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corresponding more or less to the sum of the ionization energy and the electron
affinity (Flynn
1972
; Kittel
2005
; Samsonov
1968
). Clearly, the degree of ionic
character (ionicity) will tend to increase with increasing difference in electroneg-
ativities of anion and cation but there is no general agreement on how to express the
ionicity quantitatively in terms of electronegativities or of other parameters. The
usual approach has been to try to identify measures of the homopolar and ionic
components of the bonding based on observed properties that reflect the distribution
of electron density; thus the definitions of Pauling (
1960
,
1971
), Phillips (
1968
,
1969
,
1970
,
1973
), van Vechten (
1969a
,
b
), Kowalczyk et al. (
1974
), Hübner and Leon-
hardt (
1975
), Stewart et al. (
1980
) and Guo et al. (
1999
) are variously derived from
thermochemically determined electronegativities, dielectric constant, spectroscopic
parameters and ''orbital electronegativities'' calculated from ionization potentials
and electron affinities.
A generally useful scale for comparing ionicities appears to be that of Phillips
and Van Vechten, initially only applied to the binary compounds A
N
B
8-N
(N = group in the periodic table) but extended to other compounds by Levine
(
1973a
,
b
); as well as the references above, see Ramakrishnan (
1974
) for a simple
exposition and Madelung (
1978
, pp. 331-352) for further discussion of this and
other measures; also Catlow and Stoneham (
1983
). The Phillips-Van Vechten
ionicities are obtained as follows:
1. Resolving the crystal potential into a covalent component, corresponding to an
average of the properties of the two atoms, and an ionic component, corre-
sponding to their difference, an average band gap E
g
is defined as E
g
¼
E
c
þ
E
i
Þ
2
;
where E
c
;
E
i
are components of the band gap expressing the covalent and
ionic character, respectively.
2. E
g
is obtained from the observed static dielectric constant.
3. E
c
is determined from an empirical formula relating it to the interatomic
spacing, using the purely covalent C and Si to calibrate this relationship; thence
E
i
¼
E
g
E
c
is obtained.
4. The ionicity parameter f
i
is defined as f
i
¼
E
i
=
E
g
;
0
f
i
1
:
Selected values of f
i
are given in Table
1
from Levine (
1973a
,
b
).
The general trends and relative positions are similar to those given by Pauling
(
1960
), Kowalczyk et al. (
1974
), and Hubner and Leonhardt (
1975
), although there
are a few discrepancies.
An alternative approach to determining the degree of ionicity in bonding is to
start with the electron density distribution from an accurate X-ray structure
determination and resolve it into spherically averaged components (''pseudo
atoms'') centered on each site and a non-spherical component representing the
covalent bonding; this enables one to determine a net or residual charge for each
atom, from which an ionicity may be derived by comparing this charge with the
formal charge corresponding to full ionization according to the chemical valency
(for example, Stewart
1976
). In this way the net charge on Si in a-quartz has been
determined to be about 1 electron unit, compared with a formal charge of 4 for
