PHYS 5003
Condensed Matter Physics
Lecture 1
Ch. 0. Introduction
• Modern technologies from chips to bodies of aircrafts
are based on materials science.
• A piece of a material exists in one of different phases
depending on the temperature T and pressure P as
described by the general phase diagram below.
Fig. 0.1: 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".
¾ The three areas:
• Suppose you have a pure substance at three different sets of
conditions of temperature and pressure 1, 2 and 3, namely (T1,P1),
(T2,P2) and (T3,P3) as shown below:
• Under the set of conditions at 1 (T1,P1), in the diagram, the substance
would be a solid because it falls into that area of the phase diagram.
At 2, (T2,P2), it would be a liquid; and at 3, (T3,P3), it would be a
vapour (a gas).
¾ 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 N contains the properties of the material
Recall: Ohm’s law ( J = VE , where V 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). r
The models of condensed matter physics attempt to evaluate
the constant N 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