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Atoms


Contents

Periodic Table
Band Theory, Metal
Solid State
X-ray Diffraction
Specific Heats of Solids and Phonons
Superconductivity
Laser
Plasma
Quantum Computing (see appendix)
Footnotes
References
Index

Periodic Table

In the mid 19th century, scientists were confronted with a mountain of seemingly unconnected chemical data - a situation similar to the particle physics in mid 20th century. In 1869 the Russian chemist Mendeleyev successfully organized the various chemical elements into a Periodic Table. Similar elements are arranged in vertical columns and the properties of the elements change
Periodic Table 1 Periodic Table 2 progressively across the row. The Periodic Table in Figure 13-01a is the modern version; while Figure 12-19 depicts the simpler one. The atomic number is the number of positive charges in the atomic nucleus. Atomic masses refer to the masses of neutral atoms, including the masses of the nucleus, the electrons and the mass equivalent of their binding energies. It is expressed in mass units such that the mass of the most abundant type of carbon is exactly 12.00 u (1 u = 1.66x10-24 gm).

Figure 13-01a Periodic Table,
Modern [view large image, 1 MB]

Figure 13-01b Periodic Table,
Unconventional [view large image]

Also see "Extension of the Periodic Table".

It was discovered later that not all of the atoms of a particular element have the same mass. The different varieties (different number of neutrons, same number of protons) of the same element are called its isotopes. The atomic masses now appear in the Periodic Table is the average atomic mass weighted by the abundance of each isotope. Unfortunately, the abundance depends on location where the sample is taken (ultimately depends on the process that created, transported or aggregated the material). The International Union of Pure and Applied Chemistry (IUPAC) has decided in 2011 to list atomic weight in lower and upper bounds, e.g., (1.00784;1.00811) for hydrogen. The affected elements include H, Li, B, C, S, and N. Elements with only one stable isotope such as F, Al, Na, Au and 17 others, are exempted from this ongoing change. And some highly radioactive elements exist too fleetingly for their atomic weights even to be defined.

Periodic Table, Comical Figure 13-01a includes data for the boiling point, melting point, density, acidity, basicity, crystal structure, and electronegativity (tendency to keep electrons) of the elements. The s, p, d, and f letters in the electronic configuration designate the orbital quantum number l = 0, 1, 2, 3, ... respectively for the outer shell electrons. A new designation of the groups has a number ranged from 1 to 18. Figure 13-01b is an unconventional Periodic Table. It specifies the phase (solid, liquid, or gas) of the element at room temperature, whether the element is radioactive or man-made, as well as its usage (in daily life) or occurrence (in nature). The original version in pdf format, and other Periodic Table in words are available from: http://elements.wlonk.com. Other kinds of Periodic Table may incorporate properties such as atomic radius, covalent radius, ionization potential, specific heat, heat of vaporization, heat of fusion, electrical conductivity,

Figure 13-01c Periodic Table, Comical [view large image]

and thermal conductivity etc. None of the elements are edible (as suggested in Figure 13-01c). They could be burning, toxic, poisonous, radioactive or metallic (Figure 13-01d). Human consume mostly organic compounds such as proteins, carbohydrate, or fat. We also take in some
inorganic compounds, e.g., the "Calcium, Magnesium, Zinc" pills, which actually contain Calcium Carbonate (CaCO3), Magnesium Oxide (MgO), and Zinc Gluconate (C12H22O14Zn). Perhaps the table salt (NaCl) is the most favorite inorganic substance. Water (H2O) is very important, but tasteless.

The regular pattern in the periodic table is related to the states of the electrons in an atom. It is specified by four quantum numbers. The principal quantum number n determines the energy level; its value runs from 1, 2, 3, ... For each n, the orbital quantum number l = 0, 1, 2, ... (n-1); it is related to the magnitude of angular momentum. Then for each l, the magnetic quantum number m can be -l, -l+1, ...l-1, l; it is related to the z component of the angular momentum. The spin quantum number s is either +1/2 or -1/2.

For n = 1, l = 0, m = 0, there is only 2 possible quantum states for the electron, with s = +1/2 and -1/2 respectively. For n = 2, l = 0, m = 0 and l =1, m = -1, 0, +1; there is a total of 2 + 6 = 8 possible quantum states. Therefore, it requires 2 electrons to complete the shell for n = 1, and 8 electrons to complete the shell for n = 2, ...and so on. The orbital quantum number l is often designated by a letter, s for l = 0, p for l = 1, d for l = 2, and f for l = 3 ...

The quantum number l is non-additive (e.g., two of the quantum numbers l1, l2 are added as vectors, they can take on the values of l1+l2, l1+l2-1, ..., |l1-l2| ) while m is additive (e.g., m' = m1 + m2 only) and relates to an Abelian group (e.g., the two dimensional rotation about the z-axis). States having the same non-additive quantum numbers but differing from each other by their additive quantum numbers are said to belong to the same multiplet. The number of members of a multiplet is called its multiplicity. For a given multiplet l the multiplictiy is equal to 2l+1.

The atom tends to lost the outer electrons if the number is far from a complete shell or sub-shell such as the elements in the beginning of a series. It gradually develops a preference for accepting more electrons to complete the outer shell as the progression moves toward the end of a series. This property is responsible for all the chemical reactions, which form molecules with a tendency of completing the shell (energy levels with similar energy, usually with the same value of n) or subshell (energy levels having almost the same energy, usually with the same values of l). A stable atomic configuration is also achieved by completing a shell or sub-shell as illustrated in Table 13-01 below by the inert elements (the rule becomes more complicated in the advanced series as the electrons with high l tend to intermingle with each others), which do not react chemically:

n ..., l ..., (2l+1)x2 Electron Configuration of the Inert Element
1 0 2 He (2)=2
2 0, 1 2, 6 Ne (2)+(2+6)=10
3 0, 1, 2 2, 6, 10 Ar (2)+(2+6)+(2+6)=18
4 0, 1, 2, 3 2, 6, 10, 14 Kr (2)+(2+6)+(2+6+10)+(2+6)=36
5 0, 1, 2, 3, 4 2, 6, 10, 14, 18 Xe (2)+(2+6)+(2+6+10)+(2+6+10)+(2+6)=54
6 0, 1, 2, 3, 4, 5 2, 6, 10, 14, 18, 22 Rn (2)+(2+6)+(2+6+10)+(2+6+10+14)+(2+6+10)+(2+6)=86

Table 13-01 Electron Configuration of the Inert Elements

Note: Small inserts in the 2nd column depict the corresponding atomic structures with the semi-classical view in term of orbital motion, and quantum view in term of probability density.
High-tech Elements Export Quota The 21st century ushers in an era of handheld electronics and green machines. The new technologies use materials other than the traditional steel or gold. Suddenly some obscure metals appear on the scene (or laterally on the touchscreen). These elements used to be the by-products of smelting. Now they are the primary ores in short supplies as demand soared.

Figure 13-02j High-tech Elements [view large image]

Figure 13-02k Export Quota [view large image]

In 2010, the US Department of Energy compiled a list of 14 high-tech elements in danger of supply disruption for the green technology (Figure 13-02j).
Electronic Junks One of the problems is the introduction of export quotas by China (Figure 13-02k), which currently mines over 90% of the supply of rare earth elements. The insert in Figure 13-02k shows the low-tech smelting of lanthanum in Inner Mongolia. In theory the shortfall could be covered by reopening some of those closed ores suspended over environmental concerns about radioactive contamination or toxicity. Another way is to recycle the used parts.

Figure 13-02l Recycling Electronic Junks [view large image]

But the process would ruin the place and poison its inhabitants as shown in Figures 13-02l taken from a remote village in South-East China. Figure 13-02j also shows the special (and wonderful) properties of some high-tech elements.
On March 13 2012, the U.S., Japan and EU filed a WTO (World Trade Organization) complaint vs. China. They accuse China of hoarding the valuable minerals for its own use. The aim is to pressure China to lift export limits on rare earth minerals. But the Chinese government retorts that, the restrictions are motivated by environmental concerns (?).

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Band Theory, Metal

Energy Bands Band Theory About 80% of the free elements at room temperature exists in the form of metal. The conditions to form metal are vacant valence orbitals and low ionization energies. Similar to the splitting of energy levels when two or more atoms come close to each other; (See Figure 12-15.) energy levels broadened to a band (many closely spaced energy levels) for an aggregate

Figure 13-03a Energy Bands
[view large image]

Figure 13-03b Band Theory
[view large image]

of many atoms as shown in Figure 13-03a. In this example, the valence electrons occupy the energy bands up to half of the 3s band at 0oK, at an energy called Fermi energy Ef. Figure 13-03b shows that if there is empty levels available in the energy band, valence electrons will be able to roam among the space in between the atoms by absorbing energy from the environment when the temperature is above 0oK. With a few exceptions, metals have a silvery-white color because they reflect all frequencies of light. They have high electrical and thermal conductivity and all metals can be drawn into wires or hammered into sheets without shattering -- that is, they are ductile and malleable. All these attributes are the result of mobile, non-rigid electron gas within the lattice. Most metals (except gold, silver, platinum, and diamond) do not occur as free elements in the Earth's crust. They are usually found in chemical combination with other elements as mineral ores.

Figure 13-03b shows that in an insulator, the valence band is full and the next empty energy band is separated by a large energy gap. Conduction cannot occur unless some of the electrons in the valence band are promoted to the conduction band. Energy needed to promote a few electrons might be provided by heating the solid to a very high temperature or by shining X rays on it. No solid can remain as a good insulator while it is exposed to X rays. A semicon-ductor has a small energy gap. Electrons can be promoted to the conduction band as a result of irradiation such as the conversion of sunlight to electricity by means of a silicon cell.

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Solid State

Condensed matter encompasses both liquid and solid (Figure 13-03c). Solid state physics is the study of rigid matter or solids. It is
Condensed Matter Phase Diagram the major branch of condensed matter physics including both crystalline solids such as insulator, metal, semiconductor as mentioned above; and non-crystalline solids (Soft Matter) such as amorphous solid, granular matter, quasi-crystal, and polymer. Solid materials are formed from densely-packed atoms, with strong interacting forces between them. For example, sodium chloride (NaCl) is held together by ionic bonds, it is the covalent bonds responsible for metallic bonding, and the van der Waals forces provide the bonding to the

Figure 13-03c Condensed Matter
[view large image]

Figure 13-03d Phase Diagram [view large image]

noble gases (in solid form). These interactions are responsible for the mechanical, thermal, electrical, magnetic and optical properties of solids.
Theoretically, such system of atoms or molecules is described by :

where the sum and interaction V include all the constituents in the system. There are usually about 1023 particles in the system making solution of these equations impracticable. Approximations to alleviate the problem are introduced such that the energy scale under consideration is below 1 ev, while the interacting distance smaller than 10-8 cm is ignored. This is appropriate for ordinary solids which are insensitive to the details outside these scales. Under these assumptions it is possible to introduce macroscopic quantity such as density by averaging over the individual behavior of the particles. Actually many properties in solids are emergent resulting from interactions among large numbers of particles. For example, water and ice are governed by the same equation but exhibit completely different properties. Such phenomena have something to do with the phase (Figure 13-03d) rather than the basic equation, which is highly symmetrical. Water exhibits the translational and rotational symmetry of the basic laws, while ice is only invariant under the discrete translational and rotational group of its crystalline lattice. In other words, the translational and rotational symmetries of the microscopic equations have been spontaneously broken in solid phase.

    Some experimental methods to measure the macroscopic properties of solids:

  1. Scattering - Use neutrons or X-rays to discover the structure of the solid (see X-ray Diffraction).
  2. NMR - Apply static magnetic field B and measure the absorption or emission frequency of electromagnetic radiation = geB/m to calculate the charge to mass ratio e/m, where g 2 is the electron spin correction.
  3. Thermodynamics - Measure the response of macroscopic variables (energy, volume, etc.) to variations of temperature, pressure, etc. to derive quantities such as specific heat (Cv = U/T) etc.
  4. Transport - Measure the gradient of heat or electrical current to determine the thermal or electrical conductivity.

Table 13-02 below lists some macroscopic properties of solid at 293oK and 1 atm 101 kpa (1 pa = 1 kg/m-s2). Examples are given for the high and low limits.

Property Definition Unit Example (High) Example (Low)
Density Amount of Mass within a volume gm/cm3 Platinum (21.45) Kapok (0.050)
Melting Point Temperature for solid turning into Liquid oK Graphite (3800) Ice (273)
Heat of Fusion Heat/mass to completely convert solid to liquid (107) ergs/gm Quartz (~830) Lead (25)
Specific Heat Amount of heat to raise 1oK in unit mass (104) ergs/gm-K Concrete (3350) Iron, Pure (106)
Thermal Conductivity Rate of heat flow through temperature gradient (104) ergs/sec-cm-K Diamond (900) Kapok (0.03)
Electrical Resistivity Resistance of Current flow (10-6) ohms-cm Paraffin (3x1018) Silver (1.6)
Linear Expansivity Linear expansion (%) at the raise of 1oK (10-6) 1/K Plastic (250) Diamond (~0)
Tensile Strength Maximum stress before yielding Mpa Steel (3000) Concrete (~4)
Elongation Deformation/original-length before fracture % Plastic (800) Iron, cast (~0)
Young's Modulus Ratio of stress to strain Gpa Diamond (1200) Rubber (0.02)

Table 13-02 Some Macroscopic Properties of Solid

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X-ray Diffraction

X-ray Diffraction XRD Pattern The Bragg (father and son) pioneered the discovery to discern the structure of crystals in early 20th century. They took the diffraction pattern resulting from the interaction between the atoms (in the crystal) and X-ray and developed a formula to find out the inter-atomic distance. The method is

Figure 13-04a X-ray Diffraction [view large image]


Figure 13-04b XRD Pattern

now widely used in molecular biology and biochemistry as well. The following provides a brief explanation for the process.
  1. Incident X-ray is collimated into plane wave and hits the crystal either in one piece or in powdery form. X-ray is used because its wavelength is in the same order of magnitude of the inter-atomic distance.


  2. The atoms become polarized into dipoles. Each dipole oscillates under the influence of the electromagnetic waves. The oscillations in term re-emit radiation in all directions in the form of spherical waves. The un-scattered incident waves appear as a bright spot (black in a photographic plate) at the center (Figure 13-04a).


  3. At certain incident angles to the crystal planes (Bragg planes) the scattered beams add together constructively to form bright
  4. Miller Indices spots around the central point. The formula for such constructive interference is :
    2d sin() = n
    where d is the spacing between Bragg planes, is the incident angle, is the wavelength, and the integer n is the order of the scattered beam, e.g., higher number of n corresponds to bright spot further away from the incident direction. The angular range of the diffractometer usually restricts n to be 1.

    Figure 13-04c Miller Indices
    [view large image]

  5. The spacing between the Bragg planes "d" is related to the inter-atomic distance "a" by the formula:
    a = d (h2+k2+l2)1/2
    where the Miller indices (h k l) are defined as the reciprocals of the fractional intercepts (see Figure 13-04c for a graphical explanation).


  6. The diffraction pattern for a piece of amorphous material (such as glass) usually appears as concentric rings around the un-scattered beam image. For crystal with regular spacing between atoms, the ring breaks up into spots as shown in Figure 13-04a. Another method is to grind the specimen into powder (to the size of about 10-4 cm) and put them in a holder. In this way
  7. Powder Diffraction it is not necessary to orient the crystal in various positions to obtain diffraction patterns for different Bragg planes. Figure 13-04b plots the intensity of the scattered waves versus twice the incident angles obtained by the diffractometer similar to the one shown in Figure 13-04a. The graph shows the intensity variation produced by the various Bragg planes. The International Centre for Diffraction Data maintains JCPDS (Joint Committee on Powder Diffraction Standards) cards for about 500,000 powder diffraction patterns (as of 2006), which can be used to identify substances in a given diffraction pattern such as shown in Figure 13-04d (CPS stands for counts of X-ray photons per second).

    Figure 13-04d Powder Diffraction [view large image]

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Specific Heats of Solids and Phonons

Beside the metallic bond, atoms and their compounds can form crystal by other types of bond as shown in Figure 13-05. It is expected that vibrations of the constituent atoms would determine the physical properties of the crystal (solid). For example, the specific heat cv, which is the energy that must be added to raise the temperature by 1oC (at constant volume) in one kmole of the substance, would have a value of about 3R (where R is the gas constant equal to 1.99 kcal/kmole-oK). This is indeed the case for most solids at room temperature and above as shown in Figure 13-06. However, it failed to account for the drip at low temperature. In 1907 Eistein derived an improved theoretical formula by considering the vibration to be quantized in multiples of hv, where v is the frequency of the vibration. The idea is similar to the quantized electromagnetic wave in blackbody radiation. But it still failed to describe the behavior of the specific heat at very low temperature. The discrepancy is finally resolved in 1912 by considering a solid as a continuous elastic body. Instead of residing in the vibrations of individual atoms, the internal energy of a solid is assumed to
Crystal Types Specific Heats reside in elastic standing waves. These waves, like electromagnetic waves in a cavity, have quantized energy contents. A quantum of vibrational energy in a solid is called a "phonon", and it travels with the speed of sound. The concept of phonones is quite general and has applications in connection with the thermal conductivity of some solids, the way electrons in the crystal structure interact with sound waves, and in superconductivity.

Figure 13-05 Crystal Types [view large image]

Figure 13-06 Specific Heats
[view large image]

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Superconductivity

Superconducting Elements If mercury is cooled below 4.1 K, it loses all electric resistance. This discovery of superconductivity by H. Kammerlingh Onnes in 1911 was followed by the observation of other metals and intermetallic compounds (made of two or more metallic elements) which exhibit zero resistivity below a certain critical temperature Tc. The fact that the resistance is zero has been demonstrated by sustaining currents in superconducting lead rings for many years with no measurable reduction. Table 13-03 shows the elements, which can become superconducting at the indicated critical temperature.

[view large image]

Table 13-03 Super-conducting Elements

Superconducting Compounds Ceramic materials are expected to be insulators -- certainly not superconductors, but that is just what Georg Bednorz and Alex Muller found when they studied the conductivity of a lanthanum-strontium-copper oxide ceramic in 1986. Its critical temperature of 30 K was the highest, which had been measured to date. Their discovery started a surge of activity which discovered superconducting behavior as high as 125 K. However, these compounds are hard to make and difficult to shape. They pose a multitude of physical challenges to researchers and engineers.

Figure 13-07 High Temperature Superconductors [view large image]

Figure 13-07 lists the high temperature (above 4o K) superconductors discovered during the last one hundred years.

Superconductivity Meissner Effect

The effect of superconducting is often demonstrated by cooling a disk made of superconducting material with liquid nitrogen to below the critical temperature Tc. A magnet placed above the disk is repelled, i.e., it is levitated above the superconductor. (See Figure 13-08a.) This phenomenon is caused by the Meissner effect which is related to the fact that a superconductor will exclude magnetic fields within the superconducting material (see Figure 13-08b).

Figure 13-08a Superconductivity

Figure 13-08b Meissner Effect

Suppose, as in Figure 13-08a, a magnet is placed above a superconductor. The induced magnetic field inside the superconductor is exactly equal and opposite in direction to the applied magnetic field, so that they cancel within the superconductor. The result are two magnets equal in strength with poles of the same type facing each other. These poles will repel each other, and the force of repulsion is enough to float the magnet. However, the magnet's magnetic field must be below the superconductor's critical magnetic field Hc. If the magnetic field is stronger than Hc it would penetrate the superconductor and extinguish the superconductivity.

In 1956 L. Cooper offered an explanation for this phenomenon of superconductivity. The process starts in some materials at very low temperature when two electrons near the Fermi energy level could couple to form an effective new particle, under a
Cooper Pair very weak attractive force. This particle was subsequently called the Cooper pair (Figure 13-08c). It can be shown that the most energetically favourable situation for this to occur was when the two electrons had a total spin of zero. Since the Exclusion principle does not apply to particle with integer spin, there is no restriction on the energy state that the Cooper pair can occupy. In particular, at low temperatures thermal agitation is minimal, and all of the Cooper pairs can occupy the lowest possible energy state. Thus no energy exchanges can take place (nothing to give), the normal resistive energy losses are not possible. The Cooper pairs move

Figure 13-08c Cooper Pair [view large image]

unimpeded through the superconducting material: it has zero electrical resistance and exhibits superconductivity. The weak attractive force between the electrons in the Cooper pair has its origin in the induced polarization (of the atoms in the lattice, see Figure 13-08c).
An equivalent description is to consider the attraction as the result of the emission of a virtual phonon by one electron and its absorption by another one as shown by the Feynman diagram in Figure 13-08c.

This is known as the BCS theory. It does not explain the absence of resistance in copper oxide based compounds. There is still no definitive theory of how or why these compounds become superconductivity.

It has been shown that the exclusion of magnetic flux (Meissner effect) corresponds to a finite range for the electromagnetic field and hence to a `massive photon'. In the context of quantum field theory, the meissner effect in a superconductor occurs because the U(1) gauge symmetry is broken in a superconductor. The photon acquires a mass through the Higgs mechanism and the Higgs bosons are the Cooper pairs.

Super-conductivity is often cited as an example of emergent phenomenon when novel property appears in an ensemble of individual parts. The human brain is another example where ensemble of molecules and atoms becomes a conscious whole. Very often the emergent property is the result of internal force (between the parts) winning over thermal motion (ultimately the tendency toward higher entropy - more disorder).
Strange Metal Entenglement It was discovered in 2008 that some materials such as the barium iron arsenide (BaFe2As2) behave strangely at low temperature. It starts out in a state of spin-density wave (SDW) in which the charge density (of the conduction electrons) has a sinusoidal modulation out of step from the periodicity of the crystal lattice. This material become super-conductive with doping (substituting arsenic with phosphorus as illustrated in Figure 13-08d) but only up to about 30% beyond which it turns to the normal state of Fermi liquid (free Fermi gas). Another interesting property is displayed by increasing the temperature at 30% doping level, the result is neither a superconductor nor SDW but something called strange metal. This phenomenon

Figure 13-08d Stange Metal [view large image]

Figure 13-08e Entanglement [view large image]

cannot be explained by the BCS theory. It seems that all the electrons in the solid entangled together as a single indivisible whole. It turns out that such complicated system has a counter
part in Superstring theory, from which a simpler formulation can be found by the method of duality. According to the Superstring theory, the entanglement acts as an addition spatial dimension above and beyond the three dimensions where the electrons reside (Figure 13-08e). However, scientists still don't understand how such state occurs in actual materials. Explaining what is really going on is still in its infancy. It should be emphasized that this is just a mathematical analogy; the wholesale entanglement does not constitute a proof for the existence of extra-dimensional space.

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Laser

Laser, Ruby Laser, Energy Levels Finding substances in which a population inversion can be set up is central to the development of new kinds of laser. The first material used was synthetic ruby. Ruby is crystalline aluminum (Al2O3) in which a small fraction of the Al3+ ions have been replaced by chromium ions, Cr3+. It is the chromium ions that give rise to the characteristic pink or red colour of ruby and it is in these ions that a population inversion is set up in a ruby laser.

Figure 13-09 Ruby Laser
[view large image]

Figure 13-10 Laser, Energy
Levels [view large image]

In a ruby laser, a rod of ruby is irradiated with the intense flash of light from xenon-filled flashtubes. (See Figure 13-09.) Light in the green and blue regions of the spectrum is absorbed by chromium ions, raising the energy of electrons of the ions from the ground state level to the broad F bands (See Figure 13-10). Electrons in the F bands rapidly undergo non-radiative transitions to the two metastable E levels. A non-radiative transition does not result in the emission of light; the energy released in the transition is dissipated as heat in the ruby crystal. The metastable levels are unusual in that they have a relatively long lifetime of about 4 milliseconds (4 x 10-3 s), the major decay process being a transition from the metastable level to the ground state. This long lifetime allows a high proportion (more than a half) of the chromium ions to build up in the metastable levels so that a population inversion is set up between these levels and the ground state level. This population inversion is the condition required for stimulated emission to overcome absorption and so give rise to the amplification of light. Since photons are bosons, which do not obey the Pauli exclusion principle, they can occupy the same state. The stimluating photon and the stimulated photon leave the atom in the same direction, same frequency, same polarization and in phase. This light can then interact with other chromium ions that are in the metastable levels causing them to repeat the same process. As each stimulating photon leads to the emission of two photons, the intensity of the light emitted will build up quickly. This cascade process in which photons emitted from excited chromium ions cause stimulated emission from other excited ion, will create a very intense and coherent red light beam of wavelengths 694.3 and 692.7 nm.

Laser Cooling Laser cooling utilizes the collective momentum of many photons to reduce the thermal motion of an atom. Since the approaching and recessing speed of the atoms differs slightly due to the Doppler effect and the atoms can only absorb a certain frequency, the laser beam can be tuned such that it slows down only the approaching atoms. The six crossed laser beams shown in Figure 13-10a create a space in which atoms moving in this region (the bright area in the center of the picture) are trapped and cooled by absorption of photons from the crossed beams. With this technique, researchers have already reached temperatures lower than a millionth of a degree Kelvin. That's an average atomic speed on the order of a few cm/sec.

Figure 13-10a Laser Cooling

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Plasma

Phases, the Three Fourth Phase In the solid state, the atoms are firmly imprisoned inside a rigid network (like ice for example). When we raise the temperature, they go into a liquid state (the ice melts), where the atoms may slide around in relation to the others, thus enabling a liquid to adapt to the shape of a container. If we heat it up even more, we arrive at the gas state: atoms then move around freely and independently of each other (water turns into steam). (See Figure 13-11.) Finally, when we get to very high temperatures (typically several million degrees), the ingredients of the atom separate, nuclei and electrons move around independently and form

Figure 13-11 The Three Phases
[view large image]

Figure 13-12 The Fourth
Phase [view large image]

a globally neutral mixture: this is the plasma state (See Figure 13-12).

This fourth state of matter, found in the stars and the interstellar environment, makes up most of our universe (around 99 %). On Earth, it does not exist in a natural form, apart in lightning and the Aurora Borealis. In our everyday life, plasmas have many applications (micro-electronics, television flat screens and so on), of which the commonest is the neon tube. (See Figure 13-13.)
Plasma Depending on the temperature, the atoms may be partially or wholly ionized. A plasma may thus be considered as a mixture of positively charged ions and negatively charged electrons, possibly co-existing with neutral atoms and molecules. For example, in our luminescent tube, the ions and electrons is a small proportion in relation to atoms and molecules. On the other hand, in plasmas produced for fusion experiments, the gas is strongly ionised, and the atoms and molecules are in low proportion, even completely absent in the heart of the pulse. In both cases, the description of plasmas comes from the physics of fluid mechanics and controlled by the force of electromagnetic interaction. The system is described by the usual macroscopic features such as density, temperature, pressure and rate of flow.

Figure 13-13 Plasma Occurrence

See "Application to Thermo-nuclear Fusion".

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Quantum Computing (see appendix)

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Footnotes

1Deuterium and tritium are the isotopes of hydrogen. While the hydrogen nucleus contains only 1 proton, the deuterium contains 1 proton and 1 neutron, and the tritium contains 1 proton and 2 neutrons.

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Index

Atomic mass
Atomic number
Band theory, metal
Bell state measurement
Bell states
Carbon
Conduction band
Cooper pair
Deuterium-tritium fuel
Einstein-Podolsky-Rosen (EPR) source
Entanglement
Fermi energy
Fourier series
Fusion
Glass
Instabilities
Insulator
Isotopes
Laser
Laser Cooling
Meisser effect
Metastable levels
Periodic table
Phonon
Plasma
Population inversion
Quantum computing
Quantum encryption
Quantum error correction
Qubits
Ruby laser
Semiconductor
Solid state
Specific Heats of Solids
Stimulation emission
Superconductivity
Superposition
Teleportation
Tokamak
Valence Band
Valence electrons
X-ray diffraction

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