Crystal Affairs

Rhombic dipyramid is designated by the general form {hkl} and consists of 8 triangular faces, each of which intersects all 3 crystallographic axes. This pyramid may have several different appearances due to the variability of the axial lengths.
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The formation of a crystalline solid is a highly cooperative process in comparison to a reaction between two discrete molecules—of the order of 10^23 particles need to be arranged with translational symmetry as part of the transformation, with new bonding patterns both established locally and propagated in an ordered manner throughout the solid.

Matthew J. Rosseinsky,(2008), Opening the “Stable” Door, Wiley



Crystal system: each of seven categories of crystals (cubic, tetragonal, orthorhombic, trigonal, hexagonal, monoclinic, and triclinic) classified according to the possible relations of the crystal axes.

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Researchers have reported the first stable silicon (0) compound to contain a silicon-silicon double bond. The disilicon molecule (Si=Si) is far too reactive to exist in isolation. Disilenes (R2Si=SiR2) and disilynes do exist, but the cores in these compounds are no longer in the elemental, highly active, zero oxidation state; their silicon atoms have lost their lone pairs by combining with other molecular fragments. The researchers managed to synthesise a dark red crystal complex whose core effectively has the properties of a diatomic silicon unit. They stabilized the electron-deficient core with a bulky carbene - a coordinating ligand that the group has previously used to isolate diborene. The unusual molecule could kickstart the development of new reaction strategies using highly reactive silicon compounds.

A Stable Silicon(0) Compound with a Si=Si Double Bond, Science, Vol. 321. no. 5892, pp. 1069 - 1071, DOI: 10.1126/science.1160768], (August 26, 2008)


Double bonding with silicon

In a landmark for silicon chemistry, US researchers have reported the first stable silicon (0) compound to contain a silicon-silicon double bond. The unusual molecule could kickstart the development of new reaction strategies using highly reactive silicon compounds, the researchers suggest.

The disilicon molecule (Si=Si) is far too reactive to exist in isolation. Disilenes (R2Si=SiR2) and disilynes do exist, but the cores in these compounds are no longer in the elemental, highly active, zero oxidation state; their silicon atoms have lost their lone pairs by combining with other molecular fragments.

But Yuzhong Wang and colleagues at the University of Georgia have managed to synthesise a dark red crystal complex whose core effectively has the properties of a diatomic silicon unit. The researchers stabilise the electron-deficient core with a bulky carbene - a coordinating ligand that the group has previously used to isolate diborene.

'The diatomic core of our complex can be considered to be a silicon allotrope with two distinct reactive handles: a lone pair of electrons and a double bond.' says principal investigator Gregory Robinson. 'We predict that in combination, these two factors will result in this compound being highly reactive.'

'What baffles me is that this complex is a truly stable, "bottleable" species, not just a molecule which is observed in a low-temperature matrix,' comments Gernot Frenking, professor of theoretical chemistry at the Philipps-Universität in Marburg, Germany.

Guy Bertrand, of the University of California, Riverside, says such molecules, and other zero-oxidation state clusters of main-group elements such as boron and phosphorus, are not just academic curiosities. 'One of the obvious advantages of base-stabillised element(0) compounds is their greater solubility, which facilitates further chemical transformation,' he says.

The intermediate could lead to new ring, polymer and organometallic systems with potentially exciting properties. But the researchers stress that the research is in its infancy and many more studies are required to assess the reactivity and potential applications of the new silicon species.

Fred Campbell
http://www.rsc.org/chemistryworld/News/2008/August/21080804.asp


Miller Indices

We must touch on a type of notation often seen in mineral literature known as Miller Indices.....So the problem was really one of how to bring order to the literature's chaos. To the problem, Miller applied relatively simple mathematics - the Universal Language. To the lettering systems, Miller described the a,b,c (for hexagonal crystals his notation is four numbers long) intercepts of each planar crystal form as numbers and also made note of the form letter. His numbering system became widely accepted and is known as Miller indices. The numbers are presented as whole numbers (fractions are not allowed) and are the reciprocal of the actual intercept number, all whole numbers being reduced by their lowest common denominator. Here's a couple of simple examples from the cubic system.


Let us first describe a face of an octahedron and later a cube using Miller's indices. First, we should realize that an octahedron is an eight-sided crystal form that is the simple repetition of an equilateral triangle about our 3 crystallographic axes. The triangle is oriented so that it crosses the a1, a2, and a3 axes all at the same distance from the axial cross. This unit distance is given as 1. Dividing 1 into the whole number 1 (it's a reciprocal, remember?) yields a value of 1 for each Miller number. So the Miller indices is (111) for the face that intercepts the positive end of each of the 3 axes. See Figure 3 for all possible numbers for the 8 faces. Note: A bar over the number tells me that the intercept was across the negative end of the particular crystallographic axis. The octahedral form is given the letter designation of "o".




Now to the cube face. A cube face that intercepts the a3 (vertical) axis on the + end will not intercept the a1 and a2 axes. If the face does not intercept an axis, then we assign a mathematical value of infinity to it. So we start with Infinity, Infinity, 1 (a1, a2, a3). Infinity divided into 0 = 0 (any number divided into zero equals zero). So the Miller indices of the +a3 intercept face equals (001). See the drawing for all possible Miller indices for the 6 faces of a cube (Figure 4).

I think we should briefly mention cleavage at this point. CLEAVAGE is the preferred planar direction of breakage that many minerals possess. It is due to planes of weakness that exist in some minerals because the bonding strength between the atoms or molecules is not the same in every direction. Because crystals are composed of orderly arrangements of atoms or molecules, we really should expect cleavage to be present in many crystals. The notation that denotes cleavage is derived in much the same manner as Miller indices, but is expressed in braces. So a cubic crystal, say diamond, no matter whether it exhibits cubic {001} or octahedral {111} crystal form, has an octahedral cleavage form that is given as {111}.

Note: The Miller indices when used as face symbols are enclosed in parentheses, as the (111) face for example. Form symbols are enclosed in braces, as the {111} form for example. Zone symbols are enclosed in brackets, [111] for example and denote a zone axis in the crystal. So in the discussion of cleavage (above), you must use braces to denote cleavage. Cleavage is analogous to form as cubic, octahedral, or pinacoidal cleavage and does not refer to just one face of a form.



I want to consider the tetragonal prisms. There are 3 of these open forms consisting of the 1st order, 2nd order, and ditetragonal prisms. Because they are not closed forms, in our figures we will add a simple pinacoid termination, designated as c. The pinacoid form intersects only the c axis, so its Miller indices notation is {001}. It is a simple open 2-faced form.

The first order prism is a form having 4 faces that are parallel to the c axis and having each face intersect the a1 and a2 axes at the same distance (unity). These faces are designated by the letter m (given with Miller indices in fig. 4.2a and by m in fig. 4.2c) and the form symbol is {110}. The second order prism is essentially identical to the first order prism, but rotated about the c axis to where the faces are parallel to one of the a axes (fig. 4.2b), thus being perpendicular to the other a axis. The faces of the second order prism are designated as a and their form symbol is {100}.

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Bravais lattice



In geometry and crystallography, a Bravais lattice, named after Auguste Bravais,[1] is an infinite set of points generated by a set of discrete translation operations. A crystal is made up of one or more atoms (the basis) which is repeated at each lattice point. The crystal then looks the same when viewed from any of the lattice points. In all, there are 14 possible Bravais lattices that fill three-dimensional space. Related to Bravais lattices are Crystallographic point groups of which there are 32 and Space groups of which there are 230.

It was pointed out in 1845, that there are 14 unique Bravais lattices in three dimensional crystalline systems, adjusting the previously existent result 15 lattices.

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