Cross Pollination Works

"You really never know where your next great idea is going to come from."

Michelle Borkin of Harvard University combines astronomy and medical imaging to advance both fields and proves that interdisciplinary collaboration helps people develop great ideas otherwise undiscovered  . . . and save lives along the way.

The Nobel Prize in Physics 1914 Max von Laue

Laue diagram of a crystal  See: Experimental diffraction

The Laue method in transmission mode

The Laue method in reflection mode

There are two different geometries in the Laue method, depending on the crystal position with regard to the photographic plate: transmission or reflection.

Concerning the Detection of X-ray Interferences

***

Max Theodor Felix von Laue (9 October 1879 – 24 April 1960) was a Germanphysicist who won the Nobel Prize in Physics in 1914 for his discovery of the diffraction of X-rays by crystals. In addition to his scientific endeavors with contributions in optics, crystallography, quantum theory, superconductivity, and the theory of relativity, he had a number of administrative positions which advanced and guided German scientific research and development during four decades. A strong objector to National Socialism, he was instrumental in re-establishing and organizing German science after World War II.

Max von Laue
Laue in 1929

Contents   1 Biography 1.1 Early years 1.2 Career 1.2.1 Opposition to Nazism 1.2.2 Hidden Nobel prize 1.2.3 Post-war 1.3 Personal life 2 Organizations 3 Honours and awards 4 See also 5 Publications 6 Selected literature 7 Bibliography 8 References 9 External links

See:

• Quasicrystal: Prof. Dan Shechtman

Also See:

• Physical geodesy: A Condensative Result

• Quasicrystal and Information
  
  

The Belle B Factory Experiment

Existing standard hadrons and exotic hadrons. At the B Factory experiment, a series of new exotic mesons containing charm quarks (c) have been discovered. Unlike these exotic mesons, the newly discovered Z_b particles contain bottom quarks (b) and have an electric charge. If only one bottom quark and one anti-bottom quark ( b ) are contained, the resulting particle is electrically neutral. Thus, the Z_b must also contain at least two more quarks (e.g., one up quark (u) and one anti-down quark ( d )).

The Belle B Factory experiment, which began in 1999 with the aim of elucidating the origin of particle-anti-particle symmetry breaking (CP violation), has contributed to the Nobel Prize in Physics in 2008 awarded to Drs. Kobayashi and Maskawa. Moreover, data obtained from electron--positron collisions with the world's highest luminosity achieved at the KEKB accelerator have resulted in a series of unexpected discoveries of exotic hadrons, opening a new research frontier in particle physics. Data taking at the Belle Experiment has already been completed, but a vast amount of data is still awaiting detailed analysis. Moreover, an upgraded version of the KEKB/Belle Experiment, called SuperKEKB/Belle II is currently being prepared. Belle II aims to collect 50 times more data than the earlier experiment......... See: Belle Discovers New Heavy 'Exotic Hadrons'

Also See:

•  Belle Discovers New Heavy ‘Exotic Hadrons’

• Belle experiment makes exotic discovery

 ***

The Belle experiment is a particle physics experiment conducted by the Belle Collaboration, an international collaboration of more than 400 physicists and engineers investigating CP-violation effects at the High Energy Accelerator Research Organisation (KEK) in Tsukuba, Ibaraki Prefecture, Japan

The Belle detector, located at the collision point of the e−e+ asymmetric-energy collider (KEKB), is a multilayer particle detector. Its large solid angle coverage, vertex location with precision on the order of tens of micrometres (provided by a silicon vertex detector), good pion–kaon separation at the momenta range from 100 MeV/c till few GeV/c (provided by a novel Cherenkov detector), and few-percent precision electromagnetic calorimetry (CsI(Tl) scintillating crystals) allow for many other scientific searches apart from CP-violation. Extensive studies of rare decays, searches for exotic particles and precision measurements of B mesons, D mesons, and tau particles have been carried out and have resulted in almost 300 publications in physics journals.

Highlights of the Belle experiment so far include

• the first observation of CP-violation outside of the kaon system (2001)
• observation of: and
• measurement of ϕ₃ using the Dalitz plot
• measurement of the CKM quark mixing matrix elements | V_ub | and | V_cb |
• observation of direct CP-violation in and
• observation of transitions
• evidence for
• observations of a number of new particles including the X(3872)

The Belle experiment operated at the KEKB accelerator, the world's highest luminosity machine. The instantaneous luminosity exceeded 2.11×10³⁴ cm⁻²·s⁻¹. The integrated luminosity collected at the ?(4S) resonance mass is ~710 fb⁻¹ (corresponds to 771 million BB meson pairs). Most data is recorded on the ?(4S) resonance, which decays to pairs of B mesons. About 10% of the data is recorded below the ?(4S) resonance in order to study backgrounds. In addition, Belle has carried out special short runs at the ?(5S) resonance to study B
s mesons as well as on the ?(3S) resonance to search for evidence of Dark Matter and the Higgs Boson.

The Belle II B-factory, an upgraded facility with two orders of magnitude more luminosity, has been approved in June 2010.^[1] The design and construction work is ongoing.

 See also

• B-factory
• B–B oscillation

 External links

• Official Belle Website

 References

1. ^ KEK press release

Loci: A Gallery of Ray Tracing for Geometers

The crystalline state is the simplest known example of a quantum , a stable state of matter whose generic low-energy properties are determined by a higher organizing principle and nothing else. Robert Laughlin

Figure 10 with linked animation: Five-fold rotational symmetry of the dodecahedron

Modern expositors of mathematics, with computers and open source ray tracing software at their disposal, have the tools necessary to create vivid and effective geometric constructions in 3-space. With a little additional effort, animations can be generated, adding the fourth dimension of time. The web provides a viable medium for enhancing mathematical presentations with photo-realistic graphics and video. A Gallery of Ray Tracing for Geometers

See Also: Creating Photo-realistic Images and Animations

A Walk Through Dimensions

Control the Medium, You Control the Product?

The historical record, as I’ve also argued, is also quite unequivocal on the folly of allowing those who own the medium to control the message See: The Vertical Integration Elephant in the Room

 For differing points of view some might have a take on the process unfolding in our society today as a sign of the way things have always gone? Do you feel the same?

A Thomas Nast cartoon shortly after the Supreme Court affirmed Alexander Graham Bell's patents (library of congress)

Strike!

At least seven major cities adopted measured service in the 1880s: Boston; San Francisco; Buffalo; Pittsburgh; Indianapolis; Washington, DC; and Rochester, New York. The policy had a pro-consumer aspect; it expanded the market of any local exchange carrier to people who didn't want to pay a big monthly service fee, thus extending the circle of individuals any rate payer could call.

But while measured service initially succeeded in San Francisco and Buffalo, it failed everywhere else throughout the decade. Consumers could not shake the suspicion that its real purpose was to get them to pay more money to the telephone company. And so they resorted to what we would call boycotts and they called "strikes" to make their dissatisfaction known.

"The term 'strike' has come to be associated primarily with a work stoppage," John notes, but "in the 1880s its meaning was broader. A corporation could be struck not only by workers, but also by consumers and even lawmakers."

As early as 1881, for example, Washington, DC's "Telephone Subscribers Protective Association" launched a boycott of its exchange when the company adopted measured billing. It wasn't very long affair, just twelve days. But 300 out of the city's 700 phone subscribers participated. That was all it took for the firm to surrender and bring back flat rates. See: Mad about metered billing? They were in 1886, too

Crystal Structure

In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry. Patterns are located upon the points of a lattice, which is an array of points repeating periodically in three dimensions. The points can be thought of as forming identical tiny boxes, called unit cells, that fill the space of the lattice. The lengths of the edges of a unit cell and the angles between them are called the lattice parameters. The symmetry properties of the crystal are embodied in its space group.

A crystal's structure and symmetry play a role in determining many of its physical properties, such as cleavage, electronic band structure, and optical transparency.

Insulin crystals.

Contents  1 Unit cell 1.1 Miller indices 1.2 Planes and directions 1.2.1 Cubic structures 2 Classification 2.1 Lattice systems 2.2 Atomic coordination 2.2.1 Close packing 2.3 Bravais lattices 2.4 Point groups 2.5 Space groups 3 Grain boundaries 4 Defects and impurities 5 Prediction of structure 6 Polymorphism 7 Physical properties 8 See also 9 References 10 External links

Unit cell

 

The crystal structure of a material or the arrangement of atoms within a given type of crystal structure can be described in terms of its unit cell. The unit cell is a small box containing one or more atoms, a spatial arrangement of atoms. The unit cells stacked in three-dimensional space describe the bulk arrangement of atoms of the crystal. The crystal structure has a three-dimensional shape. The unit cell is given by its lattice parameters, which are the length of the cell edges and the angles between them, while the positions of the atoms inside the unit cell are described by the set of atomic positions (x_i  , y_i  , z_i) measured from a lattice point.

• 

  Simple cubic (P)
• 

  Body-centered cubic (I)
• 

  Face-centered cubic (F)

 Miller indices

 

Main article: Miller index

Planes with different Miller indices in cubic crystals

Vectors and atomic planes in a crystal lattice can be described by a three-value Miller index notation (ℓmn). The ℓ, m, and n directional indices are separated by 90°, and are thus orthogonal. In fact, the ℓ component is mutually perpendicular to the m and n indices.

By definition, (ℓmn) denotes a plane that intercepts the three points a₁/ℓ, a₂/m, and a₃/n, or some multiple thereof. That is, the Miller indices are proportional to the inverses of the intercepts of the plane with the unit cell (in the basis of the lattice vectors). If one or more of the indices is zero, it simply means that the planes do not intersect that axis (i.e., the intercept is "at infinity").

Considering only (ℓmn) planes intersecting one or more lattice points (the lattice planes), the perpendicular distance d between adjacent lattice planes is related to the (shortest) reciprocal lattice vector orthogonal to the planes by the formula:

 

Planes and directions

 

The crystallographic directions are fictitious lines linking nodes (atoms, ions or molecules) of a crystal. Likewise, the crystallographic planes are fictitious planes linking nodes. Some directions and planes have a higher density of nodes. These high density planes have an influence on the behavior of the crystal as follows:

• Optical properties: Refractive index is directly related to density (or periodic density fluctuations).

• Adsorption and reactivity: Physical adsorption and chemical reactions occur at or near surface atoms or molecules. These phenomena are thus sensitive to the density of nodes.

• Surface tension: The condensation of a material means that the atoms, ions or molecules are more stable if they are surrounded by other similar species. The surface tension of an interface thus varies according to the density on the surface.
•  

Dense crystallographic planes

• Microstructural defects: Pores and crystallites tend to have straight grain boundaries following higher density planes.

• Cleavage: This typically occurs preferentially parallel to higher density planes.

• Plastic deformation: Dislocation glide occurs preferentially parallel to higher density planes. The perturbation carried by the dislocation (Burgers vector) is along a dense direction. The shift of one node in a more dense direction requires a lesser distortion of the crystal lattice.

In the rhombohedral, hexagonal, and tetragonal systems, the basal plane is the plane perpendicular to the principal axis.

Cubic structures

 

For the special case of simple cubic crystals, the lattice vectors are orthogonal and of equal length (usually denoted a); similarly for the reciprocal lattice. So, in this common case, the Miller indices (ℓmn) and [ℓmn] both simply denote normals/directions in Cartesian coordinates. For cubic crystals with lattice constant a, the spacing d between adjacent (ℓmn) lattice planes is (from above):






Because of the symmetry of cubic crystals, it is possible to change the place and sign of the integers and have equivalent directions and planes:

• Coordinates in angle brackets such as <100> denote a family of directions that are equivalent due to symmetry operations, such as [100], [010], [001] or the negative of any of those directions.

• Coordinates in curly brackets or braces such as {100} denote a family of plane normals that are equivalent due to symmetry operations, much the way angle brackets denote a family of directions.

For face-centered cubic (fcc) and body-centered cubic (bcc) lattices, the primitive lattice vectors are not orthogonal. However, in these cases the Miller indices are conventionally defined relative to the lattice vectors of the cubic supercell and hence are again simply the Cartesian directions.

 Classification

 

The defining property of a crystal is its inherent symmetry, by which we mean that under certain 'operations' the crystal remains unchanged. For example, rotating the crystal 180° about a certain axis may result in an atomic configuration that is identical to the original configuration. The crystal is then said to have a twofold rotational symmetry about this axis. In addition to rotational symmetries like this, a crystal may have symmetries in the form of mirror planes and translational symmetries, and also the so-called "compound symmetries," which are a combination of translation and rotation/mirror symmetries. A full classification of a crystal is achieved when all of these inherent symmetries of the crystal are identified.^[1]

Lattice systems

 

These lattice systems are a grouping of crystal structures according to the axial system used to describe their lattice. Each lattice system consists of a set of three axes in a particular geometrical arrangement. There are seven lattice systems. They are similar to but not quite the same as the seven crystal systems and the six crystal families.

The 7 lattice systems (From least to most symmetric)	The 14 Bravais Lattices				Examples
1. triclinic (none)
2. monoclinic (1 diad)	simple	base-centered
3. orthorhombic (3 perpendicular diads)	simple	base-centered	body-centered	face-centered
4. rhombohedral (1 triad)
5. tetragonal (1 tetrad)	simple	body-centered
6. hexagonal (1 hexad)
7. cubic (4 triads)	simple (SC)	body-centered (bcc)	face-centered (fcc)

The simplest and most symmetric, the cubic (or isometric) system, has the symmetry of a cube, that is, it exhibits four threefold rotational axes oriented at 109.5° (the tetrahedral angle) with respect to each other. These threefold axes lie along the body diagonals of the cube. The other six lattice systems, are hexagonal, tetragonal, rhombohedral (often confused with the trigonal crystal system), orthorhombic, monoclinic and triclinic.

 

 Atomic coordination

By considering the arrangement of atoms relative to each other, their coordination numbers (or number of nearest neighbors), interatomic distances, types of bonding, etc., it is possible to form a general view of the structures and alternative ways of visualizing then.

HCP lattice (left) and the fcc lattice (right).

 Close packing

 

The principles involved can be understood by considering the most efficient way of packing together equal-sized spheres and stacking close-packed atomic planes in three dimensions. For example, if plane A lies beneath plane B, there are two possible ways of placing an additional atom on top of layer B. If an additional layer was placed directly over plane A, this would give rise to the following series :




...ABABABAB....  This type of crystal structure is known as hexagonal close packing (hcp).

If however, all three planes are staggered relative to each other and it is not until the fourth layer is positioned directly over plane A that the sequence is repeated, then the following sequence arises:



...ABCABCABC...  This type of crystal structure is known as cubic close packing (ccp)


The unit cell of the ccp arrangement is the face-centered cubic (fcc) unit cell. This is not immediately obvious as the closely packed layers are parallel to the {111} planes of the fcc unit cell. There are four different orientations of the close-packed layers.

The packing efficiency could be worked out by calculating the total volume of the spheres and dividing that by the volume of the cell as follows:






The 74% packing efficiency is the maximum density possible in unit cells constructed of spheres of only one size. Most crystalline forms of metallic elements are hcp, fcc, or bcc (body-centered cubic). The coordination number of hcp and fcc is 12 and its atomic packing factor (APF) is the number mentioned above, 0.74. The APF of bcc is 0.68 for comparison.

 Bravais lattices

 

When the crystal systems are combined with the various possible lattice centerings, we arrive at the Bravais lattices. They describe the geometric arrangement of the lattice points, and thereby the translational symmetry of the crystal. In three dimensions, there are 14 unique Bravais lattices that are distinct from one another in the translational symmetry they contain. All crystalline materials recognized until now (not including quasicrystals) fit in one of these arrangements. The fourteen three-dimensional lattices, classified by crystal system, are shown above. The Bravais lattices are sometimes referred to as space lattices.

The crystal structure consists of the same group of atoms, the basis, positioned around each and every lattice point. This group of atoms therefore repeats indefinitely in three dimensions according to the arrangement of one of the 14 Bravais lattices. The characteristic rotation and mirror symmetries of the group of atoms, or unit cell, is described by its crystallographic point group.

Point groups

The crystallographic point group or crystal class is the mathematical group comprising the symmetry operations that leave at least one point unmoved and that leave the appearance of the crystal structure unchanged. These symmetry operations include

• Reflection, which reflects the structure across a reflection plane
• Rotation, which rotates the structure a specified portion of a circle about a rotation axis
• Inversion, which changes the sign of the coordinate of each point with respect to a center of symmetry or inversion point
• Improper rotation, which consists of a rotation about an axis followed by an inversion.

Rotation axes (proper and improper), reflection planes, and centers of symmetry are collectively called symmetry elements. There are 32 possible crystal classes. Each one can be classified into one of the seven crystal systems.

 Space groups

 

The space group of the crystal structure is composed of the translational symmetry operations in addition to the operations of the point group. These include:

• Pure translations, which move a point along a vector
• Screw axes, which rotate a point around an axis while translating parallel to the axis
• Glide planes, which reflect a point through a plane while translating it parallel to the plane.

There are 230 distinct space groups.

Grain boundaries

 

Grain boundaries are interfaces where crystals of different orientations meet. A grain boundary is a single-phase interface, with crystals on each side of the boundary being identical except in orientation. The term "crystallite boundary" is sometimes, though rarely, used. Grain boundary areas contain those atoms that have been perturbed from their original lattice sites, dislocations, and impurities that have migrated to the lower energy grain boundary.

Treating a grain boundary geometrically as an interface of a single crystal cut into two parts, one of which is rotated, we see that there are five variables required to define a grain boundary. The first two numbers come from the unit vector that specifies a rotation axis. The third number designates the angle of rotation of the grain. The final two numbers specify the plane of the grain boundary (or a unit vector that is normal to this plane).

Grain boundaries disrupt the motion of dislocations through a material, so reducing crystallite size is a common way to improve strength, as described by the Hall–Petch relationship. Since grain boundaries are defects in the crystal structure they tend to decrease the electrical and thermal conductivity of the material. The high interfacial energy and relatively weak bonding in most grain boundaries often makes them preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. They are also important to many of the mechanisms of creep.

Grain boundaries are in general only a few nanometers wide. In common materials, crystallites are large enough that grain boundaries account for a small fraction of the material. However, very small grain sizes are achievable. In nanocrystalline solids, grain boundaries become a significant volume fraction of the material, with profound effects on such properties as diffusion and plasticity. In the limit of small crystallites, as the volume fraction of grain boundaries approaches 100%, the material ceases to have any crystalline character, and thus becomes an amorphous solid.

Defects and impurities

 

Real crystals feature defects or irregularities in the ideal arrangements described above and it is these defects that critically determine many of the electrical and mechanical properties of real materials. When one atom substitutes for one of the principal atomic components within the crystal structure, alteration in the electrical and thermal properties of the material may ensue.^[2] Impurities may also manifest as spin impurities in certain materials. Research on magnetic impurities demonstrates that substantial alteration of certain properties such as specific heat may be affected by small concentrations of an impurity, as for example impurities in semiconducting ferromagnetic alloys may lead to different properties as first predicted in the late 1960s.^[3][4] Dislocations in the crystal lattice allow shear at lower stress than that needed for a perfect crystal structure.^[5]

Prediction of structure

 

Main article: Crystal structure prediction

Crystal structure of sodium chloride (table salt)

The difficulty of predicting stable crystal structures based on the knowledge of only the chemical composition has long been a stumbling block on the way to fully computational materials design. Now, with more powerful algorithms and high-performance computing, structures of medium complexity can be predicted using such approaches as evolutionary algorithms, random sampling, or metadynamics.

The crystal structures of simple ionic solids (e.g., NaCl or table salt) have long been rationalized in terms of Pauling's rules, first set out in 1929 by Linus Pauling, referred to by many since as the "father of the chemical bond".^[6] Pauling also considered the nature of the interatomic forces in metals, and concluded that about half of the five d-orbitals in the transition metals are involved in bonding, with the remaining nonbonding d-orbitals being responsible for the magnetic properties. He, therefore, was able to correlate the number of d-orbitals in bond formation with the bond length as well as many of the physical properties of the substance. He subsequently introduced the metallic orbital, an extra orbital necessary to permit uninhibited resonance of valence bonds among various electronic structures.^[7]

In the resonating valence bond theory, the factors that determine the choice of one from among alternative crystal structures of a metal or intermetallic compound revolve around the energy of resonance of bonds among interatomic positions. It is clear that some modes of resonance would make larger contributions (be more mechanically stable than others), and that in particular a simple ratio of number of bonds to number of positions would be exceptional. The resulting principle is that a special stability is associated with the simplest ratios or "bond numbers": 1/2, 1/3, 2/3, 1/4, 3/4, etc. The choice of structure and the value of the axial ratio (which determines the relative bond lengths) are thus a result of the effort of an atom to use its valency in the formation of stable bonds with simple fractional bond numbers.^[8][9]

After postulating a direct correlation between electron concentration and crystal structure in beta-phase alloys, Hume-Rothery analyzed the trends in melting points, compressibilities and bond lengths as a function of group number in the periodic table in order to establish a system of valencies of the transition elements in the metallic state. This treatment thus emphasized the increasing bond strength as a function of group number.^[10] The operation of directional forces were emphasized in one article on the relation between bond hybrids and the metallic structures. The resulting correlation between electronic and crystalline structures is summarized by a single parameter, the weight of the d-electrons per hybridized metallic orbital. The “d-weight” calculates out to 0.5, 0.7 and 0.9 for the fcc, hcp and bcc structures respectively. The relationship between d-electrons and crystal structure thus becomes apparent.^[11]

Polymorphism

 

Quartz is one of the several thermodynamically stable crystalline forms of silica, SiO₂. The most important forms of silica include: α-quartz, β-quartz, tridymite, cristobalite, coesite, and stishovite.

Polymorphism refers to the ability of a solid to exist in more than one crystalline form or structure. According to Gibbs' rules of phase equilibria, these unique crystalline phases will be dependent on intensive variables such as pressure and temperature. Polymorphism can potentially be found in many crystalline materials including polymers, minerals, and metals, and is related to allotropy, which refers to elemental solids. The complete morphology of a material is described by polymorphism and other variables such as crystal habit, amorphous fraction or crystallographic defects. Polymorphs have different stabilities and may spontaneously convert from a metastable form (or thermodynamically unstable form) to the stable form at a particular temperature. They also exhibit different melting points, solubilities, and X-ray diffraction patterns.

One good example of this is the quartz form of silicon dioxide, or SiO₂. In the vast majority of silicates, the Si atom shows tetrahedral coordination by 4 oxygens. All but one of the crystalline forms involve tetrahedral SiO₄ units linked together by shared vertices in different arrangements. In different minerals the tetrahedra show different degrees of networking and polymerization. For example, they occur singly, joined together in pairs, in larger finite clusters including rings, in chains, double chains, sheets, and three-dimensional frameworks. The minerals are classified into groups based on these structures. In each of its 7 thermodynamically stable crystalline forms or polymorphs of crystalline quartz, only 2 out of 4 of each the edges of the SiO₄ tetrahedra are shared with others, yielding the net chemical formula for silica: SiO₂.
Another example is elemental tin (Sn), which is malleable near ambient temperatures but is brittle when cooled. This change in mechanical properties due to existence of its two major allotropes, α- and β-tin. The two allotropes that are encountered at normal pressure and temperature, α-tin and β-tin, are more commonly known as gray tin and white tin respectively. Two more allotropes, γ and σ, exist at temperatures above 161 °C and pressures above several GPa.^[12] White tin is metallic, and is the stable crystalline form at or above room temperature. Below 13.2 °C, tin exists in the gray form, which has a diamond cubic crystal structure, similar to diamond, silicon or germanium. Gray tin has no metallic properties at all, is a dull-gray powdery material, and has few uses, other than a few specialized semiconductor applications.^[13] Although the α-β transformation temperature of tin is nominally 13.2 °C, impurities (e.g. Al, Zn, etc.) lower the transition temperature well below 0 °C, and upon addition of Sb or Bi the transformation may not occur at all.^[14]

Physical properties

 

Twenty of the 32 crystal classes are so-called piezoelectric, and crystals belonging to one of these classes (point groups) display piezoelectricity. All piezoelectric classes lack a centre of symmetry. Any material develops a dielectric polarization when an electric field is applied, but a substance that has such a natural charge separation even in the absence of a field is called a polar material. Whether or not a material is polar is determined solely by its crystal structure. Only 10 of the 32 point groups are polar. All polar crystals are pyroelectric, so the 10 polar crystal classes are sometimes referred to as the pyroelectric classes.

There are a few crystal structures, notably the perovskite structure, which exhibit ferroelectric behavior. This is analogous to ferromagnetism, in that, in the absence of an electric field during production, the ferroelectric crystal does not exhibit a polarization. Upon the application of an electric field of sufficient magnitude, the crystal becomes permanently polarized. This polarization can be reversed by a sufficiently large counter-charge, in the same way that a ferromagnet can be reversed. However, it is important to note that, although they are called ferroelectrics, the effect is due to the crystal structure (not the presence of a ferrous metal).

See also

 

For more detailed information in specific technology applications see Materials science, Ceramic engineering, or Metallurgy.

• Bravais lattice
• Brillouin zone
• Cleavage (crystal)
• Crystal
• Crystal engineering
• Crystal growth
• Crystal system
• Crystallographic database
• Crystallographic defect
• Crystallographic point group
• Crystallography
• Fractional coordinates
• Hermann–Mauguin notation
• Laser-heated pedestal growth
• Lattice constant
• Liquid crystal
• Miller index
• Patterson function
• Quasicrystals
• Schoenflies notation
• Seed crystal
• Solid
• Wigner–Seitz cell

 

References

 

1. ^ Ashcroft, N.; Mermin, D. (1976) Solid State Physics, Brooks/Cole (Thomson Learning, Inc.), Chapter 7, ISBN 0030493463
2. ^ Nikola Kallay (2000) Interfacial Dynamics, CRC Press, ISBN 0824700066
3. ^ Hogan, C. M. (1969). "Density of States of an Insulating Ferromagnetic Alloy". Physical Review 188 (2): 870. Bibcode 1969PhRv..188..870H. doi:10.1103/PhysRev.188.870.
4. ^ Zhang, X. Y.; Suhl, H (1985). "Spin-wave-related period doublings and chaos under transverse pumping". Physical Review a 32 (4): 2530–2533. Bibcode 1985PhRvA..32.2530Z. doi:10.1103/PhysRevA.32.2530. PMID 9896377.
5. ^ Courtney, Thomas (2000). Mechanical Behavior of Materials. Long Grove, IL: Waveland Press. pp. 85. ISBN 1-57766-425-6.
6. ^ L. Pauling (1929). "The principles determining the structure of complex ionic crystals". J. Am. Chem. Soc. 51 (4): 1010–1026. doi:10.1021/ja01379a006.
7. ^ Pauling, Linus (1938). "The Nature of the Interatomic Forces in Metals". Physical Review 54 (11): 899. Bibcode 1938PhRv...54..899P. doi:10.1103/PhysRev.54.899.
8. ^ Pauling, Linus (1947). Journal of the American Chemical Society 69 (3): 542. doi:10.1021/ja01195a024.
9. ^ Pauling, L. (1949). "A Resonating-Valence-Bond Theory of Metals and Intermetallic Compounds". Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934-1990) 196 (1046): 343. Bibcode 1949RSPSA.196..343P. doi:10.1098/rspa.1949.0032.
10. ^ Hume-rothery, W.; Irving, H. M.; Williams, R. J. P. (1951). "The Valencies of the Transition Elements in the Metallic State". Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934-1990) 208 (1095): 431. Bibcode 1951RSPSA.208..431H. doi:10.1098/rspa.1951.0172.
11. ^ Altmann, S. L.; Coulson, C. A.; Hume-Rothery, W. (1957). "On the Relation between Bond Hybrids and the Metallic Structures". Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934–1990) 240 (1221): 145. Bibcode 1957RSPSA.240..145A. doi:10.1098/rspa.1957.0073.
12. ^ Molodets, A. M.; Nabatov, S. S. (2000). "Thermodynamic Potentials, Diagram of State, and Phase Transitions of Tin on Shock Compression". High Temperature 38 (5): 715–721. doi:10.1007/BF02755923.
13. ^ Holleman, Arnold F.; Wiberg, Egon; Wiberg, Nils; (1985). "Tin" (in German). Lehrbuch der Anorganischen Chemie (91–100 ed.). Walter de Gruyter. pp. 793–800. ISBN 3110075113.
14. ^ Schwartz, Mel (2002). "Tin and Alloys, Properties". Encyclopedia of Materials, Parts and Finishes (2nd ed.). CRC Press. ISBN 1566766613.

 

External links

 

• The internal structure of crystals... Crystallography for beginners
• Appendix A from the manual for Atoms, software for XAFS
• Intro to Minerals: Crystal Class and System
• Introduction to Crystallography and Mineral Crystal Systems
• Crystal planes and Miller indices
• Interactive 3D Crystal models
• Specific Crystal 3D models
• Crystallography Open Database (with more than 140.000 crystal structures)
• Crystal Lattice Structures: Other Crystal Structure Web Sites