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Introduction to Inorganic Chemistry
Published in Caroline Desgranges, Jerome Delhommelle, A Mole of Chemistry, 2020
Caroline Desgranges, Jerome Delhommelle
Finally, a last application of group theory is the study of crystal structures. For instance, let us have a look at the crystal of water, known as ice. The most common form of ice is known as hexagonal ice (Ih). The crystal structure of Ih is defined by the space group P63/mmc (number 194) and its crystallographic point group is D6h. Ice Ih is the form of ice found in nature, for instance in snow. Let us add that are many other crystal structures for ice that can be obtained at high pressure or very low temperature, leading to the 18 different ice crystals known today!
Nineteen Phases of Ice and Counting
Published in Fausto Martelli, Properties of Water from Numerical and Experimental Perspectives, 2022
Alfred Amon, Bharvi Chikani, Siriney O. Halukeerthi, Carissa Ponan, Alexander Rosu-Finsen, Zainab Sharif, Rachael L. Smith, Sukhpreet K. Talewar, Christoph G. Salzmann
The familiar hexagonal phase of ice is called ice Ih. Based on X-ray diffraction, it was established that the oxygen atoms in ice Ih are arranged in tetrahedral coordination environments (Dennison 1921, Bragg 1921, Barnes and Bragg 1929). However, the positions of the hydrogen atoms remained unresolved and even controversial until the late 1940s when neutron diffraction became available (Wollan et al. 1949). Four of the debated structural models are shown in Fig. 1. According to the Barnes model (Barnes and Bragg 1929), the water molecules lose their molecular character in ice with hydrogen atoms located halfway between the oxygen atoms. The Bernal-Fowler model on the other hand suggested intact and orientationally ordered H2O molecules (Bernal and Fowler 1933). Pauling proposed a structural model with two half-occupied hydrogen sites along each of the hydrogen bonds (Pauling 1935). Finally, rotating water molecules, in what would now be considered a plastic phase of ice, were considered as well (Wollan et al. 1949). The analysis of the powder neutron diffraction of data of D2O ice Ih revealed that Pauling’s model provided the best match to the recorded intensities of the Bragg peaks. The half-occupied hydrogen sites thereby reflect the average structure of ice in which the orientations of the fully hydrogen-bonded water molecules are random. Such an ice structure is commonly described as hydrogen disordered. The molar configurational entropy of such a phase of ice was estimated by Pauling as R ln (3/2) (Pauling 1935). The frequently used term “proton disordered” is chemically incorrect since the water molecule contains hydrogen atoms and not H+ ions.
Enhancing the formation of ionic defects to study the ice Ih/XI transition with molecular dynamics simulations
Published in Molecular Physics, 2021
These global order parameters are restricted to one of the variants of ice XI. We can also define an order parameter akin to the one used in Landau's theory of phase transitions [58], that satisfies in ice Ih (the disordered phase), in the ↑ variant of ice XI, and in the ↓ variant of ice XI. This order parameter is able to distinguish the two variants of ice XI. However, both variants are equivalent by symmetry and therefore thermodynamic properties, such as, e.g. the free energy, as a function of must be even functions. It is convenient to include this symmetry in the order parameter using that satisfies in ice Ih, and in ice XI. We shall see that better resolution of the local changes in structure can be achieved using It is easy to see that in ice Ih, and in ice XI. We will use a continuous and differentiable version of to construct a bias potential with the VES framework (see reference [51] for details).
Theoretical analyses of pressure induced glass transition in water: Signatures of surprising diffusion-entropy scaling across the transition
Published in Molecular Physics, 2021
Saumyak Mukherjee, Biman Bagchi
In both the ice Ih crystal and the molten glassy phase the diffusion coefficient (D) of water molecules is zero. With further increase in pressure, the value of D remains zero and does not reveal the formation of a new state at very high pressures (Figure 6(c) inset). Consequently, diffusion is unable to detect either of the two glass transitions at 80 K. Melting results in a substantial decrease in the mean square fluctuation (MSF) of the positions of water molecules. here, N is the total number of water molecules in the system, τ is the total time, ri(t) is the instantaneous position of the ith molecule (O atom) at time t and is a reference position (e.g. the initial position of that molecule). We plot against pressure in Figure 6(c). In the crystalline ice Ih state, the MSF increases with an increase in compression. At the melting pressure, its experiences a sharp decrease when the system enters the glassy phase. This justifies the entropic behaviour of the system. Thereafter MSF exhibits a small decrease with pressure, without any further crossover. Hence, MSF distinctly determines the 1st glass transition. However, it fails to denote any subsequent transitions.
Freeze-drying process for the design of porous formulations based on bismuth-potassium-ammonium citrate
Published in Journal of Dispersion Science and Technology, 2021
Ekaterina S. Naydenko, Tatyana Yu. Podlipskaya, Yurii M. Yukhin, Andrey G. Ogienko
Low-temperature powder x-ray diffraction experiments (details are given in ESI), carried out with samples of frozen BPAC aqueous solution and BPAC solution in the TBA/water co-solvent system (Figure 1), revealed that BPAC formed an amorphous freeze concentrate under conditions (freezing at −20 °C) provided by typical laboratory freeze-dryers. For the aqueous solution, ice Ih is the only crystalline phase in the whole temperature range studied; for the TBA/water co-solvent system the diffraction patterns, in addition to ice Ih reflections, exhibit reflections of the TBA·2H2O hydrate; the increase in temperature (from −100 to −5 °C) did not result in the appearance of any reflections corresponding to BPAC or any other crystalline phases. On the diffraction patterns recorded at −5 °C only reflections corresponding to ice Ih were present (ice Ih coexists with the aqueous solution of BPAC and with BPAC solution in TBA/water).