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Model Answer Written Assignment_Group B

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    This alignment is due to the presence of hydrogen bonds in the Truckee, which align the individual Sees tetrahedrons nicely. As seen in figure 2(a), the structure possesses rotational symmetry around the center of order 2, and it is also symmetric horizontally and vertically, with 2 unique mirrors. It also forms a nice tessellation, indicating plane symmetry. In phase 2, the alignment is approximately along the [3-1 0] and [3 1 0] directions. This reduces the symmetry by removing the reflection across the horizontal, as well as rotational symmetry. It however, retains the vertical reflective symmetry and plane symmetry.

    In phase 1, structure changes, and only plane symmetry is present. This change in symmetry is due to how the hydrogen bonding changes at different temperatures. By measuring the proton conductivity; through proton mobility, the symmetry can be deduced. In phase 3, in order for protons to migrate, the simultaneous break and re-form of 2 hydrogen bonds is required, which is not easily done. However, if the structure shifts, such as in phase 2, it makes it easier to break and re-form a single hydrogen bond at a time, which leads to more mobile protons, as proton movement is not hindered by the presence of another hydrogen bond.

    This suggests that at higher temperatures, if the rend continues, the structure will lose most of its symmetry as protons get more mobile. This also corroborates with thermal motion of atoms, where atoms at higher temperatures possess more energy, and vibrate with higher frequency and amplitude. This causes more disorder in the system, leading to less symmetry. Likewise, in this crystal structure, the higher temperature causes the protons to become more energetic, which makes it easier to break and re- form hydrogen bonds.

    Also, the tetrahedral themselves possess more energy, which might contribute to their De-alignment away from the axes. The De- alignment makes it even easier for hydrogen bonds to break and re-form, and so more proton movement occurs, leading to higher proton conductivity. There are three phases whereby each has a different crystal structure at three different temperatures. At room temperature (KICK), Phase Ill is present whereby Cash(Sees)2 has a crystal structure of a monoclinic with a space group of CO/ m.

    At KICK, Phase II is present whereby Cash(Sees)2 has a crystal structure of a monoclinic-AU symmetry. At KICK, Phase I is present whereby Cash(Sees)2 has a crystal structure of a trillion with a space group of RE-m. In Phase Ill, as we can see in Figure 2(a), the positioning of the tetrahedrons is parallel to the a-axis, and in between these Sees tetrahedrons are the hydrogen bonds. Looking at a 2-dimensional perspective, we can also see that there is a translation movement of the Sees tetrahedrons along the a-axis; hence the symmetry operator would be a glide line parallel to a-axis.

    In a 3-dimensional perspective, we can see that Phase Ill has a 2-fold rotation axis and contains glide planes. In Phase II, from Figure 2(b), we can see that the positioning of the Sees tetrahedrons are along the approximate direction [310]. Observing the schematic of the crystal structure in Phase II, we can see that there is a vertical mirror line in between the Sees tetrahedrons. There is also an a-glide reflection vertically. In Phase l, from Figure 2(c), the positioning of Sees tetrahedron is similar to that of Phase II, however the difference is the crystal structure and the hydrogen bonding.

    Comparing both Phase II and Phase Ill crystal structures of the compound, Phase II contains two-fold screw axis, inversion center and a two-fold rotation axis, which is the sole reason for Phase II to be twice of that of Phase Ill in terms of geometrical arrangement of hydrogen bonds. From the above analysis of the symmetry of the crystals structures in different phases, we can tell that Phase Ill has the most symmetry operators and hence achieving the highest crystal symmetry generating a low geometrical arrangement of hydrogen bonds.

    Due to the low geometrical arrangement of hydrogen bonds, the mobility of protons decreases giving the result of ferroelectric. The drastic change from superscription conductivity to forecasting happens when there is a change from Phase II to Phase Ill. The major difference between theses 2 phases is the hydrogen bond arrangement. Due to the presence of a mobile proton, the hydrogen bonds will undergo break-and-recombination phenomena. Shown in Figure 5(c), the proton has to move from i-site to k-site, j-site proton hast to move to I-site.

    As it is harder to move 2 protons at once, the hydrogen bond in Phase Ill is relatively stable compared to Phase II and Phase l. On the other hand, Phase II provides a even more flexible path for the mobile proton to maneuver as it is not restrained by another hydrogen bond. Therefore, Phase II has lower crystal symmetry at higher temperatures. Paragraph 2 The crystal structure in phase II and Ill is a monoclinic system while phase I belongs to a trillion system. The crystal is optically biaxial in both phase II and Ill.

    Due to the same crystal structures in phase II and Ill, both phases have similar domain structure consisting off. Three different types of domains called Del, DO and DO which is separated by two types of domain boundaries called W- and W’-. The W- domain boundary was aligned along the plane of {311} whereas W’- boundary belonged to the plane {1 In}, in which n is determined by the strain compatibility condition. In both phases II and Ill, the observed angles 0 between the all (or ball) axes of neighboring two domains for both domain boundaries are close to each other at about ј = 1200.

    These also agree with theoretical values calculated from the lattice constants. This can be explained in terms of crystal structure: phases II and Ill both have monoclinic systems made up of hexagonal lattice in which C] (angle between vectors a and b) is 1200. Therefore, the crystal structure can account for the angles between the domains, that is, domain structure. However, there is still a change in domain pattern at the II-Ill phase transition. This is most likely due to the orientation of he hydrogen bonds formed between the Sees tetrahedrons.

    In phase Ill, the hydrogen bonds are parallel to the direction along the a-axis while the hydrogen bonds in phase II are aligned to the [31 0] or [3 -1 0] directions. At the I-II phase transition, domain boundaries disappear above the critical temperature and the crystal becomes optically unsocial. The crystal structure in all domains in phase II is averaged and superposed with the symmetry of domain boundary to give the crystal structure in phase l. Paragraph 3 The efficiency of fuel cell depends on the number of mobile charged particles, which is needed to conduct electric current.

    Proton transport efficiency defines the number of mobile proton that can be generated from the breaking and recombination of hydrogen bond. This can be observed when the three domains (D 1, DO, and DO) from each phase (Ill, II, and l) are superimposed to make possible geometrical arrangement. The study focuses only in the region between TIT-III and TTL-al, because phase II was observed to have flexibility in proton migration which also means proton conductivity. In order to transport one proton in phase Ill, two hydrogen bonds have to move and arrange themselves o its allowable geometrical position.

    In comparison, it only needs recombination of one hydrogen bond in phase II. Therefore, phase II is a precursor motion of superscription motion. The recombination in phase II is easier to occur than in phase Ill. Phase Ill has higher crystal symmetry where the number of possible geometrical arrangement is limited. As an example, if a proton moves from I-site to j-site, a proton in k-site must be moved to i-site. It is required as the hydrogen bonds in phase Ill must be paralleled and it is difficult to move two hydrogen bonds at a same time.

    When temperature reaches T II-Ill and above, phase II lowers the crystal symmetry and raises the number of possible geometrical arrangement where the hydrogen bond does not need to be paralleled to any directions. As an example, if a proton moves from j’-site to k’-site, the proton at i’-site is already at the right position following the possible geometrical arrangement. Hence, it can be deduced that by lowering the crystal symmetry, it will increase the number of possible geometrical arrangement which leads to higher proton transport efficiency. This phase II is appropriate for fuel cell as an electrolyte.

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