1.2 Bragg Scattering and Bernal–Fowler Water
7
intense X-rays from synchrotrons (SAXS) and from free-electron lasers (XFEL)
look promising [17]. These techniques have much shorter exposure time than in the
original Bragg experiments, and thus they are getting closer to the I-structure.
A century of X-ray studies after Bernal and Fowler has shown that the short-order
arrangement in water is similar to that in ice crystals. However, the microscopic
dynamics, which cannot be studied by this method, were still missing. In order to
introduce dynamics to Bernal and Fowler’s concept, Frenkel (1946) proposed the
idea of the simultaneous vibrational and translational motion of molecules, which
is suitable for liquids [18]. The idea was that the oscillations of the molecules in
quasi-crystalline cells have been assumed to be similar to those in solids, but the
translational displacements of the cell as a whole with the corresponding free path
were equal to the first step of diffusion (see Sect. 1.3 for details). Such dynamics
were proposed to account for a distinctive feature of liquids, and were well suited to
the molecular dynamics in water. This model has crystalline and gas-like properties
at the same time. This can explain the X-ray diffraction data and leaves space for
dynamics. Frenkel’s classical model was effectively used to interpret quasi-elastic
neutron scattering data (see Sect. 1.2.3), but was not further developed because in
the 1970s, the main focus was turned to simulations of quantum-mechanical molecular dynamics (see Sect. 1.6), where the calculated volume of water is too small
to model Frenkel’s dynamics, which require significantly higher computational cost
than computers could afford.
1.2.2 X-Ray Crystallography of Ice
X-ray interaction with ice was historically studied separately from that for liquid
water. The method dates back to the first systematic detection of the diffraction patterns of ice crystals by Rinne [19], and their interpretation in relation to the geometrical arrangement of oxygen atoms by Bragg [20]. A large inaccuracy remained in the
arrangement of atoms and molecules in ice, until it was clarified by neutron scattering
(see Sect. 1.5), and infrared and dielectric spectroscopy (see Chap. 2). Nowadays,
although the average position of oxygen atoms has been defined in detail, there are
still many questions concerning the details of ice’s structure and atomic dynamics.
The problem is that it is difficult to prepare a homogeneous ice sample, and then
establish its crystal symmetry, which corresponds to the ice lattice. The scattered
intensity of X-rays depends on the orientation of the sample relative to the incident
beam, as shown in Fig. 1.6. Thus, a lot of initial assumptions are needed in the
interpretation of X-ray diffraction data. The construction of the model is additionally complicated by the fact that the crystal growing process is time dependent, and
the crystal structure is significantly dependent on the boundary conditions.
5 Never5 It should be noted that a single crystal of ice Ih (hexagonal) cannot appear upon cooling a hypothetical infinite volume of water, since the latter does not have a distinguished axis. Ideal ice Ih
crystals grow on cooled surfaces with a surface-dependent structure (see, for example, [24]).
7
intense X-rays from synchrotrons (SAXS) and from free-electron lasers (XFEL)
look promising [17]. These techniques have much shorter exposure time than in the
original Bragg experiments, and thus they are getting closer to the I-structure.
A century of X-ray studies after Bernal and Fowler has shown that the short-order
arrangement in water is similar to that in ice crystals. However, the microscopic
dynamics, which cannot be studied by this method, were still missing. In order to
introduce dynamics to Bernal and Fowler’s concept, Frenkel (1946) proposed the
idea of the simultaneous vibrational and translational motion of molecules, which
is suitable for liquids [18]. The idea was that the oscillations of the molecules in
quasi-crystalline cells have been assumed to be similar to those in solids, but the
translational displacements of the cell as a whole with the corresponding free path
were equal to the first step of diffusion (see Sect. 1.3 for details). Such dynamics
were proposed to account for a distinctive feature of liquids, and were well suited to
the molecular dynamics in water. This model has crystalline and gas-like properties
at the same time. This can explain the X-ray diffraction data and leaves space for
dynamics. Frenkel’s classical model was effectively used to interpret quasi-elastic
neutron scattering data (see Sect. 1.2.3), but was not further developed because in
the 1970s, the main focus was turned to simulations of quantum-mechanical molecular dynamics (see Sect. 1.6), where the calculated volume of water is too small
to model Frenkel’s dynamics, which require significantly higher computational cost
than computers could afford.
1.2.2 X-Ray Crystallography of Ice
X-ray interaction with ice was historically studied separately from that for liquid
water. The method dates back to the first systematic detection of the diffraction patterns of ice crystals by Rinne [19], and their interpretation in relation to the geometrical arrangement of oxygen atoms by Bragg [20]. A large inaccuracy remained in the
arrangement of atoms and molecules in ice, until it was clarified by neutron scattering
(see Sect. 1.5), and infrared and dielectric spectroscopy (see Chap. 2). Nowadays,
although the average position of oxygen atoms has been defined in detail, there are
still many questions concerning the details of ice’s structure and atomic dynamics.
The problem is that it is difficult to prepare a homogeneous ice sample, and then
establish its crystal symmetry, which corresponds to the ice lattice. The scattered
intensity of X-rays depends on the orientation of the sample relative to the incident
beam, as shown in Fig. 1.6. Thus, a lot of initial assumptions are needed in the
interpretation of X-ray diffraction data. The construction of the model is additionally complicated by the fact that the crystal growing process is time dependent, and
the crystal structure is significantly dependent on the boundary conditions.
5 Never5 It should be noted that a single crystal of ice Ih (hexagonal) cannot appear upon cooling a hypothetical infinite volume of water, since the latter does not have a distinguished axis. Ideal ice Ih
crystals grow on cooled surfaces with a surface-dependent structure (see, for example, [24]).