Introduction

Half-Heusler (HH) phases are an intermetallic structure type with unique properties. Generally, the HH chemical formula can be written as XYZ, where X and Y are usually transition metals or rare-earth metals, and Z is a main-group element for example from p-block^[1][2] The HH structure is a derivative of Heusler alloys, where the chemical formula is X₂YZ; hence the name Half-Heusler. Half-Heusler phases are interesting due to their increased thermoelectric (TE) properties: converting heat into electricity. Besides TE properties, studies have shown that certain HH phases can be used as topological insulators^[3], meaning that the surface behaves like a conductor and the bulk behaves as an insulator. These properties open up new possibilities, for example, in the field of thermoelectric conversion technologies. The most common information about the Half-Heusler can be found from the table 1 below.

Table1. Information about the Half-Heusler.

Structure

The Half-Heusler crystal structure differs from Heusler alloys; however, it is still a cubic structure. Compared to the Heusler alloy's Fm-3m (255) space group, the symmetry of Half-Heusler is lowered to F-43m (space group number 216) when half of the X element is removed/left out. Figure 1 shows the structural difference between Heusler and Half-Heusler, where half of the X element (grey) is absent. In Half-Heusler phases, the Wyckoff positions for the elements are as follows: X (1/4, 1/4, 1/4), Y (0, 0, 0), and Z (1/2, 1/2, 1/2). There is also the fourth position (3/4, 3/4, 3/4); however, in Half-Heusler, that is unoccupied. 

The positions of elements Y and Z can be switched if it's fully done. This would result in an inverse structure, and it would still be considered the same Half-Heusler. However, if you swap either one of the elements Y or Z with the element X, you would result in a completely different material. The reason why the material changes is that the element X with tetrahedral coordination would change. In the first scenario of swapping Y and Z, it would keep the tetrahedral coordination at element X. This said, the composition XYZ could have three different structures depending on the tetrahedrally coordinated element.^[1][2][4]

Figure 1. Crystal structure difference between Ni₂TiSn Heusler alloy (a) and NiTiSn Half-Heusler (b). Ni: gray, Ti: blue, Sn: purple (Figure: Joona Pystynen)

Properties

Semiconduction

Half-Heusler's have a valence electron count of 18 (8 with e.g. LiAlSi^[5]) , which makes them possible semiconductors: all of the elements have either a filled or an empty valence shell. ^{[1][2][4][6][7]} For example with a HH compound such as NbFeSb the oxidation states for these elements are Nb⁵⁺, Fe^2-, and Sb^3-, thus the overall material is neutral and and all of the elements are filled or empty respectively to their valence shell. Their band structures are typically more towards an indirect semconductor than a direct one and calculated band gaps are typically around 0.5 - 1 eV. Figure 2 shows examples of band structures and band gaps for different Half-Heusler compounds. Carrier pockets are different between HH compounds because different elements contributes differently to the overall orbitals.

Figure 2. Band structures and band gaps of different Half-Heusler materials.^[6] (Lisence: CC BY 4.0)

Thermoelectricity

Half-Heusler's can be either n-type or p-type doped. This feature allows for the optimization of thermoelectric properties through targeted alterations of charge carriers and possible creation of disorder and these alterations can decrease thermal conductivity. For example doping on the Z position can alter the number of charge carriers, while doping on the X and Y positions can simultaneously introduce disorder. Half-Heusler materials are especially attractive for thermoelectric applications due to their remarkable properties, including high Seebeck coefficients and high electrical conductivity. The only drawback to these materials is at the moment their relatively high thermal conductivity.^[1] However, ongoing research efforts are seeking to address this limitation and improve the overall thermoelectric performance of Half-Heusler compounds.

References