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.

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  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.
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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

Quasicrystal: Prof. Dan Shechtman

A quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two, three, four, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders, for instance five-fold.

Aperiodic tilings were discovered by mathematicians in the early 1960s, and, some twenty years later, they were found to apply to the study of quasicrystals. The discovery of these aperiodic forms in nature has produced a paradigm shift in the fields of crystallography. Quasicrystals had been investigated and observed earlier,^[2] but, until the 1980s, they were disregarded in favor of the prevailing views about the atomic structure of matter.

Roughly, an ordering is non-periodic if it lacks translational symmetry, which means that a shifted copy will never match exactly with its original. The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled; i.e. the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two dimensions. The ability to diffract comes from the existence of an indefinitely large number of elements with a regular spacing, a property loosely described as long-range order. Experimentally, the aperiodicity is revealed in the unusual symmetry of the diffraction pattern, that is, symmetry of orders other than two, three, four, or six. The first experimental observation of what came to be known as quasicrystals was made by Dan Shechtman and coworkers in 1982 and it was reported in print two years later.^[3] Shechtman received the Nobel Prize in Chemistry in 2011 for his findings.^[4].

In 2009, following a decade long search, a group of scientists from University of Florence in Italy reported the existence of a natural quasicrystals in mineral samples from the Koryak mountains in Russia's far east, named icosahedrite.^[5][6] It was further claimed by scientists from Princeton University that icosahedrite is extra-terrestrial in origin, possibly delivered to Earth by a CV3 carbonaceous chondrite asteroid.^[7]

240 E₈ polytope vertices using 5D orthographic_projection to 2D using 5-cube (Penteract) Petrie_polygon basis_vectors overlaid on electron diffraction pattern of an Icosahedron Zn-Mg-Ho Quasicrystal.

• E8_(mathematics) and Quasicrystals

The Lived Past and the Anticipated Future.

the autobiographical self has prompted extended memory, reasoning, imagination, creativity and language. And out of that came the instruments of culture --religions, justice,trade, the arts, science, technology. And it is within that culture that we really can get -- and this is the novelty --something that is not entirely set by our biology. It is developed in the cultures. It developed in collectives of human beings. And this is, of course, the culturewhere we have developed something that I like to call socio-cultural regulation.

***

Plato prove that justice does not depend upon a chance, convention or upon external force. It is the right condition of the human soul by the very nature of man when seen in the fullness of his environment. It is in this way that Plato condemned the position taken by Glaucon that justice is something which is external. According to Plato, it is internal as it resides in the human soul. "It is now regarded as an inward grace and its understanding is shown to involve a study of the inner man." It is, therefore, natural and no artificial. It is therefore, not born of fear of the weak but of the longing of the human soul to do a duty according to its nature.

Plato's Concept Of Justice: An Analysis  Bold was added by me for emphasis.

***

 See Also:

•  What is Good Governance

ATLAS discovers its first new particle

String theory isn't just another quantum field theory, another particular finite list of elementary particles with some interactions. It's an intellectually and literally multi-dimensional reservoir of wisdom that has taught us many things of completely new kinds that we couldn't foresee. The Reference Frame: LHC: is a new particle?: LHC: is χb(3P) a new particle?

When you hold a particular point of view about nature it is important in my mind to know where the search is going and what this means overall. How we look at reality and how we look at nature.

The spectrum of the _b states: the leftmost peak is the _b(1P), the middle one the _b(2P), and the rightmost the new _b(3P). The upper plot shows the spectrum for decays involving unconverted photons, while th lower plot shows the spectra for decays involving converted photons. In the lower plot, the upper (red) curve shows the spectrum for _b decays to (1S), while the lower (brown) curve shows the spectrum for decays to (2S). (Only the _b(3P) peak appears distinctly in the lower spectrum because it is the only _b state with decays involving enough energy to be detected in this study.) See: Atlas News

Also See: LHC heads into new year with first particle discovery

I understand how my own life can be changed from experiencing an anomaly in the everyday world? It is not proof enough. All scientists know this.

Is it better then for those who visit to know that such a thing in a condense matter view can can govern the matter states? This is part of recognizing the geometrical structure that Plato sought to establish as an underlying reality to nature? While it does not all define the matter states so successful we could attribute the universe to a soccer ball? No. For those of you who need more proof seek to find the subject of allotrope or polytopes here and you will understand what I mean.
 
How it can have such an impact, and to search, where our sciences have gone. I hope one day it offers up an answer. I suspect that the research in science experimentally will most likely lead the way.  I believe we will discover something quite dramatic in the coming years that seems now very unlikely.

The lure to write my experience as a truth and to offer it up as a question, is on my mind. I believe we are much closely attached to the depth of reality then we currently know. I can only write it up as fiction then.

This is part of the idea I have about the move into the cosmos as part of our education as civilians of a new cultural thematic that we will make our home out in the stars as a result of this.

Clearly I speak of the elemental nature and gravity, and this too is a pursuit in today's science that is underway. So while I speak in advance of such things, clearly it must be highlighted that this has not been accomplished yet either.

Of course there are theories out there and using them provide for a better perspective about our cosmos and the birth of it. In theory then, there is much that makes sense. In theory, it has to be experimentally proven. In theory, we construct the parameters?

If you have a particle that travels a distance and you use a calorimeter instrument to measure it's identity, then can you not seek to find a representative of calorimeter design that would suit the "time differences of something that would amount to a faster then light"....other then recognize existing mediums as a sure sign of Cerenkov?

You use the space station then? If you follow the history of high energy particles from space this left you with no alternative but to leave the domain of earth to establish some insight into the applicability of the AMS program and particle research? Dark matter research?

Google Books Library Project

What's the goal of this project?

The Library Project's aim is simple: make it easier for people to find relevant books – specifically, books they wouldn't find any other way such as those that are out of print – while carefully respecting authors' and publishers' copyrights. Our ultimate goal is to work with publishers and libraries to create a comprehensive, searchable, virtual card catalog of all books in all languages that helps users discover new books and publishers discover new readers. See: Google Books

I was asked by my daughter about one of these devices whether I preferred the new device or the paper books. I would have to say I do favor the paperback but also look for advantages as to provide access to information as detrimental to providing society with the tools necessary. Receiving a gift certificate for 50 dollars to one of the books stores I might add this for a electronic purchase.

What brought this subject up was the update on the new electronic devices out there that allow you to read and download books for reading. Over the years being an advocate of sorts for the electronic development of our cultures I could see where such devices would allow extraordinary freedom to carry's a lot of books in one location. So there has to be lots said about not being in in the mood for reading one book while being attentive to others for research material. Sort of like closing in on a cold case file or something like that may have been missed supportive by research material.

So under the auspice of attaining a library of sorts was appealing to me and I thought advantages to society that cold not travel distances to the libraries yet have access from the rural locations.

***

The Google Books Library Project is an effort by Google to scan and make searchable the collections of several major research libraries.^[1] The project, along with Google's Partner Program, comprise Google Books (formerly Google Book Search). Along with bibliographic information, snippets of text from a book are often viewable. If a book is out of copyright and in the public domain, the book is fully available to read or to download.^[2]

1 Participants 1.1 Initial Project Partners 1.1.1 Harvard University 1.1.2 New York Public Library 1.1.3 Stanford University 1.1.4 University of Michigan 1.1.5 University of Oxford 1.2 Additional Project Partners 1.2.1 Bavarian State Library 1.2.2 Columbia University 1.2.3 Committee on Institutional Cooperation (CIC) 1.2.4 Complutense University of Madrid 1.2.5 Cornell University 1.2.6 Ghent University Library 1.2.7 Keio University 1.2.8 National Library of Catalonia 1.2.9 Princeton University 1.2.10 University of California 1.2.11 University Library of Lausanne 1.2.12 University of Mysore 1.2.13 University of Texas at Austin 1.2.14 University of Virginia 1.2.15 University of Wisconsin–Madison 2 See also 3 Notes 4 References 5 External links

 Participants

The Google Books Library Project continues to evolve;^[3] however, only some of the institutional partners are listed on the web page currently maintained by Google:^[4]

 Initial Project Partners

The number of academic libraries participating in the digitization and uploading of books from their collections has grown beyond the original five: Harvard, Michigan, Stanford, Oxford, and the New York Public Library.

 Harvard University

Harvard University (and Harvard University Library) is an institutional participant in the project.^[5] The Harvard University Library (HUL) today is best understood as a coordinated system of more than 80 libraries with shared holdings. The University Library is also a department of the University's central administration through which the libraries collaborate in the areas of digital acquisitions and collections, information technology, high-density storage, and preservation.^[6]
The Harvard University Library and Google are building on a successful pilot conducted by Harvard and Google throughout 2005. The project will increase Internet access to the holdings of the Harvard University Library, which includes more than 15.8 million volumes. While physical access to Harvard's library materials generally is restricted to current Harvard students, faculty, and researchers, or to scholars who can come to Cambridge, the Harvard-Google Project has been designed to enable both members of the Harvard community and users everywhere to discover works in the Harvard collection.

"The new century presents important new opportunities for libraries, including Harvard's, and for those individuals who use them. The collaboration between major research libraries and Google will create an important public good of benefit to students, teachers, scholars, and readers everywhere. The project harnesses the power of the Internet to allow users to identify books of interest with a precision and at a speed previously unimaginable. The user will then be guided to find books in local libraries or to purchase them from publishers and book vendors. And, for books in the public domain, there will be even broader access."^[4]

"The Harvard-Google Project links the search power of the Internet to the depth of knowledge in Harvard's world-renowned libraries. Harvard has been collecting books for nearly four centuries. Among our out-of-copyright books are countless unique copies, unusual editions, and neglected or forgotten works. Our efforts with Google will bring about the broad dissemination of the knowledge contained in those books and, with it, significant information about the world views that those books represent .... By working with Google, Harvard is furthering an essential aspect of the University Library's mission, which is to serve scholars around the world."

-- Sidney Verba, the former Carl H. Pforzheimer University Professor and former Director of the University Library.^[5]

 New York Public Library

The New York Public Library (NYPL) is an institutional participant in the project.^[7]
In this pilot program, NYPL is working with Google to offer a collection of its public domain books, which will be scanned in their entirety and made available for free to the public online. Users will be able to search and browse the full text of these works. When the scanning process is complete, the books may be accessed from both The New York Public Library's website and from the Google search engine. ^[7]

"The New York Public Library Research Libraries were struck by the convergence of Google's mission with their own. We see the digitization project as a transformational moment in the access to information and wanted not only to learn from it but also to influence it. Our response at present is a conservative one, with a limited number of volumes in excellent condition, in selected languages and in the public domain. With appropriate evaluation of this limited participation, we look forward to a more expansive collaboration in the future."

-– David Ferriero, Andrew W. Mellon Director and Chief Executive of the Research Libraries, The New York Public Library.^[4]

 Stanford University

Stanford University (and Stanford University Libraries/SULAIR) is an institutional participant in the project.^[8]

"Stanford has been digitizing texts for years now to make them more accessible and searchable, but with books, as opposed to journals, such efforts have been severely limited in scope for both technical and financial reasons. The Google arrangement catapults our effective digital output from the boutique scale to the truly industrial. Through this program and others like it, Stanford intends to promote learning and stimulate innovation."

-– Michael A. Keller, University Librarian.^[4]

 University of Michigan

Notice about the project

The University of Michigan (and the University of Michigan Library) is an institutional participant in the project.^[9]

"The project with Google is core to our mission as a great public university to advance knowledge — on campus and beyond. By joining this partnership that makes our library holdings searchable through Google, UM serves as an agent in an initiative that radically increases the availability of information to the public. The University of Michigan embraces this project as a means to make information available as broadly and conveniently as possible. Moreover, the UM Library embarked on this ground-breaking partnership for a number of very compelling reasons:

• "We believe that, beyond providing basic access to library collections, this activity is critically transformative, enabling the University Library to build on and re-conceive vital library services for the new millennium.
• "This work will create new ways for users to search and access library content, opening up our collections to our own users and to users throughout the world.
• "Although we have engaged in large-scale, preservation-based conversion of materials in the Library's collection for several years, and have been a leader in digital preservation efforts among research libraries, we know that only through partnerships of this sort can conversion of this scale be achieved. Our program is strong, and we have been able to digitize approximately 5,000 volumes/year; nevertheless, at this rate, it would take us more than a thousand years to digitize our entire collection."

-– John P. Wilkin, Associate University Librarian.^[4]

University of Oxford

University of Oxford is an institutional participant in this project.^[10] Oxford is the oldest university in the English-speaking world, and its historic Bodleian Library is the oldest university library.

"The Bodleian Library's mission, from its founding in 1602, has been based on Sir Thomas Bodley's vision of a library serving the worldwide 'Republic of Letters', with the Library's collections open to all who have need to use them. To this day over 60% of readers who use and work in the Bodleian Library have no direct affiliation with the University of Oxford . The Google Library Project in Oxford testifies to our ongoing commitment to enable and facilitate access to our content for the scholarly community and beyond. The initiative will carry forward Sir Thomas Bodley's vision and the ethos of the Bodleian Library into the digital age, allowing readers from around the world to access the Library's collections over the World Wide Web."

-– Ronald Milne, former Director of Oxford University Library & Bodleian Librarian.^[4]

 Additional Project Partners

Other institutional partners have joined the Project in the years since the partnership was first announced.

 Bavarian State Library

The Bavarian State Library (Bayerische Staatsbibliothek or BSB) is an institutional participant in the project.^[11]

"With today's announcement we are opening our library to the world and bringing the true purpose of libraries — the discovery of books and knowledge — a decisive step further in into the digital era. This is an exciting effort to help readers around the world discover and access Germany's rich literary tradition online — whenever and wherever they want."

— Dr. Rolf Griebel, Director General of the Bavarian State Library.^[4]

 Columbia University

Columbia University (and Columbia University Library System) is an institutional participant in the project.^[4]

"Our participation in the Google Book Search Library Project will add significantly to the extensive digital resources the Libraries already deliver," said James Neal, Columbia's vice president for information services and university librarian. "It will enable the Libraries to make available more significant portions of its extraordinary archival and special collections to scholars and researchers worldwide in ways that will ultimately change the nature of scholarship."

— James G. Neal, University Librarian and Vice-President for Information Services at Columbia University.^[4]

 Committee on Institutional Cooperation (CIC)

The Committee on Institutional Cooperation (CIC) is an institutional participant in the project.^[12] The CIC developed in the late 1950s from a cautious exploration of the ways in which 11 major universities — two private and nine state-supported — might pool their resources for the common good. Today the CIC is an active participant in the Google Books Library Project, which becomes something of a logical extension of the initial working relationships forged a half century ago amongst Big Ten universities and the University of Chicago.

• The CIC is a consortium of 12 research universities:
  • Indiana University, Bloomington, Indiana
  • Michigan State University
  • Northwestern University
  • Ohio State University
  • Pennsylvania State University
  • Purdue University
  • University of Chicago
  • University of Illinois
  • University of Iowa
  • University of Michigan
  • University of Minnesota
  • University of Wisconsin–Madison

The CIC is guided by the Provosts of the member universities; and the CIC Digital Library Initiatives Overview Committee monitors the digitization and dissemination of books in the CIC collections.^[13]

"This partnership with Google is one of the most ambitious undertakings in the history of the CIC, and sets the stage for a remarkable transformation of library services and information access. We're opening up these resources as both a common good shared among the universities, as well as a public good available more broadly. "

— Barbara McFadden Allen, Director of the CIC.^[4]

 Complutense University of Madrid

The Complutense University of Madrid (Universidad Complutense) is an institutional participant in the project.^[14]

"Out-of-copyright books previously only available to people with access to the University Complutense of Madrid's Library, or the money to travel, will now be accessible to everyone with an Internet connection, wherever they live. We are quite literally opening our library to the world. The opportunities for education are phenomenal and we are delighted to be working with Google on this project."

— Carlos Berzosa, Chancellor.^[4]

 Cornell University

Cornell University (and Cornell University Library) is an institutional participant in the project.^[15]

"Research libraries today are integral partners in the academic enterprise through their support of research, teaching and learning. They also serve a public good by enhancing access to the works of the world's best minds. As a major research library, Cornell University Library is pleased to join its peer institutions in this partnership with Google. The outcome of this relationship is a significant reduction in the time and effort associated with providing scholarly full-text resources online."

— Ann R. Kenney, Interim Cornell University Librarian.^[4]

 Ghent University Library

Ghent University (and Boekentoren/Ghent University Library) is an institutional participant in the project.^[16]

'We are thrilled to open our books and our library to the world through this project. This is an exciting effort to help readers — no matter where they are — discover and access part of Belgium and Europe's rich literary tradition and culture. In addition, we are about to start a multi-year project to renovate our library building, and while our library's doors will be closed, its books will remain open to students and academics through Google Book Search."

— Sylvia Van Peteghem, Chief Librarian, Ghent University Library.^[4]

 Keio University

Keio University (and Keio Media Centers (Libraries)) is an institutional participant in the project.^[17]

"The Google project allows us to make our collections visible worldwide, so that our books will contribute to research and education on a global scale. Our university was founded in 1858 by Yukichi Fukuzawa, who was well known for his commitment to bringing information and media forward in modern Japan. This makes Keio ideally suited to be the first Japanese library to participate in Google Book Search."

— Professor S. Sugiyama, Director, Keio University Library.^[4]

National Library of Catalonia

The National Library of Catalonia (Biblioteca de Catalunya) is an institutional participant in the project.^[18]

"It once was the case that only those who could visit our library were able to 'visit' our books. Now, anyone interested in the vast number of titles our library houses will be able to find and access them online–or perhaps just discover them by chance via a simple search of the Google Book Search index. This is a tremendous step forward for enabling readers all around the world to discover and access the rich history of Catalonian, Castilian, and Latin American literature."

-- Dolors Lamarca, Director of the National Library of Barcelona.^[4]

 Princeton University

Princeton University (and Princeton University Library) is an institutional participant in the project.^[19]

"Generations of Princeton librarians have devoted themselves to building a remarkable collection of books in thousands of subjects and dozens of languages. Having the portion of that collection not covered by copyright available online will make it easier for Princeton students and faculty to do research, and joining the Google partnership allows us to share our collection with researchers worldwide, a step very much in keeping with the University's unofficial motto of Princeton in the nation's service and in the service of all nations."

— Karin Trainer, Princeton University Librarian.^[4]

 University of California

The University of California is an institutional participant in the project.^[20]

"By unlocking the wealth of information maintained within our libraries and exposing it to the latest that search technologies have to offer, the University of California is continuing its work to harness technology and our library collections in support of research, learning, patient care, and cultural engagement. In this new world, people will make connections between information and ideas that were hitherto inaccessible, driving the pace of innovation in all areas of life – academic, economic, and civic – and enhancing the use of the world's great libraries.

"With digital copies of our library holdings, we will also provide a safeguard for the countless thousands of authors, publishers, and readers who would be devastated by catastrophic loss occasioned, for example, by natural disaster. Anyone who doubts the impact that such disaster can have on our cultural memory need look no further than the devastation wrought by Hurricane Katrina on our sister libraries in the Gulf States.

"As an institution that has built these vast collections as a public good and in the public trust, joining the Google library partnership was the right thing to do."

— Daniel Greenstein, Associate Vice Provost for Scholarly Information and University Librarian.^[4]

University Library of Lausanne

The University of Lausanne (and the Cantonal and University Library of Lausanne) is an institutional participant in the project.^[21]

"Out of copyright books previously only available to people with access to Lausanne's university library, will now be accessible to everyone with an Internet connection, wherever they live. We are quite literally opening our library to the world. The opportunities for education are phenomenal and we are delighted to be working with Google on this project".

— Hubert A. Villard, Director of the Cantonal and University Library of Lausanne.^[4]

 University of Mysore

The University of Mysore (and the Mysore University Library) is an institutional participant in the project.^[22]

 University of Texas at Austin

The University of Texas at Austin (and the University of Texas Libraries) is an institutional participant in this project.^[23]

"University libraries in our society are entrusted with the critical mission of collecting and providing access to information spanning the entire range of human knowledge. Our libraries are also responsible for effectively preserving this knowledge and ensuring access to it over vast periods of time. At the University of Texas at Austin, we hold a deep commitment to each of these objectives and believe that participating in this venture will help ensure our ability to meet those commitments far into the future."

— Fred Heath, Vice Provost and Director of Libraries.^[4]

 University of Virginia

The University of Virginia (and the University of Virginia Library) is an institutional participant in this project.^[24]

"The U.Va. Library was a pioneer in digitizing public domain materials. We started with printed texts in 1992, and faculty and students quickly discovered that long-forgotten and out-of-print texts could reach new audiences and spark new scholarship. We have often talked about libraries without walls, but now we are even closer to realizing that vision, thanks to this partnership."

— Karin Wittenborg, University Librarian, University of Virginia.^[4]

 University of Wisconsin–Madison

The University of Wisconsin–Madison (and the University of Wisconsin Digital Collection) is an institutional participant in this project.^[25]

"The combined library collections of the University of Wisconsin–Madison Libraries and the Wisconsin Historical Society Library comprise one of the largest collections of documents and historical materials in the United States. Through this landmark partnership with Google, Wisconsin is taking a leading role in preserving public domain works for future generations and making the Library's resources widely available for education and research. This effort truly exemplifies the vision of The Wisconsin Idea—the notion that the boundaries of the university are limitless. The Wisconsin libraries have been following in this tradition. The Google digitization efforts will enable the libraries to expand access to public domain materials that have heretofore only been accessible in the libraries. Much of this material is rare and one-of-a-kind, providing a rich, open source of information for educational, research and general public use."

— Edward Van Gemert, Interim Director, UW–Madison Libraries.^[4]

 See also

• HathiTrust
• Google Book Search Settlement

 Notes

1. ^ Stein, Linda L. et al. (2009). Literary Research and the American Realism and Naturalism Period: Strategies and Sources, p. 261.
2. ^ Google Books Library Project – An enhanced card catalog of the world's books
3. ^ O'Sullivan, Joseph and Adam Smith. "All booked up," Googleblog. December 14, 2004.
4. ^ ^{a b c d e f g h i j k l m n o p q r s t u} Google Library Partners
5. ^ ^{a b} Harvard + Google
6. ^ HUL summary/overview
7. ^ ^{a b} New York Public Library + Google
8. ^ Stanford + Google
9. ^ Michigan + Google
10. ^ Oxford + Google
11. ^ Bavaria + Google (in English); Staatsbibliothek + Google (in German)
12. ^ CIC + Google
13. ^ CIC overview
14. ^ Madrid + Google (in English); Complutense Universidad + Google (in Spanish)
15. ^ Cornell + Google
16. ^ Ghent/Gent + Google
17. ^ Keio + Google (in English); Keio + Google (in Japanese)
18. ^ Biblioteca de Catalunya (BNC) + Google (in Spanish)
19. ^ Princeton + Google
20. ^ California + Google
21. ^ Bibliothèque Cantonale et Universitaire/BCU + Google (in French)
22. ^ Mysore + Google
23. ^ Texas + Google
24. ^ Virginia + Google
25. ^ Wisconsin + Google

 References

• Lester, June and Wallace C. Koehler. (2007). Fundamentals of Information Studies: Understanding Information and Its Environment. New York: Neal-Schuman Publishers. 13-ISBN 978-1-555-70594-7/10-ISBN 1-555-70594-4; OCLC 122526045
• Miller, Michael. (2007). Googlepedia: the Ultimate Google Resource. Indianapolis, Indiana: Que. 13-ISBN 978-0-789-73639-0/10-ISBN 0-789-73639-X; OCLC 224762694
• Stein, Linda L, and Peter J. Lehu. (2009). Literary Research and the American Realism and Naturalism Period: Strategies and Sources. Lanham, Maryland: Scarecrow Press. 13-ISBN 978-0-810-86141-1/10-ISBN 0-810-86141-0; 13-ISBN 978-0-810-86242-5/10-ISBN 0-810-86242-5; OCLC 233798804

 External links

• Google Books website
• Google Library Partners
• Digital Library Federation
• The European Library

Grail: Gravity Recovery and Interior Laboratory

GRAIL Spacecraft Logo

NASA's Gravity Recovery and Interior Laboratory, or GRAIL, spacecraft logo is emblazoned on the first stage of a United Launch Alliance Delta II launch vehicle, now secured in the gantry at Cape Canaveral Air Force Station's Space Launch Complex 17B.

Image credit: NASA/Jim Grossmann

Mission Overview

The GRAIL mission will place two spacecraft into the same orbit around the Moon. As they fly over areas of greater and lesser gravity, caused both by visible features such as mountains and craters and by masses hidden beneath the lunar surface, they will move slightly toward and away from each other. An instrument aboard each spacecraft will measure the changes in their relative velocity very precisely, and scientists will translate this information into a high-resolution map of the Moon's gravitational field. 


This gravity-measuring technique is essentially the same as that of the Gravity Recovery And Climate Experiment (GRACE), which has been mapping Earth's gravity since 2002. See: Grail: Gravity Recovery and Interior Laboratory

See Also: Time-Variable Gravity Measurements





Mean Gravity Field

Who of us could forget what the earth looks like after it has been mapped.

 On planet Earth, we tend to think of the gravitational effect as being the same no matter where we are on the planet. We certainly don't see variations anywhere near as dramatic as those between the Earth and the Moon. But the truth is, the Earth's topography is highly variable with mountains, valleys, plains, and deep ocean trenches. As a consequence of this variable topography, the density of Earth's surface varies. These fluctuations in density cause slight variations in the gravity field, which, remarkably, GRACE can detect from space.

Our views in terms of the gravity field becomes part and parcel of our assessment as we venture out into space. So why not the Moon.

Image Credit: NASA/Goddard

Early assessment of Clementine along with LCROSS paints a interesting feature of our Moon as we look to understand the matter constituent makeup of the moon,  along with what it's gravity field.

Here at Dialogos of Eide I am concerned about this relationship. Such mapping not only becomes useful in the determination of the gravity field but it also heightens the understanding of relating to the elemental.

Future moon missions will need to understand the elemental makeup (while quantum gravity and relativity have not been joined experimentally) in order to use the elements to assist the colony in providing the tools necessary for it's survival there. With a Treaty established,  such claims to the moon become a societal move beyond earth's domain and truly moves us to civilization that will habitat the stars.

Part of this move into the cosmos will be the need to understand "something spiritual about ourselves and while ethereal in it's assessment this relationship to gravity."  It is also necessary to go "even deeper" to understand our ability to manipulate the force of gravity as a product of the mechanism of the Higg's field as we move through our own psychological underpinnings with the way in which we choose to live. (I know we have yet to proof this connection).

I give some inkling with the four links below. This is my assessment of the relationship toward "my gravity"  as I choose to live in the world of reality.

• Colour of Gravity 4 
• Colour of Gravity 3
• Colour of Gravity 2
• Colour of Gravity 1