1 X-Ray Birefringence Imaging (XBI): A New Technique …
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to study birefringence of anisotropic materials using linearly polarized X-rays [4–12]
has remained remarkably neglected, despite the fact that linearly polarized X-rays,
tunable to any desired X-ray energy, have been readily accessible for the last 50 years
or so with the availability of synchrotron radiation facilities. Indeed, the first definitive
demonstration of X-ray birefringence was reported only recently [8], as discussed in
more detail below.
In recent years, our research group has been exploring the phenomenon of X-ray
birefringence (and the related phenomenon of X-ray dichroism), which led to the
development of an imaging technique—called X-ray birefringence imaging (XBI)—
that allows X-ray birefringence of materials to be studied in a spatially resolved
manner. In many respects, the XBI technique represents the X-ray analogue of the
polarizing optical microscope.
This chapter presents a basic introduction to the XBI technique, giving a qualitative
description of the fundamentals of the technique and presenting several examples
to demonstrate the utility of the technique to yield information on the orientational
properties of anisotropic materials. Several applications of the technique to study
organic materials are described, including characterization of changes in molecular
orientational ordering associated with solid-state phase transitions, characterization
of liquid crystal phases, and studies of materials in which the molecules undergo
anisotropic molecular dynamics.
1.2 Background to X-Ray Birefringence Imaging
The phenomenon of X-ray birefringence is closely related to the much more widely
studied phenomenon of X-ray dichroism [13–17], both of which concern the interaction of linearly polarized X-rays with anisotropic materials. In particular, X-ray
dichroism relates to the way in which X-ray absorption depends on the orientation of
a material relative to the direction of polarization of a linearly polarized incident Xray beam, whereas X-ray birefringence relates to the way in which the real part of the
complex refractive index (and hence the speed of wave propagation) depends on the
orientation of a material relative to the direction of polarization of a linearly polarized
incident X-ray beam. Although X-ray dichroism and X-ray birefringence give rise to
different effects on the propagation of linearly polarized X-rays through a material,
they are related by a Kramers–Kronig transform [18] and the two phenomena depend
on the same structural and symmetry properties of the material.
While X-ray birefringence (as studied using XBI) and optical birefringence (as
studied using the polarizing optical microscope) share several common characteristics, they also differ in some fundamentally important aspects. Thus, optical birefringence depends on the anisotropy of the material as a whole (e.g., in the case
of a crystal, it depends on the symmetry of the crystal structure), whereas X-ray
birefringence, when studied using an X-ray energy close to the absorption edge of a
specific type of atom in the material, depends on the local anisotropy in the vicinity
of the selected type of atom. As X-ray birefringence depends on the orientational
5
to study birefringence of anisotropic materials using linearly polarized X-rays [4–12]
has remained remarkably neglected, despite the fact that linearly polarized X-rays,
tunable to any desired X-ray energy, have been readily accessible for the last 50 years
or so with the availability of synchrotron radiation facilities. Indeed, the first definitive
demonstration of X-ray birefringence was reported only recently [8], as discussed in
more detail below.
In recent years, our research group has been exploring the phenomenon of X-ray
birefringence (and the related phenomenon of X-ray dichroism), which led to the
development of an imaging technique—called X-ray birefringence imaging (XBI)—
that allows X-ray birefringence of materials to be studied in a spatially resolved
manner. In many respects, the XBI technique represents the X-ray analogue of the
polarizing optical microscope.
This chapter presents a basic introduction to the XBI technique, giving a qualitative
description of the fundamentals of the technique and presenting several examples
to demonstrate the utility of the technique to yield information on the orientational
properties of anisotropic materials. Several applications of the technique to study
organic materials are described, including characterization of changes in molecular
orientational ordering associated with solid-state phase transitions, characterization
of liquid crystal phases, and studies of materials in which the molecules undergo
anisotropic molecular dynamics.
1.2 Background to X-Ray Birefringence Imaging
The phenomenon of X-ray birefringence is closely related to the much more widely
studied phenomenon of X-ray dichroism [13–17], both of which concern the interaction of linearly polarized X-rays with anisotropic materials. In particular, X-ray
dichroism relates to the way in which X-ray absorption depends on the orientation of
a material relative to the direction of polarization of a linearly polarized incident Xray beam, whereas X-ray birefringence relates to the way in which the real part of the
complex refractive index (and hence the speed of wave propagation) depends on the
orientation of a material relative to the direction of polarization of a linearly polarized
incident X-ray beam. Although X-ray dichroism and X-ray birefringence give rise to
different effects on the propagation of linearly polarized X-rays through a material,
they are related by a Kramers–Kronig transform [18] and the two phenomena depend
on the same structural and symmetry properties of the material.
While X-ray birefringence (as studied using XBI) and optical birefringence (as
studied using the polarizing optical microscope) share several common characteristics, they also differ in some fundamentally important aspects. Thus, optical birefringence depends on the anisotropy of the material as a whole (e.g., in the case
of a crystal, it depends on the symmetry of the crystal structure), whereas X-ray
birefringence, when studied using an X-ray energy close to the absorption edge of a
specific type of atom in the material, depends on the local anisotropy in the vicinity
of the selected type of atom. As X-ray birefringence depends on the orientational