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Alkali Metal Trielides Fei Wang Iowa State University Chemistry Publications Chemistry 2011 Revisiting the Zintl–Klemm Concept: Alkali Metal Trielides Fei Wang Iowa State University Gordon J. Miller Iowa State University, [email protected] Follow this and additional works at: http://lib.dr.iastate.edu/chem_pubs Part of the Materials Chemistry Commons, Other Chemistry Commons, and the Physical Chemistry Commons The ompc lete bibliographic information for this item can be found at http://lib.dr.iastate.edu/ chem_pubs/652. For information on how to cite this item, please visit http://lib.dr.iastate.edu/ howtocite.html. This Article is brought to you for free and open access by the Chemistry at Iowa State University Digital Repository. It has been accepted for inclusion in Chemistry Publications by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Revisiting the Zintl–Klemm Concept: Alkali Metal Trielides Abstract To enhance understanding of the Zintl–Klemm concept, which is useful for characterizing chemical bonding in semimetallic and semiconducting valence compounds, and to more effectively rationalize the structures of Zintl phases, we present a partitioning scheme of the total energy calculated on numerous possible structures of the alkali metal trielides, LiAl, LiTl, NaTl, and KTl, using first-principles quantum mechanical calculations. This assessment of the total energy considers the relative effects of covalent, ionic, and metallic interactions, all of which are important to understand the complete structural behavior of Zintl phases. In particular, valence electron transfer and anisotropic covalent interactions, explicitly employed by the Zintl–Klemm concept, are often in competition with isotropic, volume-dependent metallic and ionic interaction terms. Furthermore, factors including relativistic effects, electronegativity differences, and atomic size ratios between the alkali metal and triel atoms can affect the competition by enhancing or weakening one of the three energetic contributors and thus cause structural variations. This partitioning of the total energy, coupled with analysis of the electronic density of states curves, correctly predicts and rationalizes the structures of LiAl, LiTl, NaTl, and KTl, as well as identifies a pressure-induced phase transition in KTl from its structure, based 6– on [Tl6] distorted octahedra, to the double diamond NaTl-type. Disciplines Materials Chemistry | Other Chemistry | Physical Chemistry Comments Reprinted (adapted) with permission from Inorg. Chem., 2011, 50 (16), pp 7625–7636. Copyright 2011 American Chemical Society. This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/chem_pubs/652 ARTICLE pubs.acs.org/IC Revisiting the ZintlÀKlemm Concept: Alkali Metal Trielides Fei Wang and Gordon J. Miller* Department of Chemistry, Iowa State University, Ames, Iowa 50011, United States bS Supporting Information ABSTRACT: To enhance understanding of the ZintlÀKlemm concept, which is useful for characterizing chemical bonding in semimetallic and semiconducting valence compounds, and to more effectively rationalize the structures of Zintl phases, we present a partitioning scheme of the total energy calculated on numerous possible structures of the alkali metal trielides, LiAl, LiTl, NaTl, and KTl, using first-principles quantum mechanical calculations. This assessment of the total energy considers the relative effects of covalent, ionic, and metallic interactions, all of which are important to understand the complete structural behavior of Zintl phases. In particular, valence electron transfer and anisotropic covalent interactions, explicitly employed by the ZintlÀKlemm concept, are often in competition with isotropic, volume-dependent metallic and ionic interaction terms. Furthermore, factors including relativistic effects, electronega- tivity differences, and atomic size ratios between the alkali metal and triel atoms can affect the competition by enhancing or weakening one of the three energetic contributors and thus cause structural variations. This partitioning of the total energy, coupled with analysis of the electronic density of states curves, correctly predicts and rationalizes the structures of LiAl, LiTl, NaTl, and KTl, 6À as well as identifies a pressure-induced phase transition in KTl from its structure, based on [Tl6] distorted octahedra, to the double diamond NaTl-type. ’ INTRODUCTION that is, the line dividing groups 13 and 14.2À9 They keep in- One significant goal of solid-state science is to design and triguing solid-state chemists for many reasons, one of which is that they are promising in many applications especially as prepare materials with desired properties. Because properties are 10À15 the expression of crystal and electronic structures, with the latter thermoelectric materials. The structures of Zintl phases deduced from the former through quantum mechanics, it is can be understood using the ZintlÀKlemm concept. As an example, consider the most frequently quoted Zintl phase, essential to possess a sound understanding of the structures of 16 solids, as well as the forces that govern the aggregation of atoms NaTl, which adopts a double diamond structure with Na and into structures, which can change in response to variations in Tl forming interpenetrating diamond substructures. The ZintlÀ Klemm rationalization of NaTl is that Na donates its 3s electron chemical composition and external conditions. Solids have been À traditionally categorized into three model classes, ionic, metallic, to Tl, resulting in a formal Tl anion with 4 valence electrons. This “anion” behaves as a pseudotetrel atom, each of which forms and covalent, each of which employs different structural ratio- + nalizations. However, there are no clear dividing lines because the 4 covalent bonds and adopts the diamond structure. Each Na variations among the three classes are gradual rather than abrupt. “cation” acts as a charge balancer and space filler. They can even be described using the same theoretical model. Although simplistic, the ZintlÀKlemm concept decently Burdett1 has argued that metals, just like covalent species, can be rationalizes the structures of Zintl phases. The validity of this concept was confirmed by first-principles calculations on described with a tight-binding scheme; their energy bands are 17 18 19 also formed through orbital overlap. So, there is no essential KÀSb, KÀSn, and KÀTe systems. Its success stems from difference between “covalent bonds” and “metallic bonds”, its consideration of charge transfer and covalent interactions in except that in metals the driving force for distortions of the intermetallic compounds, implying that Zintl phases, although electron density is too small to cause electron localization and composed of metallic or semimetallic elements, also involve ionic opening of band gaps in the electronic density of states. Such and covalent interactions. Thus, Zintl phases are a compound continuities among metallic, ionic, and covalent interactions class bridging metallic, ionic, and covalent substances. Also, mean that there are solids that can exhibit metallicity, ionicity, indeed, Zintl phases exhibit features resembling nonmetallic solids, for example, narrow homogeneity ranges or “precise” and covalency simultaneously and cannot be approximated into 14 any one of these three model classes, for instance, Zintl phases. compositions and poor conductivity or semiconductivity. The ZintlÀKlemm concept, however, also has limitations. For For such intermediate solids, the complete structural rationaliza- 20 tion becomes challenging. instance, LiTl, isoelectronic with NaTl, adopts a CsCl-type Zintl phases are compounds composed of electropositive metals (e.g., alkali, alkaline earth, or rare earth metals) and Received: March 29, 2011 electronegative metals or semimetals around the “Zintl line”, Published: July 20, 2011 r 2011 American Chemical Society 7625 dx.doi.org/10.1021/ic200643f | Inorg. Chem. 2011, 50, 7625–7636 Inorganic Chemistry ARTICLE structure, which defies the ZintlÀKlemm concept, whereas LiAl,21 LiGa,22 and LiIn23 all adopt the NaTl-type structure at ambient conditions. Moreover, the ZintlÀKlemm concept does not predict a unique structure for a given chemical composition. For example, besides the cubic diamond structure, the hexagonal diamond or lonsdaleite structure also satisfies the ZintlÀKlemm formalism for TlÀ. Also, KTl adopts a structure thoroughly different from LiTl or NaTl and contains Tl6 distorted octahedra24 with local point symmetry . Every Tl atom can C2h still be perceived as four-bonded, and, indeed, Si atoms form similar octahedral clusters in the gas phase.25 So, the ZintlÀ Klemm rule in KTl is formally obeyed, but it cannot explain the Figure 1. The seven structure types investigated. Blue, Li/Na/K; cause of the difference between KTl and NaTl, which become green, Al/Tl. isostructural under pressures higher than 2 kbar.26 Such structur- al effects of external pressure on Zintl phases have not yet been band structures and valence electron maps for LiAl, LiTl, and NaTl discussed. These limitations stem from the oversimplification of in the NaTl-type structure, the energy cutoffs are set to higher values: 300.4 eV for LiAl, 175.0 eV for LiTl, and 127.5 eV for NaTl. All band the ZintlÀKlemm concept, which considers charge transfer but structures and valence electron density maps were plotted with does not take into complete account the subsequent interactions wxDragon.35
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