The Lattice Symmetry Of Quartz Α-Fepo4 Lab Analysis

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The lattice symmetry of quartz α-FePO4 is trigonal. Its space group is P3121. The lattice symmetry of quartz β-FePO4 is hexagonal. It space group is P6422.
According to the article, only two of the various quartz homeotypes which exhibit alpha-beta transitions have been studied in detail at high temperature. One of them is Silicon Dioxide. As such, it is possible for silicon dioxide to have the same structure when the chemistry is completely different.
Since iron is trivalent and phosphorus is pentavalent, an equation of the following can be written to explain the chemical substitution which takes place to maintain the same symmetry:
Here, the total charge on each side has a charge of 8+ and
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For example, as temperature increases, the degree increases as well. At a temperature of 294K, the θ average is 137.9 degree and at a temperature of 465K, θ becomes 140.0 degree. The temperature dependence of the volume strongly follows the behavior of the average θ as a function of temperature.
The relationship between the unit cells is as follow:
Both are seen from the C axis. These results show that α- FePO4 has a trigonal unit cell whereas β- FePO4 has a hexagonal unit cell. In both cases, the actual dimensions remain the same. This is despite the change in temperature. The dimensions remain the same even though there is a change in symmetry.
The symmetrical differences between α-FePO4 and β-FePO4 are that α-FePO4 is trigonal and β-FePO4 is hexagonal. When temperature increases, the volume expands. The tilt angle, δ, has an inverse relationship with temperature. As temperature approaches the alpha to beta phase, the tilt angle decreases. This can be attributed to the increasing disorder at high temperature arising from excited low energy, high
amplitude
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Base on the article, it has been shown that the alpha-beta transition in quartz can be modeled using a single order parameter, the tilt angle. The overall average tilt angle is used for FePO4 as both the individual average tilt angles of the FeO4 and PO4 tetrahedral depend on the fractional atomic coordinates of O1 and O2 and are thus correlated. The temperature dependence of this angle described using this Landau-type model can be expressed as follows:
As temperature increases, the structure becomes larger. This is achieved by changing the angles in the relationship between Fe04 and PO4 tetrahedral. Given that the increase in volume is only affected by the change in tilt angle or the angles between the tetrahedral, we should not be expecting a further change in volume.
This tells us that once we convert to the high temperature beta phase, it should not be able to expand anymore. There should not be a further change in volume.
When we look at the details of the unit cell volume for beta phase, at a high temperature form, we see that the volume doesn’t expand anymore because it the structure is fully

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