
Topologically close pack (TCP) phases, also known as Frank-Kasper (FK) phases, are one of the largest groups of
intermetallic
An intermetallic (also called an intermetallic compound, intermetallic alloy, ordered intermetallic alloy, and a long-range-ordered alloy) is a type of metallic alloy that forms an ordered solid-state compound between two or more metallic elemen ...
compounds, known for their complex
crystallographic structure
In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns th ...
and physical properties. Owing to their combination of periodic and aperiodic structure, some TCP phases belong to the class of
quasicrystals. Applications of TCP phases as high-temperature structural and
superconducting materials have been highlighted; however, they have not yet been sufficiently investigated for details of their physical properties. Also, their complex and often
non-stoichiometric
In chemistry, non-stoichiometric compounds are chemical compounds, almost always solid inorganic compounds, having elemental composition whose proportions cannot be represented by a ratio of small natural numbers (i.e. an empirical formula); mos ...
structure makes them good subjects for theoretical calculations.
History
In 1958,
Frederick C. Frank and John S. Kasper, in their original work investigating many complex
alloy
An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductility, ...
structures,
showed that non-icosahedral environments form an open-end network which they called the major skeleton, and is now identified as the declination locus. They came up with the methodology to pack asymmetric
icosahedra
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons".
There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
into crystals using other polyhedra with larger
coordination numbers. These coordination
polyhedra were constructed to maintain topological close packing (TCP).
Unit-cell geometries classification
Based on the
tetrahedral units, FK
crystallographic
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The word ...
structures are classified into low and high polyhedral groups denoted by their
coordination numbers (CN) referring to the number of atom centering the polyhedron.
Some atoms have an
icosahedral
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons".
There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
structure with low coordination, labeled CN12. Some others have higher coordination numbers of 14, 15 and 16, labeled CN14, CN15, and CN16, respectively. These atoms with higher coordination numbers form uninterrupted networks connected along the directions where the five-fold icosahedral symmetry is replaced by six-fold local symmetry. The sites of 12-coordination are called minor sites and those with more than 12-fold coordination are major sites.
Classic FK phases
The most common members of a FK-phases family are:
A15,
Laves phase
Laves phases are intermetallic phase (matter), phases that have composition AB2 and are named for Fritz Laves who first described them. The phases are classified on the basis of geometry alone. While the problem of Close-packing of equal spheres, ...
s, σ, μ, M, P, and R.
A15 phases
A15 phases are
intermetallic
An intermetallic (also called an intermetallic compound, intermetallic alloy, ordered intermetallic alloy, and a long-range-ordered alloy) is a type of metallic alloy that forms an ordered solid-state compound between two or more metallic elemen ...
alloys with an average coordination number (ACN) of 13.5 and eight A
3B
stoichiometry
Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions.
Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equal ...
atoms per unit cell where two B atoms are surrounded by CN12 polyhedral (icosahedra), and six A atoms are surrounded by CN14 polyhedral. Nb
3Ge is a superconductor with A15 structure.
Laves phases
The three
Laves phase
Laves phases are intermetallic phase (matter), phases that have composition AB2 and are named for Fritz Laves who first described them. The phases are classified on the basis of geometry alone. While the problem of Close-packing of equal spheres, ...
s are intermetallic compounds composed of CN12 and CN16 polyhedra with AB
2 stoichiometry, commonly seen in binary metal systems like MgZn
2. Due to the small
solubility
In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution.
The extent of the solubil ...
of AB
2 structures, Laves phases are almost line compounds, though sometimes they can have a wide homogeneity region.
σ, μ, M, P, and R phases
The sigma (σ) phase is an intermetallic compound known as the one without definite stoichiometric composition and formed at the
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
/atom ratio range of 6.2 to 7. It has a primitive
tetragonal unit cell with 30 atoms. CrFe is a typical alloy
crystallizing in the σ phase at the equiatomic composition. With physical properties adjustable based on its structural components, or its chemical composition provided a given structure.
The μ phase has an ideal A
6B
7 stoichiometry, with its prototype W
6Fe
7, containing
rhombohedral cell with 13 atoms. While many other Frank-Kasper alloy types have been identified, more continue to be found. The alloy Nb
10Ni
9Al
3 is the prototype for the M phase. It has
orthorhombic
In crystallography, the orthorhombic crystal system is one of the 7 crystal systems. Orthorhombic lattices result from stretching a cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular prism with a r ...
space group with 52 atoms per unit cell. The alloy Cr
9Mo
21Ni
20 is the prototype for the P-phase. It has a primitive orthorhombic cell with 56 atoms. The alloy Co
5Cr
2Mo
3 is the prototype for the R-phase which belongs to the rhombohedral space group with 53 atoms per cell.
Applications
FK phase materials have been pointed out for their high-temperature structure and as superconducting materials. Their complex and often non-stoichiometric structure makes them good subjects for theoretical calculations.
A15, Laves and σ are the most applicable FK structures with interesting fundamental properties. The A15 compounds are forming important intermetallic
superconductor with major applications in materials used in wires for superconducting such as: Nb
3Sn, Nb
3Zr, and Nb
3Ti. A majority of superconducting magnets are constructed out of Nb
3Ti alloy.
Small extents of σ phase considerably decreases the flexibility and impairment in erosion
resistance
Resistance may refer to:
Arts, entertainment, and media Comics
* Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm:
** ''Resistance'' (comics), based on the video game of the same title
** ''T ...
. While addition of refractory elements like
W,
Mo, or Re to FK phases helps to enhance the thermal properties in such alloys as steels or nickel-based
superalloy
A superalloy, or high-performance alloy, is an alloy with the ability to operate at a high fraction of its melting point. Several key characteristics of a superalloy are excellent mechanical strength, resistance to thermal creep deformation, g ...
s, it increases the risk of unwanted precipitation in intermetallic compounds.
See also
*
Complex metallic alloys
References
{{DEFAULTSORT:Frank-Kasper phases
Crystal structure types