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Cubic crystal system

Lattice point group

Science Physics Condensed matter physics Crystallography

In crystallography, the cubic (or isometric) crystal system features a unit cell shaped like a cube, making it one of the simplest and most common forms in crystals and minerals. The system includes three main types: primitive cubic (cP), body-centered cubic (cI or bcc), and face-centered cubic (cF or fcc). While fcc often refers to the cubic close-packed structure in metals, it's technically a face-centered cubic Bravais lattice, which isn’t always close-packed, as seen in diamond and zincblende lattices. Though unit cells are usually cubic, their primitive unit cells may differ in shape.

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Bravais lattices

Further information: Bravais lattice

The three Bravais latices in the cubic crystal system are:

Bravais lattice	Primitivecubic	Body-centeredcubic	Face-centeredcubic
Pearson symbol	cP	cI	cF
Unit cell

The primitive cubic lattice (cP) consists of one lattice point on each corner of the cube; this means each simple cubic unit cell has in total one lattice point. Each atom at a lattice point is then shared equally between eight adjacent cubes, and the unit cell therefore contains in total one atom (1⁄8 × 8).¹

The body-centered cubic lattice (cI) has one lattice point in the center of the unit cell in addition to the eight corner points. It has a net total of two lattice points per unit cell (1⁄8 × 8 + 1).²

The face-centered cubic lattice (cF) has lattice points on the faces of the cube, that each gives exactly one half contribution, in addition to the corner lattice points, giving a total of four lattice points per unit cell (1⁄8 × 8 from the corners plus 1⁄2 × 6 from the faces).

The face-centered cubic lattice is closely related to the hexagonal close packed (hcp) system, where two systems differ only in the relative placements of their hexagonal layers. The [111] plane of a face-centered cubic lattice is a hexagonal grid.

Attempting to create a base-centered cubic lattice (i.e., putting an extra lattice point in the center of each horizontal face) results in a simple tetragonal Bravais lattice.

Coordination number (CN) is the number of nearest neighbors of a central atom in the structure.³ Each sphere in a cP lattice has coordination number 6, in a cI lattice 8, and in a cF lattice 12.

Atomic packing factor (APF) is the fraction of volume that is occupied by atoms. The cP lattice has an APF of about 0.524, the cI lattice an APF of about 0.680, and the cF lattice an APF of about 0.740.

Crystal classes

Further information: Crystallographic point group

The isometric crystal system class names, point groups (in Schönflies notation, Hermann–Mauguin notation, orbifold, and Coxeter notation), type, examples, international tables for crystallography space group number,⁴ and space groups are listed in the table below. There are a total 36 cubic space groups.

No.	Point group					Type	Example	Space groups
No.	Name⁵	Schön.	Intl	Orb.	Cox.	Type	Example	Primitive	Face-centered	Body-centered
195–197	Tetartoidal	T	23	332	[3,3]+	enantiomorphic	Ullmannite, Sodium chlorate	P23	F23	I23
198–199	Tetartoidal	T	23	332	[3,3]+	enantiomorphic	Ullmannite, Sodium chlorate	P213		I213
200–204	Diploidal	Th	2/m3(m3)	3*2	[3+,4]	centrosymmetric	Pyrite	Pm3, Pn3	Fm3, Fd3	I3
205–206	Diploidal	Th	2/m3(m3)	3*2	[3+,4]	centrosymmetric	Pyrite	Pa3		Ia3
207–211	Gyroidal	O	432	432	[3,4]+	enantiomorphic	Petzite	P432, P4232	F432, F4132	I432
212–214	Gyroidal	O	432	432	[3,4]+	enantiomorphic	Petzite	P4332, P4132		I4132
215–217	Hextetrahedral	Td	43m	*332	[3,3]		Sphalerite	P43m	F43m	I43m
218–220	Hextetrahedral	Td	43m	*332	[3,3]		Sphalerite	P43n	F43c	I43d
221–230	Hexoctahedral	Oh	4/m32/m(m3m)	*432	[3,4]	centrosymmetric	Galena, Halite	Pm3m, Pn3n, Pm3n, Pn3m	Fm3m, Fm3c, Fd3m, Fd3c	Im3m, Ia3d

Other terms for hexoctahedral are: normal class, holohedral, ditesseral central class, galena type.

Single element structures

As a rule, since atoms in a solid attract each other, the more tightly packed arrangements of atoms tend to be more common. (Loosely packed arrangements do occur, though, for example if the orbital hybridization demands certain bond angles.) Accordingly, the primitive cubic structure, with especially low atomic packing factor, is rare in nature, but is found in polonium.⁶ ⁷ The bcc and fcc, with their higher densities, are both quite common in nature. Examples of bcc include iron, chromium, tungsten, and niobium. Examples of fcc include aluminium, copper, gold and silver.

Another important cubic crystal structure is the diamond cubic structure, which can appear in carbon, silicon, germanium, and tin. Unlike fcc and bcc, this structure is not a lattice, since it contains multiple atoms in its primitive cell. Other cubic elemental structures include the A15 structure found in tungsten, and the extremely complicated structure of manganese.

Multi-element structures

Compounds that consist of more than one element (e.g. binary compounds) often have crystal structures based on the cubic crystal system. Some of the more common ones are listed here. These structures can be viewed as two or more interpenetrating sublattices where each sublattice occupies the interstitial sites of the others.

Caesium chloride structure

See also: Category:Caesium chloride crystal structure

One structure is the "interpenetrating primitive cubic" structure, also called a "caesium chloride" or B2 structure. This structure is often confused for a body-centered cubic structure because the arrangement of atoms is the same. However, the caesium chloride structure has a basis composed of two different atomic species. In a body-centered cubic structure, there would be translational symmetry along the [111] direction. In the caesium chloride structure, translation along the [111] direction results in a change of species. The structure can also be thought of as two separate simple cubic structures, one of each species, that are superimposed within each other. The corner of the chloride cube is the center of the caesium cube, and vice versa.⁸

It works the same way for the NaCl structure described in the next section. If you take out the Cl atoms, the leftover Na atoms still form an FCC structure, not a simple cubic structure.

In the unit cell of CsCl, each ion is at the center of a cube of ions of the opposite kind, so the coordination number is eight. The central cation is coordinated to 8 anions on the corners of a cube as shown, and similarly, the central anion is coordinated to 8 cations on the corners of a cube. Alternately, one could view this lattice as a simple cubic structure with a secondary atom in its cubic void.

In addition to caesium chloride itself, the structure also appears in certain other alkali halides when prepared at low temperatures or high pressures.⁹ Generally, this structure is more likely to be formed from two elements whose ions are of roughly the same size (for example, ionic radius of Cs+ = 167 pm, and Cl− = 181 pm).

The space group of the caesium chloride (CsCl) structure is called Pm3m (in Hermann–Mauguin notation), or "221" (in the International Tables for Crystallography). The Strukturbericht designation is "B2".¹⁰

There are nearly a hundred rare earth intermetallic compounds that crystallize in the CsCl structure, including many binary compounds of rare earths with magnesium,¹¹ and with elements in groups 11, 12,¹² ¹³ and 13. Other compounds showing caesium chloride like structure are CsBr, CsI, high-temperature RbCl, AlCo, AgZn, BeCu, MgCe, RuAl and SrTl.

Rock-salt structure

See also: Category:Rock salt crystal structure

The space group of the rock-salt or halite (sodium chloride) structure is denoted as Fm3m (in Hermann–Mauguin notation), or "225" (in the International Tables for Crystallography). The Strukturbericht designation is "B1".¹⁴

In the rock-salt structure, each of the two atom types forms a separate face-centered cubic lattice, with the two lattices interpenetrating so as to form a 3D checkerboard pattern. The rock-salt structure has octahedral coordination: Each atom's nearest neighbors consist of six atoms of the opposite type, positioned like the six vertices of a regular octahedron. In sodium chloride there is a 1:1 ratio of sodium to chlorine atoms. The structure can also be described as an FCC lattice of sodium with chlorine occupying each octahedral void or vice versa.¹⁵

Examples of compounds with this structure include sodium chloride itself, along with almost all other alkali halides, and "many divalent metal oxides, sulfides, selenides, and tellurides".¹⁶ According to the radius ratio rule, this structure is more likely to be formed if the cation is somewhat smaller than the anion (a cation/anion radius ratio of 0.414 to 0.732).

The interatomic distance (distance between cation and anion, or half the unit cell length a) in some rock-salt-structure crystals are: 2.3 Å (2.3 × 10−10 m) for NaF,¹⁷ 2.8 Å for NaCl,¹⁸ and 3.2 Å for SnTe.¹⁹ Most of the alkali metal hydrides and halides have the rock salt structure, though a few have the caesium chloride structure instead.

Alkali metal hydrides and halides with the rock salt structure

	Hydrides	Fluorides	Chlorides	Bromides	Iodides
Lithium	Lithium hydride	Lithium fluoride ²⁰	Lithium chloride	Lithium bromide	Lithium iodide
Sodium	Sodium hydride	Sodium fluoride ²¹	Sodium chloride	Sodium bromide	Sodium iodide
Potassium	Potassium hydride	Potassium fluoride ²²	Potassium chloride	Potassium bromide	Potassium iodide
Rubidium	Rubidium hydride	Rubidium fluoride	Rubidium chloride	Rubidium bromide	Rubidium iodide
Caesium	Caesium hydride	Caesium fluoride	(CsCl structure)

Alkaline earth metal chalcogenides with the rock salt structure

	Oxides	Sulfides	Selenides	Tellurides	Polonides
Magnesium	Magnesium oxide	Magnesium sulfide	Magnesium selenide ²³	Magnesium telluride²⁴	(NiAs structure)
Calcium	Calcium oxide	Calcium sulfide	Calcium selenide ²⁵	Calcium telluride	Calcium polonide ²⁶
Strontium	Strontium oxide	Strontium sulfide	Strontium selenide	Strontium telluride	Strontium polonide²⁷
Barium	Barium oxide	Barium sulfide	Barium selenide	Barium telluride	Barium polonide²⁸

Rare-earth ²⁹ and actinoid pnictides with the rock salt structure

	Nitrides	Phosphides	Arsenides	Antimonides	Bismuthides
Scandium	Scandium nitride	Scandium phosphide	Scandium arsenide³⁰	Scandium antimonide³¹	Scandium bismuthide³²
Yttrium	Yttrium nitride	Yttrium phosphide	Yttrium arsenide ³³	Yttrium antimonide	Yttrium bismuthide³⁴
Lanthanum	Lanthanum nitride ³⁵	Lanthanum phosphide ³⁶	Lanthanum arsenide³⁷	Lanthanum antimonide	Lanthanum bismuthide³⁸
Cerium	Cerium nitride ³⁹	Cerium phosphide ⁴⁰	Cerium arsenide⁴¹	Cerium antimonide	Cerium bismuthide⁴²
Praseodymium	Praseodymium nitride ⁴³	Praseodymium phosphide ⁴⁴	Praseodymium arsenide ⁴⁵	Praseodymium antimonide ⁴⁶	Praseodymium bismuthide ⁴⁷
Neodymium	Neodymium nitride ⁴⁸	Neodymium phosphide ⁴⁹	Neodymium arsenide⁵⁰	Neodymium antimonide⁵¹	Neodymium bismuthide ⁵²
Promethium	?	?	?	?	?
Samarium	Samarium nitride ⁵³	Samarium phosphide ⁵⁴	Samarium arsenide ⁵⁵	Samarium antimonide ⁵⁶	Samarium bismuthide⁵⁷
Europium	Europium nitride ⁵⁸	Europium phosphide	(Na2O2 structure)⁵⁹	(unstable)⁶⁰
Gadolinium	Gadolinium nitride ⁶¹	Gadolinium phosphide	Gadolinium arsenide⁶²	Gadolinium antimonide⁶³	Gadolinium bismuthide⁶⁴
Terbium	Terbium nitride ⁶⁵	Terbium phosphide	Terbium arsenide⁶⁶	Terbium antimonide⁶⁷	Terbium bismuthide⁶⁸
Dysprosium	Dysprosium nitride ⁶⁹	Dysprosium phosphide	Dysprosium arsenide	Dysprosium antimonide	Dysprosium bismuthide ⁷⁰
Holmium	Holmium nitride ⁷¹	Holmium phosphide	Holmium arsenide ⁷²	Holmium antimonide	Holmium bismuthide ⁷³
Erbium	Erbium nitride ⁷⁴	Erbium phosphide	Erbium arsenide⁷⁵	Erbium antimonide	Erbium bismuthide⁷⁶
Thulium	Thulium nitride ⁷⁷	Thulium phosphide	Thulium arsenide	Thulium antimonide	Thulium bismuthide⁷⁸
Ytterbium	Ytterbium nitride ⁷⁹	Ytterbium phosphide	Ytterbium arsenide⁸⁰	Ytterbium antimonide	(unstable)⁸¹ ⁸²
Lutetium	Lutetium nitride ⁸³	Lutetium phosphide	Lutetium arsenide	Lutetium antimonide	Lutetium bismuthide
Actinium	?	?	?	?	?
Thorium	Thorium nitride ⁸⁴	Thorium phosphide⁸⁵	Thorium arsenide⁸⁶	Thorium antimonide⁸⁷	(CsCl structure)
Protactinium	?	?	?	?	?
Uranium	Uranium nitride ⁸⁸	Uranium monophosphide ⁸⁹	Uranium arsenide⁹⁰	Uranium antimonide⁹¹	Uranium bismuthide⁹²
Neptunium	Neptunium nitride	Neptunium phosphide	Neptunium arsenide	Neptunium antimonide	Neptunium bismuthide⁹³
Plutonium	Plutonium nitride ⁹⁴	Plutonium phosphide ⁹⁵	Plutonium arsenide ⁹⁶	Plutonium antimonide⁹⁷	Plutonium bismuthide⁹⁸
Americium	Americium nitride ⁹⁹	Americium phosphide¹⁰⁰	Americium arsenide¹⁰¹	Americium antimonide¹⁰²	Americium bismuthide¹⁰³
Curium	Curium nitride ¹⁰⁴	Curium phosphide¹⁰⁵	Curium arsenide¹⁰⁶	Curium antimonide¹⁰⁷	Curium bismuthide¹⁰⁸
Berkelium	Berkelium nitride¹⁰⁹	Berkelium phosphide¹¹⁰	Berkelium arsenide¹¹¹	?	Berkelium bismuthide¹¹²
Californium	?	?	Californium arsenide¹¹³	?	Californium bismuthide¹¹⁴

Rare-earth and actinoid chalcogenides with the rock salt structure

	Oxides	Sulfides	Selenides	Tellurides	Polonides
Scandium	(unstable)¹¹⁵	Scandium monosulfide
Yttrium		Yttrium monosulfide¹¹⁶
Lanthanum		Lanthanum monosulfide ¹¹⁷
Cerium		Cerium monosulfide ¹¹⁸	Cerium monoselenide ¹¹⁹	Cerium monotelluride¹²⁰
Praseodymium		Praseodymium monosulfide ¹²¹	Praseodymium monoselenide ¹²²	Praseodymium monotelluride¹²³
Neodymium		Neodymium monosulfide ¹²⁴	Neodymium monoselenide¹²⁵	Neodymium monotelluride¹²⁶
Promethium		?	?	?	?
Samarium		Samarium monosulfide ¹²⁷	Samarium monoselenide	Samarium monotelluride	Samarium monopolonide¹²⁸
Europium	Europium monoxide	Europium monosulfide ¹²⁹	Europium monoselenide ¹³⁰	Europium monotelluride ¹³¹	Europium monopolonide¹³²
Gadolinium	(unstable)¹³³	Gadolinium monosulfide ¹³⁴
Terbium		Terbium monosulfide ¹³⁵			Terbium monopolonide¹³⁶
Dysprosium		Dysprosium monosulfide ¹³⁷			Dysprosium monopolonide¹³⁸
Holmium		Holmium monosulfide ¹³⁹			Holmium monopolonide¹⁴⁰
Erbium		Erbium monosulfide¹⁴¹
Thulium		Thulium monosulfide¹⁴²			Thulium monopolonide¹⁴³
Ytterbium	Ytterbium monoxide	Ytterbium monosulfide ¹⁴⁴			Ytterbium monopolonide¹⁴⁵
Lutetium	(unstable)¹⁴⁶ ¹⁴⁷	Lutetium monosulfide¹⁴⁸			Lutetium monopolonide¹⁴⁹
Actinium		?	?	?	?
Thorium		Thorium monosulfide¹⁵⁰	Thorium monoselenide¹⁵¹	(CsCl structure)¹⁵²
Protactinium		?	?	?	?
Uranium		Uranium monosulfide ¹⁵³	Uranium monoselenide¹⁵⁴	Uranium monotelluride¹⁵⁵
Neptunium		Neptunium monosulfide	Neptunium monoselenide	Neptunium monotelluride
Plutonium		Plutonium monosulfide¹⁵⁶	Plutonium monoselenide ¹⁵⁷	Plutonium monotelluride¹⁵⁸
Americium		Americium monosulfide¹⁵⁹	Americium monoselenide¹⁶⁰	Americium monotelluride¹⁶¹
Curium		Curium monosulfide¹⁶²	Curium monoselenide¹⁶³	Curium monotelluride¹⁶⁴

Transition metal carbides and nitrides with the rock salt structure

	Carbides	Nitrides
Titanium	Titanium carbide	Titanium nitride
Zirconium	Zirconium carbide	Zirconium nitride
Hafnium	Hafnium carbide	Hafnium nitride¹⁶⁵
Vanadium	Vanadium carbide	Vanadium nitride
Niobium	Niobium carbide	Niobium nitride
Tantalum	Tantalum carbide	(CoSn structure)
Chromium	(unstable)¹⁶⁶	Chromium nitride

Many transition metal monoxides also have the rock salt structure (TiO, VO, CrO, MnO, FeO, CoO, NiO, CdO). The early actinoid monocarbides also have this structure (ThC, PaC, UC, NpC, PuC).¹⁶⁷

Fluorite structure

Main article: Fluorite structure

See also: Category:Fluorite crystal structure

Much like the rock salt structure, the fluorite structure (AB2) is also an Fm3m structure but has 1:2 ratio of ions. The anti-fluorite structure is nearly identical, except the positions of the anions and cations are switched in the structure. They are designated Wyckoff positions 4a and 8c whereas the rock-salt structure positions are 4a and 4b.¹⁶⁸ ¹⁶⁹

Zincblende structure

See also: Category:Zincblende crystal structure

The space group of the Zincblende structure is called F43m (in Hermann–Mauguin notation), or 216.¹⁷⁰ ¹⁷¹ The Strukturbericht designation is "B3".¹⁷²

The Zincblende structure (also written "zinc blende") is named after the mineral zincblende (sphalerite), one form of zinc sulfide (β-ZnS). As in the rock-salt structure, the two atom types form two interpenetrating face-centered cubic lattices. However, it differs from rock-salt structure in how the two lattices are positioned relative to one another. The zincblende structure has tetrahedral coordination: Each atom's nearest neighbors consist of four atoms of the opposite type, positioned like the four vertices of a regular tetrahedron. In zinc sulfide the ratio of zinc to sulfur is 1:1.¹⁷³ Altogether, the arrangement of atoms in zincblende structure is the same as diamond cubic structure, but with alternating types of atoms at the different lattice sites. The structure can also be described as an FCC lattice of zinc with sulfur atoms occupying half of the tetrahedral voids or vice versa.¹⁷⁴

Examples of compounds with this structure include zincblende itself, lead(II) nitrate, many compound semiconductors (such as gallium arsenide and cadmium telluride), and a wide array of other binary compounds. The boron group pnictogenides usually have a zincblende structure, though the nitrides are more common in the wurtzite structure, and their zincblende forms are less well known polymorphs.¹⁷⁵ ¹⁷⁶

Copper halides with the zincblende structure

	Fluorides	Chlorides	Bromides	Iodides
Copper	Copper(I) fluoride	Copper(I) chloride	Copper(I) bromide	Copper(I) iodide

Beryllium and Group 12 chalcogenides with the zincblende structure

	Sulfides	Selenides	Tellurides	Polonides
Beryllium	Beryllium sulfide	Beryllium selenide	Beryllium telluride	Beryllium polonide¹⁷⁷ ¹⁷⁸
Zinc	Zinc sulfide	Zinc selenide	Zinc telluride	Zinc polonide
Cadmium	Cadmium sulfide	Cadmium selenide	Cadmium telluride	Cadmium polonide
Mercury	Mercury sulfide	Mercury selenide	Mercury telluride	–

This group is also known as the II-VI family of compounds, most of which can be made in both the zincblende (cubic) or wurtzite (hexagonal) form.

Group 13 pnictogenides with the zincblende structure

	Nitrides	Phosphides	Arsenides	Antimonides
Boron	Boron nitride*	Boron phosphide	Boron arsenide	Boron antimonide
Aluminium	Aluminium nitride*	Aluminium phosphide	Aluminium arsenide	Aluminium antimonide
Gallium	Gallium nitride*	Gallium phosphide	Gallium arsenide	Gallium antimonide
Indium	Indium nitride*	Indium phosphide	Indium arsenide	Indium antimonide

This group is also known as the III-V family of compounds.

Heusler structure

Main article: Heusler compound

The Heusler structure, based on the structure of Cu2MnAl, is a common structure for ternary compounds involving transition metals. It has the space group Fm3m (No. 225), and the Strukturbericht designation is L21. Together with the closely related half-Heusler and inverse-Huesler compounds, there are hundreds of examples.

Iron monosilicide structure

See also: Category:Iron monosilicide structure type

The space group of the iron monosilicide structure is P213 (No. 198), and the Strukturbericht designation is B20. This is a chiral structure, and is sometimes associated with helimagnetic properties. There are four atoms of each element for a total of eight atoms in the unit cell.

Examples occur among the transition metal silicides and germanides, as well as a few other compounds such as gallium palladide.

Transition metal silicides and germanides with the FeSi structure

	Silicides	Germanides
Manganese	Manganese monosilicide	Manganese germanide
Iron	Iron monosilicide	Iron germanide
Cobalt	Cobalt monosilicide	Cobalt germanide
Chromium	Chromium(IV) silicide	Chromium(IV) germanide

Weaire–Phelan structure

A Weaire–Phelan structure has Pm3n (223) symmetry.

It has three orientations of stacked tetradecahedrons with pyritohedral cells in the gaps. It is found as a crystal structure in chemistry where it is usually known as a "type I clathrate structure". Gas hydrates formed by methane, propane, and carbon dioxide at low temperatures have a structure in which water molecules lie at the nodes of the Weaire–Phelan structure and are hydrogen bonded together, and the larger gas molecules are trapped in the polyhedral cages.

External links

JMol simulations by Graz University:
- Simple cubic
- BCC
- FCC
- HCP
Making crystal structure with Molview

References

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Vogt, O.; Mattenberger, K. (1995). "The magnetism of localized or nearly localized 4f and 5f shells". Journal of Alloys and Compounds. 223 (2): 226–236. doi:10.1016/0925-8388(94)09005-x. /wiki/Doi_(identifier) ↩
Vogt, O.; Mattenberger, K. (1995). "The magnetism of localized or nearly localized 4f and 5f shells". Journal of Alloys and Compounds. 223 (2): 226–236. doi:10.1016/0925-8388(94)09005-x. /wiki/Doi_(identifier) ↩
Vogt, O.; Mattenberger, K. (1995). "The magnetism of localized or nearly localized 4f and 5f shells". Journal of Alloys and Compounds. 223 (2): 226–236. doi:10.1016/0925-8388(94)09005-x. /wiki/Doi_(identifier) ↩
Vogt, O.; Mattenberger, K. (1995). "The magnetism of localized or nearly localized 4f and 5f shells". Journal of Alloys and Compounds. 223 (2): 226–236. doi:10.1016/0925-8388(94)09005-x. /wiki/Doi_(identifier) ↩
Benedict, U.; Holzapfel, W.B. (1993). "Chapter 113 High-pressure studies — Structural aspects". Lanthanides/Actinides: Physics I. Handbook on the Physics and Chemistry of Rare Earths. Vol. 17. Elsevier. pp. 245–300. doi:10.1016/s0168-1273(05)80030-3. ISBN 9780444815026. 9780444815026 ↩
Benedict, U.; Holzapfel, W.B. (1993). "Chapter 113 High-pressure studies — Structural aspects". Lanthanides/Actinides: Physics I. Handbook on the Physics and Chemistry of Rare Earths. Vol. 17. Elsevier. pp. 245–300. doi:10.1016/s0168-1273(05)80030-3. ISBN 9780444815026. 9780444815026 ↩
Benedict, U.; Holzapfel, W.B. (1993). "Chapter 113 High-pressure studies — Structural aspects". Lanthanides/Actinides: Physics I. Handbook on the Physics and Chemistry of Rare Earths. Vol. 17. Elsevier. pp. 245–300. doi:10.1016/s0168-1273(05)80030-3. ISBN 9780444815026. 9780444815026 ↩
Benedict, U.; Holzapfel, W.B. (1993). "Chapter 113 High-pressure studies — Structural aspects". Lanthanides/Actinides: Physics I. Handbook on the Physics and Chemistry of Rare Earths. Vol. 17. Elsevier. pp. 245–300. doi:10.1016/s0168-1273(05)80030-3. ISBN 9780444815026. 9780444815026 ↩
Benedict, U.; Holzapfel, W.B. (1993). "Chapter 113 High-pressure studies — Structural aspects". Lanthanides/Actinides: Physics I. Handbook on the Physics and Chemistry of Rare Earths. Vol. 17. Elsevier. pp. 245–300. doi:10.1016/s0168-1273(05)80030-3. ISBN 9780444815026. 9780444815026 ↩
Benedict, U.; Holzapfel, W.B. (1993). "Chapter 113 High-pressure studies — Structural aspects". Lanthanides/Actinides: Physics I. Handbook on the Physics and Chemistry of Rare Earths. Vol. 17. Elsevier. pp. 245–300. doi:10.1016/s0168-1273(05)80030-3. ISBN 9780444815026. 9780444815026 ↩
Benedict, U.; Holzapfel, W.B. (1993). "Chapter 113 High-pressure studies — Structural aspects". Lanthanides/Actinides: Physics I. Handbook on the Physics and Chemistry of Rare Earths. Vol. 17. Elsevier. pp. 245–300. doi:10.1016/s0168-1273(05)80030-3. ISBN 9780444815026. 9780444815026 ↩
Benedict, U.; Holzapfel, W.B. (1993). "Chapter 113 High-pressure studies — Structural aspects". Lanthanides/Actinides: Physics I. Handbook on the Physics and Chemistry of Rare Earths. Vol. 17. Elsevier. pp. 245–300. doi:10.1016/s0168-1273(05)80030-3. ISBN 9780444815026. 9780444815026 ↩
Benedict, U.; Holzapfel, W.B. (1993). "Chapter 113 High-pressure studies — Structural aspects". Lanthanides/Actinides: Physics I. Handbook on the Physics and Chemistry of Rare Earths. Vol. 17. Elsevier. pp. 245–300. doi:10.1016/s0168-1273(05)80030-3. ISBN 9780444815026. 9780444815026 ↩
Benedict, U.; Holzapfel, W.B. (1993). "Chapter 113 High-pressure studies — Structural aspects". Lanthanides/Actinides: Physics I. Handbook on the Physics and Chemistry of Rare Earths. Vol. 17. Elsevier. pp. 245–300. doi:10.1016/s0168-1273(05)80030-3. ISBN 9780444815026. 9780444815026 ↩
Benedict, U.; Holzapfel, W.B. (1993). "Chapter 113 High-pressure studies — Structural aspects". Lanthanides/Actinides: Physics I. Handbook on the Physics and Chemistry of Rare Earths. Vol. 17. Elsevier. pp. 245–300. doi:10.1016/s0168-1273(05)80030-3. ISBN 9780444815026. 9780444815026 ↩
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Didchenko, R.; Gortsema, F.P. (1963). "Some electric and magnetic properties of rare earth monosulfides and nitrides". Journal of Physics and Chemistry of Solids. 24 (7): 863–870. Bibcode:1963JPCS...24..863D. doi:10.1016/0022-3697(63)90062-3. /wiki/Bibcode_(identifier) ↩
Kershner, C.J.; DeSando, R.J.; Heidelberg, R.F.; Steinmeyer, R.H. (1966). "Rare earth polonides". Journal of Inorganic and Nuclear Chemistry. 28 (8): 1581–1588. doi:10.1016/0022-1902(66)80054-4. /wiki/Doi_(identifier) ↩
Didchenko, R.; Gortsema, F.P. (1963). "Some electric and magnetic properties of rare earth monosulfides and nitrides". Journal of Physics and Chemistry of Solids. 24 (7): 863–870. Bibcode:1963JPCS...24..863D. doi:10.1016/0022-3697(63)90062-3. /wiki/Bibcode_(identifier) ↩
Didchenko, R.; Gortsema, F.P. (1963). "Some electric and magnetic properties of rare earth monosulfides and nitrides". Journal of Physics and Chemistry of Solids. 24 (7): 863–870. Bibcode:1963JPCS...24..863D. doi:10.1016/0022-3697(63)90062-3. /wiki/Bibcode_(identifier) ↩
Kershner, C.J.; DeSando, R.J.; Heidelberg, R.F.; Steinmeyer, R.H. (1966). "Rare earth polonides". Journal of Inorganic and Nuclear Chemistry. 28 (8): 1581–1588. doi:10.1016/0022-1902(66)80054-4. /wiki/Doi_(identifier) ↩
Didchenko, R.; Gortsema, F.P. (1963). "Some electric and magnetic properties of rare earth monosulfides and nitrides". Journal of Physics and Chemistry of Solids. 24 (7): 863–870. Bibcode:1963JPCS...24..863D. doi:10.1016/0022-3697(63)90062-3. /wiki/Bibcode_(identifier) ↩
Kershner, C.J.; DeSando, R.J.; Heidelberg, R.F.; Steinmeyer, R.H. (1966). "Rare earth polonides". Journal of Inorganic and Nuclear Chemistry. 28 (8): 1581–1588. doi:10.1016/0022-1902(66)80054-4. /wiki/Doi_(identifier) ↩
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Kruger, O.L.; Moser, J.B. (1967). "Lattice constants and melting points of actinide-group IVA-VIA compounds with NaCl-type structures". Journal of Physics and Chemistry of Solids. 28 (11): 2321–2325. Bibcode:1967JPCS...28.2321K. doi:10.1016/0022-3697(67)90257-0. /wiki/Bibcode_(identifier) ↩
Kruger, O.L.; Moser, J.B. (1967). "Lattice constants and melting points of actinide-group IVA-VIA compounds with NaCl-type structures". Journal of Physics and Chemistry of Solids. 28 (11): 2321–2325. Bibcode:1967JPCS...28.2321K. doi:10.1016/0022-3697(67)90257-0. /wiki/Bibcode_(identifier) ↩
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Bravais lattices

Crystal classes

Single element structures

Multi-element structures

Caesium chloride structure

Rock-salt structure

Fluorite structure

Zincblende structure

Heusler structure

Iron monosilicide structure

Weaire–Phelan structure

See also

Further reading

External links

References