14
K. D. M. Harris et al.
depends on the overall crystal symmetry, which is rhombohedral for BrCH/thiourea in
the HT phase (for a rhombohedral host structure containing guest molecules undergoing isotropic molecular motion, the overall symmetry is rhombohedral), giving
uni-axial behavior in optical birefringence (Fig. 1.5b). In contrast, X-ray birefringence at the Br K-edge depends only on the orientational properties of the C–Br
bonds; as the BrCH guest molecules undergo isotropic reorientational motion in the
HT phase, the orientational distribution of the C–Br bonds is isotropic, and no X-ray
birefringence is observed (Fig. 1.5a).
For BrCH/thiourea in the LT phase, the XBI behavior [19] (see Fig. 1.6, which
shows XBI data recorded at 20 K as a function of χ, with φ fixed at φ = 0°) is
significantly different from that in the HT phase. First, we consider the large central
region of the crystal (i.e., the bright region in the top XBI image in Fig. 1.6); at φ = 0°,
the C–Br bonds in this region of the crystal are nearly perpendicular to the direction
of propagation of the incident X-ray beam. The X-ray intensity for this region varies
significantly as a function of χ, with intensity maxima and minima separated by χ
≈ 45°. In the LT phase, it is known from X-ray diffraction [21] that the C–Br bonds
adopt a well-defined orientation within the crystal (see Fig. 1.3b), with an angle ψ
≈ 52.5° between the C–Br bond direction and the tunnel axis (c-axis) of the thiourea
host structure. For the large central region of the crystal, the maximum intensity in the
XBI images in Fig. 1.6 occurs at χ ≈ 82°, because for this orientation of the crystal,
the angle between the C–Br bond direction and the direction of linear polarization of
the incident X-ray beam is ca. 45° (see Fig. 1.6). Similarly, the minimum intensity
arises at χ ≈ 38°, because for this orientation of the crystal, the angle between the
C–Br bond direction and the direction of linear polarization of the incident X-ray
beam is ca. 90°. Thus, the χ-dependence of the XBI data for BrCH/thiourea in the LT
phase (for φ = 0°) is analogous to the behavior of a uni-axial crystal in the polarizing
optical microscope, with the direction of the C–Br bonds representing the “X-ray
optic axis.” More details of the geometric properties of the BrCH/thiourea inclusion
compound in the LT phase that underpin this interpretation of the XBI data are given
in the original paper [19].
Furthermore, it is clear from the XBI data in Fig. 1.6 that the crystal of
BrCH/thiourea in the LT phase contains orientationally distinct domains, highlighted
in Fig. 1.7 (which shows an expanded view of the XBI image recorded for χ = 10°
and φ = 0° in Fig. 1.6). In Fig. 1.7, the large central region of the crystal comprises
a large parallelogram-shaped domain (the bright region), with two smaller domains
(dark regions) at each end of the crystal. These distinct domains contain the same
crystal structure of the LT phase, but with different orientations relative to the laboratory reference frame. The domain boundaries between the major domain and the
two minor domains are parallel to each other and intersect the c-axis at an angle of
ca. 136°, allowing the domain boundary to be assigned as the crystallographic (101)
plane. Further XBI images recorded as a function of temperature indicate that there is
K. D. M. Harris et al.
depends on the overall crystal symmetry, which is rhombohedral for BrCH/thiourea in
the HT phase (for a rhombohedral host structure containing guest molecules undergoing isotropic molecular motion, the overall symmetry is rhombohedral), giving
uni-axial behavior in optical birefringence (Fig. 1.5b). In contrast, X-ray birefringence at the Br K-edge depends only on the orientational properties of the C–Br
bonds; as the BrCH guest molecules undergo isotropic reorientational motion in the
HT phase, the orientational distribution of the C–Br bonds is isotropic, and no X-ray
birefringence is observed (Fig. 1.5a).
For BrCH/thiourea in the LT phase, the XBI behavior [19] (see Fig. 1.6, which
shows XBI data recorded at 20 K as a function of χ, with φ fixed at φ = 0°) is
significantly different from that in the HT phase. First, we consider the large central
region of the crystal (i.e., the bright region in the top XBI image in Fig. 1.6); at φ = 0°,
the C–Br bonds in this region of the crystal are nearly perpendicular to the direction
of propagation of the incident X-ray beam. The X-ray intensity for this region varies
significantly as a function of χ, with intensity maxima and minima separated by χ
≈ 45°. In the LT phase, it is known from X-ray diffraction [21] that the C–Br bonds
adopt a well-defined orientation within the crystal (see Fig. 1.3b), with an angle ψ
≈ 52.5° between the C–Br bond direction and the tunnel axis (c-axis) of the thiourea
host structure. For the large central region of the crystal, the maximum intensity in the
XBI images in Fig. 1.6 occurs at χ ≈ 82°, because for this orientation of the crystal,
the angle between the C–Br bond direction and the direction of linear polarization of
the incident X-ray beam is ca. 45° (see Fig. 1.6). Similarly, the minimum intensity
arises at χ ≈ 38°, because for this orientation of the crystal, the angle between the
C–Br bond direction and the direction of linear polarization of the incident X-ray
beam is ca. 90°. Thus, the χ-dependence of the XBI data for BrCH/thiourea in the LT
phase (for φ = 0°) is analogous to the behavior of a uni-axial crystal in the polarizing
optical microscope, with the direction of the C–Br bonds representing the “X-ray
optic axis.” More details of the geometric properties of the BrCH/thiourea inclusion
compound in the LT phase that underpin this interpretation of the XBI data are given
in the original paper [19].
Furthermore, it is clear from the XBI data in Fig. 1.6 that the crystal of
BrCH/thiourea in the LT phase contains orientationally distinct domains, highlighted
in Fig. 1.7 (which shows an expanded view of the XBI image recorded for χ = 10°
and φ = 0° in Fig. 1.6). In Fig. 1.7, the large central region of the crystal comprises
a large parallelogram-shaped domain (the bright region), with two smaller domains
(dark regions) at each end of the crystal. These distinct domains contain the same
crystal structure of the LT phase, but with different orientations relative to the laboratory reference frame. The domain boundaries between the major domain and the
two minor domains are parallel to each other and intersect the c-axis at an angle of
ca. 136°, allowing the domain boundary to be assigned as the crystallographic (101)
plane. Further XBI images recorded as a function of temperature indicate that there is