Frank–Kasper Phases
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Topologically close pack (TCP) phases, also known as Frank-Kasper (FK) phases, are one of the largest groups of
intermetallic An intermetallic (also called intermetallic compound, intermetallic alloy, ordered intermetallic alloy, long-range-ordered alloy) is a type of metallic alloy that forms an ordered solid-state compound between two or more metallic elements. Inte ...
compounds, known for their complex crystallographic structure and physical properties. Owing to their combination of periodic and aperiodic structure, some TCP phases belong to the class of
quasicrystal A quasiperiodicity, quasiperiodic crystal, or quasicrystal, is a structure that is Order and disorder (physics), ordered but not Bravais lattice, periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks trans ...
s. 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 Non-stoichiometric compounds are chemical compounds, almost always solid inorganic compounds, having chemical element, elemental composition whose proportions cannot be represented by a ratio of small natural numbers (i.e. an empirical formula); ...
structure makes them good subjects for theoretical calculations.


History

In 1958, Charles Frank and John S. Kasper, in their original work investigating many complex
alloy An alloy is a mixture of chemical elements of which in most cases at least one is a metal, metallic element, although it is also sometimes used for mixtures of elements; herein only metallic alloys are described. Metallic alloys often have prop ...
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 into crystals using other polyhedra with larger
coordination number In chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it. The ion/molecule/atom surrounding the central ion ...
s. These coordination
polyhedra In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary su ...
were constructed to maintain topological close packing (TCP).


Unit-cell geometries classification

Based on the
tetrahedral In geometry, a tetrahedron (: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular Face (geometry), faces, six straight Edge (geometry), edges, and four vertex (geometry), vertices. The tet ...
units, FK crystallographic structures are classified into low and high polyhedral groups denoted by their
coordination number In chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it. The ion/molecule/atom surrounding the central ion ...
s (CN) referring to the number of atom centering the polyhedron. Some atoms have an icosahedral 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 phases, σ, μ, M, P, and R.


A15 phases

A15 phases are
intermetallic An intermetallic (also called intermetallic compound, intermetallic alloy, ordered intermetallic alloy, long-range-ordered alloy) is a type of metallic alloy that forms an ordered solid-state compound between two or more metallic elements. Inte ...
alloys with an average coordination number (ACN) of 13.5 and eight A3B
stoichiometry Stoichiometry () is the relationships between the masses of reactants and Product (chemistry), products before, during, and following chemical reactions. Stoichiometry is based on the law of conservation of mass; the total mass of reactants must ...
atoms per unit cell where two B atoms are surrounded by CN12 polyhedral (icosahedra), and six A atoms are surrounded by CN14 polyhedral. Nb3Ge is a superconductor with A15 structure.


Laves phases

The three Laves phases are intermetallic compounds composed of CN12 and CN16 polyhedra with AB2 stoichiometry, commonly seen in binary metal systems like MgZn2. Due to the small
solubility In chemistry, solubility is the ability of a chemical substance, substance, the solute, to form a solution (chemistry), solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form su ...
of AB2 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 in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
/atom ratio range of 6.2 to 7. It has a primitive
tetragonal In crystallography, the tetragonal crystal system is one of the 7 crystal systems. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the Cube (geometry), cube becomes a rectangular Pri ...
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 A6B7 stoichiometry, with its prototype W6Fe7, containing
rhombohedral In geometry, a rhombohedron (also called a rhombic hexahedron or, inaccurately, a rhomboid) is a special case of a parallelepiped in which all six faces are congruent rhombus, rhombi. It can be used to define the rhombohedral lattice system, a Ho ...
cell with 13 atoms. While many other Frank-Kasper alloy types have been identified, more continue to be found. The alloy Nb10Ni9Al3 is the prototype for the M phase. It has
orthorhombic In crystallography, the orthorhombic crystal system is one of the 7 crystal systems. Orthorhombic Lattice (group), lattices result from stretching a cubic crystal system, cubic lattice along two of its orthogonal pairs by two different factors, res ...
space group with 52 atoms per unit cell. The alloy Cr9Mo21Ni20 is the prototype for the P-phase. It has a primitive orthorhombic cell with 56 atoms. The alloy Co5Cr2Mo3 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 include important intermetallic
superconductors Superconductivity is a set of physical properties observed in superconductors: materials where electrical resistance vanishes and magnetic fields are expelled from the material. Unlike an ordinary metallic conductor, whose resistance decreases ...
such as: Nb3Sn, Nb3Al, and V3Ga with applications including wires for high-field superconducting magnets. Nb3Sn is also being investigated as a potential material for fabricating superconducting radio frequency cavities. Small extents of σ phase considerably decreases the flexibility and impairment in erosion resistance. 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 superalloys, it increases the risk of unwanted precipitation in intermetallic compounds.


See also

*
Complex metallic alloys Complex metallic alloys (CMAs) or complex intermetallics (CIMs) are intermetallic compounds characterized by the following structural features: #large unit cells, comprising some tens up to thousands of atoms, #the presence of well-defined atom ...


References

{{DEFAULTSORT:Frank-Kasper phases Crystal structure types