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Thermoelectric Materials and Devices

The Royal Society of Chemistry

Zintl Phases: Recent Developments in Thermoelectrics and Future Outlook

SUSAN M. KAUZLARICH, ALEX ZEVALKINK, ERIC TOBERERAND G. JEFF SNYDER

1.1.1 Introduction

Definition of Zintl Phases

The term Zintl phase was first used by F. Laves to indicate a subset of compounds within the general class of intermetallics, named after Eduard Zintl, a German scientist who was the first to systematically prepare and structurally characterize these phases. Zintl's interest was in determining what combination of elements would form salt-like structures, focusing on the heavier elements of group 13, 14 and 15. During this time, Hume-Rothery and Westgren had demonstrated the correlation of structure and valence electron concentration for intermetallics, and the compounds that Zintl studied did not fall within those structure-electron count rules. As more compounds were discovered and the transition between salt-like and metallic structures became less clear, this definition proved to be too limiting. Schäfer, Eisenmann, and Müller proposed a more general definition where electron transfer is essentially complete between the alkali or alkaline earth cation and the electronegative elements that utilize the electrons such that they achieve a filled valence either by covalent bonding or by the formation of lone pairs of electrons. Therefore, these phases exhibit salt-like characteristics from the ionic bonding between the cation and the anionic unit. The anionic unit can be isolated anions; if there are not enough electrons for a filled octet, then they form covalent bonds and polyanionic units. The Zintl concept provides a simple idea concerning ionic and covalent bonding within intermetallic phases, allowing for a simple description of bonding that provides insight into the structure and properties of intermetallic phases. One simple way to define a Zintl phase was articulated by Nesper and Miller as the following: there exists a well-defined relationship between chemical and electronic structures in a Zintl phase and a chemist can understand the structure by using simple electron counting rules.

1.1.2 Charge Counting/Formal Valence Rules

Since Zintl phases fall between insulators and metals, it can be difficult to devise a consistent set of rules governing their classification. The salt-like nature of these phases often results in high melting points, high heats of formation, poor conductivities and greater brittleness than many intermetallics. There is the requirement for a well-defined relationship between their chemical and electronic structures, but that can also be a difficult criterion to implement since it requires a detailed knowledge of the structure and bonding. This particular criterion implies that Zintl phases are line compounds with narrow homogeneity widths, a restriction that would make this classification of compounds difficult to dope or manipulate electronically, and therefore uninteresting to those pursuing optimization of thermoelectric properties. In order to understand how to think about these phases, let's start by restating the obvious: all Zintl phases are composed of an electropositive atom, which is treated like a fully ionized element that provides its electrons to the more electronegative elements in the structure. These electronegative elements either use those electrons to form a closed-shell ion or, if there are not enough electrons for this, to form bonds in order to achieve a full octet of electrons. These compounds are distinguished from insulators by the size of the band gap and are typically considered to be semiconductors.

In binary Zintl phases, AaXx (A = electropositive metal, X = electronegative element) 8x electrons are required in order to achieve an octet (or closed shell) for the x X atoms, e(A) and e(X) are the number of valence electrons of A and X.

a • e(A) + x • e(X) = 8x (1.1)

Typically, it is assumed that there are no bonds between A atoms and that X can have X-X bonds that are considered to be two-centre, two-electron bonds, and that the octet rule is satisfied for both elements. If this is the case, then the number of the valence electron count per formula unit of AaXx(VEC) is:

[FORMULA OMITTED] (1.2)

While this equation provides the VEC for the compound formula, the term in the parentheses represents the average number of valence electrons per anion, Nx. In general, this results in the classical valence rule for insulators — the 8 — N rule proposed by Mooser and Pearson — which provides the number of covalent bonds required to satisfy the anion valence. W. Klemm proposed an additional nuance where the more electronegative partner is described as an element with the same number of electrons: a pseudoatom concept. Consider the charged X(aeA / x) — unit: if Nx is non-integral, then a set of pseudoatoms is required to describe the observed coordination environments. For example, heteroanions with tetrahedral units can be described as the analogous orthooxosilicate or germanate anions: [SiP4]8- [SiA4]8- or [GeP4]8- and [GeAs4]8- where the large formal charge is balanced by means of the alkaline earth metal cation. The combination of Zintl's original proposal and Klemm's pseudoatom description is now called the Zintl-Klemm concept. Based on this electron counting model, these compounds should all be semiconductors. However, the difference between insulators and semiconductors is somewhat arbitrarily based on the bandgap and there are suggestions in the literature of either 2.5 eV10 or 2.0 eV. Because of the simple electron counting scheme, the Zintl-Klemm concept is a powerful tool for the assessment of complex main group solids and there are a number of groups working to put this on firm theoretical grounds.

The incorporation of transition metals into these structures adds complexity and has expanded the original criteria. Some of the first research in this area focused on transition metal containing compounds that are isostructural to known main group Zintl compounds. Analogous to main group compounds, these compounds contained anionic units that showed isoelectronic relationships with transition metal halides and chalcogenides. The Zintl-Klemm idea of bonding has been successfully used to probe changes in electronics and bonding within the ThCrSi structure type. Using the Zintl concept, totally new compounds have been prepared and novel properties obtained. The addition of both transition metals and rare earth ions have expanded this area considerably.

1.1.3 Thermoelectric Zintl Compounds

Good thermoelectric materials have low electrical resistivity, low thermal conductivity and a large Seebeck coefficient. Typically, small band-gap semiconductors with carrier concentrations within 10-19 - 1021 cm-3 work better than metals or insulators. Also, a large unit cell, heavy atoms, and structural complexity generally result in good thermoelectric (TE) efficiency.

Many Zintl materials fulfill these qualifications; however, relatively few were investigated for their thermoelectric properties until the last few years. Since these compounds are valence precise and possess the requisite small band gap as well as having complex structures, it is expected that new thermoelectrics with high efficiency may be discovered. The potential of this area for further research is demonstrated so far with a few structure types that will be described below.

1.1.3.1 Yb14MnSb11 Structure Type

Yb14MnSb11 is one of the first recognized phases with excellent thermoelectric performance (zT ~ 1 at 1200 K). This compound is of the Ca14AlSb11 structure type (shown in Figure 1.1). A variety of compounds of this structure type have been reported for the heavier alkaline earth cations (Ca, Sr, Ba) with Al, Ga, In, Zn, Cd, Mn, and Nb and the pnictides from P to Bi. The rare earths, Eu and Yb, have also been prepared, along with isovalent solid solutions of a variety of compounds. This structure type has also been prepared with a small amount of Ln3+ replacing some of the Yb2+ and a small amount of Te replacing some Sb in Yb14MnSb11. In general, all of the compounds can be synthesized by reacting the elements in sealed Nb or Ta tubes. The tubes are sealed in fused silica tubes either under vacuum or 0.25 atmosphere of Ar and heated to temperatures of up to 1250 °C for periods of 24-300 h. There is evidence for reaction of the Nb tubes with some of the elements, so Ta is considered the more ideal container. Quantitative yields can be obtained at low temperatures for some of the phases, but X-ray quality single crystals are formed only at higher temperatures. Yb14MnSb11 can be prepared by high temperature inductive heating. In addition to direct reaction of the elements, large crystals can be prepared from Sn flux; this work provided the initial steps forward for preparing large amounts of phase pure material for detailed property measurements, including thermoelectric properties.

The compounds crystallize in the tetragonal system, I41/acd (Z = 8). In the framework of valence rules, the structure of these compounds can be understood according to one formula unit (A14MPn11) corresponding to 14A2+ cations + 4 Pn3- anions + MPn49- tetrahedron + Pn37- linear unit. The tetrahedron has 4 point symmetry and is translated by half along the c axis, while the Pn3 units have 222 point symmetry and are staggered by 90° along the c axis with respect to each other. The isolated Pn atoms are 6-coordinated by cations and are located between the tetrahedral and the Pn3 units, forming a spiral along a screw axis coincident with the c axis. The linear anion, Pn37- unit, can be either symmetric or asymmetric, depending on both the identity of the cation and anion. The lighter pnictides with large cations tend to be asymmetric. The structure can also be related to the Cu2O structure type, but forming two interpenetrating networks. The oxygen atoms are substituted by the tetrahedron and the Cu atoms are substituted by the pnictide octahedron. The central Pn atoms of the linear polyanions connect the nets with the remaining cations.

CaAl2Si2 Structure Type

The CaAl2Si2 structure type (space group P3m1, Z = 1) is prevalent for compounds with the AB2X2 composition. There has been extensive research into compounds of this structure type. An apparent requirement for this structure type is that the B atoms are either main group or transition metals with d0, d5, or d10 electronic configuration. Several of the compounds with the CaAl2Si2 structure type have been shown to have zT values near unity. In particular, the solid solution of Ca1-xYbxZn2Sb2 was first shown to have promise. The layered structure can be described as consisting of two adjacent puckered hexagonal nets of alternating Al and Si. The An+ cations alternate between the [B2Xx]n- double layers (Figure 1.2). Structural relationships to other structure types, such as BaAl3 and CaSi2, have been described.

1.1.3.3 Sr3GaSb3 Structure Type

Compounds with the A3MPn3 stoichiometry can crystallize in four different structure types. Sr3GaSb3 crystallizes in the monoclinic crystal system (space group P21/n) and the three other structure types include orthorhombic Ba3GaSb3 (Z = 8) and Ca3InP3 (Z = 4) both in space group Puma and Ba3AlSb3, which crystallizes in the space group Cmca, Z = 8. All structures of A3MPn3 contain MPn4 tetrahedra and the structures differ depending on how these tetrahedra are connected. Sr3GaSb3, shown in Figure 1.3, contains infinite non-linear chains of corner sharing tetrahedra. Various combinations of A = Ca, Sr, Ba, Eu; M = Al, Ga, In; Pn = P, As, Sb have been reported; however, a systematic study has not been performed. For example, A3GaSb3 (A = Sr, Ba) have been reported, but Ca3GaSb3 or Eu3GaSb3 have not. The only Eu containing phase reported is Eu3InP3, which is described as very air-sensitive with high electrical resistivity. To date, the thermoelectric properties of Ca3AlSb3, Sr3GaSb3, and Sr3AlSb3 have been reported.

1.1.3.4 Ca5Ga2As6 Structure Type

The Zintl compound, Ca5Al2Sb6, is well known and crystallizes in the Ca5Ga2As6 structure type (space group Pbam, Z = 2) Compounds of Ca5M2Sb6 formula (with M = Al, Ga, In) have been prepared and all belong to this structure type. Similar to the SrGaSb compound, this structure type is another example of MSb4 tetrahedra that are connected in a unique fashion. The structure type is composed of chains of corner-linked MSb4 tetrahedra, connected through Sb-Sb bonds to form ladder-like moieties (Figure 1.4).

1.2 Thermal Properties

The thermal conductivity of Zintl compounds is found to be extremely low, particularly at high temperature. This low thermal conductivity generally overcomes the lower electronic mobility found in these materials and provides the foundation for high zT. Additionally, the complex structures enable phonon behaviour not observed in more simple lattices.

Figure 1.5 shows that the lattice thermal conductivity, κL, for many Zintl compounds is significantly below that of heritage Si0.8Ge0.2. Near room temperature, many of these materials show a decaying lattice thermal conductivity due to increased phonon-phonon scattering, while others exhibit thermal conductivity values with little temperature dependence. The latter behaviour will be explored below. Many of these materials display a slight upturn in thermal conductivity near their maximum measurement temperature. At these high temperatures, minority carrier contributions to the conductivity become significant, leading to a bipolar contribution. The standard Wiedemann-Franz approach to removing the electronic contribution does not capture this contribution.

1.2.1 Theory behind Low [Kappa]L in Complex Materials

A simple kinetic theory approach to phonon transport and heat conduction reveals that the three primary descriptors of thermal conductivity are the volumetric heat capacity (Cv), phonon group velocity (v) and mean free path between collisions (l). As Zintl compounds are largely dense materials, there is relatively minor variation in the heat capacity. However, the group velocity and phonon relaxation time (τph = l/v) are critically dependent on material composition and crystal structure.

The phonon relaxation time is determined by several scattering sources, including phonon-phonon, defect, and boundary scattering. In most materials at high temperature, Umklapp (phonon-phonon) scattering is the dominant scattering mechanism. Shown in Figure 1.5, κL in Ca5Al2Sb6 provides an excellent example of the 1/T temperature dependence expected when Umklapp scattering dominates. Umklapp scattering is governed by the anharmonicity of the lattice, typically parameterized by the Grüneisen parameter. The Grüneisen parameter has been characterized using thermal expansion measurements for few Zintl compounds to date, and moderate values between 1.5-2 have been found. However, in 'rattling' compounds, the mode-specific Grüneisen parameter can be quite high near the rattling frequency and leads to increased scattering of phonons in that frequency regime. Such mode-specific values are obtained from temperature dependent inelastic scattering measurements.

In addition to Umklapp scattering, point defect scattering in Zintl compounds has been harnessed to scatter high frequency phonons. One early example is Yb1-xCaxZn2Sb2. Here, the thermal conductivity responds as predicted from classic thermal scattering theory (Figure 1.6), with the most substantial reduction to κl occurring at 300 K near x = 0.5. Likewise, Yb9Mn4.2Sb9 has Mn interstitials that act as scattering sources and also reduce κL at room temperature. To scatter low frequency phonons, boundary scattering from grain boundaries, nanostructures, for example, can be used. Despite the success of nanostructures in reducing κL in other materials, little work has been devoted to nano-structuring Zintl compounds. Extended defects (stacking faults) have been observed in the layered Zintl compound SrZnSb2, and have been shown to significantly reduce κL near room temperature.

Phonon group velocity, υg, has been found to play a critical role in explaining the low thermal conductivity in Zintl compounds. Like many thermoelectric materials, the low frequency limit of υg, (speed of sound) in many Zintl compounds is quite low, arising from a combination of heavy atoms and soft bonding between covalent moieties. Furthermore, Zintl compounds often possess large mass contrast, which increases the gap between phonon modes at the Brillouin zone edges and at the zone centre. Such large gaps flatten the phonon modes and lead to reduced group velocity. When this phenomenon is combined with extremely complex structures (here, complexity refers to the number of atoms within the primitive cell), the group velocity throughout much of the dispersion can be significantly suppressed. As the size of the real-space cell grows, the Brillouin zone shrinks, and the fraction of optical phonon modes with low velocity increases rapidly. As the number of atoms in the primitive cell (N) increases, the acoustic contribution to kl shrinks, scaling roughly as 1/N1/3. Figure 1.7 shows the experimental κL in selected Zintl phases as a function of N, illustrating the benefit of a large unit cell and correspondingly small contribution from acoustic phonons. Further reduction in the acoustic group velocity can be achieved through the inclusion of 'rattling' modes that flatten the phonon dispersion near the resonant frequency of the rattling species.

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Excerpted from Thermoelectric Materials and Devices by Iris Nandhakumar, Neil M. White, Stephen Beeby. Copyright © 2017 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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