular scales and their macroscopic properties. It incorporates elements of applied physics and chemistry.) A piece of material exists in different phases depending on the temperature T and pressure P as described by the general phase diagram below. This is the phase diagram for a typical pure substance  There are three lines, three areas marked "solid", "liquid" and "vapour", and two special points marked "C" and "T". The three areas Suppose you have a pure substance at three different sets of conditions of temperature and pressure 1, 2 and 3 (below) Under the set of conditions at 1 in the diagram, the substance would be a solid because it falls into that area of the phase diagram. At 2, it would be a liquid; and at 3, it would be a vapour (a gas).  The three lines Suppose you had a solid and increased the temperature while keeping the pressure constant (diagram). As the temperature increases to the point where it crosses the line, the solid will turn to liquid. In other words, it melts. If you repeated this at a higher fixed pressure, the melting temperature would be higher because the line between the solid and liquid areas slopes slightly forward. The lines simply show the effect of pressure on melting point. Anywhere on the line, there is an equilibrium between phases it separates. The two points Above the critical temperature C, it is impossible to condense a gas into a liquid just by increasing the pressure. All you get is a highly compressed gas. The particles have too much energy for the intermolecular attractions to hold them together as a liquid. Where all three lines meet, you have a unique combination of temperature and pressure where all three phases are in equilibrium together. That's why it is called a triple point T.  A condensed system consists of aggregates of atoms or molecules in a solid or a liquid phase where the interatomic distances are smaller than the corresponding gas phase. The constituent atoms and molecules are in general interacting. When the interactions are negligible the corresponding matter forms an ideal gas. When the atoms in a solid are regularly arranged the solid is crystalline else it is non-crystalline or amorphous. Hence a crystalline solid consists of regular arrangement of atoms, which repeat again and again over the whole space. The interatomic distances in the condensed system are of order of few angstroms. This is why we see these systems as continuous because the visible light has wavelengths of order of few thousands angstroms. X-rays of wavelength of order of angstrom are needed to observe the internal structure of a condensed phase.  The arrangement of atoms in a solid is determined by the interatomic interactions. The realized structure corresponds to the lowest energy of the aggregate of atoms. However, metastable states of different arrangements do exist.  To study a piece of material in general, an external force F is applied to the material and resulting response R is measured. For weak forces these quantities are linearly related R=κF The constant  contains the properties of the material Recall: Ohm’s law ( J = E , where  is the electrical conductivity) and similarly the relations for thermal conduction (Q = kAdT/s) , magnetic susceptibility (M = H), elasticity (Hooke’s law: F =k x), heat capacity ( T=(I/C ) Q). The models of condensed matter physics attempt to evaluate the constant  and to explain the observed behavior. The condensed phases we study here are very large in extent. We refer to them as bulk materials. However, these materials possess surfaces and the area of surface physics deals in particular with the structure and properties of surfaces. Recent progress in the study of condensed phases led to emphasis on nano-systems. Here the size of the system is of order of few nanometers and they are studied under nano-science or nanotechnology. The properties of nano-systems are different from the bulk systems. This course deals with description of crystalline solids, their elastic, thermal, electronic and magnetic properties. The treatment uses both classical and quantum theories. The general objectives of the course include the following Introduction of the required terminology to describe a crystal and its use in cubic and hexagonal crystal systems Explain the elastic response of solids and how sound travels in solids Understand the thermal properties of solids and find out how solids respond to heating. Explain why solids are classified into metals, insulators and semiconductors Understand the semiconducting nature of solids and how to change current carriers. Understand why some materials are magnetic and other not and explain the magnetic properties of materials