10
K. D. M. Harris et al.
1.3.4 The Detector
The experimental setup for XBI measurements requires a two-dimensional X-ray
detector (typically a charge-coupled device detector or a hybrid pixel detector) to
allow the X-ray intensity diffracted by the analyzer to be measured in a spatially
resolved manner. The resolution of the measured XBI images depends primarily on
the resolution of the two-dimensional X-ray detector and is typically of the order
of 10 μm (for the charge-coupled device detector currently used in the XBI setup
on beamline B16, the pixel size is 6.4 μm, and the image dimensions are 1392 ×
1040 pixels). However, the resolution of the XBI images in the horizontal direction
also depends on the penetration depth of the X-rays at the polarization analyzer.
Ideally, diffraction at the analyzer should occur only close to the surface; however,
if the penetration depth at the analyzer is significant, the horizontal resolution of the
XBI images is degraded. Minimizing the penetration depth, for example using an
analyzer containing heavier elements, is clearly advantageous in terms of optimizing
resolution.
1.4 Examples of Applications of the XBI Technique
1.4.1 XBI Study of a Model Material with All C–Br Bonds
Parallel
The first XBI experiment [19] studied a thiourea inclusion compound containing 1bromoadamantane (1-BrA) guest molecules, selected as a model material in which
all C–Br bonds are known to be parallel (Fig. 1.3a). This material allowed a test of
the hypothesis that X-ray birefringence at the Br K-edge depends specifically on the
orientations of the C–Br bonds within the material. In the 1-BrA/thiourea inclusion
compound [16], the thiourea molecules are arranged in a tunnel “host” structure,
within which the 1-BrA “guest” molecules are located. It is established from X-ray
diffraction that the C–Br bonds of all 1-BrA guest molecules in this material are
oriented parallel to each other along the tunnel axis of the host structure (Fig. 1.3a).
XBI data for a single crystal of 1-BrA/thiourea, recorded as a function of χ, are
shown in Fig. 1.4. The sample reference axis (z s -axis) is the long axis of the crystal
morphology, which is parallel to the thiourea host tunnel (c-axis) and hence parallel
to the C–Br bonds in the material. Each image in Fig. 1.4 shows a spatially resolved
map of X-ray intensity for a specific orientation of the crystal. Clearly, the X-ray
intensity varies significantly as a function of χ, with maximum intensity at χ ≈ 45°;
in this orientation, the C–Br bonds are oriented at ca. 45° with respect to the direction
of linear polarization of the incident X-ray beam. Minimum intensity occurs at χ ≈ 0°
and χ ≈ 90°, when the C–Br bonds are either parallel (χ = 0°) or perpendicular (χ =
90°) to the direction of linear polarization of the incident X-ray beam. The observed
dependence of intensity on χ [i.e., I(χ ) = I o sin
2 (2χ )] is directly analogous to the
K. D. M. Harris et al.
1.3.4 The Detector
The experimental setup for XBI measurements requires a two-dimensional X-ray
detector (typically a charge-coupled device detector or a hybrid pixel detector) to
allow the X-ray intensity diffracted by the analyzer to be measured in a spatially
resolved manner. The resolution of the measured XBI images depends primarily on
the resolution of the two-dimensional X-ray detector and is typically of the order
of 10 μm (for the charge-coupled device detector currently used in the XBI setup
on beamline B16, the pixel size is 6.4 μm, and the image dimensions are 1392 ×
1040 pixels). However, the resolution of the XBI images in the horizontal direction
also depends on the penetration depth of the X-rays at the polarization analyzer.
Ideally, diffraction at the analyzer should occur only close to the surface; however,
if the penetration depth at the analyzer is significant, the horizontal resolution of the
XBI images is degraded. Minimizing the penetration depth, for example using an
analyzer containing heavier elements, is clearly advantageous in terms of optimizing
resolution.
1.4 Examples of Applications of the XBI Technique
1.4.1 XBI Study of a Model Material with All C–Br Bonds
Parallel
The first XBI experiment [19] studied a thiourea inclusion compound containing 1bromoadamantane (1-BrA) guest molecules, selected as a model material in which
all C–Br bonds are known to be parallel (Fig. 1.3a). This material allowed a test of
the hypothesis that X-ray birefringence at the Br K-edge depends specifically on the
orientations of the C–Br bonds within the material. In the 1-BrA/thiourea inclusion
compound [16], the thiourea molecules are arranged in a tunnel “host” structure,
within which the 1-BrA “guest” molecules are located. It is established from X-ray
diffraction that the C–Br bonds of all 1-BrA guest molecules in this material are
oriented parallel to each other along the tunnel axis of the host structure (Fig. 1.3a).
XBI data for a single crystal of 1-BrA/thiourea, recorded as a function of χ, are
shown in Fig. 1.4. The sample reference axis (z s -axis) is the long axis of the crystal
morphology, which is parallel to the thiourea host tunnel (c-axis) and hence parallel
to the C–Br bonds in the material. Each image in Fig. 1.4 shows a spatially resolved
map of X-ray intensity for a specific orientation of the crystal. Clearly, the X-ray
intensity varies significantly as a function of χ, with maximum intensity at χ ≈ 45°;
in this orientation, the C–Br bonds are oriented at ca. 45° with respect to the direction
of linear polarization of the incident X-ray beam. Minimum intensity occurs at χ ≈ 0°
and χ ≈ 90°, when the C–Br bonds are either parallel (χ = 0°) or perpendicular (χ =
90°) to the direction of linear polarization of the incident X-ray beam. The observed
dependence of intensity on χ [i.e., I(χ ) = I o sin
2 (2χ )] is directly analogous to the