Before embarking on a study of solid state physics, perhaps we should ask
what we even mean by the "solid state". Although the
distinctions between the solid, liquid, and vapor states of matter have
been a part of our common experience for a very long time, the very nature
of solids has been dramatically revealed only over the last half-century
in ways that were previously unimaginable and technologies have been
developed that allow new structures and even new materials to be created.
At the very core of the question of the nature of solids is the atomic
hypothesis. For well over two millenia, since the time of Democritus and
Lucretius, the idea that everything is made of distinct atoms has been a
part of natural philosophy, although neither understood nor accepted even
by many natural philosophers and scientists over much of the intervening
time. Even as recently as the beginning of the twentieth century - within
the lifetime of some humans - the existence of atoms as individual
constituents of matter could not be verified without some doubt, and it
had been assumed that any direct observation would be impossible.
Einstein's explanation, in 1905, of Brownian motion as indirect evidence
of the effects of individual atoms and molecules was a significant
contribution to the idea that all matter, even the air we breathe, is made
of atoms and combinations of atoms. And the observation of the diffraction
of x-rays by crystalline solids was even stronger evidence of the
microscopic structure of materials. And now, only a lifetime later,
distinct materials can be identified in terms of the arrangement of their
constituent atoms. In our own conscious lifetimes (even those of the
students reading this), it has become possible to observe individual atoms
using scanning tunneling microscopy and even create and study new atomic
structures by placing individual atoms. The atomic hypothesis has become
the atomic fact - and we now know that all materials are constructed of
individual atoms that are distinguishable and distinct. Furthermore, the
study of atoms in the first half of the last century has led to an
understanding of the very structure of the atoms themselves and to the
remarkable conclusion that we now know the characteristics of every type
of atom that is even possible in the entire universe with atomic number
less than 110 and the organizing principles for any that are either
discovered or manufactured that are heavier - even in the core of some
distant supernova. Even if the "modern physics" concepts of
quantum mechanics and relativity - which changed our worldview from the
classical physics of the previous centuries - are replaced by a
"new" physics, it will not change what we know about the
possible atoms that can exist. All that can be changed are the underlying
descriptions - the mathematical formalism that describes nature at the
atomic level - but not the knowledge of the nature of the atoms
themselves.
So the discussion of the nature of solids has to be the discussion of how
the individual atoms coelesce into larger structures and take on the
characteristics and properties of the many possible solids. The first
question, I suppose, is "Why should atoms attract each other in order
to form solids?" And the answer, of course, as it is for all
"why" questions, is that it is energetically preferable for them
to do so. That is not a very satisfying answer, in itself, and we should
only be satisfied when we know why forming solids lowers the energy of the
collection of constituent atoms. To deal with such questions will require
dealing with the bonding mechanisms. And the bonding mechanisms between
atoms is intimately related to the very structure of the atoms themselves.
For that reason, we will begin our study with a review of atomic structure
- how the quantum theory predicts how the electrons fill atomic orbitals
(which leads to the structure of the periodic table) and then how that in
turn predicts how atoms interact with each other in order to complete
their atomic shells thus forming either molecules or the larger structures
which we call solids. As we will see, there are a number of different
possible bonding mechanisms, and which occur will determine the atomic
arrangements and the physicsl properties of the resulting solids.
What IS the solid state of matter? Do all substances even exist as solids?
It is useful to categorize or separate matter into several states or
phases - which, in general, behave quite differently from one another. The
three obvious states of matter, which we all recognize in our normal
experience are the solid, liquid, and vapor phases. We can use water as
the common example - with the three states of water being ice, water, and
steam. And our normal experience also indicates what determines the state
- or phase - in which we can find that substance. Below the freezing point
it is ice, above the boiling point it is steam - or vapor, and in between
it is in the liquid form. And we also notice, from our own experience,
that at the ice-point water and ice can exist in equilibrium just as water
and steam can co-exist at boiling. But it is also true that changing the
pressure can also change the temperatures at which those phase transitions
occur. So the phases or states of matter for some chosen material depends
both on temperature and on pressure. For that reason, absolute temperature
and absolute pressure are referred to as state variables - that is,
controlling them for some substance controls the state of the substance
(liquid, solid, vapor).
A phase diagram is a useful way to display the states of matter for some
substance. The curves which separate the phases represent the combinations
of temperature and pressure for which the two phases which border that
branch of the diagram are in equilibrium. There is also a triple point - a
particular temperature and pressure at which all three of the phases are
in equilibium. Materials for which the triple point pressure is less than
atmospheric pressure will exhibit all three phases - solid, liquid, and
vapor - at atmospheric pressure depending on the temperature (again, water
being an obvious example). And that is the case for most, but certainly
not all, materials. Carbon dioxide, for example, has a triple point
pressure well above atmospheric pressure. As a consequence, CO2 exists in
solid form (dry ice) at atomospheric pressure and as a gas, depending on
the temperature, but does not have a separate liquid phase unless the
pressure is raised above the triple point pressure. All of the elements
will solidify at some temperature at atmospheric pressure except helium.
Helium gas liquifies only when the temperature is lowered to 4.2 K - the
lowest boiling point of any material - and will not solidify except at
high pressures with the temperature maintained below one Kelvin.
How these 'factoids" are useful to us are to remind us of the nature
of solids. If all materials are made of atoms, whether the material is a
solid or a liquid or a vapor depends on whether the atoms form some
relatively rigid bond with respect to their neighboring atoms or whether
that bond is such that the atoms or molecules can move with respect to
each other, yet form a surface (as in a condensed droplet), or whether
they behave independently of each other and can only be contained with a
closed volume. And the conditions that determine which of those states
occur are temperature and pressure.
But even though atomic bonding and the structure of the resulting solids
is important, we ultimately want to discuss the properties of the various
types of solids that can form. Closely related to the atomic bonding are
the mechanical properties of solids - how rigid or pliable the solid would
be or how readily vibrations could be propagated through it. And closely
related to how the atoms vibrate are the thermal properties of solids -
thermal expansion, for example, or thermal conductivity and molar heat
capacity. (And as we will see, the heat capacity of a solid will become an
important measure of how the atoms vibrate.) But it is the electrical (or
the electronic) properties of solids that will hold most of our interest.
That is, depending on the bonding mechanisms that allow atoms to coelesce
into solid form, there may be electrons that can migrate among the atoms
or ions which then render the solid to be an electrical conductor. On the
other hand, if the outer electrons of the atoms that form the solid are
all participating in the bonding - in order to complete closed shells on
the atoms - then the material would not be inherently conductive. These
distinctions will need to be made carefully to fully understand the
characteristics of metals, insulators, and semiconductors. In attempting
to understand the behavior of the electrons in solids, we will find that
our classical assumptions will be inadequate - that is, assuming that the
electrons behave classically (like charged b-b's moving among the
"bowling ball" atoms or ions) will yield behaviors that are not
consistent with experiments. And resolving the inconsistencies will
require applying quantum theory to the electrons and that in turn will
give us a language to discuss the distinctions between metals, insulators,
and semiconductors - and hence the language to deal with the properties of
semiconductors and the devices that can be made from those materials.
Finally, there are some "special states" that can be discussed -
and a study of solid state physics would be remiss if those special states
were not included. Magnetic materials and superconductors are intriguing
and important types of solids that can only be understood following the
discussion of normal solids. |