Soluble direct-band-gap semiconductors LiAsS2 and NaAsS 2: Large electronic structure effects from weak As...S interactions and strong nonlinear optical response

Article abstract of DOI:10.1002/anie.200801392

Bridging the gap: Li_1-xNa_xAsS₂ (x=0-1) species are found to be a new class of polar direct-gap semiconductors, which display a strong second harmonic generator (SHG) response. The anomalous band-gap trend and their direct-band-gap nature was studied by calculations. The 1.6 eV direct energy gap of LiAsS₂ coupled with its high solubility makes it promising as an efficient light harvesting component in solar cells. (Graph Presented)

Full text of DOI:10.1002/anie.200801392

Communications
DOI: 10.1002/anie.200801392
Direct-Gap Semiconductors
Soluble Direct-Band-Gap Semiconductors LiAsS2 and
NaAsS2: Large Electronic Structure Effects from Weak
As···S Interactions and Strong Nonlinear Optical Response**
Tarun K. Bera, Jung-Hwan Song, Arthur J. Freeman, Joon I. Jang,
John B. Ketterson, and Mercouri G. Kanatzidis*
Angewandte
Chemie
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Chemie
Polarity is essential for various technologically important
properties, such as nonlinear optics (NLO), piezoelectricity,
and ferroelectricity,[1] and a direct gap is important for
optoelectronic applications, such as light-emitting diodes
(LED), lasers, and solar cells.[2] Chalcopyrite-based materials
are polar direct-gap semiconductors that are used both in
optoelectronic and NLO applications as second harmonic
generators (SHGs) in the IR region,[3] where the use of oxides
such as BaBa2O4, LiNbO3, or KTiOPO3 is limited. The non-
centrosymmetric packing of asymmetric building units can
result in highly polar compounds.[4] Today, materials design
exploiting asymmetric building units, such as Jahn–Teller-
distorted d0 metal centers (e.g. Ti4+, Nb5+, Mo6+),[5] anionic
groups with stereochemically active lone pairs (e.g. (IO3)ꢀ,
(TeOx)nꢀ),[6] and non-centrosymmetric p-orbital systems (e.g.
(BO3)3ꢀ, (B3O6)3ꢀ),[7] is of broad scientific and technological
interest. Corresponding units of the heavier chalcogenides
have been little explored. These would be the trigonal-
pyramidal building anions (e.g. [AsS3]3ꢀ, [SbS3]3ꢀ, [TeS3]2ꢀ).[4]
Herein we present the unusual properties of the new
thioarsenate LiAsS2 (I) and its analogue NaAsS2 (II),[8] which
LiAsS2 (I) was first prepared by the alkali metal poly-
chalcogenide flux method,[10] but it can also be prepared by
the direct reaction of Li2S, As, and S. Li1ꢀxNaxAsS2 (x = 0.4,
0.5) and NaAsS2 (II) were also synthesized by direct
combination reactions. The crystal structures were deter-
mined with single-crystal X-ray diffraction analysis. Differ-
ential thermal analyses (DTA) show that I and II melt
congruently, as indicated by the full recovery of the com-
pounds upon cooling the melts.[11] The compounds are stable
in air and water.
LiAsS2 (I) crystallizes in the space group Cc[12] and
NaAsS2 (II) in P21/b.[8] Both I and II feature the same
polymeric 11[AsS2 ] chains, but these are stacked in a different
ꢀ
manner (Figure 1a,b). The chains are made from corner-
sharing AsS3 trigonal pyramids having two different sulfur
atoms:
a
bridging atom S2 and a terminal atom S1
ꢀ
(Figure 1c). A non-centrosymmetric packing of the 11[AsS2 ]
chains in I and the corresponding centrosymmetric packing in
II are shown in Figure 1a,b.
The arsenic-centered trigonal pyramids are distorted, as
ꢀ
evidenced by the As S bond lengths (2.176(2)–2.331(2) Š)
have 1[AsS2 ] chains made of condensed trigonal-pyramidal
and S-As-S angles (94.52–102.648). By comparison, the As S
ꢀ
ꢀ
1
units [AsS3]3ꢀ. From a combined experimental and theoretical
and S-As-S metrics in As2S3 are 2.243–2.293 Š and 92.76–
investigation, we find that the size of the alkali metal
influences the symmetry and polarity of the structure.
Remarkably, it also leads to unexpected trends in the size of
the band gap in these compounds. The polar LiAsS2 and the
centrosymmetric NaAsS2 are found to be direct-gap semi-
conductors, with the lithium analogue having a substantially
narrower energy gap. Surprisingly, the band gap of both
compounds is substantially narrower than that of the parent
binary compound As2S3, a trend which, as we will explain
below, is opposite to what is expected. Our ab initio density
functional calculations of their ground- and excited-state
properties with the full-potential linearized augmented plane
wave method (FLAPW)[9a] reveal that the anomalously large
differences in the energy band gap of the two compounds are
mainly due to the weak interchain As···S interactions. We also
report a strong SHG response for LiAsS2 and its dramatic
enhancement in the solid solutions Li1ꢀxNaxAsS2 up to 30
times larger than the benchmark material AgGaSe2 and 120
times larger than LiNbO3.
[*] T. K. Bera, Prof. Dr. M. G. Kanatzidis
Department of Chemistry, Northwestern University
2145 Sheridan Rd., Evanston, IL 60208 (USA)
Fax: (+1)847-491-5937
E-mail: m-kanatzidis@northwestern.edu
Dr. J.-H. Song, Prof. A. J. Freeman, Dr. J. I. Jang, Prof. J. B. Ketterson
Department of Physics and Astronomy, Northwestern University
2145 Sheridan Rd., Evanston, IL 60208 (USA)
[**] Financial support from the NSF (DMR-0801855 and DMR-0306731)
and through its MRSEC program (DMR-0076097) at the Materials
Research Center of Northwestern University is acknowledged. This
work made use of the Analytical Service Laboratory (ASL) and the
Electron Probe Instrumentation Center (EPIC), Northwestern Uni-
versity.
Figure 1. Extended unit cell view of a) LiAsS2 with non-centrosymmet-
ric packing of 1[AsS2ꢀ] chains, and b) centrosymmetric packing in
1
NaAsS2. c) A single 11[AsS2ꢀ] chain. d, e) The coordination environment
ꢀ
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/anie.200801392.
of As in LiAsS2 (d) and NaAsS2 (e), showing three strong As S
interactions (solid lines) and three weak interactions (dashed lines).
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104.998, respectively.[13] Each arsenic atom has three weakly
interacting sulfur atoms in addition to the three covalently
bonded sulfur atoms (a so-called [3+3] coordination, Fig-
ure 1d,e).
The alkali-metal ions in I and II are in a distorted
ꢀ
octahedral environment of sulfur atoms with A S (A = alkali
metal) distances of 2.620(12)–2.880(12) Š in I and 2.800(12)–
3.060(13) Š in II. The AS6 octahedron forms a three-dimen-
sional network by itself through edge sharing in the bc plane
and corner sharing along the a direction.[11] The NaS6
octahedron is much more distorted than the LiS6 octahedron.
The influence of the alkali metal (Li and Na) on the
crystal symmetry was further investigated by studying the
mixed alkali-metal system Li1ꢀxNaxAsS2. The non-centrosym-
metric structure of I holds up to 40% sodium.[14] The resultant
Li0.6Na0.4AsS2 (referred to as Ia) is isostructural with I. A
further increase in the sodium fraction leads to a structural
transition from monoclinic Cc to orthorhombic Pbca.
The 50% sodium-substituted compound Li0.5Na0.5AsS2
(referred to as IIa) is centrosymmetric and very closely
related to II. Structure solutions and refinements of Ia and IIa
reveal that the alkali-metal site has a mixed occupation of
both lithium and sodium. Following the VØgard law,[15] there is
a linear increase of the unit cell volume with increasing x, as
expected from the fact that sodium is larger than lithium
(Figure 2a). The slope of the plot (normalized unit cell
volume vs. composition x) in the composition range 0 ꢁ x ꢁ
0.4 is different from that in the composition range 0.5 ꢁ x ꢁ 1
(Figure 2a). A sudden increase of the unit cell volume on
going from x = 0.4 to 0.5 signifies the structural change and
also reveals that the polar structure is more dense than the
centrosymmetric one.
Figure 2. a) Normalized unit cell volume versus composition in the
Li1ꢀxNaxAsS2 system. The vertical line indicates the region of the
structural transition. b) Solid-state UV/Vis absorption spectra of I, II,
Ia, IIa, and As2S3. c) Photos of the as-synthesized powdered materials
showing color trend. d) Solution UV/Vis absorption spectrum of I.
Inset shows the clear solution of I in hydrazine. e) A plot of the relative
SHG efficiency of I and Ia compared with that of AgGaSe2 (particle
sizes of 45–63 mm were used for the SHG efficiency comparison).
The denser packing of 1[AsS2ꢀ] chains in I leads to a
1
shortening of the weaker interchain As···S interactions (3.091,
3.200, and 3.305 Š in LiAsS2) compared to those in NaAsS2
(3.304, 3.513, and 3.707 Š; Figure 1d,e). These weak As···S
interactions turn out to have a considerable effect on the
electronic structures and the band gaps of the compounds.
The solid-state UV/Vis optical absorption spectra of I, II,
Ia, IIa, and As2S3 show very strong and steep absorption
onsets almost parallel to the absorption axis, suggestive of
direct band-edge absorption (Figure 2b). A striking contrast
in the spectra is that the band gap of LiAsS2 (I) at 1.60 eV is
anomalously smaller than that of NaAsS2 (II) at 2.23 eV,
which can be seen visually in Figure 2c. Generally, changes in
the alkali metal do not have a profound influence on the
energy gap of the covalent network structure because of the
generally ionic bonding with the network. Thus, the observed
0.63 eV difference in band gap is too large for such a
compositional change.
material.[16] In other words, the introduction of ionic A2Q
dismantles the dense MQ framework to a less dense
2ꢀ
[MmQm+1
[MmQm+1
]
]
framework of lower dimensionality. The
framework has less dispersed energy bands
2ꢀ
than MQ and consequently a larger band gap. Therefore, it
is surprising that LiAsS2 and NaAsS2 (which derive from
A2S + As2S3!2AAsS2) absorb light at lower energies than
As2S3 itself. The structures of the two compounds appear to
meet the lower dimensionality characteristic, yet they possess
a lower-energy gap compared to the binary material. This
result may be attributed to the different hybridization of
arsenic associated with the weak As···S interactions between
the derived (interchain in LiAsS2 and NaAsS2) and the parent
(interlayer in As2S3) compounds, as explained below.
To understand these unusual optical properties, we
performed band-structure calculations for the ground and
excited states using the highly precise full-potential linearized
augmented plane wave (FLAPW) method[9a] with the
screened-exchange local density approximation (sX-
LDA)[9b] as well as the Hedin–Lundqvist form of the
exchange-correlation potential (LDA).[9c]
Another unexpected finding is that the energy gaps of the
two ternary compounds are found to be smaller than that of
the parent As2S3 (ca. 2.44 eV). Generally, when the structure
of a binary solid is modified by the introduction of a
nucleophilic agent, as for example in the case of A2Q +
2ꢀ
mMQ!A2MmQm+1, the [MmQm+1
]
part of the structure is
The results show the title compounds to be direct-gap
materials, and the reasons for the narrower gaps are highly
insightful. Here too, the sX-LDA method with the FLAPW
approach shows great improvements of the excited electronic
generally typified by two prominent characteristics 1) less
dense structure with same dimensionality or lower dimen-
sionality and 2) higher-energy gap compared to the binary
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ꢀ
states over the LDA and again has yielded excellent estimates
of the band gaps and band dispersions.[17] Careful investigation
of the band structure revealed that the fundamental absorption
edge in As2S3 corresponds to an indirect gap, but with several
other indirect and direct transitions within a few tenths of an
electronvolt of the indirect edge, consistent with previous
studies and also in accord with most of the optical absorption
studies.[18] Interestingly, the fundamental absorption edges in
both LiAsS2 (I) and NaAsS2 (II) correspond to direct gaps.
The band structure of I is shown in Figure 3a (for II, see the
Supporting Information). The DOS plots (see the Supporting
Information) show that the bands around the Fermi level (EF)
are predominantly As and S states. The valence band edge is
mainly S 3p in nature, whereas the conduction band edge has
mainly As 4p character in all three compounds. The funda-
mental band edge excitation is mostly from the S 3p to the
As 4p orbital. The calculated band gaps (Ecalcd =1.68 eV for
LiAsS2, 2.19 eV for NaAsS2, and 2.7 eV for As2S3) show very
good agreement with the measured band gaps (1.60, 2.23, and
2.44 eV, respectively). A direct band gap of 1.6 eV is nearly
ideal for maximum capture of solar radiation, suggesting
LiAsS2 could be promising for solar-cell investigations.
and interchain). The differences in the average As S
separations and the S-As-S bond angles[11] on going from
As2S3 to NaAsS2 to LiAsS2 were insufficient to explain the
ꢀ
band-gap variation. Then the role of the weak As S
interactions (mainly interchain) was investigated by calculat-
ing the band structures of the individual 11[AsS2 ] chains. This
ꢀ
calculation was done on a model system in which the chains
were set apart from each other by up to approximately 8 Š, to
essentially eliminate any interaction between them. The
calculated band gap of this model system is approximately
3.5 eV (Figure 3b), which is considerably larger than the band
gaps of all three compounds (including As2S3). This finding
suggests a dominant role for interchain interactions on
defining the band gap. The single-chain band structure in
Figure 3b shows the same gross features along G-B-D-Y as in
Figure 3a of the real compounds, but the flat bands along G-
X-S-Y-G are due to a lack of interchain interactions.[19] The
shorter interchain separations in LiAsS2 than NaAsS2 result in
stronger hybridization between the weakly interacting As 4p
and S 3p states, which results in more dispersive bands
(Figure 3a) and consequently narrower band gaps.
LiAsS2 and NaAsS2 are highly soluble (ca. 0.3 molLꢀ1) in
hydrazine and produce yellow solutions (inset in Figure 2d)
with identical optical absorption maxima at 3.05 eV (Fig-
ure 2d). This finding suggests that the two solutions contain
To explain the anomalous band-gap difference between
LiAsS2 and NaAsS2, three factors were considered: 1) the
ꢀ
strong As S covalent interactions, 2) the average S-As-S
the same separated 1[AsS2 ] chains. Good agreement
ꢀ
bond angles, and 3) the weak As···S interactions (intrachain
1
between the measured solution UV/Vis absorption and the
calculated energy gap (ca. 3.5 eV) for the separated 11[AsS2 ]
ꢀ
chains (Figure 3b) suggests well-separated 11[AsS2 ] chains in
ꢀ
dilute solution and confirms the significant role of the
interchain interactions on the band-edge formation.[11] The
lmax in the spectra of these solutions shifts progressively to
longer wavelengths with increasing concentration, indicative
of chain–chain interactions at higher concentration. The high
solubility of these compounds makes them good candidates
for solution processing investigations to fabricate thin films of
the materials.[20] The polarity and one-dimensional structure
could be helpful to prepare highly oriented films.[21]
The nonlinear optical SHG efficiency of the polar LiAsS2
(I) and Li0.6Na0.4AsS2 (Ia) was measured with a modified
Kurtz–NLO system using a 1580 nm laser.[22a] The particle size
versus SHG efficiency measurement revealed that these
compounds are not type I phase-matchable.[11,22b] An effi-
ciency comparison with the commercially used material
AgGaSe2 was also made (Figure 2e), because the transpar-
ency window for I and Ia is in the same region as for
AgGaSe2.[11] We found that I is about 10 times and compound
Ia is about 30 times more efficient than AgGaSe2. The highly
polar structure that results from the alignment of dipoles in
LiAsS2 is responsible for the enhanced SHG intensity
compared to weakly polar AgGaSe2. This enhanced SHG
intensity of the sodium-substituted Ia could be attributed to
the higher polarizability of sodium vis-à-vis lithium in the
structure; this conclusion is supported by the progressive
SHG intensity enhancement observed in Li1ꢀxNaxAsS2 with
increasing x.[11]
Figure 3. The calculated band structures of a) LiAsS2, Ecalcd =1.68 eV
and b) a single 11[AsS2ꢀ] chain, Ecalcd =3.36 eV. See the Supporting
Information for calculated band structures of NaAsS2, Ecalcd =2.19 eV,
and the projection of the electronic density-of-states (DOS) of LiAsS2
for individual elements (As and S).
In conclusion, LiAsS2 and NaAsS2 are direct-gap semi-
conductors with a band gap which is anomalously lower than
that of As2S3. The SHG response of LiAsS2 is up to 30 times
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Communications
[11] See the Supporting Information.
larger than AgGaSe2. The 1.6 eV direct energy gap of LiAsS2
[12] Crystal data for LiAsS2 (I): Monoclinic space group Cc, Z = 4;
a = 11.847(4), b = 5.4076(10), c = 5.3508(18) Š, b = 113.25(3)8,
coupled with its high solubility makes it promising as an
efficient light-harvesting component in solar cells.
3
V= 315 Š at 100 K; qmax (MoKa) = 29.158; number of data
measured: 1416; number of unique data F2o > 2s(Fo2): 755;
Received: March 23, 2008
Revised: May 25, 2008
Published online: August 28, 2008
number of variables: 37; m = 11.794 mmꢀ1; 1calcd = 3.079 gcmꢀ3
;
Rint = 2.87%; GOF = 1.078; R1 = 2.22%; Rw = 4.33 for I > 2s(I).
[13] D. J. E. Mullen, W. Nowacki, Z. Kristallogr. 1972, 136, 48.
[14] Crystal data for Li1ꢀxNaxAsS2(x = 0.4, Ia): Monoclinic space
group Cc, Z = 4; a = 12.104(3), b = 5.4839(9), c = 5.4176(14) Š,
Keywords: chalcogenides · electronic structure ·
nonlinear optics · semiconductors · thioarsenates
.
3
b = 113.188(19)8, V= 330.54(13) Š at 100 K; qmax (MoKa) =
29.038; number of data measured: 1487; number of unique
data F2o > 2s(F2o): 827; number of variables: 38; m = 11.293 mmꢀ1
;
1calcd = 3.062 gcmꢀ3
; Rint = 2.86%; GOF = 1.088; R1 = 2.36%;
[1] a) D. N. Nikogosyan, Nonlinear optical crystals: a complete
survey, Springer, New York, 2005; b) J. H. Liao, G. M. Marking,
K. F. Hsu, Y. Matsushita, M. D. Ewbank, R. Borwick, P.
Cunningham, M. J. Rosker, M. G. Kanatzidis, J. Am. Chem.
Soc. 2003, 125, 9484; c) I. Chung, C. D. Malliakas, J. I. Jang, C. G.
Canlas, D. P. Weliky, M. G. Kanatzidis, J. Am. Chem. Soc. 2007,
129, 14996; d) S. Fossier, et al., J. Opt. Soc. Am. B 2004, 21, 1981
(see Supporting Information).
[2] a) J. L. Shay, J. H. Wernick, Ternary Chalcopyrite Semiconduc-
tors: Growth, Electronic Properties, and Applications, Pergamon,
Oxford, 1975; b) H. J. Lewerenz, Sol. Energy Mater. Sol. Cells
2004, 83, 395.
[3] a) C. H. L. Goodman, Semicond. Sci. Technol. 1991, 6, 725;
b) G. C. Bhar, Jpn. J. Appl. Phys. Part 1 1993, 32, 653; c) P. G.
Schunemann, Proc. SPIE-Int. Soc. Opt. Eng. 2007, 6455,
64550R-1.
[4] a) N. Ye, Q. Chen, B. Wu, C. T. Chen, J. Appl. Phys. 1998, 84,
555; b) J. D. Feichtner, G. W. Roland, Appl. Opt. 1972, 11, 993;
c) K. F. Hulme, O. Jones, P. H. Davies, M. V. Hobden, Appl.
Phys. Lett. 1967, 10, 133; d) J. G. Bergman, G. D. Boyd, A.
Ashkin, S. K. Kurtz, J. Appl. Phys. 1969, 40, 2860.
Rw = 5.62% for I > 2s(I). Crystal data for Li1ꢀxNaxAsS2(x = 0.5,
IIa): Orthorhombic Pbca, Z = 8; a = 11.0913(6), b = 5.4291(2),
c = 22.5383(12) Š, V= 1357.16(11) Š3 at 100 K; qmax (MoKa) = to
29.178; number of data measured: 11222; number of unique data
F2o > 2s(F2o): 1824; number of variables: 73; m = 11.015 mmꢀ1
;
1calcd = 3.015 gcmꢀ3
; Rint = 4.70%; GOF = 1.168; R1 = 3.91%;
Rw = 6.40% for I > 2s(I). Further details on the crystal structure
investigation may be obtained from the Fachinformationszen-
trum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany
(fax: (+ 49)7247-808-666; e-mail: crysdata@fiz-karlsruhe.de),
on quoting the depository numbers CSD-419059, 419060, and
419061 for LiNaAs2S4, Li1ꢀxNaxAsS2, and LiAsS2, respectively.
[15] L. Vegard, Z. Phys. 1921, 5, 17.
[16] a) E. A. Axtell III, Y. Park, K. Chondroudis, M. G. Kanatzidis, J.
Am. Chem. Soc. 1998, 120, 124; b) E. A. Axtell III, J. H. Liao, Z.
Pikramenou, M. G. Kanatzidis, Chem. Eur. J. 1996, 2, 656;
c) J. H. Liao, C. Varotsis, M. G. Kanatzidis, Inorg. Chem. 1993,
32, 2453; d) G. A. Marking, M. Evain, V. Petricek, M. G.
Kanatzidis, J. Solid State Chem. 1998, 141, 17; e) E. Ruzin, A.
Kracke, S. Dehnen, Z. Anorg. Allg. Chem. 2006, 632, 1018.
[17] a) D. M. Bylander, L. Kleinman, Phys. Rev. B 1990, 41, 7868;
b) R. Asahi, W. Mannstadt, A. J. Freeman, Phys. Rev. B 1999, 59,
7486.
[5] P. S. Halasyamani, Chem. Mater. 2004, 16, 3586.
[6] a) K. M. Ok, P. S. Halasyamani, Angew. Chem. 2004, 116, 5605;
Angew. Chem. Int. Ed. 2004, 43, 5489; b) H. S. Ra, K. M. Ok, P. S.
Halasyamani, J. Am. Chem. Soc. 2003, 125, 7764; c) D. Phanon, I.
Gautier-Luneau, Angew. Chem. 2007, 119, 8640; Angew. Chem.
Int. Ed. 2007, 46, 8488.
[18] a) T. Shimizu, N. Ishii, J. Non-Cryst. Solids 1978, 27, 109; b) J. Li,
D. A. Drabold, S. Krishnaswami, G. Chen, H. Jain, Phys. Rev.
Lett. 2002, 88, 046803.
[19] The weak interaction between layers of As2Se3 is also known to
be a key factor for band edge properties: a) E. Tarnow, A.
Antonelli, J. D. Joannopoulos, Phys. Rev. 1986, 34, 4059.
[20] a) D. B. Mitzi, L. L. Kosbar, C. E. Murray, M. Copel, A. Afzali,
Nature 2004, 428, 299; b) D. B. Mitzi, S. Raoux, A. G. Schrott, M.
Copel, A. Kellock, J. Jordan-Sweet, Chem. Mater. 2006, 18, 6278;
c) D. B. Mitzi, M. Copel, C. E. Murray, Adv. Mater. 2006, 18,
2448.
[21] a) J. C. P. Gabriel, P. Davidson, Adv. Mater. 2000, 12, 9; b) J. H.
Golden, F. J. DiSalvo, J. M. J. Frechet, Chem. Mater. 1995, 7, 232;
c) J. H. Golden, F. J. DiSalvo, J. M. J. Frechet, J. Silcox, M.
Thomas, J. Elman, Science 1996, 273, 782.
[7] S. Pan, J. P. Smit, B. Watkins, M. R. Marvel, C. L. Stern, K. R.
Poeppelmeier, J. Am. Chem. Soc. 2006, 128, 11631.
[8] a) M. Palazzi, S. Jaulmes, Acta Crystallogr. Sect. B 1977, 33, 908;
b) W. S. Sheldrick, M. Wachhold, Coord. Chem. Rev. 1998, 176,
211.
[9] a) E. Wimmer, H. Krakauer, M. Weinert, A. J. Freeman, Phys.
Rev. B 1981, 24, 864; b) D. M. Bylander, L. Kleinman, Phys. Rev.
B 1990, 41, 7868; c) L. Hedin, B. I. Lundqvist, J. Phys. C 1971, 4,
2064.
[10] a) M. G. Kanatzidis, A. C. Sutorik, Prog. Inorg. Chem. 1995, 43,
151; b) M. G. Kanatzidis, Curr. Opin. Solid State Mater. Sci. 1997,
2, 139; c) T. J. McCarthy, M. G. Kanatzidis, Chem. Mater. 1993, 5,
1061; d) T. K. Bera, R. G. Iyer, C. D. Malliakas, M. G. Kanatzi-
dis, Inorg. Chem. 2007, 46, 8466.
[22] a) S. K. Kurtz, T. T. Perry, J. Appl. Phys. 1968, 39, 3798; b) K. M.
Ok, E. O. Chi, P. S. Halasyamani, Chem. Soc. Rev. 2006, 35, 710.
7832
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