Atoms

Contents

Periodic Table

		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".

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

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

The elements in the periodic table has been classified broadly into metals, non-metals and metalloids as discussed in Topic-12. The more refined classification is to categorize according to groups (in new designation from 1 to 18). A summary is given for each group here. It then follows with a table (attached to the main text as a "flap") listing the elements within. For Groups 3 - 12 only the more common elements are presented. The table is intended to supplement the conventional periodic table with information on electron orbitals, emission spectrum, some common chemical compounds, the application to nature and in our daily life. The pictures on orbitals and spectrum are taken from "The Elements, A Visual Exploration of Every Known Atom in the Universe" by Theodore Gray. The followings is a summary of the information in these tables:

		1. The atomic radius is not well defined as the electron density does not have a sharp boundary in quantum theory. Theoretical calculation defines it as the maximum radial density in the outermost shells. The result is shown in Figure 13-01d for most of the elements. Measured radii are added (within parenthses) for those with missing data. Experimental data are usually obtained by measuring the distance
Figure 13-01d Atomic Radii [view large image]	Figure 13-01e Subshell Energy Levels [view large image]	between two atoms (and then divided by 2). It is rather obvious that there are discrepancies in these two kinds of measurements. Figure 13-01e depicts the energy levels of the subshells and the outermost filling blocks (subshells) in the periodic table.


2. The general trends of the radii are decreasing size from Group 1 to Group 18 and the reverse from Period 1 to 7. Such phenomena are the results of three competing causes :
• Electron shells increase the radii down each period (column).
• Nuclear charge attracts the electrons to make the radii smaller along each column and row.
• Electron shielding by inner electrons reduces the effect of increasing nuclear charge.

3. Figure 13-01e shows the increase in energy (less binding) as more subshells are filled by electrons. Thus, the ionization energies (binding energy) are inversely proportion to the radii of the atoms (such relationship is exact for the Bohr model of the hydrogen atom). Consequently, most of the metallic elements are good electric and thermal conductors since they possess loosely bound outermost electrons to move up to the conduction band. Near the end of the d-block transition metals (Group 11 and 12), they all become excellent conductors as there are 10 valence electrons available for the conduction band. Some of the Group 13 to 17 elements is high in electronegativity - meaning that they rather accept electrons than donate them to the conduction band - and thus turn into metalloids or diatomic gases. The Group 18 elements of inert gases have fully occupied shells or subshells, they don't interact with other elements and not even to themselves. Thus they exist as monoatomic gases.

4. The emission spectrum of the elements is used to identify unknown substance. A crude and cheap method to detect metal ions is the flame test, which heats the sample on a loop of platinum wire moistened with hydrochloric acid (HCl) in a colorless flame. Figure 13-01f shows the color of the flame from sodium carbonate (Na₂CO₃) and copper sulfate (CuSO₄). The color of the flame is determined by the dominant emission line of the metallic element. However, the color is only a

		qualitative indicator, since many different metals may emit similar color. A more reliable method is the spectroscope shown in Figure 13-01g. The source is in the form of low pressure gas inside a discharge tube . A slit or two is used to collimate the light into parallel beam (for a sharp image). The different emission lines are separated by a prism. It is widely used in
Figure 13-01f Flame Test	Figure 13-01g Spectroscope [view large image]	science and engineering. For example, the emission spectrum of the quasar 3C273 looks suspiciously like the Balmer series spectrum of the hydrogen atom but the wavelength of each

		line is not the same as the one shown in Figure 13-01h taken in the laboratory. It turns out that the ratios of the wavelengths are identical, the lines has been red shifted by a factor of (1 + z), where z is the amount of redshift, as the quasar
Figure 13-01h Hydrogen Emission Spectrum [view large image]	Figure 13-01i 3C273 Emission Spectrum [view large image]	is recessing from us in the cosmic expansion (Figure 13-01i).

5. The quantum theory of hydrogen atom has related the energy levels of the electron to the wavelength of the emission lines in well organized series. Most of the other elements produce randomly distributed emission lines since the displacement of just one electron opening up numerous ways the other electron(s) can jump from one energy level to another. The group 13 elements and a few others seem to be the exception. They appear to be hydrogen-like with one

Figure 13-01j Orbitals and Spectrum [view large image]

outer electron moving around a core. Figure 13-01j illustrates a few of the possible ways the electrons can move around generating a number of emission lines after an electron at the core has been excited to higher energy level.




• Group 1 elements (known as alkali metals) are silvery colored, soft, low density metals, which react readily with halogens to form ionic salts, and with water to form strongly alkaline (basic) hydroxides. These elements all have one electron in their outermost shell, so the energetically preferred state of achieving a filled electron shell is to lose one electron to form a singly charged positive ion. Their softness and ractivity increase down the group. Lithium is a soft metal (see Figure 13-02a) with such low density that it floats in water. It reacts vigorously with water to produce hydrogen gas, and with oxygen to form

Li2O, such that it is never found in its free state in nature. Hydrogen (water creator in Greek), with a solitary electron, nominally belongs in the alkali metals group. However, removal of that single electron requires considerably more energy than for the other alkali metals. Like the halogens, only one additional electron is required to fill in the outermost shell of the hydrogen atom, so hydrogen can be regarded in some respects as behaving like a halogen; its elemental form is a diatomic gas, and it can even form salts (called hydrides) with the alkali metals, where the metal has donated an electron to the hydrogen, almost as if hydrogen were actually a halogen.

Figure 13-02a Lithium

See more in Group 01 Elements.



Group 2 elements have one more electron in their outer shells than group 1 elements. Although they are reactive, the extra electron makes them less reactive than group 1 elements. The reactivity of these elements increases down the group. They are found in compounds, which form important rocks in the Earth's crust. This gives rise to the group's alternative name, the "alkaline earth" metals. The emerald (Be3(Al,Cr)2Si6O18) is the green variety of beryl (see Figure 13-02b), the mineral that is the principal source of beryllium.

Figure 13-02b Beryl

See more in Group 02 Elements.


• Group 3 -12 are the transition elements, which are usually hard, tough and shiny. They are less reactive and have greater

  densities than group 1 or 2 elements. Group 11 includes the traditional coinage metals such as copper, silver, and gold (see Figure 13-02c). They are also known as the "noble metals". They are all relatively inert, hard-to-corrode metals which have been used for minting coins, hence their name. Many metals form coloured compounds, (e.g., iron pyrite), and many metals have a coloured sheen. These metals, especially silver, have unusual properties that make them essential for industrial applications outside of their monetary or decorative value. They are all excellent conductors of electricity. The most conductive of all metals are silver, copper and gold in that order. Silver is the most

  Figure 13-02c Gold

  thermally conductive element, and is also the most light reflecting element. Silver also has the unusual property that the tarnish on the surface is still highly electrically conductive.

  See more in Groups 03-12 Elements.
  
  
• Group 13 elements are called light metals. Boron is a hard, brittle, non-metallic element. It is found in nature usually in combination with oxygen. The compound boric oxide is important in making heat-resistant glass. Boric acid is commonly used as eyewash and antiseptic. The compound borax (boron combined with oxygen, water, and sodium) is

useful as a cleaning agent and water softener. Aluminum, which is right beneath boron, is by its position a metalloid. But the properties of aluminum are usually those of metals. Aluminum is the most abundant metal and the third most abundant element in the earth's crust. Aluminum is found as aluminum oxide in the ore called bauxite. Aluminum is extremely valuable in industry (see Figure 13-02d). It is light, strong, and does not tarnish in air. It is a good conductor and is used in wiring, airplane parts, household items. The other members of the boron family ...gallium, indium, and thallium, are metals. Gallium shares many chemical properties with aluminum. It is an extremely soft metal that can be cut with a knife. It also has an extremely low melting point of 29.8oC. Gallium

Figure 13-02d Aluminum

arsenide (GaAs) can function as a "laser diode" and convert electricity directly into a beam of laser light.

See more in group 13 Elements.


• Group 14 is the carbon family. It includes the elements carbon, silicon, germanium, tin, and lead. Carbon can combine with other elements in a great variety of ways - in millions of carbon compounds called "organic compounds", which form the basis for life. Carbon exists in its free state in several different forms. The most spectacular of these forms is diamond, the hardest of materials (see Figure 13-02e1). In the form of graphite, the carbon atoms arrange themselves in layer, like the pages of a book. Because the forces between them are not very strong, the layers slide easily over one another, making graphite soft and slippery. It is useful as a lubricant and as a writing material in pencils. Silicon is the second most abundant element in the earth's crust. Silicon is used in glass and in cement. Glass is produced by

		mixing silica (sand - SiO2), soda ash (sodium carbonate - Na2CO3) and limestone (calcium carbonate - CaCO3) in a ratio of 60:80:5 and heated to the melting point of 2500oF. The final product is a supercooled liquid called glass which can be made to be colourful or to have special property by adding impurities (see Figure 13-02e2). Silicon is also used in solar cells, which convert the energy of sunlight into electric energy. Germanium is a metalloid used in transistors, which are devices found in many electronic instruments, such as radios and
Figure 13-02e1 Carbon [view large image]	Figure 13-02e2 Glass	televisions. Tin is a metal which resists rusting and corrosion. The most dense element in the carbon family is the metal lead (Pb), which can form poisonous compounds.

See more in group 14 Elements.


• Group 15 is the nitrogen family. This group is sometimes referred to as pnictogens (choke generator in Greek as nitrogen was discovered in 1772 by demonstrating that it can asphyxiate a mouse). It consists of nitrogen, phosphorus, arsenic, antimony, and bismuth. Although a relatively unreactive gas, nitrogen forms hundreds of thousands of compounds that are of crucial importance for agriculture and industry. Considering the stability of nitrogen itself, some of these compounds are, ironically, extremely unstable and explosive. Despite the lack of reactivity of nitrogen, nature has developed several mechanisms (such as lightning) for converting nitrogen for use by living cells. The process of converting nitrogen from the atmosphere into usable nitrogen compounds is called nitrogen "fixing". Phosphorus (bearer of light in Greek) is a non-metal that glows in dark and bursts into flames in warm air (see Figure 13-02f). It is used in

the military to make incendiary bomb. Arsenic is a brittle, crystalline solid at room temperature. It is often thought of as a semi-metal, or metalloid. For example, it is a poor conductor of electricity, yet it has a steel-gray color. In the form of arsenious oxide, it is a well-known poison. It is used as a weed killer and insecticide. Arsenic has become a material of great importance in the world of solid-state electronics. Small amounts of arsenic are added to such semi-conductors as germanium and silicon to transform them into transistors.

Figure 13-02f Phosphorus

See more in group 15 Elements.


• Group 16 consists of the elements Oxygen (O), Sulfur (S), Selenium (Se), Tellurium (Te), and the radioactive Polonium (Po). Their compounds, particularly the sulfides, selenides and tellurides are collectively known as chalcogenides. The

name is generally considered to mean "ore former" (from the Greek chalcos "ore" and -gen "formation"). Oxygen and sulfur (see Figure 13-02g) are nonmetals, polonium is a true metal, and selenium and tellurium are metalloid semiconductors (i.e., their electrical properties are between those of a metal and an insulator). Nevertheless, tellurium, as well as selenium, is often referred to as a metal when in elemental form. Chalcogenides are quite common as minerals, e.g., FeS2 pyrite is an iron ore and AuTe2 gave its name to the gold rush town of Telluride, Colorado in the USA. The oxidation number of the chalcogen is generally -2 in a chalcogenide but other values (e.g. -1 in pyrite) can be attained. The highest oxidation number +6 is found in sulfates, selenates and tellurates, e.g., in Na2SeO4 - sodium selenate.

Figure 13-02g Sulfur

See more in group 16 Elements.


• Group 17 elements are known as the halogens (salt creator). These elements are diatomic molecules in their natural form. They require one more electron to fill their outer electron shells, and so have a tendency to form a singly-charged negative ion. This negative ion is referred to as a halide ion, which tend to form ionic compounds with metals. Salts containing these ions are known as halides. Halogens form covalent compounds with non-metals. Examples include

  most carbon-containing, or organohalogen, molecules. Organohalogen chemicals (such as DDT, PCB, CFC, ...) are often believed to be solely industrial compounds, but many living organisms and geological phenomena also produce them naturally. In the case of plants and animls (such as sponges, corals, seaweeds, evergreen trees, some arthropods, and some frogs), the substance is produced for defence against predators and parasites. The halogens become less reactive, and their melting points increase further down the group. For example, fluorine is a yellow gas at room temperature, whereas bromine is a liquid, and iodine is a black solid (see Figure 13-02h).

  Figure 13-

  02h Iodine

  See more in group 17 Elements.
  
  

  Group 18 contains the noble or inert gases. Their outer electron shells are full, which makes it difficult for them to gain or lose electrons. They are therefore almost totally unreactive and non-flammable. The neon signs contain neon gas that glows in orange-red color (see Figure 13-02i) when it is energized by an electrical discharge. Every gas, when excited, radiates its own characteristic color. Argon, for example, produces a purple light, while xenon produces a blue-green light.

  Figure 13-02i Neon

  See more in group 18 Elements.
  
  

		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).

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.

Band Theory, Metal

		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]

Solid State

		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.

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 (C_v = U/T) etc.
4. Transport - Measure the gradient of heat or electrical current to determine the thermal or electrical conductivity.

Table 13-02 Some Macroscopic Properties of Solid

X-ray Diffraction

		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

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]

4. 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).



5. 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

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]

Specific Heats of Solids and Phonons

		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]

Superconductivity

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

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.

		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

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).

		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

Laser

		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]

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

Plasma

		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).

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

Quantum Computing (see appendix)

Footnotes

References:

• Periodic Table -- http://chemserv.bc.edu/web-elements/
• Band Theory -- http://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html
• Band Theory, Metal -- http://www.owlnet.rice.edu/~chem152/lecture/Reading/bands.html
• Superconductivity -- http://www.physics.carleton.ca/courses/75.364/mp-2html/node16.html
• Laser -- http://www.hk-phy.org/articles/laser/laser_e.html
• Plasma Physics -- http://www.fys.uio.no/plasma/english/texts/plsmgenintro/plsmgenintro.html
• Quantum Computing, Centre for Quantum Computation -- http://www.qubit.org/

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