8
K. D. M. Harris et al.
As shown in Fig. 1.2, the definition of the laboratory reference frame (X, Y, Z)
in the experimental XBI setup is based on the incident X-ray beam; specifically,
the direction of propagation of the incident beam is parallel to the Z-axis and the
direction of linear polarization of the incident beam is parallel to the X-axis (thus,
the XZ-plane is horizontal). For XBI measurements, a wide-area incident beam is
used (by appropriate selection of slits on the synchrotron beamline). To date, all our
XBI experiments have been carried out on beamline B16 at Diamond Light Source
(the UK synchrotron radiation facility), with a beam area that is typically ca. 4 mm
horizontally and ca. 1 mm vertically.
Clearly, the range of X-ray energies that can be accessed depends on the characteristics of the beamline used for the XBI experiments. On beamline B16 at Diamond
Light Source, X-ray energies corresponding to the K-edges of elements from Cr to
Ag in the Periodic Table are readily accessed, including the Br K-edge which was
used in recording all the XBI data discussed in this chapter.
After selecting the absorption edge of a particular element in the material of
interest, the optimal X-ray energy for the XBI experiment is established by initially
measuring X-ray dichroism data for the material, and then using the dichroism data
to determine the specific X-ray energy that corresponds to maximum birefringence,
following the procedure described previously [8].
1.3.2 The Sample
As X-ray birefringence is sensitive to local molecular orientational properties, there
is no requirement that the sample under investigation must be crystalline. Thus, in
principle, the XBI technique may be applied to probe the distribution of molecular orientations in any anisotropic material, provided it contains a suitable X-ray
absorbing element.
The sample is mounted on a goniometer, allowing the orientation of the sample
to be changed relative to the direction of propagation (Z-axis) and direction of linear
polarization (X-axis) of the incident X-ray beam. First of all, a reference axis for the
sample is defined, typically corresponding to: (i) a known crystallographic axis, (ii)
a well-defined feature of the sample morphology (e.g., the long axis of a needle-like
crystal), or (iii) a well-defined feature of the experimental setup (e.g., the magnetic
field in the setup to study liquid-crystal samples discussed in Sect. 1.4.3). It is convenient to define an orthogonal axis system (x s , y s , z s ) for the sample, with the z s -axis
taken as the reference axis. The reference axis is maintained in the laboratory XYplane (i.e., the vertical plane perpendicular to the direction of propagation of the
incident X-ray beam) throughout the XBI experiment (Fig. 1.2), and there are two
ways in which the orientation of the sample is changed relative to the fixed laboratory
reference frame (X, Y, Z), called χ-rotation and φ-rotation.
Rotation of the sample around the laboratory Z-axis is called χ-rotation, with the
sample rotated in a plane perpendicular to the direction of propagation of the incident
K. D. M. Harris et al.
As shown in Fig. 1.2, the definition of the laboratory reference frame (X, Y, Z)
in the experimental XBI setup is based on the incident X-ray beam; specifically,
the direction of propagation of the incident beam is parallel to the Z-axis and the
direction of linear polarization of the incident beam is parallel to the X-axis (thus,
the XZ-plane is horizontal). For XBI measurements, a wide-area incident beam is
used (by appropriate selection of slits on the synchrotron beamline). To date, all our
XBI experiments have been carried out on beamline B16 at Diamond Light Source
(the UK synchrotron radiation facility), with a beam area that is typically ca. 4 mm
horizontally and ca. 1 mm vertically.
Clearly, the range of X-ray energies that can be accessed depends on the characteristics of the beamline used for the XBI experiments. On beamline B16 at Diamond
Light Source, X-ray energies corresponding to the K-edges of elements from Cr to
Ag in the Periodic Table are readily accessed, including the Br K-edge which was
used in recording all the XBI data discussed in this chapter.
After selecting the absorption edge of a particular element in the material of
interest, the optimal X-ray energy for the XBI experiment is established by initially
measuring X-ray dichroism data for the material, and then using the dichroism data
to determine the specific X-ray energy that corresponds to maximum birefringence,
following the procedure described previously [8].
1.3.2 The Sample
As X-ray birefringence is sensitive to local molecular orientational properties, there
is no requirement that the sample under investigation must be crystalline. Thus, in
principle, the XBI technique may be applied to probe the distribution of molecular orientations in any anisotropic material, provided it contains a suitable X-ray
absorbing element.
The sample is mounted on a goniometer, allowing the orientation of the sample
to be changed relative to the direction of propagation (Z-axis) and direction of linear
polarization (X-axis) of the incident X-ray beam. First of all, a reference axis for the
sample is defined, typically corresponding to: (i) a known crystallographic axis, (ii)
a well-defined feature of the sample morphology (e.g., the long axis of a needle-like
crystal), or (iii) a well-defined feature of the experimental setup (e.g., the magnetic
field in the setup to study liquid-crystal samples discussed in Sect. 1.4.3). It is convenient to define an orthogonal axis system (x s , y s , z s ) for the sample, with the z s -axis
taken as the reference axis. The reference axis is maintained in the laboratory XYplane (i.e., the vertical plane perpendicular to the direction of propagation of the
incident X-ray beam) throughout the XBI experiment (Fig. 1.2), and there are two
ways in which the orientation of the sample is changed relative to the fixed laboratory
reference frame (X, Y, Z), called χ-rotation and φ-rotation.
Rotation of the sample around the laboratory Z-axis is called χ-rotation, with the
sample rotated in a plane perpendicular to the direction of propagation of the incident