Syntheses, Crystal and Electronic Structures, and Linear
Optics of LiMBO3 (M ) Sr, Ba) Orthoborates
W.-D. Cheng,* H. Zhang, Q.-S. Lin, F.-K. Zheng, and J.-T. Chen
Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, State
Key Laboratory of Structural Chemistry, Fuzhou, Fujian 350002, People’s Republic of China
Received October 10, 2000. Revised Manuscript Received March 7, 2001
The syntheses, crystal and electronic structures, and linear optical properties of the new
orthoborates LiMBO3 (M ) Sr, Ba) are reported here. These compounds, which crystallize
in the monoclinic space group P21/n with cell dimensions a ) 6.476(2), b ) 6.684(3), c )
6.843(3) Å, â ) 109.41(3)°, and Z ) 4 for M ) Sr, a ) 6.372(1), b ) 7.022(3), c ) 7.058(1) Å,
â ) 113.89(1)°, and Z ) 4 for M ) Ba, are modeled in terms of the cluster units (LiMBO3)2.
The calculated electronic structures show that the top of the valence band consists of mostly
the O 2p orbitals and the bottom of the conduction band consists of cationic orbitals. The
dynamic refractive indices of these orthoborates are obtained in the framework of the INDO/
SCI approximation together with the “sum-over-states” method. It is found that the refractive
index is larger for LiSrBO3 than for LiBaBO3 and the charge transfer from O2- anionic
orbitals to cationic orbitals appears to provide significant contribution to the linear
polarizability of these compounds.
1. Introduction
Research efforts have been directed at solid-state
borates due to a variety of physical and chemical
features exhibited by these compounds, such as lumi-
nescence of doped borates SrB4O71,2 and X2Z(BO3)2
(X ) Ba, Sr, Ca; Z ) Ca, Mg),3 nonlinear optical
properties4 of borate compounds including the (B3O6)3-
group, and catalytic activity of the zinc-copper borate
ZnCu2(BO3)2.5 Among nonlinear optical crystals, solid-
state borates have emerged as the pre-eminent materi-
als for high-power applications, and now, they are being
utilized in the manufacture of components in essentially
all complex microprocessor-based devices from PCs to
cellular phones. An understanding of the relationship
between microscopic structure and macroscopic proper-
ties has been recognized as an important aid in the
design and improvement of materials.6 Cheng et al. have
calculated the electronic structures and nonlinear opti-
cal coefficients of MB6O10 (M ) Cs2, Li2, CsLi) with an
aim to understand the electronic origin of their optical
susceptibility.7 Keszler and co-workers have systemati-
cally investigated the syntheses, structures, and proper-
ties of alkali-metal borates searching for a trend in the
structure-property relationship.8,9
In this study, we first report the syntheses and single-
crystal structural determinations for mixed alkaline and
alkaline-earth metal orthoborates LiMBO3 (M ) Sr, Ba),
and we find that the structural types of our obtained
compounds are different from those of the LiABO3
orthoborates (A ) Mg, Mn, Co, Zn, and Cd) reported in
references.10-13 Belkebir and co-workers have calculated
the crystallographic cell of the phases of LiZnBO3
obtained by solid-state reaction without melting by
indexing their X-ray power diffraction patterns, and the
two structures found are monoclinic probably with the
same Li-Zn cationic disorder as evidenced by vibra-
tional behavior.13 Piffard and co-workers have deter-
mined the structure of LiCoBO3 to be of the space group
C2/c and indicated that the Co and Zn cations have
occupied similar positions within the trigonal bipyr-
amids above and below the center plane in LiCoBO3 and
LiZnBO3, respectively.10 Then, we use a cluster unit
representing the crystalline orthoborate lattice to cal-
culate the electronic structure and refractive indices of
mixed alkaline-earth metal and lithium orthoborates
LiMBO3 (M ) Sr, Ba). In this way, we obtain a means
to examine structural and compositional contributions
to linear optical properties. The calculated results show
a larger refractive index for LiSrBO3 than for LiBaBO3
and indicate that the charge transfers from O 2p orbitals
to cation valence orbitals have major contributions to
the refractive indices of LiMBO3 (M ) Sr, Ba).
* To whom correspondence should be addressed.
(1) Blasse, G.; Dirksen, G. J.; Meijerink, A. Chem. Phys. Lett. 1990,
167, 41-44.
(2) Meijerink, A.; Nuyten, J.; Blasse, G. J. Lumin. 1989, 44, 19-
31.
(3) Verstegen, J. M. P. J. J. Electrochem. Soc. Solid-State Sci.
Technol. 1974, 121, 1631-1633.
(4) Chen, C.-Z.; Gao, D.-S.; Chen, C.-T. Acad. Thesis Conf. Cryst.
Growth Mater. (China) 1979, B44, 107-111.
(5) Zletz, A. U.S. Patent Application, 709, 790, March 11, 1985,
Amoco Corp.
(6) Munowitz, M.; Jarman, R. H.; Harrison, J. F. Chem. Mater.
1993, 5, 661-671; 1993, 5, 1257-1267.
(7) Cheng, W.-D.; Chen, J.-T.; Lin, Q.-S.; Zhang, Q.-E.; Lu, J.-X.
Phys. Rev. B 1999, 60, 11747-11754.
(8) Akella, A.; Keszler, D. A. J. Solid State Chem. 1995, 120, 74-
79.
(9) Smith, R. W.; Keszler, D. A. J. Solid State Chem. 1997, 129,
184-188.
(10) Piffard, Y.; Rangan, K. K.; An, Y.; Guyomard, D.; Tournoux,
M. Acta Crystallogr. 1998, C54, 1561-1563.
(11) Norrestam, R. Z. Kristallogr. 1989, 187, 103-110.
(12) Sokolova, E. V.; Simonov, M. A.; Belov, N. V. Z. Kristallogr.
1980, 25, 1285-1286.
(13) Belkebir, A.; Tarte, P.; Rulmont, A.; Gilbert, B. New J. Chem.
1996, 20, 311-316.
1841Chem. Mater. 2001, 13, 1841-1847
10.1021/cm000808i CCC: $20.00 © 2001 American Chemical Society
Published on Web 04/27/2001
2. Experimental and Computational Procedures
2.1. Syntheses and Crystal Growths. 2.1.1. LiSrBO3. A
mixture containing appropriate amounts of LiCO3 (Chemical
pure), SrCO3 (Chemical pure), and H3BO3 (Analytical reagent)
was ground into fine powder in a mortar of agate. This mixture
was heated to 450 °C in a platinum crucible and kept at this
temperature for 4 h, followed by heating at 840 °C for 10 h
and at 910 °C for 24 h. The mixture, then, was cooled from
910 to 600 °C at a rate of 2.7 °C h-1. It finally was quenched
to room temperature. A few colorless pillar crystals were found
from the melt of the mixture.
2.1.2. LiBaBO3. A stoichiometric mixture of LiCO3 (0.74 g,
chemical pure), BaF2 (1. 71 g, analytical reagent), SrCO3 (1.48
g, chemical pure), and H3BO3 (1.24 g, analytical reagent) was
ground into fine powder in a mortar of agate, then heated to
450 °C in a platinum crucible, and kept at this temperature
for 4 h, followed by heating at 840 °C for 24 h and at 910 °C
for 24 h, then cooled from 910 to 800 °C at a rate of 1.0 °C h-1
and from 800 to 600 °C at a rate of 4.0 °C h-1, and finally
air-quenched to room temperature. A few colorless pillar
crystals were found from the melt.
2.2. X-ray Determination. A single crystal of LiSrBO3 and
LiBaBO3 with approximate dimensions 0.18 � 0.08 � 0.06 and
0.30 � 0.20 � 0.10 mm3 was selected for single-crystal X-ray
diffraction, respectively. The diffraction data were collected
on an Enraf-Nonius CAD4 diffractometer with graphite mono-
chromator Mo KR radiation for these two crystals. Cell
constants were obtained from least-squares refinement, using
the setting angles of 25 reflections in the range 26° < 2ı <
48° for LiSrBO3 and 25 reflections in the range 22° < 2ı <
46° for LiBaBO3. The crystallographic parameters of these two
crystals are listed in Table 1. The intensity data were collected
at 273 K in the range -11 e h e 11, 0 e k e 12, and 0 e l e
12 for LiSrBO3 and the range 0 e h e 12, 0 e k e 13, and
-13 e l e 13 for LiBaBO3, using the ö/2ı scan technique with
a scan speed of 5°/min and a scan width of ¢ö ) (0.8 + 0.35
tan ı)°, respectively. The intensities of three standard reflec-
tions were measured every 60 min, and the intensity decay
was 0.6 and 4.7% for crystals LiSrBO3 and LiBaBO3, respec-
tively. Lorentz and polarization corrections were applied to
the data. The linear absorption coefficients are 14.3 and 135.3
mm-1 for these two crystals, respectively. An empirical absorp-
tion correction based on a ª-scan was applied and the relative
transmission coefficients ranged from 0.324 to 1.00 with an
average value of 0.662 and from 0.484 to 0.996 with an average
value of 0.740, respectively. The 1824 and 2301 reflections
were used to measured with 2ımax ) 80°; 1223 and 1490
reflections with I > 3ó(I) were used in structural determination
and refinement for LiSrBO3 and LiBaBO3 crystals, respec-
tively.
The structures of LiSrBO3 and LiBaBO3 were separately
determined by the Shelx/PC and MolEN/PC programs. From
the systematic absence of h0l: l ) 2n; 0k0: k ) 2n and from
subsequent least-squares refinement, the space group of these
two crystals was determined to be P21/n. Note that this space
group is not a standard space group. However, it is often
convenient and the angle of â will not become much larger
than 90° when we prefer the space group P21/n in determining
the crystal structures. The Sr and Ba atoms were located from
the direct method; the remaining atoms were located in
succeeding difference Fourier synthesis. The final full-matrix
least-squares refinement for 56 and 55 variable parameters
converged to R ) 4.43%, Rw ) 8.98% [in which w ) 1/(ó2(Fo2)
+ (aP)2 + bP); P ) (2Fc2 + Max(Fo2,0))/3], S ) 0.982, and (¢/
ó)max ) 0.0001 for LiSrBO3 and converged to R ) 5.51%, Rw
) 6.26% [in which w ) 1/(ó2(F) + (0.020F)2 + 1.0)], S ) 0.93,
and (¢/ó)max ) 0.0001 for LiBaBO3. Neutral atomic scattering
factors were taken from Cromer and Waber.14 The maximum
and minimum peaks on the final different Fourier map are
1.43 and -1.00 e/Å3 and 5.57 and -1.72 e/Å3 for SrLiBO3 and
BaLiBO3 crystals, respectively. The atom coordinates and
thermal parameters are listed in Table 2. Here, it is noted that
the BaF2 attempted as a flux was added into the mixture of
SrCO3, LiCO3, and H3BO3, and the variation of temperature
was controlled to try and obtain a new phase of LiSrBO3.
However, the crystal of LiBaBO3 was found in the X-ray
structural determination and the atom of Sr was not present
in this crystal. We made a trial structure including the Sr
atoms in the LiBaBO3 during the solution of crystal structure
by the Shelxtl/PC program. The result showed a large value
of R and unreasonable coordinations of metal atoms. Accord-
ingly, we believe no Sr atoms are in this crystal structure.
2.3. Computational Details. The wave functions and
energies obtained from electronic structural calculations were
employed to compute the polarizabilities of clusters, and the
electronic structural calculations of the clusters were based
on an all-valence-electron, semiempirical INDO self-consistent
field (SCF) molecular orbital (MO) procedure with configura-
tion interaction (CI) modified by Zerner and co-workers.15-18
There are the one-center core integral Uíí, resonance integral
âíî, two-electron integral çíî, overlap integral Síî, and density
matrix element Píî in the matrix element of the Fock operator
under the INDO approximation. The INDO model as employed
herein included all one-center two-electron integrals and two-
center two-electron integrals çíî. The one-center two-electron
integrals çíí were chosen from the Pariser approximation, çíí
) F0(íí) ) IPí - EAí, and the two-center two electron integrals
were calculated using the Mataga-Nishimoto formula, çíî )
1.2/[RAB + 2.4/(çíí + çîî)] in the spectroscopic version of the
INDO method. The Slater orbital exponents œ and the other
calculating parameters are listed in Table 3. The molecular
orbital calculations were performed by the restricted Hartree-
Fock method. The ground state was constructed as a single
(14) Cromer, D. T.; Waber, J. T. In International Table for X-ray
Crystallography; Kynoch Press: Birmingham, 1974; Vol. IV, Table
2.2A, p 71.
(15) Bacon, A. D.; Zerner, M. C. Theor. Chim. Acta 1979, 53, 21-
54.
(16) Zerner, M. C.; Lovw, G. H.; Kirchner, R. F.; Mueller-Westerhoff,
U. T. J. Am. Chem. Soc. 1980, 102, 589-599.
(17) Anderson, W. P.; Edwards, E. D.; Zerner, M. C. Inorg. Chem.
1986, 25, 2728-2732.
(18) Anderson, W. P.; Cundari, T. R.; Zerner, M. C. Int. J. Quantum
Chem. 1991, 39, 31-45.
Table 1. Crystal Parameters
formula LiSrBO3 LiBaBO3
fw 153.37 203.09
space group P2(1)/n P2(1)/n
a (Å) 6.4800(13) 6.372(1)
b (Å) 6.6800(13) 7.022(3)
c (Å) 6.8400(14) 7.058(1)
â (deg) 109.41(3) 113.89(1)
V (Å3) 279.25(10) 288.7(2)
Z 4 4
Dcalc (mg/m3) 3.648 4.67
R 0.0443 0.0551
Rw 0.0898 0.0626
S 0.982 0.93
Table 2. Fractional Atomic Coordinates and Equivalent
Isotropic Displacement Parameters (Å)
atom x y Z Ueqa
LiSrBO3
Sr 0.20197(5) 0.12378(5) 0.86760(5) 0.00811(9)
O(1) 0.1560(5) 0.1105(4) 1.2178(4) 0.0130(5)
O(2) 0.1073(5) 0.2993(4) 0.4940(4) 0.0109(4)
O(3) 0.1963(5) 0.4897(4) 0.9367(4) 0.0109(5)
B 0.1886(6) 0.1326(6) 0.4270(6) 0.0084(5)
Li 0.1002(13) 0.4086(10) 1.1930(11) 0.0136(13)
LiBaBO3
Ba 0.33502(8) 0.13980(7) 0.15907(6) 0.01093(6)
O(1) 0.3793(9) 0.3180(7) 0.5164(8) 0.0085(9)
O(2) 0.291(1) 0.1598(9) 0.7740(8) 0.017(1)
O(3) 0.2199(9) 0.0011(7) 0.4569(7) 0.0074(9)
B 0.296(1) 0.160(1) 0.579(1) 0.007(1)
Li 0.896(2) 0.071(2) 0.298(2) 0.009(3)
a Ueq ) 1/3∑i∑jUijRi*Rj*aiaj.
1842 Chem. Mater., Vol. 13, No. 5, 2001 Cheng et al.
determinant from the Hartree-Fock SCF calculated results.
Only single-substituted determinants relative to the ground
state configuration were considered and only singlet spin-
adapted configurations needed to be included in the CI
calculations. The ground state and all excited states had the
multiplicity of 1. The electron was promoted from the 13
highest occupied orbitals to the 13 lowest unoccupied orbitals
and the configuration space was constructed by these 26 active
orbitals. The wave functions and energy eigenvalues of the
excited states were determined by solving the secular equation
relating to configuration coefficients. The dipole and transition
moment matrix elements were expressed as a sum of one-
electron integrals.
The cluster units (LiSrBO3)2 and (LiBaBO3)2 representing
extended oxide crystals LiSrBO3 and LiBaBO3 were selected
for calculations, as shown in Figure 1. The coordinate systems
are defined in the calculations. The coordinate center is located
at the center of the ring [M1M2O3O5]. The x axis is defined
to be parallel to the connecting line between the O3 and O5
atoms, and the y axis is lain down the plane constructed by
three atoms, O3-O5-M1 in Figure 1. The z axis is defined as
the right-hand rule of the coordinate system for these two
clusters, respectively. Theoretical calculations of electronic
structures and polarizabilities are based on the crystallo-
graphic structural data for these two clusters.
The tensor components of the polarizability R(ö) with fre-
quency dependence for the clusters (LiSrBO3)2 and (LiBaBO3)2
were calculated by the sum-over-states (SOS) method as
follows:
3. Results and Discussions
3.1. Crystal Structures. Drawings of the contents
of the unit cells of compounds LiMBO3 (M ) Sr, Ba)
are shown in Figure 2. It is found that LiMBO3
structures can be constructed from a stack of [MO] and
[LiO] layers along the [101h] direction and B atoms
localized in adjacent layers as a bridging role. In the
[LiO] layers, the adjacent polyhedrons constructed from
the LiO5 form dimers by sharing edges, and each dimer
connects with the four adjacent dimers by the four O
atoms to form two-dimensional sheets along the ac
diagonal plane, as shown in Figure 3. The Li atoms are
coordinated by five O atoms and the LiO5 polyhedron
is a distorted trigonal bipyramid. For the LiSrBO3
crystal, the Li-O distances vary from 1.955(7) to
2.169(8) Å with an average value of 2.056 Å, where the
long bond lengths of Li-O are in the axial direction of
the trigonal bipyramid. An average bond length of the
Li-O in the LiBaBO3 crystal is close to that of the
LiSrBO3 one. The B-O distances vary from 1.369(4) to
1.385(6) Å with an average value of 1.377 Å and the
O-B-O angles are between 118.3(7)° and 122.6(7)°.
These values are normal in a [BO3] plane of LiMBO3
(M ) Sr, Ba). Table 4 lists the interatomic distances
and angles of LiMBO3. There are different coordinations
Table 3. INDO/S Model Parameters
parameter B O Li Sr Ba
œns,np (Å-1) 1.300 2.275 0.650 1.214 1.263
œ(n-1)d (Å-1) 2.058 2.658
-Ins (eV) 14.05 32.90 5.41 5.84 5.21
-Inp (eV) 8.70 17.28 3.61 3.76 3.43
-I(n-1)d (eV) 3.66 3.22
-âns,np (eV) 17.00 34.20 9.00 1.88 2.66
-â(n-1)d (eV) 10.05 12.50
çns,np (eV) 8.68 13.00 4.57 3.75 4.68
ç(n-1)dd (eV) 5.31 5.19
ç(n-1)dns,np 4.53 3.79
Figure 1. Selected cluster unit model of (LiMBO3).
Rij(ö) ) 1/p“mígm
iímg
j[(ömg - öp)
-1 + (ömg + öp)
-1] (1)
Figure 2. Crystal structure stacked from the [MO] and [101]
direction in [LiMBO3]. The M-O bonds are omitted for clarity.
Figure 3. Structure of the [LiO] layer along the ac diagonal
plane in [LiMBO3].
Properties of LiMBO3 (M ) Sr, Ba) Orthoborates Chem. Mater., Vol. 13, No. 5, 2001 1843
between the Sr and Ba atoms in LiMBO3 (M ) Sr, Ba)
crystals. The Sr atoms are coordinated by seven O
atoms, and the SrO7 polyhedron may be described as a
mono-capped distorted trigonal prism. The Sr-O dis-
tances vary from 2.495(3) to 2.692(3) Å with an average
value of 2.594 Å, which compared very well to the
expected value 2.590 Å calculated from the crystal radii
for the seven-coordinate Sr2+ ion.19 In the [SrO] layers,
the Sr atoms through sharing O-O edges extend along
the b direction to form chains, and the adjacent chains
link together by O atoms to form puckering sheets
parallel to the ac diagonal plane, as shown in Figure 4.
These sheets are connected along the [101h] direction to
form the three-dimensional framework by the bridging
O atoms of the [LiO] layers. For the LiBaBO3 crystal,
however, the Ba atoms are coordinated by nine O atoms
and the BaO9 polyhedron is described as a mono-capped
distorted square antiprism. The Ba-O distances vary
from 2.622(6) to 3.185(5) Å with an average value of
2.813 Å, which compared well to the expected value
2.850 Å calculated from the crystal radii for the nine-
coordinate Ba2+ ion.19 In the [BaO] layers, the Ba atoms
through sharing the planes of three oxygen atoms
extend along the ac diagonal direction to form chains,
and the adjacent chains link together by the two oxygen
atoms to form puckering sheets in the b direction, as
shown in Figure 5. These sheets are connected along
the [101h] direction to form the three-dimensional frame-
work by the bridging O atoms of the [LiO] layers.
3.2. Electronic Structures. The energy bands for
LiSrBO3 and LiBaBO3 are calculated in terms of MO
procedures. Note that the top of the valence band of
LiSrBO3 and LiBaBO3 is at -7.07 and -5.65 eV,
respectively, and is taken to be zero and regarded as a
reference in the following discussion.
The dominant contribution to the lower valence band
(i.e., -31.5 to -23.5 eV for LiSrBO3, -28.5 to -24.5 eV
for LiBaBO3) comes from O 2s orbitals along with a
relatively small (<8%) contribution from B 2s orbitals.
It is therefore assigned as an s valence band. The upper(19) Shannon, R. D. Acta Crystallogr. 1976, A32, 751-767.
Table 4. Interatomic Distances (Å) and Bond Angles (deg)
Interatomic Distances (Å) Bond Angles (deg) Interatomic Distances (Å) Bond Angles (deg)
a. LiSrBO3 b. LiBaBO3
Sr-O(1) 2.6928(7) O(1)-Sr-O(1) 79.57(2) Ba-O(1) 2.726(6) O(1)-Ba-O(1) 131.2(2)
Sr-O(1) 2.513(1) O(1)-Sr-O(2) 98.01(2) Ba-O(1) 2.670(6) O(1)-Ba-O(1) 89.3(2)
Sr-O(2) 2.689(1) O(1)-Sr-O(2) 82.02(3) Ba-O(1) 2.677(5) O(1)-Ba-O(2) 149.6(2)
Sr-O(2) 2.5171(9) O(1)-Sr-O(2) 155.856(9) Ba-O(2) 2.622(6) O(1)-Ba-O(2) 112.9(1)
Sr-O(2) 2.5297(8) O(1)-Sr-O(3) 123.03(2) Ba-O(2) 3.067(8) O(1)-Ba-O(2) 79.1(2)
Sr-O(3) 2.495(1) O(1)-Sr-O(3) 93.19(2) Ba-O(2) 3.030(8) O(1)-Ba-O(3) 53.0(2)
Sr-O(3) 2.5469(9) O(1)-Sr-O(2) 149.26(1) Ba-O(3) 2.675(6) O(1)-Ba-O(3) 78.3(2)
Li-O(1) 2.0219(9) O(1)-Sr-O(2) 79.05(1) Ba-O(3) 2.646(5) O(1)-Ba-O(3) 68.4(2)
Li-O(1) 2.0131(5) O(1)-Sr-O(2) 96.83(2) Ba-O(3) 3.185(5) O(1)-Ba-O(1) 69.3(2)
Li-O(2) 2.1664(9) O(1)-Sr-O(3) 80