I. INTRODUCTION
A. Thermoelectric (TE) materials
In recent years, partly due to rising fuel prices and concern over the role of CO2 emissions in the greenhouse atmospheric warming effect, TE material research has become increasingly important worldwide. The TE effect refers to phenomena by which either a temperature difference creates an electric potential or an electric potential creates a temperature difference (Martin et al., Reference Martin, Tritt and Uher2010). These phenomena are known as the Seebeck effect (converting temperature to current), Peltier effect (converting current to temperature), and Thomson effect (conductor heating/cooling). Although all materials have a nonzero TE effect, in most materials it is too small to be useful for practical applications. Low-cost materials that have a large TE effect have potential to be used in applications including power generation and refrigeration.
TE materials can either allow heat to be pumped from one place to another using electricity or allow electricity to be generated from heat. The efficiency and performance of TE power generation or cooling are related to the dimensionless figure of merit (ZT) of the TE materials, given by ZT = S 2σ T/k, where T is the absolute temperature, S is the Seebeck coefficient or thermopower, σ is the electrical conductivity (σ = 1/ρ, ρ is electrical resistivity), and k is the thermal conductivity (Tritt and Subramanian, Reference Tritt and Subramanian2006). In order to develop efficient TE materials, efforts have been expended on synthesizing completely new materials as well as on developing chemically doped materials with improved properties.
B. Phase diagrams and X-ray diffraction patterns
Phase diagrams contain important information for the development of new materials, control of structure and composition of critical phases, and the improvement of properties of technologically important materials. These diagrams very often can be thought of as “road maps” or “blue prints” for processing and for understanding materials' properties, as they provide the theoretical basis for synthesis of materials. Applications of phase diagrams range from preparation of high-quality single crystals and single-phase materials to controlled precipitation of second phases and formation of melts. More specifically, the phase relationships described in a phase diagram can be used to correlate the phases present in X-ray diffraction patterns of material systems, and to understand whether a single phase or a mixture has been obtained.
For over 60 years, the American Ceramic Society (ACerS), in collaboration with National Institute of Standards and Technology (NIST), has evaluated and published the Phase Diagrams for Ceramists series of compilations. A parallel program in alloy phase diagrams is currently managed by the American Society for Metals (ASM). The ASM Alloy Phase Diagrams Center is copyrighted by ASM International, and the data in this product are copyrighted by Material Phases Data System, Vitznau, Switzerland. A portion of the binary diagrams is jointly copyrighted by Material Phases Data System and Japan Science and Technology Corporation, Tokyo, Japan. The availability of phase diagrams in these databases is critical for any branch of materials research, whether it concerns energy-related materials (TEs, superconductors, fuel cells, batteries or supercapacitors), or materials for a diverse array of other applications, such as optoelectronic devices, magnetic materials, ferroelectric materials, etc.
Since X-ray diffraction provides a non-destructive “fingerprint” technique for phase identification, X-ray diffraction reference patterns are especially important for phase characterization. Therefore, it is essential to have complete coverage of experimental/calculated patterns in the Powder Diffraction File (PDF), produced by the International Centre for Diffraction Data (ICDD), to serve as references.
C. ICDD TE task group
ICDD serves a dual role in the scientific community. It is a non-profit publishing house as well as a scientific organization that sponsors diffraction-related conferences and scientific committees for ensuring the high quality of the PDF. In the past two decades, the Ceramics Subcommittee of the Technical Committee of ICDD has created a number of material task groups to ensure extensive coverage of reference diffraction patterns of ceramics phases in the PDF. One of the task groups focuses on TE materials (code “TE” in the PDF). The working definition of TE is that “Thermoelectric materials are materials that have reasonably high Figure of Merit (ZT, ZT = S 2σ/κ; materials with high Seebeck coefficient (S), high electrical conductivity (σ), and low thermal conductivity (κ)) for practical applications.” Some or all of the associated properties (Seebeck coefficient, electrical conductivity (or resistivity (1/σ)), thermal conductivity and ZT) should be added to the PDF and made available to the users.
An important activity of the TE task group is to fill in the gap of the PDF with those phases that have missing patterns and also provide added physical property information to the TE phases. A survey of the TE materials in the PDF is therefore important for the TE community (including the ICDD Grants-in-Aid recipients).
II. Surveying plan
We designed a survey with the aim of compiling the phase diagrams and X-ray diffraction patterns of TE compounds based on known TE systems. To efficiently accomplish this goal, we organized the TE materials in the PDF into five categories, namely half-Heusler compounds, skutterudites, clathrates, oxides, and other chalcogenides, silicides, and pcnitides. This classification will cover a significant number of the state-of-the-art TE materials. The chosen compounds/systems are checked against the phase diagrams databases produced by ASM or by ACerS/NIST, and also against the PDF.
In this report, we will discuss our effort at tabulating information pertaining to the half-Heusler compounds. As these half-Heusler compounds are all semiconductors/metal-alloys, the ASM database was used exclusively.
III. SURVEY OF HALF-HEUSLER COMPOUNDS
A. Background information on half-Heusler compounds
The half-Heusler structure, XYZ, was first discovered by Heusler (Heusler, Reference Heusler1903). The half-Heusler compounds possess MgAgAs type structure (Jeitschko, Reference Jeitschko1970) that is closely related to that of the full-Heusler alloys. The full-Heusler structure, X 2YZ, is built up from four interpenetrating fcc sublattices mutually shifted along the body diagonal by a ¼ distance. In other words, the unit cell of the full-Heusler structure, with space group Fm3m, consists of four inter-penetrating fcc lattices at offsets of A = (0, 0, 0) B = (¼, ¼, ¼), C = (½, ½, ½), and D = (¾, ¾, ¾), with site occupancies A = Y, B = X, and C = Z. If one of the two equivalent sites, (¼, ¼, ¼) or (¾, ¾, ¾), is empty, this will give rise to the half-Heusler XYZ structure that adopts the space group F43m. The half-Heusler structure is shown in Figure 1. These alloys, in general, have three components that often originate from different element groups. Most frequently, two of the groups are composed of transition metals and the third group consists of metals and metalloids. The structures of the full-Heusler and half-Heusler compounds exhibit different properties. For example, while the full-Heusler compounds MNi2Sn (M = Zr, Hf, Ti) are metallic, removal of one of the two Ni sublattices and replacing them by an ordered lattice of vacancies leads to the formation of the half-Heuslers with semi-conducting character (Uher et al., Reference Uher, Yang, Hu, Morelli and Meisner1999).
Structure of a half-Heusler compound XYZ that adopts the space group F43m.
Semiconductors with a small band gap in the density of states are favourable for TE applications. In recent years, half-Heusler compounds that obey the isoelectron rules (the sum of valence electron count (VEC)) of 18 per formula unit (Tobola et al., Reference Tobola, Pierre, Kaprzyk, Skolozdra and Kouacou1998) have attracted increasing attention as new TE compounds because of their high thermoelectric power (TEP = S 2σ) (Ogut and Rabe, Reference Ogut and Rabe1995; Kaczarska, et al., Reference Kaczarska, Pierre, Balla, Tobola, Skolozdra and Melnik1998; Tobola et al., Reference Tobola, Pierre, Kaprzyk, Skolozdra and Kouacou1998; Jung et al., Reference Jung, Koo and Whangbo2000; Tobola and Pierre, Reference Tobola and Pierre2000; Asahi et al., 2008) due to their narrow band gaps. Complex compounds such as TiNiSn phases are promising n-type thermoelectrical materials as illustrated by an exceptionally large figure of merit, ZT~1.5 at high temperatures (Asahi et al., Reference Asahi, Morkkawa, Hazama and Matsubara2008). Doped TiCoSb, a p-type material, exhibits a large thermopower of S = −400 μV/K at 300 K. Larson et al. (Reference Larson, Mahanti, Sportouch and Kanatzidis1999) studied the electronic structure of a class of half-Heusler compounds MNiPn where M is Y, La, Lu, and Yb, and Pn is a pnicogen Sb and Bi and found that all these systems except Yb are narrow gap semiconductors and are potential candidates for high-performance TE materials. Yang et al. (Reference Yang, Li, Wu, Zhang, Chen and Yang2008) conducted theoretical calculations on 36 representative half-Heusler compounds to determine the band structure and predicted TE properties. The dependence of Seebeck coefficient, electrical conductivity, and power factor on the Fermi level was also reported. The electronic structure results predicted the band gaps, and provided an invaluable guide for further experimental work.
B. Material selection rules
In this survey, we focus our attention on the half-Heusler compounds using the following selection rules: (1) for alkali-earth elements, only Mg and Ca are selected (so far half-Heusler compounds containing alkali-earth elements Sr and Ba have no band gap); (2) for group IVB elements Sn, Ge, and Si are used (as Pb is considered toxic and therefore has been avoided), and for VB elements, Sb and Bi were used; and (3) lanthanide elements were chosen except for Pm and Tb.
C. Results of the survey
Table I provides the results of the phase diagram and powder diffraction pattern survey. This table is divided into columns of the chemical formula XYZ; whether the ASM database provides the specific phase diagram (“Y” indicates “Yes” and “N” indicates “No”); a reference to the phase diagram cited in the ASM database if available; the structure type of the XYZ phases, whether they are “cubic,” “hexagonal,” “orthorhombic,” or other; the set number of the reference powder patterns in the PDF (xx-xxx-xxxx). If either the phase diagram or crystallographic information is missing in the PDF, the symbol “–” is used.
Survey results of 306 intermetallic compounds, XYZ, where Z is Si, Ge, Sn, Sb, Bi using the ASM phase diagram data base and the PDF.
Based on our selection rules, we found a total of 306 compounds with the chemical formula XYZ. The structures of these XYZ compounds have been found to be of several different types. Apparently, not all XYZ phases form the half-Heusler type structure (fcc, cF12, F43m), some form hexagonal structures (P63/mmc, P6/mmm, P63mc, and P62m), and some form the orthorhombic Pnam structure. The size factor of each element is of great importance in determining the structure of intermetallics. As a specific example, the structure of the members of the RNiSb family that contain lighter elements (with larger covalent radius; R = La, Ce, Pr, Nd, Sm, Gd, and Tb) is of the hexagonal (p6/mmm or P63/mmc) type, whereas the heavier Dy, Ho, Er, and Y alloys are of the cubic (F43m) type (Marazza et al., Reference Marazza, Rossi and Ferro1980). In some cases, for example, RAuSn, both the cubic and hexagonal structures of the same XYZ formula can be prepared under different conditions. In other cases, while the lighter hexagonal members in the RAuSn (R = lanthanides) compounds crystallize in the space group of P63/mmc, the heavier ones adopt the P63mc space group. In silicides, coexistence of two structure types was also reported: the Fe2P type structure with space group P62m (Dwight et al., Reference Dwight, Harper and Kimball1973) and the orthorhombic Pnam phase (Kotur and Gladyshevskij, Reference Kotur and Gladyshevskij1981). Most orthorhombic phases identified in Table I are metallic.
Among the 306 compounds, a total of 67 compounds have no information regarding phase diagrams or crystallographic data. These compounds are listed below as Sn-, Ge-, Si-, Sb, and Bi-containing compounds:
(1). NbIrSn, LaAuSn, TaCoSn, TaRhSn, TaIrSn, TiPdSn, VCoSn, VRhSn, VIrSn
(2). PrAgGe, Nd-Ag-Ge, Sm-Ag-Ge, PrAuGe, SmAuGe, TmAuGe, ScAgGe, TaIrGe, TiPtGe, VRhGe, VIrGe
(3). EuCuSi, HoAgSi, LaAuSi, CeAuSi, PrAuSi, SmAuSi, EuAuSi, GdAuSi, DyAuSi, HoAuSi, ErAuSi, TmAuSi, ScAgSi, VRhSi, VIrSi
(4). HfIrSb, MgAgSb, MgAuSb, EuNiSb, LuPdSb, TiIrSb, ZrIrSb
(5). CaAgBi, CaAuBi, HfCoBi, HfRhBi, HfIrBi, MgAgBi, MgAuBi, LaNiBi, CeNiBi, EuNiBi, YbNiBi, EuPdBi, DyPdBi, HoPdBi, YPdBi, PrPtBi, NdPtBi, SmPtBi, EuPtBi, ScPtBi, TiCoBi, TiRhBi, TiIrBi, ZrRhBi, ZrIrBi
III. CONCLUSION
We found that among 306 potential XYZ systems that we have surveyed, 234 have powder diffraction patterns in the PDF, 28 have phase diagram information, and 67 do not have any phase diagram or crystallographic information. Among the XYZ systems with powder patterns, 84 are reported with cubic F43m half-Heusler structures, and the others are hexagonal, orthorhombic or unknown. Some XYZ compounds have both the cubic half-Heusler and hexagonal structures, and others have hexagonal structure with different space groups, or both hexagonal and orthorhombic structures.
Although not all XYZ phases that we have discussed belong to the half-Heusler cubic type phase, from the point of view of filling the gap in both the phase diagram and powder diffraction databases, it is also important to fill the missing hexagonal and orthorhombic phases as well. In addition, a majority of the half-Heusler phases still need to have property data. It is hoped that this survey activity will provide a useful starting point for the TE and materials research community, phase diagram community, ICDD task group members and grants-in-aid recipients to provide missing phase diagrams, reference X-ray powder diffraction patterns, and property data to improve the coverage of the phase diagram databases and the PDF. Success of these database activities will lead to efficient and productive materials research and development.
