Written exercise
Paragraph 1 Iron phosphate, FePO4, has a very similar structure as quartz. Quartz has a trigonal lattice structure with space group P3121 (group no. 152). Similarly, at temperature below 980K, iron phosphate exists as α-FePO4, which also exhibits trigonal lattice structure with space group P3121 in which iron, phosphate and oxygen occupy Wyckoff position 3a, 3b and 6c respectively. In quartz, every silicon atom is connected to four oxygen atoms to form a network of cornerconnected tetrahedra, while in α-FePO4 each iron or phosphate atom is also connected to four oxygen atoms, forming corner-connected FeO4 and PO4 tetrahedra respectively. However, when temperature reaches and exceeds 980K, α-FePO4 exhibits α-β transition, …show more content…
Despite that silicon, iron and phosphate are distinct chemical elements, quartz and iron phosphate demonstrate very similar crystal structure, and this could be achieved through altervalent substitution based on the following equation: 2Si4+
→ Fe3+ + P5+
As such, every two silicon ions in quartz is replaced by one iron(III) ion and one phosphate(V) ion while topology and total electrical charge of the tetrahedra remain unchanged. α-FePO4 and β-FePO4 are polymorphs to each other, and the transition between the alpha and beta form is temperature dependent. As temperature increases, the atoms within the crystal vibrate more vigorously leading to an expansion of the thermal ellipsoids, and as a result, the atomic volume increases. In order to accommodate this increase in atomic volume, the internal crystal structure also changes through tetrahedral tilting. A highly ordered structure with higher level of symmetry is then formed. In the case of iron phosphate, as temperature increases from 294K to 969K, the α phase crystal shows thermal expansion in which the cell parameters and volumes increase non-linearly as a function of temperature. This is brought by the …show more content…
The variations in the tilt angles, δ, and intertetrahedral bridging angles, θ, allow the expansion of the cage and unit cell volume as atomic vibration increases with increasing temperature in the α phase with a thermal expansion coefficient: a(K-1 ) = 2.924 x 10-5 + 2.920 x 10-10 (T-300)2
. The increasing atomic vibration causes the expansion of thermal ellipsoids or spheres. When the temperature reaches the transition temperature of 980K, the bonds in tetrahedron are particularly stressed, resulting in an extreme shape of the thermal ellipsoids.
Thus there is a sharp decrease in the Fe-O bond length and the tilt angle decreases to 0, resulting in a higher level of symmetry and hence a change in the lattice structure from trigonal lattice to hexagonal lattice as well as a change in the space symmetry of the crystal. As mentioned in Paragraph 2, in the β phase, since the tilt angle has already been at the minimum value, the unit cell volume stops increasing. The α-β phase transition is first-order in character and can be modeled using a function of δ, which is the average tilt angle of FePO4, as follow: δ2 = 2
Paragraph 1 Iron phosphate, FePO4, has a very similar structure as quartz. Quartz has a trigonal lattice structure with space group P3121 (group no. 152). Similarly, at temperature below 980K, iron phosphate exists as α-FePO4, which also exhibits trigonal lattice structure with space group P3121 in which iron, phosphate and oxygen occupy Wyckoff position 3a, 3b and 6c respectively. In quartz, every silicon atom is connected to four oxygen atoms to form a network of cornerconnected tetrahedra, while in α-FePO4 each iron or phosphate atom is also connected to four oxygen atoms, forming corner-connected FeO4 and PO4 tetrahedra respectively. However, when temperature reaches and exceeds 980K, α-FePO4 exhibits α-β transition, …show more content…
Despite that silicon, iron and phosphate are distinct chemical elements, quartz and iron phosphate demonstrate very similar crystal structure, and this could be achieved through altervalent substitution based on the following equation: 2Si4+
→ Fe3+ + P5+
As such, every two silicon ions in quartz is replaced by one iron(III) ion and one phosphate(V) ion while topology and total electrical charge of the tetrahedra remain unchanged. α-FePO4 and β-FePO4 are polymorphs to each other, and the transition between the alpha and beta form is temperature dependent. As temperature increases, the atoms within the crystal vibrate more vigorously leading to an expansion of the thermal ellipsoids, and as a result, the atomic volume increases. In order to accommodate this increase in atomic volume, the internal crystal structure also changes through tetrahedral tilting. A highly ordered structure with higher level of symmetry is then formed. In the case of iron phosphate, as temperature increases from 294K to 969K, the α phase crystal shows thermal expansion in which the cell parameters and volumes increase non-linearly as a function of temperature. This is brought by the …show more content…
The variations in the tilt angles, δ, and intertetrahedral bridging angles, θ, allow the expansion of the cage and unit cell volume as atomic vibration increases with increasing temperature in the α phase with a thermal expansion coefficient: a(K-1 ) = 2.924 x 10-5 + 2.920 x 10-10 (T-300)2
. The increasing atomic vibration causes the expansion of thermal ellipsoids or spheres. When the temperature reaches the transition temperature of 980K, the bonds in tetrahedron are particularly stressed, resulting in an extreme shape of the thermal ellipsoids.
Thus there is a sharp decrease in the Fe-O bond length and the tilt angle decreases to 0, resulting in a higher level of symmetry and hence a change in the lattice structure from trigonal lattice to hexagonal lattice as well as a change in the space symmetry of the crystal. As mentioned in Paragraph 2, in the β phase, since the tilt angle has already been at the minimum value, the unit cell volume stops increasing. The α-β phase transition is first-order in character and can be modeled using a function of δ, which is the average tilt angle of FePO4, as follow: δ2 = 2