Icosahedron  Helmut Werheit | Prof. Dr. rer. nat website:   http://www.werheit.mynetcologne.de/
e-mail:   helmut.werheit@koeln.de
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Boron and boron-rich solids

The different modifications of elementary boron and numerous of its compounds belong to the group of materials called "boron-rich solids". They exhibit a close relationship in view of their crystal structures, because all of them contain B12 icosahedra or related aggregates of atoms as essential common structural elements. As these icosahedra essentially determine the electronic structure and hence the chemical bonding of these solids, a large similarity of their chemical and physical properties can be expected. Because this assumption can be taken as proved, at least as far as such investigations have been performed, the generalization of properties determined on single representatives for the entire group of solids seems admittable to a certain extend.

General properties of boron-rich solids:

  • high melting points (2000 - 4000 K); e.g. boron carbide about 2.900 K

  • great hardness; at ambient temperatures 2000 - 4500 kp/mm2. Beta-rhombohedral boron is the hardest elementary crystal after diamond, and boron carbide is after diamond and cubic boron nitride the third hardest solid at all

  • low density; e.g. boron carbide 2.5 gcm-3

  • small thermal extension coefficient; e.g. boron carbide a = 5.73 10-6 K-1

  • high resistance to chemical attack, hence low corrosivity

  • high neutron absorption cross section, caused by the 10B isotope (enrichment in natural B about 20 %).

  • semiconducting behaviour

Some of these properties offer the prerequisites for technical use under extreme conditions, which are not admittable for most other materials. Moreover, the relationship of properties of this large group of structurally related solids allows the selection or tayloring of specific properties for particular uses. But this needs a detailed knowledge on the properties and their relation to the structural details. To gain this knowledge, is the objective of present investigations.

Developement for specific applications:
For the tayloring of properties of boron-rich solids the following instruments are available:

  • The crystal structures consisting of complicated three-dimensional networks of icosahedra or related aggregates contain holes, which are large enough to accomodate foreign atoms. These solid solutions exhibit properties, which are quantitaively or even qualitatively different from those of the pure structures. E.g. the mechanical properties can be modified considerably.

  • This occupation of interstices by foreign atoms changes the electronic properties, too; e.g. the conductivity character of beta-rhombohedral boron can be changed form p- to n-type, an indispensable reqirement of many semiconductor applications, as thermoelectric equipments, too.

  • The existence of many binary boron compounds is proved in principle, e.g. in the alpha-rhombohedral boron structure group compounds of the types B12X, B12X2, and B12X3. But systematical investigations of physical properties have been performed only in very few cases, especially on boron carbide, and even in this case not in conclusion. It seems very probable that several of these compounds may have properties, which are much more favourable than those of compounds already known (e.g. boron carbide).

  • Such binary boron compounds can have considerable homogeneity ranges. In the case of boron carbide it extends from B4.3C to about B12C. The electronic properties and the thermal conductivity change within the homogeneity range considerably.

  • According to bond chemical considerations it seems probable that further binary homologous compounds with modified or modifiable properties can be synthesized.

  • Ternary compounds, which can be obtained by interstitial or by substitutional introduction of a third partner are very favourable for the conditioning of materials properties. E.g. preliminary investigations on B12CySiz and B12CyAlz have shown that the Seebeck coefficient can be considerably increased compared with boron carbide.

  • Recent investigations on orthorhombic borides have shown, that this structure group allows an extended choise of metals for doping of icosahedral structures. In particular n-type conductivity and extraordinary high Seebeck coefficients (6000 V/K or even more) have been found.

  • A further way to taylor boron-rich compounds for special applications is related to the method of preparation. Besides of melting and large scale reaction methods applied in the case of boron carbide meanwhile the formation of ceramics by hot pressing has become important. This procedure seems not to change the electronic properties considerably, at any rate not irreversibly. Therefore it can be expected that this commercially favourable production method can be used tor electronic equipments. This would be an essential advantage compared with classical semiconductors, which are often needed in the form of expensive monocrystals.

Known technical application of boron-rich materials:
Till now only scarce advantage has been taken from the favourable prereqisites for the technical application of boron-rich materials mentioned. They are largely limited on boron carbide, and even in this case on the chemical composition B
4C at the carbon-rich limit of the homogeneity range. Such applications are:

  • Use for abrasive material (grinding, lapping and polishing); much cheaper than diamond

  • Tools for metalworking

  • Lightweight armor for persons and helicopters

  • Surface hardening by coating of tools

  • Effective fibre reinforcement of polymers

  • Shielding of neutrons.

  • Control rods in nuclear reactors

  • Industrial ceramics (nozzles for sand-blaster, turbines for turbojet enginess, mortars and pestles)

  • Boron carbid/graphite thermocouples

Expected applications of electronic properties:
Applications of boron-rich solids with respect to their electronic properties have been missing besides of the mentioned thermocouple, though the properties are very favourable, because they allow use under extreme conditions (high temperatures, high pressures, strong abrasive loading, chemically agressive surrounding), which are not accessable for the most other materials. In this connection fundamental investigations on boron carbide have shown that it has very favourable prerequisites for the application in the thermoelectric energy conversion, at any rate more favourable than any other semiconductor known.
The Seebeck coefficient of boron carbide is rather high, similar to those usually found in semiconductors. But contrary to all the other semiconductors hitherto known, in boron carbide it increases monotonously up to very high temperatures (> 2300 K). Hence in connection with the normal electrical and the low thermal conductivity very favourable prerequisites for a highly efficient direct thermoelectric energy conversion are available, e.g. to recycle waste heat or to transform solar thermal energy immediately into electrical energy. One essential problem in this respect hitherto unsolved is the n-type doping of boron carbide; but qualitative investigations have already led to the conclusion, that this is possible in principle, and moreover the Seebeck coefficient in ternary compounds of the same structure as boron carbide or of related structures can be increased essentially by suitable doping.
Because of the similarity of properties caused by closely related structures, boron-rich refractory compounds in general are very promising candidate materials for the improvement of the thermoelectric properties. The boron-rich compounds include mainly binary and ternary boron-rich borides (e.g. MeB
12, MeB66 (Na,Mg,Ln)MeB14, the boron modifications and solid solutions of transition elements in beta-rhombohedral boron, boron carbides, and structurally related phases.



(For details and references see

H. Werheit, R. Schmechel, Boron, in Landolt-Börnstein, Numerical Data and functional relationships in Science and Technology Group III, Vol. 41C, Springer, Berlin, 1998, p. 3 - 149)


Natural boron consists of 18.83% 10B and 81.17% 11B (precise masses of 10B: 1012937.32(57) mu and of 11B: 11009303.09(130) mu . The different modifications of elementary boron and the related boron-rich borides exhibit complex structures, which are essentially composed of nearly regular B12 icosahedra and of structural elements consisting of fragments or condensed systems of icosahedra. These structure elements are bonded directly to one another or via single boron or foreign atoms thus forming rigid comparably open three-dimensional frameworks with a large variety of structures. For example in the case of b-rhombohedral boron the space filling is only 36.5 % based on the boron atom radius rB = 0.88 Å. The common structural features based on B12 icosahedra are the reason for more or less close relationships of the properties and distinguish the boron-rich solids qualitatively from solids with simple periodic arrangements of atoms. Nevertheless translation symmetry is maintained in these complex crystal structures and therefore the boron-rich solids must be distinguished from amorphous solids as well, though early measurements suggested certain similarities of properties. On the other hand, the icosahedral boron-rich structures are different from molecular crystals as well, because the intericosahedral bonds are stronger than the intraicosahedral bonds.

In the open structures of all the icosahedral boron-rich solids there are voids of sufficient size to accommodate foreign atoms. This interstitial doping is very important to modify the semiconductor properties of these solids. 

The strong tendency of boron atoms to form icosahedral clusters is underlined by numerous molecular compounds, which are based on icosahedra or related structural elements. Even in boron-implanted silicon B12 icosahedra are formed.


Boron Compounds

For details and references see
H. Werheit, Boron Compounds, in Landolt-Börnstein, Numerical Data and functional relationships in Science and Technology Group III, Vol. 41D, O. Madelung ed., Springer, Berlin, 2000, p. 1- 491.



H. Werheit, Boron and Boron-Rich Compounds; in Y. Kumashiro (ed.), Electric Refractory Materials; Marcel Dekker Inc., New York, 2000, p. 589 - 653


Most important structure families of boron-rich boron compounds


a) with B12 icosahedra and related structure elements

  • alpha-rhombohedral boron structure group

  • beta-rhombohedral boron structure group

  • alpha-tetragonal boron structure group

  • beta-tetragonal boron structure group

  • orthorhombic gamma-AlB12 structure group

  • orthorhombic SiB6 structure group

  • REB50 type structure group

  • structure group of AlB10/C4AlB24-26

  • orthorhombic MgAlB14-type structure group

  • structure group of YB25

  • structure group of BeB3

  • structure group of orthorhombic SiB6

  • structure group of YB66 type borides

b) with non-icosahedral polyhedra

  • hexaborides with B6 octahedra

  • tetraborides with B6 octahedra

  • Dodecaborides with B12 cubo-octahedra (UB12 type)


Meanwhile it has become evident that compounds belonging to the same structure families are not only narrowly related in structure but also related with regard to their physical including their electronic properties. Moreover, the properties of representatives of different structure families are more or less narrowly related as well, at least regarding some specific fundamental properties. For the application of solids such relationships are essential because they facilitate to tailor these materials for specific applications. In the case of those boron compounds, whose structures are essentially determined by icosahedra, some fundamental properties like high melting point, high hardness, high resistance against chemical attack exist even irrespective of their attribution to specific structure families. Hence in the case of these boron compounds the following possibilities to modify specific properties are at disposal without losing the advantage of the fundamental properties.

  •       change of the structure family

  •       change of the elements of binary compounds within the same structure families

  •       variation of the compounds within their sometimes large homogeneity ranges

  •       formation of ternary compounds, which often seems merely to be a kind of doping

  •       doping by the interstitial accommodation of foreign atoms'