SECOND HARMONIC GENERATION IN BORACITES
395
metals forming hilgardite-structure haloborates; Ni, a
3d transition metal; and Cd, a Group IIB metal. This
allows us to draw some tentative conclusions about the
effects of cation and anion compositions on the conver-
sion efficiency of the compounds under consideration.
Note in this context that the nonlinear susceptibility
(and, accordingly, the SHG signal) of a crystalline
material is a tensor quantity, dependent on the crystal-
lographic orientation. Therefore, SHG measurements
on polycrystalline samples yield an average character-
istic, which depends on the particle size of the material.
The data presented in Table 2 were obtained on micro-
crystalline (3–5 µm) samples.
Both the experimental data and calculation results
demonstrate that the Mg and Cd boracites have compa-
rable nonlinear optical susceptibilities, which exceed
those of the Ni boracites by an order of magnitude.
The nonlinear optical properties of borates are com-
monly interpreted in terms of the number of [BO3]
groups per unit cell and their arrangement in the crystal
structure [1]. In this approach, cations are thought of as
stabilizers of the boron–oxygen subsystem [4]. Both
the boracite and hilgardite phases have a rigid, difficult-
to-deform framework. Nevertheless, in both borate
families the nonlinear optical response depends
strongly on the nature of the cation, which points to an
intricate relationship between the composition and non-
linear optical properties of these borates. In this respect,
the interpretation of experimental data in terms of the
Phillips–Van Vechten–Levine model appears more rea-
sonable.
Taking into account the above observations, we
infer from the data in Table 2 that the nature of the
halogen has little effect on the second-order nonlinear
response of the boracites studied, which is, at the same
time, very sensitive to the nature of the metal. To
establish the degree of generality of this conclusion,
experimental data must be compared to theoretical
predictions. Modern theories of nonlinear optical
effects give no way of evaluating second-order nonlin-
ear susceptibilities of multicomponent crystals in a
first-principles manner. At the same time, components
of the second-order nonlinear susceptibility tensor,
dijk, can be calculated using the model developed
in [13, 14], which represents the macroscopic property
of interest here as a combination of contributions from
all of the chemical bonds in the crystal. This approach
was shown to be applicable to borates [15, 16] and hil-
gardite-structure haloborates [17]. The calculation
procedure was described in detail in [17]. We used that
model to calculate the dijk tensor for the boracites
under consideration. To compare the calculation
results and experimental data for polycrystalline sam-
ples, it is necessary to consider average susceptibili-
ties dav (Table 2). Given that all of the boracites stud-
ied, except Ni3B7O13I, have the mm2 point group, dav
is related to dijk by [18]
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19
44
2
2
2
d2av
=
d33 +
(d32 + d31)
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--------
105
--------
105
13
105
2
--------
+
(d31 + d32 + d33) .
For Ni3B7O13I, we have
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5
--
7
2
d2av
=
d14.
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INORGANIC MATERIALS Vol. 41 No. 4 2005