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This report aims to study the symmetrical distinctions, crystal structures and chemistry of α‐FePO4 and β‐FePO4 as well as any alteration to FeO4 and PO4 when there are modifications to temperature. It also seeks to justify the tilting of the tetrahedral. The article by Haines shows that he had studied the iron phosphate, FePO4, at temperatures from 294 K to 1073 K and had found that the turning point between the
2 phases is at 980 K, where FePO4 takes on the alpha phase at lower temperatures
(below 980 K) and beta phase at higher temperatures (above 980 K).
The low temperature α‐FePO4 has been identified to be in the space group P3121 hence the lattice symmetry of the alpha polymorph is trigonal. Whereas the high temperature beta form has been identified to be in the space group P6422 hence the …show more content…
Figure 1: 294 K Figure 2: 1073 K
From the 2 figures we can observe that both unit cells contains a single formula unit.
Dimensions for both are generally the same but it can be seen to have a difference in symmetry. The difference lies in that the α‐ FePO4 is trigonal, where there is a 31 screw axis and β‐ FePO4 is hexagonal where there is a 64 screw axis. Therefore the link to 1 tetrahedron to another will alter as it move from 31 to 64 screw axis.
The ‘flexibility’ allows the tetrahedron to tilt and when one tetrahedron tilts, the surrounding tetrahedron will tilt in the other direction in a cooperative manner. The tilting of the tetrahedral will only change the angle and will not make any difference to the shape of the unit cell. Both alpha and beta phase will still have the same shape unit cell where a = b ≠ c and that γ = 120°.
As seen from the above table, the cell parameter rises noticeably as temperature surges which will result in an increase in cell volume. In addition, the Fe‐O‐P bond …show more content…
PO4 is significant in determining the structural integrity and properties.
Rising temperatures will cause the bond length to change. This along with the tilt angle, bridging angle and the O‐P‐O angle are the possible reasons for causing the distortions in the tetrahedral. The tetrahedral distortion is caused by a tetrahedral tilt where it is quantified by the tilt angle and affected by temperature. The cell parameters and volume of α‐ FePO4 rises noticeably and in a non‐linear way as a function of temperature. Thermal expansion is mainly due to angular variations ascertained in the Fe‐O‐P bridging angles as well as the correlated tilt angles.
Therefore temperature dependence of the thermal expansion could be the temperature dependence of angular variations ascertained in the Fe‐O‐P bridging angles as well as the correlated tilt angles. The temperature dependence of this angle can be exhibited using the equation as shown below: δ2 = 2/3 δ0 2 [1 + (1 – ¾ (T – Tc/T0 – Tc))1/2]
Where δ0 represents the decline in tilt angle at the temperature of 980 K which is the turning point and Tc represents temperature for the second‐order
This report aims to study the symmetrical distinctions, crystal structures and chemistry of α‐FePO4 and β‐FePO4 as well as any alteration to FeO4 and PO4 when there are modifications to temperature. It also seeks to justify the tilting of the tetrahedral. The article by Haines shows that he had studied the iron phosphate, FePO4, at temperatures from 294 K to 1073 K and had found that the turning point between the
2 phases is at 980 K, where FePO4 takes on the alpha phase at lower temperatures
(below 980 K) and beta phase at higher temperatures (above 980 K).
The low temperature α‐FePO4 has been identified to be in the space group P3121 hence the lattice symmetry of the alpha polymorph is trigonal. Whereas the high temperature beta form has been identified to be in the space group P6422 hence the …show more content…
Figure 1: 294 K Figure 2: 1073 K
From the 2 figures we can observe that both unit cells contains a single formula unit.
Dimensions for both are generally the same but it can be seen to have a difference in symmetry. The difference lies in that the α‐ FePO4 is trigonal, where there is a 31 screw axis and β‐ FePO4 is hexagonal where there is a 64 screw axis. Therefore the link to 1 tetrahedron to another will alter as it move from 31 to 64 screw axis.
The ‘flexibility’ allows the tetrahedron to tilt and when one tetrahedron tilts, the surrounding tetrahedron will tilt in the other direction in a cooperative manner. The tilting of the tetrahedral will only change the angle and will not make any difference to the shape of the unit cell. Both alpha and beta phase will still have the same shape unit cell where a = b ≠ c and that γ = 120°.
As seen from the above table, the cell parameter rises noticeably as temperature surges which will result in an increase in cell volume. In addition, the Fe‐O‐P bond …show more content…
PO4 is significant in determining the structural integrity and properties.
Rising temperatures will cause the bond length to change. This along with the tilt angle, bridging angle and the O‐P‐O angle are the possible reasons for causing the distortions in the tetrahedral. The tetrahedral distortion is caused by a tetrahedral tilt where it is quantified by the tilt angle and affected by temperature. The cell parameters and volume of α‐ FePO4 rises noticeably and in a non‐linear way as a function of temperature. Thermal expansion is mainly due to angular variations ascertained in the Fe‐O‐P bridging angles as well as the correlated tilt angles.
Therefore temperature dependence of the thermal expansion could be the temperature dependence of angular variations ascertained in the Fe‐O‐P bridging angles as well as the correlated tilt angles. The temperature dependence of this angle can be exhibited using the equation as shown below: δ2 = 2/3 δ0 2 [1 + (1 – ¾ (T – Tc/T0 – Tc))1/2]
Where δ0 represents the decline in tilt angle at the temperature of 980 K which is the turning point and Tc represents temperature for the second‐order