NationMaster - Encyclopedia: Cubic crystal system

The cubic crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in metallic crystals. In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ... In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ... A cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. ...

1 Bravais lattices and point/space groups
2 Atomic packing factors and examples
3 Single-element compounds
4 Multi-element compounds
5 See also
6 References

Bravais lattices and point/space groups

The three Bravais lattices that form the cubic crystal system are: In geometry and crystallography, a Bravais lattice, named after Auguste Bravais, is an infinite set of points generated by a set of discrete translation operations. ...

Simple cubic Image File history File links Lattic_simple_cubic. ...

Body-centered cubic Image File history File links Lattice_body_centered_cubic. ...

Face-centered cubic Image File history File links Lattice_face_centered_cubic. ...

The simple cubic system consists of one lattice point on each corner of the cube. Each lattice point is then shared equally between eight adjacent cubes, and the unit cell therefore contains in total one lattice point (1/8 * 8). The body centered cubic system has one lattice point in the center of the unit cell in addition to the eight corner points. It has in total 2 lattice points per cell ((1/8)*8 + 1). Finally, the face centered cubic lattice has lattice points on the faces of the cube, giving a total of 4 lattice points per unit cell ((1/8) * 8 + (1/2) * 6).

The point groups and space groups that fall under this crystal system are listed below, using the international notation. In crystallography, a crystallographic point group or crystal class is a set of symmetry operations that leave a point fixed, like rotations or reflections, which leave the crystal unchanged. ... The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ...

Point group	#	Cubic space groups
$23,!$	195-199	P23	F23	I23	P2₁3	I2₁3
$mbar3,!$	200-206	Pm $bar3$	Pn $bar3$	Fm $bar3$	Fd $bar3$	I $bar3$	Pa $bar3$	Ia $bar3$
$432,!$	207-214	P432	P4₂32	F432	F4₁32	I432	P4₃32	P4₁32	I4₁32
$bar4 3m,!$	215-220	P $bar4$ 3m	F $bar4$ 3m	I $bar4$ 3m	P $bar4$ 3n	F $bar4$ 3c	I $bar4$ 3d
$mbar3 m,!$	221-230	Pm $bar3$ m	Pn $bar3$ n	Pm $bar3$ n	Pn $bar3$ m	Fm $bar3$ m	Fm $bar3$ c	Fd $bar3$ m	Fd $bar3$ c
$mbar3 m,!$	221-230	Im $bar3$ m	Ia $bar3$ d

There are 36 cubic space groups, of which 10 are hexoctahedral: Fd3c, Fd3m, Fm3c, Fm3m, Ia3d, Im3m, Pm3m, Pm3n, Pn3m, and Pn3n. Other terms for hexoctahedral are normal class, holohedral, ditesseral central class, galena type.

Atomic packing factors and examples

The cubic crystal system is one of the most common crystal systems found in elemental metals, and naturally occurring crystals and minerals. One very useful way to analyse a crystal is to consider the atomic packing factor. In this approach, the amount of space which is filled by the atoms is calculated under the assumption that they are spherical. In crystallography, atomic packing factor is the fraction of volume in a crystal structure that is occupied by atoms. ...

Single-element compounds

Assuming one atom per lattice point, the atomic packing factor of the simple cubic system is only 0.524. Due to its low density, this is a high energy structure and is rare in nature, but is found in Polonium ^{[citation needed]}. Similarly, the body centered structure has a density of 0.680. The higher density makes this a low energy structure which is fairly common in nature. Examples include iron, chromium, and tungsten. In physics, Density is defined as mass m per unit volume V. Mathematically, it is expressed as where, in SI units: Ï (rho) is the density of the substance, measured in kg m-3 m is the mass of the substance, measured in kg v is the volume of the substance... General Name, Symbol, Number polonium, Po, 84 Chemical series metalloids Group, Period, Block 16, 6, p Appearance silvery Atomic mass (209) gÂ·molâˆ’1 Electron configuration [Xe] 4f14 5d10 6s2 6p4 Electrons per shell 2, 8, 18, 32, 18, 6 Physical properties Phase solid Density (near r. ... General Name, Symbol, Number iron, Fe, 26 Chemical series transition metals Group, Period, Block 8, 4, d Appearance lustrous metallic with a grayish tinge Atomic mass 55. ... General Name, Symbol, Number chromium, Cr, 24 Chemical series transition metals Group, Period, Block 6, 4, d Appearance silvery metallic Atomic mass 51. ... General Name, Symbol, Number tungsten, W, 74 Chemical series transition metals Group, Period, Block 6, 6, d Appearance grayish white, lustrous Atomic mass 183. ...

Finally, the face centered cubic crystals have a density of 0.741, a ratio that it shares with several other systems, including hexagonal close packed and one version of tetrahedral BCC. This is the most tightly packed crystal possible with spherical atoms. Due to its low energy, FCC is extremely common, examples include lead (for example in lead(II) nitrate), aluminum, copper, and gold. Close-packing of spheres is the arranging of an infinite lattice of spheres so that they take up the greatest possible fraction of an infinite 3-dimensional space. ... For PB or pb as an abbreviation, see PB. General Name, Symbol, Number lead, Pb, 82 Chemical series poor metals Group, Period, Block 14, 6, p Appearance bluish gray Atomic mass 207. ... R/S statement R: , , , , S: , , , Flash point non-flammable RTECS number OG2100000 Supplementary data page Structure and properties n, Îµr, etc. ... Aluminum is a soft and lightweight metal with a dull silvery appearance, due to a thin layer of oxidation that forms quickly when it is exposed to air. ... General Name, Symbol, Number copper, Cu, 29 Chemical series transition metals Group, Period, Block 11, 4, d Appearance metallic pinkish red Atomic mass 63. ... General Name, Symbol, Number gold, Au, 79 Chemical series transition metals Group, Period, Block 11, 6, d Appearance metallic yellow Atomic mass 196. ...

Multi-element compounds

The Sodium Chloride Crystal Structure of type fcc. Each atom has six nearest neighbors, with octahedral geometry. The arrangement of the atoms of each type is known as cubic close packed (ccp).
Light blue = Na⁺ (Sodium ion)
Dark green = Cl⁻ (Chloride ion)

When the compound is formed of two elements whose ions are of roughly the same size, they have what is called the interpenetrating simple cubic structure, where two atoms of a different type have individual simple cubic crystals. However, the unit cell consists of the atom of one being in the middle of the 8 vertices, structurally resembling body centered cubic. The most common example is caesium chloride CsCl. Crystal structure for sodium chloride Drawn using IsisDraw by User:Walkerma Sodium Chloride Smells File links The following pages link to this file: Ionic crystal Sodium chloride Categories: Public domain images ... Crystal structure for sodium chloride Drawn using IsisDraw by User:Walkerma Sodium Chloride Smells File links The following pages link to this file: Ionic crystal Sodium chloride Categories: Public domain images ... This articles section called Other facts does not cite its references or sources. ... Close-packing of spheres refers to arranging an infinite lattice of spheres so that they take up the greatest possible fraction of an infinite 3-dimensional space. ... General Name, Symbol, Number sodium, Na, 11 Chemical series alkali metals Group, Period, Block 1, 3, s Appearance silvery white Atomic mass 22. ... The chloride ion is formed when the element chlorine picks up one electron to form an anion (negatively-charged ion) Clâˆ’. The salts of hydrochloric acid HCl contain chloride ions and are also called chlorides. ... Caesium chloride is an ionic compound best known as a structural type. ...

However, if the cation is slightly smaller than the anion (a cation/anion radius ratio of 0.414 to 0.732), the crystal forms a different structure, interpenetrating FCC. When drawn separately, both atoms are arranged in an FCC structure. The unit cell for this is shown to the left.

References

Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., Wiley, ISBN 0-471-80580-7

Categories: Articles with unsourced statements since February 2007 | All articles with unsourced statements | Crystallography

Results from FactBites:

The Isometric (Cubic) Crystal System (0 words)
	Of the seven crystal systems, the isometric system possesses the highest symmetry.
	Keep in mind that cell parameters do not define the crystal class, but are a consequence of the symmetry elements that define the system.
	In the cubic system there will always be at least one 2, 4, 2bar, or 4bar axis and one 3 or 3bar axis.

Crystal (mineral) - MSN Encarta (876 words)
	Crystals are produced whenever a solid is formed gradually from a fluid, whether the formation results from the freezing of a liquid, the deposition of dissolved matter, or the direct condensation of a gas into solid form.
	The thirty-two classes are grouped into six crystal systems, based on the length and position of the crystal axes, imaginary lines passing through the center of the crystal, intersecting the faces, and bearing definite relations to the symmetry of the crystal.
	The six crystal systems are of great importance to mineralogists and gemologists; specification of the system is necessary in the description of any mineral (see Mineralogy).

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Contents

Atomic packing factors and examples

Single-element compounds

Multi-element compounds

See also

References