Lattice Symmetry Of Quartz, Fepo4 And Α-Fepo4?

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1. Lattice symmetry of quartz, α-FePO4 and β-FePO4:
Quartz has a trigonal lattice structure with space group P3121 (group no. 152).
At any temperature below 980K, Iron phosphate exists as α-FePO4, which has a trigonal lattice structure with space group P3121 (group no. 152) where iron, phosphate and oxygen occupy Wyckoff position 3a, 3b and 6c respectively. As the temperature rises up to and above 980K, α-FePO4 exhibits α-β transition and becomes β-FePO4 that shows a distinct lattice and space symmetry from α-FePO4. β-FePO4 has hexagonal lattice structure with space group P6422 (group no. 181), in which iron, phosphate and oxygen occupy Wyckoff position 3d, 3c and 12k respectively.

2. Crystal chemistry and
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Three mirror lines are present in the trigonal shape at the origin of the unit cell.
However, at temperature above 980K (β-FePO4), 64 screw axis is present in the unit cell. A regular hexagon is observed around the origin of each unit cell.
3. Relationship between temperature, polymorph formation, and tetrahedral tilting:
An increase in temperature leads to increasing atomic vibrations and subsequently an increase in unit cell volume. For example, as given in the data table from the experiment study, an increase in temperature from 294K to 865K leads to an increase in cell parameter a from 5.0314 Å to 5.0985 Å and c from 11.2465 Å to 11.3113 Å. The unit cell volume also increases from 246.56 Å3 to 254.64 Å3. Such thermal expansion is brought by tetrahedral tilting. A clear illustration is shown by comparing Figure 1 and Figure 5 below.

Interestingly, the tilt angle shows an inverse relationship with temperature. By comparing Figure 1, 5 and 6, we can see that the tilt angle at 456K is larger than that at 865K and smaller than that at 294K, suggesting that the tetrahedral tilting decreases as temperature increases. This observation is also supported by the data given in the experiment study. When temperature increases from 294K to 865K, δavPO4 and δdavFeO4 decrease from 23.7° to 16.2° and from 19.2° to 16.2°
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For instance, when temperature increases from 1005K to 1073K, the unit cell volume only increases slightly from 262.12 Å3to 262.30 Å3. A possible explanation for this observation is that the tilt angles have already reached their minimum value, 0° in β-FePO4. Thus there is no further expansion in volume as temperature increases. Paragraph 3
1. Difference between FeO4 and PO4 tetrahedral distortion and tetrahedral tilting:
As temperature increases, FeO4 tetrahedra experiences great distortions than that of PO4 in terms of bond length. Extracted from the data table, when temperature increases from 294K to 969K, the Fe-O bond distance decreases from 1.858 Å to 1.818 Å. However after the α-β phase transition at 980K, the Fe-O bond distance decreases to 1.73 Å when temperature increases to 1073K. Such decrease in bond length is not observed in PO4 tetrahedron.

By and large, the PO4 tetrahedra exhibit greater tilting than the FeO4 tetrahedra. This is because that the P5+ ion has a smaller ionic radius (0.17 Å) than that of the Fe3+ ion (0.49 Å), thus the PO4 tetrahedron is smaller than the FeO4 tetrahedron and manifests larger tilt

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