Written Exercise
Paragraph 1
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 space symmetry of quartz, α- FePO4 and β-FePO4: In quartz, every silicon atom is connected to four oxygen atoms to form a structure of corner-connected tetrahedral. Similarly in α-FePO4, each iron or phosphate atom is also connected to four oxygen atoms, forming corner-connected FeO4 and PO4 tetrahedra respectively. However, β-FePO4 exhibits totally different chemistry and space symmetry from either quartz or α-FePO4. According to altervalent substitution effect, quartz and iron phosphate demonstrate very similar crystal structure even though silicon, iron and phosphate are distinct chemical elements. Fe3+ + P5+ → 2Si¬4+ As seen from the equation above, two silicon ions replace one iron(III) ion and one phosphate(V) ion. The total charge (8+) and total number of ions (2) on each side of the equation are equal. 3. Crystallochemical relationships and the temperature dependence of polymorphism: The transition between polymorphs α-FePO4 and β-FePO4 is dependent on temperature. …show more content…
With a rise in temperature, the atoms with in crystal vibrate more vigorously, resulting in an expansion of thermal ellipsoids. As such, the atomic volume increases and the internal crystal structure changes through tetrahedral tilting. An ordered structure with high level of symmetry is formed.
As temperature increases from 294K to 969K, α-FePO4 undergoes thermal expansion in which the cell parameters and volumes increases in a non-linear manner. This is due to a change in the intertetrahedral Fe-O-P angles and the tilt angles. As temperature exceeds 980K, α-FePO4 is transited to β-FePO4 with a change in lattice structure from trigonal to hexagonal. There is still increase in cell parameters and expansion in cell volume as temperature continues to increase, yet the increment is much smaller compared to α-FePO4. The bond angles and bond distances decrease in β-FePO4.
Paragraph 2
1. Unit cell relationship between α-FePO4 and β-FePO4: α-FePO4 has a trigonal unit cell with lattice structure a = b = c; α = β = γ ≠ 90° and β-FePO4 has hexagonal unit cell with a lattice structure a = b ≠ c; α = β = 90°, γ = 120°. The dimensions are broadly the same even though there is a temperature change. 2. Symmetrical differences between α-FePO4 and β-FePO4: α-FePO4 belongs to space group P3121 and β-FePO4 belongs to space group P6422. The difference in symmetry is shown in Figure 3 and 4 below. At temperature below 980K (α-FePO4), 31 screw axis is present in the unit cell. 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
Paragraph 1
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 space symmetry of quartz, α- FePO4 and β-FePO4: In quartz, every silicon atom is connected to four oxygen atoms to form a structure of corner-connected tetrahedral. Similarly in α-FePO4, each iron or phosphate atom is also connected to four oxygen atoms, forming corner-connected FeO4 and PO4 tetrahedra respectively. However, β-FePO4 exhibits totally different chemistry and space symmetry from either quartz or α-FePO4. According to altervalent substitution effect, quartz and iron phosphate demonstrate very similar crystal structure even though silicon, iron and phosphate are distinct chemical elements. Fe3+ + P5+ → 2Si¬4+ As seen from the equation above, two silicon ions replace one iron(III) ion and one phosphate(V) ion. The total charge (8+) and total number of ions (2) on each side of the equation are equal. 3. Crystallochemical relationships and the temperature dependence of polymorphism: The transition between polymorphs α-FePO4 and β-FePO4 is dependent on temperature. …show more content…
With a rise in temperature, the atoms with in crystal vibrate more vigorously, resulting in an expansion of thermal ellipsoids. As such, the atomic volume increases and the internal crystal structure changes through tetrahedral tilting. An ordered structure with high level of symmetry is formed.
As temperature increases from 294K to 969K, α-FePO4 undergoes thermal expansion in which the cell parameters and volumes increases in a non-linear manner. This is due to a change in the intertetrahedral Fe-O-P angles and the tilt angles. As temperature exceeds 980K, α-FePO4 is transited to β-FePO4 with a change in lattice structure from trigonal to hexagonal. There is still increase in cell parameters and expansion in cell volume as temperature continues to increase, yet the increment is much smaller compared to α-FePO4. The bond angles and bond distances decrease in β-FePO4.
Paragraph 2
1. Unit cell relationship between α-FePO4 and β-FePO4: α-FePO4 has a trigonal unit cell with lattice structure a = b = c; α = β = γ ≠ 90° and β-FePO4 has hexagonal unit cell with a lattice structure a = b ≠ c; α = β = 90°, γ = 120°. The dimensions are broadly the same even though there is a temperature change. 2. Symmetrical differences between α-FePO4 and β-FePO4: α-FePO4 belongs to space group P3121 and β-FePO4 belongs to space group P6422. The difference in symmetry is shown in Figure 3 and 4 below. At temperature below 980K (α-FePO4), 31 screw axis is present in the unit cell. 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