Frank–Kasper phases

Last updated
Unit cell of the A15 phases of Nb3Sn Nb3Sn-unit-cell-from-xtal-1991-3D-SF-B.png
Unit cell of the A15 phases of Nb3Sn
Unit cell of Laves phase with MgZn2 structure (Mg atoms are green). C14-MgZn2.jpg
Unit cell of Laves phase with MgZn2 structure (Mg atoms are green).
Projection of unit cell of sigma phase with CrFe structure along c axis Projection of unit cell of sigma phase with CrFe structure along c axis (Fe atoms are orange).png
Projection of unit cell of sigma phase with CrFe structure along c axis
Unit cell of m phase with W6Fe7 structure projected along c-axis. W6Fe7 uc.png
Unit cell of μ phase with W6Fe7 structure projected along c-axis.

Topologically close pack (TCP) phases, also known as Frank-Kasper (FK) phases, are one of the largest groups of intermetallic 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 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 structure makes them good subjects for theoretical calculations.

Contents

History

In 1958, Frederick C. Frank and John S. Kasper, in their original work investigating many complex alloy structures, [1] [2] 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 numbers. These coordination polyhedra were constructed to maintain topological close packing (TCP). [3]

Unit-cell geometries classification

Based on the tetrahedral units, FK crystallographic 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 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. [4] The sites of 12-coordination are called minor sites and those with more than 12-fold coordination are major sites. [1]

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 alloys with an average coordination number (ACN) of 13.5 and eight A3B stoichiometry 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 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/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 A6B7 stoichiometry, with its prototype W6Fe7, containing rhombohedral 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 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. [5] [1]

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 such as: Nb3Sn, Nb3Al, and V3Ga with applications including wires for high-field superconducting magnets. [6] 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. [7]

See also

Related Research Articles

<span class="mw-page-title-main">Carbide</span> Inorganic compound group

In chemistry, a carbide usually describes a compound composed of carbon and a metal. In metallurgy, carbiding or carburizing is the process for producing carbide coatings on a metal piece.

The lanthanide or lanthanoid series of chemical elements comprises the 14 metallic chemical elements with atomic numbers 57–70, from lanthanum through ytterbium. Lutetium is also sometimes considered a lanthanide, despite being a d-block element and a transition metal. These elements are often collectively known as the rare-earth elements or rare-earth metals.

<span class="mw-page-title-main">Cubic crystal system</span> Crystallographic system where the unit cell is in the shape of a cube

In crystallography, the cubiccrystal 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 crystals and minerals.

<span class="mw-page-title-main">Intermetallic</span> Type of metallic alloy

An intermetallic is a type of metallic alloy that forms an ordered solid-state compound between two or more metallic elements. Intermetallics are generally hard and brittle, with good high-temperature mechanical properties. They can be classified as stoichiometric or nonstoichiometic intermetallic compounds.

A boride is a compound between boron and a less electronegative element, for example silicon boride (SiB3 and SiB6). The borides are a very large group of compounds that are generally high melting and are covalent more than ionic in nature. Some borides exhibit very useful physical properties. The term boride is also loosely applied to compounds such as B12As2 (N.B. Arsenic has an electronegativity higher than boron) that is often referred to as icosahedral boride.

<span class="mw-page-title-main">Weaire–Phelan structure</span>

In geometry, the Weaire–Phelan structure is a three-dimensional structure representing an idealised foam of equal-sized bubbles, with two different shapes. In 1993, Denis Weaire and Robert Phelan found that this structure was a better solution of the Kelvin problem of tiling space by equal volume cells of minimum surface area than the previous best-known solution, the Kelvin structure.

<span class="mw-page-title-main">Niobium–tin</span> Superconducting intermetallic compound

Niobium–tin is an intermetallic compound of niobium (Nb) and tin (Sn), used industrially as a type-II superconductor. This intermetallic compound has a simple structure: A3B. It is more expensive than niobium–titanium (NbTi), but remains superconducting up to a magnetic flux density of 30 teslas [T] (300,000 G), compared to a limit of roughly 15 T for NbTi.

<span class="mw-page-title-main">A15 phases</span>

The A15 phases (also known as β-W or Cr3Si structure types) are series of intermetallic compounds with the chemical formula A3B (where A is a transition metal and B can be any element) and a specific structure. The A15 phase is also one of the members in the Frank–Kasper phases family. Many of these compounds have superconductivity at around 20 K (−253 °C; −424 °F), which is comparatively high, and remain superconductive in magnetic fields of tens of teslas (hundreds of kilogauss). This kind of superconductivity (Type-II superconductivity) is an important area of study as it has several practical applications.

Magnesium aluminide is an intermetallic compound of magnesium and aluminium. Common phases (molecular structures) include the beta phase (Mg2Al3) and the gamma phase (Mg17Al12), which both have cubic crystal structures. Magnesium aluminides are important constituents of 5XXX aluminium alloys (aluminium-magnesium) and magnesium-aluminium alloys, determining many of their engineering properties. Due to the advantage of low density and being strong, magnesium aluminide is important for aircraft engines. MgAl has also been investigated for use as a reactant to produce metal hydrides in hydrogen storage technology. Like many intermetallics, MgAl compounds often have unusual stoichiometries with large and complex unit cells.

<span class="mw-page-title-main">Non-stoichiometric compound</span> Chemical compounds that cannot be represented by an empirical formula

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 ; most often, in such materials, some small percentage of atoms are missing or too many atoms are packed into an otherwise perfect lattice work.

Complex metallic alloys (CMAs) or complex intermetallics (CIMs) are intermetallic compounds characterized by the following structural features:

  1. large unit cells, comprising some tens up to thousands of atoms,
  2. the presence of well-defined atom clusters, frequently of icosahedral point group symmetry,
  3. the occurrence of inherent disorder in the ideal structure.

In chemistry, a Zintl phase is a product of a reaction between a group 1 or group 2 and main group metal or metalloid. It is characterized by intermediate metallic/ionic bonding. Zintl phases are a subgroup of brittle, high-melting intermetallic compounds that are diamagnetic or exhibit temperature-independent paramagnetism and are poor conductors or semiconductors.

A crystallographic database is a database specifically designed to store information about the structure of molecules and crystals. Crystals are solids having, in all three dimensions of space, a regularly repeating arrangement of atoms, ions, or molecules. They are characterized by symmetry, morphology, and directionally dependent physical properties. A crystal structure describes the arrangement of atoms, ions, or molecules in a crystal.

<span class="mw-page-title-main">Copper(I) sulfide</span> Chemical compound

Copper(I) sulfide is a copper sulfide, a chemical compound of copper and sulfur. It has the chemical compound Cu2S. It is found in nature as the mineral chalcocite. It has a narrow range of stoichiometry ranging from Cu1.997S to Cu2.000S. Samples are typically black.

<span class="mw-page-title-main">Chemical compound</span> Substance composed of multiple elements that are chemically bonded

A chemical compound is a chemical substance composed of many identical molecules containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element is therefore not a compound. A compound can be transformed into a different substance by a chemical reaction, which may involve interactions with other substances. In this process, bonds between atoms may be broken and/or new bonds formed.

A stannide can refer to an intermetallic compound containing tin combined with one or more other metals; an anion consisting solely of tin atoms or a compound containing such an anion, or, in the field of organometallic chemistry an ionic compound containing an organotin anion

<span class="mw-page-title-main">Crystal structure of boron-rich metal borides</span> Boron chemical complexes

Metals, and specifically rare-earth elements, form numerous chemical complexes with boron. Their crystal structure and chemical bonding depend strongly on the metal element M and on its atomic ratio to boron. When B/M ratio exceeds 12, boron atoms form B12 icosahedra which are linked into a three-dimensional boron framework, and the metal atoms reside in the voids of this framework. Those icosahedra are basic structural units of most allotropes of boron and boron-rich rare-earth borides. In such borides, metal atoms donate electrons to the boron polyhedra, and thus these compounds are regarded as electron-deficient solids.

Cr<sub>23</sub>C<sub>6</sub> crystal structure

Cr23C6 is the prototypical compound of a common crystal structure, discovered in 1933 as part of the chromium-carbon binary phase diagram. Over 85 known compounds adopt this structure type, which can be described as a NaCl-like packing of chromium cubes and cuboctahedra.

In crystallography, a Strukturbericht designation or Strukturbericht type is a system of detailed crystal structure classification by analogy to another known structure. The designations were intended to be comprehensive but are mainly used as supplement to space group crystal structures designations, especially historically. Each Strukturbericht designation is described by a single space group, but the designation includes additional information about the positions of the individual atoms, rather than just the symmetry of the crystal structure. While Strukturbericht symbols exist for many of the earliest observed and most common crystal structures, the system is not comprehensive, and is no longer being updated. Modern databases such as Inorganic Crystal Structure Database index thousands of structure types directly by the prototype compound. These are essentially equivalent to the old Stukturbericht designations.

UPt<sub>3</sub> Chemical compound

UPt3 is an inorganic binary intermetallic crystalline compound of platinum and uranium.

References

  1. 1 2 3 Frank, F. C.; Kasper, J. S. (1958-03-10). "Complex alloy structures regarded as sphere packings. I. Definitions and basic principles". Acta Crystallographica. International Union of Crystallography (IUCr). 11 (3): 184–190. doi: 10.1107/s0365110x58000487 . ISSN   0365-110X.
  2. Frank, F. C.; Kasper, J. S. (1959-07-10). "Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures". Acta Crystallographica. International Union of Crystallography (IUCr). 12 (7): 483–499. doi: 10.1107/s0365110x59001499 . ISSN   0365-110X.
  3. Joubert, J. M.; Crivello, J. C. (2012). "Non-Stoichiometry and Calphad Modeling of Frank-Kasper Phases". Applied Sciences. 2 (4): 669. doi: 10.3390/app2030669 .
  4. Berne, C.; Sluiter, M.; Pasturel, A. (2002). "Theoretical approach of phase selection in refractory metals and alloys". Journal of Alloys and Compounds. 334 (1–2): 27–33. doi:10.1016/S0925-8388(01)01773-X.
  5. Graef, M.D.; Henry, M.E. (2007) Structure of materials, An introduction to crystallography, diffraction and symmetry. Cambridge University Press. ISBN   1107005876. pp. 518–536
  6. Stewart, G.R. (July 2015). "Superconductivity in the A15 structure". Physica C: Superconductivity and its Applications. 514: 28–35. arXiv: 1505.06393 . doi: 10.1016/j.physc.2015.02.013 .
  7. Crivello, J. C.; Breidi, A; Joubert, J. M. (2013). "Χ and σ phases in binary rhenium-transition metal systems: A systematic first-principles investigation". Inorganic Chemistry. 52 (7): 3674–86. doi:10.1021/ic302142w. PMID   23477863.