MATTER IN SOLID FORM!

A vapor is an intermediate form between liquid and gas, consisting of microscopic liquid droplets which behave like a gas.  Familiar examples of water as a vapor are clouds, fog and steam.  The drawing is wrong, as usual on the internet!


Don't let the open lattice cell diagrams confuse you, they show the arrangements of the centers of the atoms, for clarity. The actual atoms in the crystal are touching one another, as close as the Pauli Principle lets them come to one another... as in molecules.




Even in classical antiquity, around 500 BCE, thinkers realized, seeing a huge variety of crystals which came right out of the ground with beautiful geometrical shapes, that atoms in solids must be arranged in three-dimensional geometric patterns which the overall shapes of the crystals often duplicated on a macroscopic scale!  It is no exaggeration to say that to be a solid is to be crystalline.


When individual atoms are placed in close contact with many other atoms, the electrons in each atom respond to the presence of so many surrounding nuclei. The number of possible electron states in the system grows to such a huge number that the individual energy levels of the electrons in the original atoms are spread into enormous numbers of possible states so close together that they in effect form a continuum, a band. Such bands still have gaps between them, relating back to the gaps between the original atomic energy levels. The size of these gaps is crucial in determining whether a given solid behaves as a conductor, a semi-conductor or an insulator. The importance of this gap cannot be overstated, since semiconductors are the basis of all modern electronics, and have no known practical replacement at present!  The key gap is between the “valence band,” which is occupied by bound electrons, and the “conduction band,” in which the electron state functions span the entire volume of the bulk matter, so that electrons with energies in this band can travel fairly freely throughout the solid!



Solids of vital importance throughout much of human history are the metals. Any atom which has a solitary electron outside closed shells of electrons forms a metal. Even hydrogen is a metal, although we don't live in an environment where its liquid and solid states can be seen! Copper is a metal vital for modern technology, while metals like gold, silver and platinum were coveted throughout much of human history. Approximately three-quarters of all known chemical elements are metals. The most abundant varieties in the Earth’s crust are aluminum, iron, calcium, sodium, potassium, and magnesium. The vast majority of such metals are found in ores (mineral-bearing substances), but a very few such as copper, gold, platinum, and silver frequently occur in the free state because they do not readily bond chemically, hence their availability to shape human history and the beginnings of technology.


In sharp contrast to the case of conductors and metals, only two naturally occurring atoms form solids which are useful semiconductors, namely silicon and germanium. A technique known as “doping,” in which impurities are inserted into crystals, can result in lab-created compounds that are semiconductors, such as gallium arsenide. A gigantic revolution in electronics occurred with the invention of the transistor. Its development completely revolutionized electronics. Here is a detailed discussion of how transistors work. The most titanic revolution in electronics, however, came about with the development of integrated circuits, complex and microscopically tiny electronic devices that are literally printed on a tiny silicon chip! Extreme miniaturization has now nearly reached its practical limits, and physicists are desperately seeking other technologies that don't depend on electron current... for example, one promising area is known as spintronics, and uses the spin rather than the charge of the electron.



Gives off huge amount of heat, incredibly fragile, does only one thing, like amplify a signal.  Basis of all electronics, 1890 to 1950.

An entire, complete fully functional computer on a single “board”, present day.


Easily held in one hand, a device that connects you to the internet, shows movies, shows web pages, makes phone calls, takes photographs, sends and receives e-mail and messages, creates documents, lets you read books, runs computer programs, makes credit card payments, etc., etc.

When we strike a chunk of solid matter, a compressional wave propagates through the solid. Such propagating waves of alternate high and low pressure in gases are called sound, but solids are systems that can only be described using quantum physics, so the equivalent of waves propagating through the solid is individual bosons propagating through the solid. These bosons are called phonons, and they obey all the rules of quantum physics as applied to bosonic particles. They are quantized density oscillations of the solid. There are two types of phonons, acoustic and optical. The acoustic phonons are so-called because they are quantized oscillations that are similar to the classical longitudinal sound waves in air.



Acoustic phonons are associated with long-wavelength vibrations, where neighboring particles oscillate nearly in phase. They have relatively low frequencies, typically in the gigahertz region. Optical phonons are associated with vibrations where neighboring particles oscillate nearly out of phase. The frequencies of optical phonons are in the terahertz region (leading to much higher phonon energies than for acoustic phonons), and in ionic crystals or glasses they can be involved in the absorption of infrared light. Note that due to the opposite electrical charges of neighboring ions, in ionic crystals, such vibrations can couple directly to the electromagnetic field through their oscillating electrical dipole moment.


Longitudinal sound wave in a tube full of air.  The particle is an air molecule.



One of the most important concepts in physics involved in understanding matter is the Equipartition Theorem. In the late 19th Century it was found that each degree of freedom of a system uses (1/2)kT of the available energy. Thus, a gas of N monatomic particles has a total energy of (3/2)NkT. When this idea was applied to gases consisting of diatomic or triatomic molecules, it was found that quantum physics was needed to count the actual number of degrees of freedom correctly, and the idea still worked. The specific heat capacity of matter is not a constant, as a result, but depends on temperature, and Einstein played a key role in understanding what was going on.  Note that for single atoms in solids, having three space degrees of freedom and three vibrational degrees of freedom relative to one another, we would expect a total energy per atom of 6 times (1/2)kT or 3kT.


A number of famous physicists, including Einstein, worked on the problem of understanding how the specific heat capacity of solids behaves as a function of T, actually going to zero as T goes to zero!



One of the most essential electronic components is the diode, a device that allows current to flow in only one direction through it. From 1900 into the 1950s, diodes were bulky, fragile vacuum tubes. The replacement of such tubes by tiny semiconductor diodes was the first step in the electronic revolution of the past 70 years. The light emitting diode (LED) has become, in the past few decades, the standard source of light for many purposes... my bedside reading lamp is an LED, and almost all automobile headlights are LEDs. [Doping of semiconductors with atoms having one less electron produces p-type material (containing mobile electron holes) while doping with atoms having one more electron produces n-type material, containing excess and mobile electrons.]





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