89Y MAS NMR and First-Principles Calculations
S1
89
Cation Disorder in Pyrochlore Ceramics: Y MAS NMR and First-Principles Calculations
Simon W. Reader, Martin R. Mitchell, Karen E. Johnston, Chris J. Pickard, Karl R. Whittle and Sharon E. Ashbrook,
Supporting Information
S2 1. Basic 89Y First-Principles Calculations
In order to evaluate the accuracy of the CASTEPS1 density functional theory code, using the gauge including projector augmented wave (GIPAW)S2 formalism, for the calculation of 89Y NMR parameters a series of calculations was undertaken for a set of simple inorganic materials whose NMR parameters had been determined previously experimentally.
Calculations were carried out using the GGA PBE functional with core-valence interactions described by ultrasoft pseudopotentials.S3 Integrals over the Brillouin zone were performed using a Monkhorst-Pack grid with a k-point spacing of 0.05 Å–1 and wavefunctions were expanded in planewaves with a kinetic energy smaller than the cutoff energy of 50 Ry. These parameters were determined by convergence studies on Y2O3, which possesses two distinct yttrium species. Calculations were performed on the EaStCHEM Research Computing Facility, which consists of 152 AMD Opteron processing cores partly connected by Infinipath high speed interconnects. Typical NMR calculation times were between 24 and 48 hours using 16 cores.
1.1 Y2O3
The unit cell dimensions and atomic coordinates for Y2O3 were taken from the literature.S4 Tests revealed that the 89Y and 17O NMR parameters were converged using a kpoint spacing of 0.05/0.04 Å–1 and an energy cut-off of 50/60 Ry, as shown in Figure S1. Calculated isotropic shieldings, σiso, for the two distinct Y species are given in Table S1, along with experimental isotropic chemical shifts, δiso.S5 For calculated shieldings values are given both for the initial crystal structure and after a geometry optimization (where atomic positions and unit cell size was allowed to vary). By considering the relative shift/shielding differences between the two Y species, it can be seen that the best agreement with experimental data is obtained after geometry optimization of the structure.
S3 Figure S1
Plot of (a, b) 89Y and (c, d) 17O chemical shielding (σ σiso) for Y2O3 as a function
of energy cut-off and k-point spacing. In (a, c) the k-point spacing was 0.1 Å–1 while in (b, d) the energy cut-off was 30 Ry. The blue diamonds and red squares indicate values for Y1 and Y2, respectively.
Table S1
Calculated and experimental isotropic chemical shielding/shift values for
Y2O3. The energy cut-off was 50 Ry and the k-point spacing was 0.05 Å–1.
Calculated Calculated (optimized) ExperimentalS5
Y1
Y2
Relative difference
σiso = 2384 ppm
σiso = 2321 ppm
63 ppm
σiso = 2376 ppm
σiso = 2330 ppm
46 ppm
δiso = 273 ppm
δiso = 314 ppm
41 ppm
S4 The shielding values calculated by CASTEP can be converted into chemical shifts by δiso = (σref – σiso)
(S1)
where σref is a reference shielding. This was determined by setting the mean value of the two calculated Y chemical shieldings in Y2O3 (2353 ppm) equal to the mean value of the two experimental isotropic chemical shifts (293.5 ppm). This gives a value of σref of 2646.5 ppm. This value was used to convert all subsequent shieldings into chemical shifts.
1.2 Model Compounds
A number of simple inorganic compounds (Y2O3,S4 Y2Sn2O7,S5 Y2Ti2O7,S6 Y2O2S,S7 YF3,S8 YAlO3,S9 α-Y2Si2O7 and β-Y2Si2O7S10) with known experimental NMR parameters were selected for study, and crystal structures were obtained from the literature. For α-Y2Si2O7, where a full structure is not known, the atomic coordinates for α-Ho2Si2O7 were used, as Ho and Y are of similar size.S11 All structures were geometry optimized prior to the calculation of NMR parameters. Typically, the forces upon the atoms were reduced to 0.005 eV/Å after optimization and the unit cell dimensions were increased by 1.13%. Table S2 compares the calculated and experimental NMR parameters for these compounds. In general, considering the large shift range of 89Y there is fairly good agreement between the calculations and the literature results, with the largest deviation observed for Y2Ti2O7. Further work (based on the calculation of Ti NMR parameters for a small number of model Ti-containing compounds) suggested that the problem here may actually lie with the Ti pseudopotential rather than with the Y itself, but although a number of alternative pseudopotentials were tested there was no significant improvement in the result. Further work would be required to determine if any improvement could be made, although the agreement achieved is certainly sufficient for the study here.
S5 Table S2
Calculated and experimental isotropic chemical shielding/shift values for
a range of simple Y-containing compounds. All structures were geometry optimized prior to the calculation of the NMR parameters. In all cases the energy cut-off was 50 Ry and the k-point spacing was 0.05 Å–1.
Calculated δiso (ppm)
Experimental δiso (ppm)
Y2O3
Y1
271
273S12
Y2O3
Y2
316
314S12
Y2Sn2O7
161
150S13
Y2Ti2O7
24
65S13
Y2O2S
302
277S12
YF3
–120
–112S14
YAlO3
259
215S15
α-Y2Si2O7 Y1
171
186S16
α-Y2Si2O7 Y2
133
149S16
α-Y2Si2O7 Y3
95
107S16
α-Y2Si2O7 Y4
38
56S16
β-Y2Si2O7
220
208S16
The correlation between experimental and calculated chemical shifts is plotted in Figure S2, demonstrating good qualitative agreement, particularly given the large 89Y chemical shift range (~4000 ppm).
S6 Figure S2
Plot of experimental against calculated isotropic chemical shifts for model
inorganic compounds.
2. 89Y chemical shifts in pyrochlores
As described in the main text, the investigation of the effect of Sn/Ti NNN substitution on the 89Y chemical shift was carried out in a systematic manner using cubic unit cells of either Y2Sn2O7 or Y2Ti2O7 and considering the chemical shifts of a single Y species as the NNN environment was altered. The chemical shifts of all of the Y species within the unit cells were then subsequently examined (and shown in Figure 7 of the main text). In addition to these systematic substitutions, a number of additional calculations were undertaken for a material with composition Y2SnTiO7, i.e., with 8 Sn and 8 Ti B site cations in the unit cell. The B site cations were arranged in a number of ordered structures (denoted O1, O2 and O3) or alternatively introduced into the structure entirely at random (denoted R1, R2 and R3). The occupation of the 16 B site cations for these various environments is given in Table S3 and Figure S3. Whilst containing only a few of the possible NNN environments, these structures possess a more disordered long range structure.
S7 Table S3
Occupation of the 16 B site cations in a series of calculations carried out for
pyrochlore unit cells of composition Y2TiSnO7. The position of these 16 cations within the unit cell is shown in Figure S3.
B site
O1
O2
O3
R1
R2
R3
1
Sn
Ti
Ti
Sn
Ti
Sn
2
Ti
Sn
Ti
Sn
Ti
Sn
3
Sn
Ti
Sn
Ti
Sn
Ti
4
Ti
Sn
Sn
Sn
Ti
Ti
5
Sn
Sn
Ti
Sn
Sn
Sn
6
Ti
Ti
Ti
Ti
Sn
Sn
7
Sn
Sn
Sn
Ti
Sn
Sn
8
Ti
Ti
Sn
Sn
Sn
Ti
9
Sn
Ti
Sn
Sn
Sn
Ti
10
Ti
Sn
Sn
Sn
Sn
Ti
11
Sn
Ti
Ti
Ti
Ti
Sn
12
Ti
Sn
Ti
Ti
Sn
Sn
13
Sn
Sn
Sn
Sn
Ti
Ti
14
Ti
Ti
Sn
Ti
Ti
Sn
15
Sn
Sn
Ti
Ti
Ti
Ti
16
Ti
Ti
Ti
Ti
Ti
Ti
S8 Figure S3
Position of the 16 B site cations within the pyrochlore unit cell. For the
various calculations the occupation of these sites are given in Table S3.
Figure S4 shows the calculated chemical shifts for these environments (denoted by black circles) superimposed on the shift ranges determined from the systematic series of calculations on substituted Y2Ti2O7 and Y2Sn2O7, denoted by open diamonds and open squares, respectively. For the Y2TiSnO7 composition the chemical shifts for all of the arrangements considered fall within the previously determined chemical shift ranges, with no anomalous shifts or significant structural distortions observed.
S9 Figure S4
Calculated 89Y chemical shifts as a function of the number, n, of Sn NNN
for substitutions into Y2Ti2O7 (grey squares), Y2Sn2O7 (grey diamonds), and for unit cells of composition Y2TiSnO7 (green triangles) with distributions of B site cations given in Table S3.
S10 References
S1. Segall, M. D.; Lindan, P. J. D.; Probert, M. J.; Pickard, C. J.; Hasnip, P. J.; Clark, S. J.; Payne, M. C. J. Phys. Cond. Matt. 2002, 14, 2717. S2. Pickard, C. J.; Mauri, F. Phys. Rev. B 2001, 63, 245101. S3. Yates, J. R.; Pickard, C. J.; Mauri, F. Phys. Rev. B 2007, 76, 024401. S4. Paton, M. G.; Maslen, E. N. Acta Cryst. 1965, 19, 307. S5. Brisse, F.; Knop, O. Can. J. Chem. 1968, 46, 859. S6. Knop, O.; Brisse, F.; Castelliz, L. Can. J. Chem. 1969, 47, 971. S7. Mikami, M.; Nakamura, S. J. Alloys and Compounds 2006, 408, 687. S8. Cheetham, A. K.; Norman, N. Acta. Chem. Scand. A 1980, 19, 2128. S9. Diehl, R.; Brandt, G. Mat. Res. Bull. 1975, 10, 85. S10. Redhammer, G. J.; Roth, G. Acta. Cryst. C. Cryst. Struct. Commun. 2003, 59, i103. S11. Felsche, J. Naturwissenschaften 1972, 59, 35. S12. Harazono, T.; Watanabe, T. Bull. Chem. Soc. Japan 1997, 70, 2383. S13. Grey, C. P.; Smith, M. E.; Cheetham, A. K.; Dobson, C. M.; Dupree, R. J. Am. Chem. Soc. 1990, 112, 4670-4675. S14. Wu, J.; Boyle, T. J.; Shreeve, J. L.; Ziller, J. W.; Evans, W. J. Inorg. Chem. 1993, 32, 1130. S15. Dupree, R.; Smith, M. E. Chem. Phys. Lett. 1988, 148, 41. S16. Becerro, A. I.; Escudero, A.; Florian, P.; Massiot, D.; Alba, M. D. J. Solid State Chem. 2004, 177, 2790.
89
Cation Disorder in Pyrochlore Ceramics: Y MAS NMR and First-Principles Calculations
Simon W. Reader, Martin R. Mitchell, Karen E. Johnston, Chris J. Pickard, Karl R. Whittle and Sharon E. Ashbrook,
Supporting Information
S2 1. Basic 89Y First-Principles Calculations
In order to evaluate the accuracy of the CASTEPS1 density functional theory code, using the gauge including projector augmented wave (GIPAW)S2 formalism, for the calculation of 89Y NMR parameters a series of calculations was undertaken for a set of simple inorganic materials whose NMR parameters had been determined previously experimentally.
Calculations were carried out using the GGA PBE functional with core-valence interactions described by ultrasoft pseudopotentials.S3 Integrals over the Brillouin zone were performed using a Monkhorst-Pack grid with a k-point spacing of 0.05 Å–1 and wavefunctions were expanded in planewaves with a kinetic energy smaller than the cutoff energy of 50 Ry. These parameters were determined by convergence studies on Y2O3, which possesses two distinct yttrium species. Calculations were performed on the EaStCHEM Research Computing Facility, which consists of 152 AMD Opteron processing cores partly connected by Infinipath high speed interconnects. Typical NMR calculation times were between 24 and 48 hours using 16 cores.
1.1 Y2O3
The unit cell dimensions and atomic coordinates for Y2O3 were taken from the literature.S4 Tests revealed that the 89Y and 17O NMR parameters were converged using a kpoint spacing of 0.05/0.04 Å–1 and an energy cut-off of 50/60 Ry, as shown in Figure S1. Calculated isotropic shieldings, σiso, for the two distinct Y species are given in Table S1, along with experimental isotropic chemical shifts, δiso.S5 For calculated shieldings values are given both for the initial crystal structure and after a geometry optimization (where atomic positions and unit cell size was allowed to vary). By considering the relative shift/shielding differences between the two Y species, it can be seen that the best agreement with experimental data is obtained after geometry optimization of the structure.
S3 Figure S1
Plot of (a, b) 89Y and (c, d) 17O chemical shielding (σ σiso) for Y2O3 as a function
of energy cut-off and k-point spacing. In (a, c) the k-point spacing was 0.1 Å–1 while in (b, d) the energy cut-off was 30 Ry. The blue diamonds and red squares indicate values for Y1 and Y2, respectively.
Table S1
Calculated and experimental isotropic chemical shielding/shift values for
Y2O3. The energy cut-off was 50 Ry and the k-point spacing was 0.05 Å–1.
Calculated Calculated (optimized) ExperimentalS5
Y1
Y2
Relative difference
σiso = 2384 ppm
σiso = 2321 ppm
63 ppm
σiso = 2376 ppm
σiso = 2330 ppm
46 ppm
δiso = 273 ppm
δiso = 314 ppm
41 ppm
S4 The shielding values calculated by CASTEP can be converted into chemical shifts by δiso = (σref – σiso)
(S1)
where σref is a reference shielding. This was determined by setting the mean value of the two calculated Y chemical shieldings in Y2O3 (2353 ppm) equal to the mean value of the two experimental isotropic chemical shifts (293.5 ppm). This gives a value of σref of 2646.5 ppm. This value was used to convert all subsequent shieldings into chemical shifts.
1.2 Model Compounds
A number of simple inorganic compounds (Y2O3,S4 Y2Sn2O7,S5 Y2Ti2O7,S6 Y2O2S,S7 YF3,S8 YAlO3,S9 α-Y2Si2O7 and β-Y2Si2O7S10) with known experimental NMR parameters were selected for study, and crystal structures were obtained from the literature. For α-Y2Si2O7, where a full structure is not known, the atomic coordinates for α-Ho2Si2O7 were used, as Ho and Y are of similar size.S11 All structures were geometry optimized prior to the calculation of NMR parameters. Typically, the forces upon the atoms were reduced to 0.005 eV/Å after optimization and the unit cell dimensions were increased by 1.13%. Table S2 compares the calculated and experimental NMR parameters for these compounds. In general, considering the large shift range of 89Y there is fairly good agreement between the calculations and the literature results, with the largest deviation observed for Y2Ti2O7. Further work (based on the calculation of Ti NMR parameters for a small number of model Ti-containing compounds) suggested that the problem here may actually lie with the Ti pseudopotential rather than with the Y itself, but although a number of alternative pseudopotentials were tested there was no significant improvement in the result. Further work would be required to determine if any improvement could be made, although the agreement achieved is certainly sufficient for the study here.
S5 Table S2
Calculated and experimental isotropic chemical shielding/shift values for
a range of simple Y-containing compounds. All structures were geometry optimized prior to the calculation of the NMR parameters. In all cases the energy cut-off was 50 Ry and the k-point spacing was 0.05 Å–1.
Calculated δiso (ppm)
Experimental δiso (ppm)
Y2O3
Y1
271
273S12
Y2O3
Y2
316
314S12
Y2Sn2O7
161
150S13
Y2Ti2O7
24
65S13
Y2O2S
302
277S12
YF3
–120
–112S14
YAlO3
259
215S15
α-Y2Si2O7 Y1
171
186S16
α-Y2Si2O7 Y2
133
149S16
α-Y2Si2O7 Y3
95
107S16
α-Y2Si2O7 Y4
38
56S16
β-Y2Si2O7
220
208S16
The correlation between experimental and calculated chemical shifts is plotted in Figure S2, demonstrating good qualitative agreement, particularly given the large 89Y chemical shift range (~4000 ppm).
S6 Figure S2
Plot of experimental against calculated isotropic chemical shifts for model
inorganic compounds.
2. 89Y chemical shifts in pyrochlores
As described in the main text, the investigation of the effect of Sn/Ti NNN substitution on the 89Y chemical shift was carried out in a systematic manner using cubic unit cells of either Y2Sn2O7 or Y2Ti2O7 and considering the chemical shifts of a single Y species as the NNN environment was altered. The chemical shifts of all of the Y species within the unit cells were then subsequently examined (and shown in Figure 7 of the main text). In addition to these systematic substitutions, a number of additional calculations were undertaken for a material with composition Y2SnTiO7, i.e., with 8 Sn and 8 Ti B site cations in the unit cell. The B site cations were arranged in a number of ordered structures (denoted O1, O2 and O3) or alternatively introduced into the structure entirely at random (denoted R1, R2 and R3). The occupation of the 16 B site cations for these various environments is given in Table S3 and Figure S3. Whilst containing only a few of the possible NNN environments, these structures possess a more disordered long range structure.
S7 Table S3
Occupation of the 16 B site cations in a series of calculations carried out for
pyrochlore unit cells of composition Y2TiSnO7. The position of these 16 cations within the unit cell is shown in Figure S3.
B site
O1
O2
O3
R1
R2
R3
1
Sn
Ti
Ti
Sn
Ti
Sn
2
Ti
Sn
Ti
Sn
Ti
Sn
3
Sn
Ti
Sn
Ti
Sn
Ti
4
Ti
Sn
Sn
Sn
Ti
Ti
5
Sn
Sn
Ti
Sn
Sn
Sn
6
Ti
Ti
Ti
Ti
Sn
Sn
7
Sn
Sn
Sn
Ti
Sn
Sn
8
Ti
Ti
Sn
Sn
Sn
Ti
9
Sn
Ti
Sn
Sn
Sn
Ti
10
Ti
Sn
Sn
Sn
Sn
Ti
11
Sn
Ti
Ti
Ti
Ti
Sn
12
Ti
Sn
Ti
Ti
Sn
Sn
13
Sn
Sn
Sn
Sn
Ti
Ti
14
Ti
Ti
Sn
Ti
Ti
Sn
15
Sn
Sn
Ti
Ti
Ti
Ti
16
Ti
Ti
Ti
Ti
Ti
Ti
S8 Figure S3
Position of the 16 B site cations within the pyrochlore unit cell. For the
various calculations the occupation of these sites are given in Table S3.
Figure S4 shows the calculated chemical shifts for these environments (denoted by black circles) superimposed on the shift ranges determined from the systematic series of calculations on substituted Y2Ti2O7 and Y2Sn2O7, denoted by open diamonds and open squares, respectively. For the Y2TiSnO7 composition the chemical shifts for all of the arrangements considered fall within the previously determined chemical shift ranges, with no anomalous shifts or significant structural distortions observed.
S9 Figure S4
Calculated 89Y chemical shifts as a function of the number, n, of Sn NNN
for substitutions into Y2Ti2O7 (grey squares), Y2Sn2O7 (grey diamonds), and for unit cells of composition Y2TiSnO7 (green triangles) with distributions of B site cations given in Table S3.
S10 References
S1. Segall, M. D.; Lindan, P. J. D.; Probert, M. J.; Pickard, C. J.; Hasnip, P. J.; Clark, S. J.; Payne, M. C. J. Phys. Cond. Matt. 2002, 14, 2717. S2. Pickard, C. J.; Mauri, F. Phys. Rev. B 2001, 63, 245101. S3. Yates, J. R.; Pickard, C. J.; Mauri, F. Phys. Rev. B 2007, 76, 024401. S4. Paton, M. G.; Maslen, E. N. Acta Cryst. 1965, 19, 307. S5. Brisse, F.; Knop, O. Can. J. Chem. 1968, 46, 859. S6. Knop, O.; Brisse, F.; Castelliz, L. Can. J. Chem. 1969, 47, 971. S7. Mikami, M.; Nakamura, S. J. Alloys and Compounds 2006, 408, 687. S8. Cheetham, A. K.; Norman, N. Acta. Chem. Scand. A 1980, 19, 2128. S9. Diehl, R.; Brandt, G. Mat. Res. Bull. 1975, 10, 85. S10. Redhammer, G. J.; Roth, G. Acta. Cryst. C. Cryst. Struct. Commun. 2003, 59, i103. S11. Felsche, J. Naturwissenschaften 1972, 59, 35. S12. Harazono, T.; Watanabe, T. Bull. Chem. Soc. Japan 1997, 70, 2383. S13. Grey, C. P.; Smith, M. E.; Cheetham, A. K.; Dobson, C. M.; Dupree, R. J. Am. Chem. Soc. 1990, 112, 4670-4675. S14. Wu, J.; Boyle, T. J.; Shreeve, J. L.; Ziller, J. W.; Evans, W. J. Inorg. Chem. 1993, 32, 1130. S15. Dupree, R.; Smith, M. E. Chem. Phys. Lett. 1988, 148, 41. S16. Becerro, A. I.; Escudero, A.; Florian, P.; Massiot, D.; Alba, M. D. J. Solid State Chem. 2004, 177, 2790.
