Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Covalent bonding and the nature of band gaps in some half-Heusler
  compounds   Half-Heusler compounds \textit{XYZ}, also called semi-Heusler compounds,
crystallize in the MgAgAs structure, in the space group $F\bar43m$. We report a
systematic examination of band gaps and the nature (covalent or ionic) of
bonding in semiconducting 8- and 18- electron half-Heusler compounds through
first-principles density functional calculations. We find the most appropriate
description of these compounds from the viewpoint of electronic structures is
one of a \textit{YZ} zinc blende lattice stuffed by the \textit{X} ion. Simple
valence rules are obeyed for bonding in the 8-electron compound. For example,
LiMgN can be written Li$^+$ + (MgN)$^-$, and (MgN)$^-$, which is isoelectronic
with (SiSi), forms a zinc blende lattice. The 18-electron compounds can
similarly be considered as obeying valence rules. A semiconductor such as
TiCoSb can be written Ti$^{4+}$ + (CoSb)$^{4-}$; the latter unit is
isoelectronic and isostructural with zinc-blende GaSb. For both the 8- and
18-electron compounds, when \textit{X} is fixed as some electropositive cation,
the computed band gap varies approximately as the difference in Pauling
electronegativities of \textit{Y} and \textit{Z}. What is particularly exciting
is that this simple idea of a covalently bonded \textit{YZ} lattice can also be
extended to the very important \textit{magnetic} half-Heusler phases; we
describe these as valence compounds \textit{ie.} possessing a band gap at the
Fermi energy albeit only in one spin direction. The \textit{local} moment in
these magnetic compounds resides on the \textit{X} site.

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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an