Morris, Dr. Hopkins, Dr.
Weyland, Dr. Jones Notre Dame and D. At the Florida Institute of Technology, Drs. Burns, and J. Mantovani have read parts of this book, and discussions with Dr. Raffaelle and Dr. Blatt were useful. Richards of Sandia, and Dr. Lehoczky of Marshall, were particularly helpful to JDP. Brief, but very pithy conversations of JDP with Dr. Bailey would like particularly to thank Drs.
Burns and J. Blatt for the many years of academic preparation, mentorship, and care they provided at Florida Institute of Technology. A special thanks to Dr. Patterson who, while Physics Department Head at Florida Institute of Technology, made a conscious decision to take on a coauthor for this extraordinary project. All mistakes, misconceptions and failures to communicate ideas are our own. No doubt some sign errors, misprints, incorrect shading of meanings, and perhaps more serious errors have crept in, but hopefully their frequency decreases with their gravity. Preface IX Most of the figures, for the first version of this book, were prepared in preliminary form by Mr.
However, for this book, the figures are either new or reworked by the coauthor BCB. We gratefully acknowledge the cooperation and kind support of Dr. Asheron, Ms. Sauer, and Ms. Duhm of Springer. Finally, and most importantly, JDP would like to note that without the constant encouragement and patience of his wife Marluce, this book would never have been completed. Bailey, Cape Canaveral, Florida 9.
Contents 1 Crystal Binding and Structure XII Contents 2. Contents XIII 4. XIV Contents 6 Semiconductors Contents XV 7. In that book parts of many fields such as metallurgy, crystallography, magnetism, and electronic conduction in solids were in a sense coalesced into the new field of solid-state physics.
About twenty years later, the term condensed-matter physics, which included the solid-state but also discussed liquids and related topics, gained prominent usage see, e. In this book we will fo- cus on the traditional topics of solid-state physics, but particularly in the last chap- ter consider also some more general areas. However, we will also consider, at least briefly, amorphous solids e. The physical definition of a solid has several ingredients. Addi- tionally, in this chapter, the term solid will mostly be restricted to crystalline solids.
A crystalline solid is a material whose atoms have a regular arrangement that exhibits translational symmetry. The exact meaning of translational symmetry will be given in Sect. When we say that the atoms have a regular arrange- ment, what we mean is that the equilibrium positions of the atoms have a regular arrangement. At any given temperature, the atoms may vibrate with small ampli- tudes about fixed equilibrium positions.
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For the most part, we will discuss only perfect crystalline solids, but defects will be considered later in Chap. Elements form solids because for some range of temperature and pressure, a solid has less free energy than other states of matter. It is generally supposed that at low enough temperature and with suitable external pressure helium requires external pressure to solidify everything becomes a solid.
No one has ever proved that this must happen. We cannot, in general, prove from first principles that the crystalline state is the lowest free-energy state. Anderson has made the point2 that just because a solid is complex does not mean the study of solids is less basic than other areas of physics. More is dif- ferent. For example, crystalline symmetry, perhaps the most important property discussed in this book, cannot be understood by considering only a single atom or molecule. It is an emergent property at a higher level of complexity.
Many other examples of emergent properties will be discussed as the topics of this book are elaborated.
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The goal of this chapter is three-fold. All three parts will help to define the uni- verse of crystalline solids. We start by discussing why solids form the binding , then we exhibit how they bind together their symmetries and crystal structure , and finally we describe one way we can experimentally determine their structure X-rays. Section 1. There are approximately four different forms of bonds. A bond in an actual crystal may be predominantly of one type and still show characteristics related to others, and there is really no sharp separation between the types of bonds.
In this Section, we merely hope to make the reader believe that it is not unreasonable for atoms to bind themselves into solids. Molecular crystals consist of chemically inert at- oms atoms with a rare-gas electronic configuration or chemically inert molecules neutral molecules that have little or no affinity for adding or sharing additional electrons and that have affinity for the electrons already within the molecule.
We shall call such atoms or molecules chemically saturated units. These interact weakly, and therefore their interaction can be treated by quantum-mechanical per- turbation theory. The interaction between chemically saturated units is described by the van der Waals forces. Quantum mechanics describes these forces as being due to correla- tions in the fluctuating distributions of charge on the chemically saturated units.
The appearance of virtual excited states causes transitory dipole moments to ap- pear on adjacent atoms, and if these dipole moments have the right directions, then the atoms can be attracted to one another. The quantum-mechanical descrip- tion of these forces is discussed in more detail in the example below. The van der 2 See Anderson [1. The forces in molecular crystals are almost central forces central forces act along a line joining the atoms , and they make efficient use of their binding in close-packed crystal structures.
However, the force between two atoms is somewhat changed by bringing up a third atom i. We should men- tion that there is also a repulsive force that keeps the lattice from collapsing. This force is similar to the repulsive force for ionic crystals that is discussed in the next Section. A sketch of the interatomic potential energy including the contributions from the van der Waals forces and repulsive forces is shown in Fig.
A relatively simple model [14, p. The displacements from equilibrium of the —e charges are labeled d1 and d2.
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There will also be a Coulomb coupling energy between the two oscillators. This is not necessarily physically reasonable. It is just the way we choose to build our model. The attraction be- tween these charges is taken care of by the spring. The interatomic potential V r of a rare-gas crystal. The interatomic spacing is r By defining new coordinates making a normal coordinate transformation it is easily possible to find these two frequencies.
We define. A more instructive form for the ground-state energy is obtained by making an assumption that brings a little more physics into the model. Combining this last inequality with 1. From 1. The negative sign tells us that the two dipoles attract each other.
This is a short-range force. Note that without the quantum- mechanical zero-point energy which one can think of as arising from the uncer- tainty principle there would be no binding at least in this simple model. More than one dimension must be considered, 2.
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The binding of electrons is not a harmonic oscillator binding, and 3.