Computational prediction and experimental confirmation of B-site doping in YBa2Fe3O8

Calculations were performed using the plane wave density functional theory (DFT) package, Vienna Ab-intio Simulation Package (VASP) version 4.6.26 65 with the Perdew, Burke and Ernzerhof (PBE) exchange correlation functional. For the B-site species (Fe, Co, Mn and Ni) the first sub-valence porbitals were treated as valence and for the A-site species (Y and Ba) the first sub-valence s-orbital was treated as valence. The k-point grid that was used for each calculation was determined by the first gamma centred k-point grid that fulfilled the condition:


Introduction
The properties of transition metal oxides are controllable by substitution at the metal sites. When several candidate sites are available, qualitative crystal chemical considerations may not always be capable of predicting the outcome of a substitution reaction. Here we explore the use of ab initio calculations to dene the outcome of site substitution in an ordered triple perovskite.
Complex metal oxides are important scientically because of their structural diversity and the wide range of novel phenomena they sustain, including charge ordering, colossal magnetoresistance and multiferroic behaviour. They have applications in many industrial and technological areas including catalysis, 1 solid oxide fuel cell (SOFC) 2 electrolytes and electrodes, transparent conductors, 3 superconductors, 4 ferro-and piezoelectrics, 5 dielectric materials, 6 thermoelectrics, 7 positive temperature co-efficient of resistivity materials (PTCR) 8 and ferrite permanent magnets. 9 Substitution into a parent structure permits property tuning in all of these application classesexamples are the evolution of the d.c. conductivity and area specic resistance (ASR) in the Ba 1Àx Sr x Fe 1Ày Co y O 3Àd [10][11][12][13] family of SOFC cathode materials, and band gap and resistivity tuning in the doped ZnO 14-16 family of transparent conducting oxides.
The structure of the superconductor YBa 2 Cu 3 O 7 (ref. 17) is based upon the ABO 3 perovskite structure that is extended to form a three-fold super structure in the c-axis direction, here-aer referred to as a 3a p structure. YBa 2 Fe 3 O 8 (ref. 18) (Fig. 1a) was the rst 3a p analogue of the superconductor YBa 2 Cu 3 O 7 in which Cu was fully replaced by another transition metal, and hence has been the object of considerable study. [18][19][20][21][22][23] It is a good candidate for predictive substitution as it is related to a number of other functional oxide materials in terms of system size, 17,24 structural motif 17,25 and some of the elements included in the system have been previously reported in other functional systems. 10,17,25 Long range ordering in the c direction is driven by ordering of oxygen vacancies (one ninth per triple perovskite (A 3 B 3 O 9 ) Formula Unit (FU)). These ordered vacancies create distinct A-and B-site environments within the structure. There are three A-sites, one hosting Y 3+ ions co-ordinated to eight O 2À ions and two Ba sites co-ordinated to twelve O 2À ions. The B-sites are ve co-ordinate square based pyramids and six coordinate octahedral sites, both distorted away from ideal polyhedral geometry: the octahedral site has four short and two long bonds, and the square pyramidal site has one short and four long bonds. YBa 2 Fe 3 O 8 orders antiferromagnetically at $700 K (ref. [20][21][22] with a G-type magnetic structure. 23 In this work we explore the use of Density Functional Theory (DFT) to guide the synthesis of B-site doped YBa 2 Fe 3 O 8 . 18 While previous reports exist for substitution of Co into the YBa 2 Fe 3 O 8 compound, 19 substitution with Ni or Mn is currently unreported. This allows for both the validation of the computational method for the system by calculating Co substitution and for the prediction of unreported substitutions. Irrespective of the A-site composition, no compounds containing Fe and Mn have been previously reported in this structure.
Given the multiplicity of possible sites for doping, it is not trivial to identify where a substitution will take place. Prediction of whether a dopant will favour one of the available B-site geometries by looking at known structures is not reliable as precedents exist for doping at each of the sites found in the 3a p structure. [26][27][28] It is also possible that B-site doping may occur in a disordered fashion over both B-sites. Given the widespread applicability of doped metal oxides it is highly desirable to use calculations to aid in predicting how to substitute the compound in order to reduce the number of syntheses that are required to nd new compounds.
The calculation of stable levels of doping in YBa 2 Fe 3 O 8 is a complex computational problem because of the number of metal species present and two different chemical environments for Fe 3+ . The prediction of ionic substitution based on a database of structures has been reported previously. 29 It has also been shown that all unique congurations of a structure can be generated using symmetry, and the most stable conguration determined by calculating relative energies between congurations. 30 This method has been applied in calculating the solid solutions of some binary and ternary oxides 31-33 and carbonate systems 34,35 and for a number of other system types. [36][37][38] Convex hull calculations have also been previously used in the prediction and synthesis of compounds with some success, 39 however the construction of convex hulls for systems containing four or more elements is impractical.
The complex structures of many functional transition metal oxides require large numbers of potential disordered congurations to be investigated in an exhaustive study. For example the largest super-cell used here for the composition YBa 2 Fe 2 MnO 8 has 16 Fe atoms and 8 Mn atoms distributed over 24 B-sites. Ignoring symmetry, there are 24!/16!8! ¼ 735 471 ways of arranging these atoms, which reduces to 24 371 congurations not related by symmetry. Since such an exhaustive approach is clearly unfeasible in this case, we propose a more practical, simplied model. Previously it has been shown that DFT calculations can be congured to closely reproduce experimental reaction enthalpies for previously known perovskite materials, such as the LaMO 3 system, where M indicates a transition metal species 40,41 for calculations performed at 0 K. This work utilises the capability of DFT to calculate formation energies from binary oxides as a predictive tool, and is demonstrated in a system containing four different cation species and covering three different dopants with a range of doping levels.
We begin by calculating an energy of M substitution for doped YBa 2 Fe 3Àx M x O 8 in a selected number of B-site congurations, representative of the possible orderings. We then experimentally test the following hypothesis: when this substitution energy is negative, doping will be experimentally favourable and conversely when the substitution energy is positive, doping would be unfavourable. We demonstrate the methodology for YBa 2 Fe 3Àx M x O 8 when M ¼ Co which has previously been synthesised 19 and then make predictions for doping when M ¼ Mn and Ni.

Reaction energies
We start our calculation of reaction enthalpies by dening the dopant species M* by the binary oxide of M and a required amount of O 2 gas required to balance any change in the charge state of M in the doped compound to the 3+ oxidation state: For reference calculations of the energies of binary oxides, the initial atomic coordinates and unit cells were used as reported in the literature. [42][43][44][45][46][47] Where multiple possible binary oxides are reported for the transition metals (M ¼ Co and Mn) the oxide which gave an overall charge state as close to 3+ as possible was selected in order to minimise the amount of O 2 required to balance the equation. When M ¼ Mn, no change in formal oxidation state is required, for M ¼ Co and Ni, we assume that all of the M atoms increase their average oxidation state to be formally 3+ as this is reported experimentally for Co in this system. 19 A substitution energy, DE sub , can then be dened for the formation of the doped material from the undoped parent, binary oxides and gas phase oxygen where required (Eqn (2)).
The most favoured conguration at each doping level is dened as the composition that yields the lowest substitution energy, DE sub . A negative value of DE sub is used across doping species and doping levels to predict that doping is likely to be possible. The energy DE sub is closely related to other potentially relevant reaction energies, as discussed in the ESI. † Since we are calculating energies at each end of the solid solution and values in between, we can also calculate energies relative to an ideal solid solution. Particularly stable compositions might be expected to have energies that lie below the energy of the ideal solid solution. Alternatively increases in energy indicate that the solid solution is unfavourable as has been suggested for solid solutions between binary materials, 48 which could suggest that phase separation is likely. For our systems, a solid-solution energy, DE SS , is calculated according to Eqn (3): In the system examined in this work the YBa 2 M 3 O 8 end members of the solid solutions are not reported in ordered 3a p structures (although YBa 2 Co 3 O 8+d is reported as a disordered cubic perovskite 49 ), and so the solid-solution energy is not a true prediction of phase stability (competing phase separation into the two ordered end members cannot occur experimentally). Instead we use DE sub (Eqn (2)) for our predictions of the outcomes of substitution reactions (Fig. 3a). However, for clarity in identifying the differences between congurations at each value of x we have used DE SS (Eqn (3) and Fig. 3b-d).

Doping models
The initial atomic coordinates and unit cell for the calculations were taken from the reported crystal structure of YBa 2 Fe 3 O 8 in an (a + b, a À b, 2c) super-cell of the nuclear cell (Fig. 1b). 18 This super-cell allows calculations for G-type antiferromagnetic and ferromagnetic ordering, and contains four octahedral and eight square pyramidal B-sites, over which the various transition metal cations were distributed at each level of doping.
The different B-site congurations considered for different doping levels are shown in Fig. 2. For full substitution (x ¼ 3) only one B-site conguration is possible. For x ¼ 1 and 2, three different B-site congurations were considered in order to be able to approximate the site preferences of the dopant species. In the rst conguration, which we named "Octahedral", octahedral sites are preferred for the dopant species. At the doping level of x ¼ 1 the octahedral sites are lled, and hence for x ¼ 2 the remaining dopants were distributed evenly amongst the square pyramidal sites in order to maximise the separation between the dopant atoms (Fig. 2). In the second conguration, which we name "Square Pyramidal" the dopant species were distributed amongst alternating square pyramidal site at x ¼ 1 and the square pyramidal sites were fully occupied when x ¼ 2. For the nal "Mixed" conguration the calculations were performed on a larger (2(a + b), a À b, 2c) super-cell to allow for each of the two octahedral and the four square pyramidal layers to contain the same number of dopant atoms. For both x ¼ 1 and x ¼ 2 an equal number of dopant species were placed on each type of B-site, with the atoms distributed in order to maximise their separation (Fig. 2).

Computational results
Balanced equations for the calculation of substitution energies were created taking into account the possibility of an overall change in oxygen content, depending on the dopant metal (DE sub , Eqn (2)). Calculated values of DE sub are used to predict whether a calculated composition would be stable (negative DE sub ) and therefore likely to form experimentally.
Results for the calculated substitution energies suggest that favourable doping can be achieved when M ¼ Co and Mn and no favoured doping conguration was found when M ¼ Ni. Substitution energies for the lowest energy conguration for each doping level and dopant are shown in Fig. 3a. When M ¼ Co the x ¼ 1 substitution level is favoured with DE sub ¼ À0.03 eV/FU when the dopant atoms are distributed over octahedral and square-pyramidal sites in the Mixed conguration, i.e. with no Bsite preference (Fig. 3b). At higher doping levels of x ¼ 2 and 3, doping is calculated to be unfavourable, with positive values of DE sub . The calculation of favourable doping for M ¼ Co and x ¼ 1 without any B-site preference which becomes unfavourable at a point between x ¼ 1 and 2 is in good agreement with reported experimental results. 19 Co doping within the YBa 2 Fe 3 O 8 phase has been reported for the nominal values of x ¼ 0.6, 0.9, 1.2 and 1.5, and substitution beyond x ¼ 1.5 has not been reported experimentally. In addition, experiments show no signicant cation site preference for the doped compounds. 19 The consistency between the computational results and the experimentally reported phases suggest that our approach can reliably calculate the favourability of transition metal substitution within YBa 2 Fe 3 O 8 .
For M ¼ Mn calculations suggest that substitution is favoured at x ¼ 1, with the Mn atoms in the octahedral conguration with G-type antiferromagnetic ordering on the B-site (Fig. 3c). DE sub for the substituted material was calculated to be À0.09 eV/FU. The higher x ¼ 2 substitution level is considerably unfavourable energetically; the most stable conguration has the Mn atoms in the octahedral conguration with G-type antiferromagnetic ordering but the substitution energy, DE sub , is +0.33 eV/FU.
For M ¼ Ni, no substitution level is found to have a negative value of DE sub . An interesting result to note however, is that at x ¼ 2 the Ni atoms were favoured in the square pyramidal sites and with ferromagnetic ordering (Fig. 3d). Although the x ¼ 2 conguration was found to have a positive DE sub value of +0.26 eV/ FU, if this level of doping could be synthesised in the 3a p structure, our calculations predict that the material would unusually favour ferromagnetic over G-type antiferromagnetic ordering.
In summary, the DFT calculations predict that only x ¼ 1 Mn substitution is favourable from the six Ni and Mn substitution levels examined.
As expected, of the calculated structures we observe that for each doping level, the most stable conguration also has the smallest unit cell volume (Fig. 4a-c). The single exception was when x ¼ 1 and M ¼ Ni, where the conguration with the smallest unit cell volume is 0.014 eV/FU less stable compared to the structure with the lowest energy.
In the structure of the M ¼ Mn, x ¼ 1 octahedral conguration, which is predicted to be stable, the geometries (Fig. 4d) of the fully Mn occupied octahedral sites display a sharp increase in the distortion of the octahedral coordination environment when compared to the undoped material. The axial bond length increases by 0.11Å with a concurrent shortening of the equatorial bond by 0.02Å in line with the Jahn-Teller distortion expected for Mn 3+ (Fig. 4d). When the doping level is increased (x ¼ 2 and 3) the length of the equatorial bond changes little. However, the extra Mn atoms must be placed into square pyramidal sites, shortening one axial bond of the octahedron and creating an irregular octahedral site, with two long bonds (2.00 and 2.28Å) and four short bonds with a mean length of 1.97Å. Similarly at the doping level x ¼ 2, where extra Mn atoms occupy half the square pyramidal sites, the square pyramid coordination environment distorts relative to the undoped material, resulting in four different square pyramids each with differing bond lengths. We suggest that the inclusion of Mn when x is greater than 1, forcing Mn into the square pyramidal sites and causing considerable distortion of all Bsites, is a factor which leads to the increased levels of doping becoming unfavourable.
The results presented above are based solely upon DFT ground state energies, however to predict the relative stability of phases under experimental conditions, it may be necessary to include the effects of nite temperature by calculating free energies of reaction. Free energies for the reaction shown in Eqn (2), DF sub , have been calculated including contributions from the entropy of mixing and the free energy of gas phase O 2 (see ESI † for details).
Values of DF sub calculated at the synthesis temperature of 1473 K, and with partial oxygen pressures corresponding to air and pure O 2 at atmospheric pressure are shown in Fig. 3e and f. Qualitatively, the results follow closely those calculated at 0 K. All Ni doped compositions remain unstable at atmospheric partial oxygen pressure, although the data suggest that YBa 2-Fe 2 NiO 8 may be stable under an atmosphere of pure O 2 , which is more oxidising than any conditions used experimentally in this study. Of the Mn doped compositions, YBa 2 Fe 2 MnO 8 retains a negative reaction energy and is predicted to be stable.  19 In the present study, the conclusions drawn from pure DFT data, calculated at 0 K, would have been the same as those drawn from the free energy data. This may, however, not always be the case, and as our thermodynamic analysis required very little extra computational cost, we suggest that it should be carried out in any future studies which use a similar methodology.

Experimental results
To test both positive and negative predictions of doping levels, samples were synthesised at the composition YBa 2 Fe 2 MnO 8AEd (M ¼ Mn, x ¼ 1), which is predicted to be stable, and the compositions representing YBa 2 FeNi 2 O 8AEd (M ¼ Ni, x ¼ 2) and YBa 2 FeMn 2 O 8AEd (M ¼ Mn, x ¼ 2), predicted to be unstable. Synthesis was attempted in air and under a reducing atmosphere of owing N 2 .
In the sample with the composition YBa 2 FeNi 2 O 8AEd red under owing N 2 (Fig. 5a), it is observed that the sample contains a mixture of known binary and ternary oxide phases, with no formation of phases with the 3a p structure. In the sample of composition YBa 2 FeMn 2 O 8AEd (Fig. 5b), the major phase was indexed to be a hexagonal perovskite similar to the reported 4H BaMnO 3Àd , 33 along with two tetragonal or pseudotetragonal perovskite phases. One has lattice parameters of a p ¼ 3.9270(2)Å and c p ¼ 3.8380(4)Å, consistent with the double perovskite YBaMn 2 O 5 . 28 The other has perovksite lattice parameters of a p ¼ 3.9004(9)Å and c p ¼ 3.926(1)Å which are not consistent with any known phase containing these elements. No long range order peaks arising from a 3a p phase were observed. The phases observed in YBa 2 FeNi 2 O 8AEd and YBa 2 FeMn 2 O 8AEd are in agreement with the predictions from DFT, in that a single 3a p perovskite was not formed as the major phase in either sample.
In the YBa 2 FeNi 2 O 8AEd and YBa 2 Fe 2 MnO 8AEd samples that were red under static air, no phases with the 3a p structure were observed to form. With YBa 2 FeNi 2 O 8AEd the same impurity phases were observed as for owing N 2 , although with different relative intensities in the diffraction pattern, with intensities for the reported YBa 3 Fe 2 O 7.5 phase decreasing. 50 For the YBa 2 Fe 2 MnO 8AEd sample red in static air, the two main phases were observed by XRD corresponding to YFeO 3 orthorhombic perovskite 51 and BaMnO 3 hexagonal perovskite (similar to that observed in the YBa 2 FeMn 2 O 8AEd sample described above).
Diffraction data for YBa 2 Fe 2 MnO 8AEd red under owing N 2 (Fig. 5c) shows that the major phase is 3a p perovskite, alongside a hexagonal impurity identied as similar to 10H BaMn 0.4 Fe 0.6 O 3Àd . 52 The composition for YBa 2 Fe 2 MnO 8AEd was optimised to isolate the 3a p component by altering the Y : Ba ratio. This was achieved by searching a one dimensional phase diagram covering Y y Ba 3Ày Fe 2 MnO 8 using 17 values ranging between 0.8 and 1.275 with varying intervals. The same synthetic procedure was maintained during this search under owing N 2 gas, with a reduced target mass of 0.3 g. A phase pure material with the 3a p structure was only obtained at the composition Y 1.175 Ba 1.825 Fe 2 MnO 8AEd (Fig. 5d). Relatively minor decreases or increases of 0.025 in Y content resulted in impurities of 10H hexagonal perovskite or YFeO 3 , respectively (Fig. 6a  and c). The oxygen content at the optimised composition, Y 1.175 Ba 1.825 Fe 2 MnO 8AEd , was analysed by iodometric titration. The determined oxygen content was O 8.04 (5) , giving an average transition metal charge state of 2.97(3)+, assuming charge states of 3+ and 2+ on Y and Ba respectively. Mössbauer spectroscopy (Fig. 7c) of this sample shows the material to be magnetically ordered at room temperature. The spectrum showed the presence of two Fe 3+ sites, which were rened as consistent with octahedral and square pyramidal geometries. In addition a small paramagnetic Fe 4+ signal was observed, and modelled as disordered over both sites. The distribution of Fe atoms within the structure was rened as 80(1) % in square pyramidal geometry and 20(1) % in octahedral geometry. Using the assumption that the only other species on the same sites is Mn, and that there is a xed ratio between square pyramidal and octahedral sites of 2 : 1, the distribution of Mn atoms is 40(1) % square pyramidal and 60(1)% octahedral.
Renement of the 3a p unit cell as a function of the Y content over the Y y Ba 3Ày Fe 3 O 8 range, shows that there is a small variation in the unit cell volume (Fig. 6b). The variation in the cell  volume implies that the structure should be accessible over a range of compositions; however, in our studies we only access the structure phase pure at one specic composition. This suggests that variation of the Fe : Mn ratio is also required at each Y : Ba ratio in order to synthesise the phase pure structure over a range of compositions, this was not attempted within this work as the Fe : Mn ratio was the focus of the DFT investigation, and the appropriate Y : Ba ratio was determined for the Fe : Mn ratio studied.
The results of DFT calculations were used as the basis for the structural renement of Y 1.175 Ba 1.825 Fe 2 MnO 8.04 (5) . The symmetry of the calculated YBa 2 Fe 2 MnO 8 structure with octahedrally coordinated Mn atoms was determined using the FINDSYM code 53 (version 3.2.3, with the tolerance set to 0.1Å). The highest symmetry space group was determined to be tetragonal P4/mmm (Fig. 8a) in a unit cell where a ¼ b ¼ 3.91603 and c ¼ 12.19815Å. In order to be consistent with reported structures for the undoped material the origin of the unit cell was set to be at the octahedral B-site. The observed B-site occupancies from Mössbauer spectroscopy were used as the starting model for B-site ordering within the structure.
For the Rietveld renement of Y 1.175 Ba 1.825 Fe 2 MnO 8.04 (5) , the structure was entered into GSAS 64,65 as separate nuclear (PXRD and NPD) and magnetic (NPD only) phases. Following earlier renements of the magnetic structure of YBa 2 Fe 3 O 8 , 54 the magnetic cell was rened as a (2a, 2b, 2c) super-cell of the orthorhombic nuclear cell, in the orthorhombic Fmm 0 m 0 magnetic space group congured in a G-type antiferromagnetic structure (see ESI † for further details). Constraints were setup between the two phases in order to keep the B-site atoms consistent (positions, occupancies and thermal parameters were constrained) and the unit cells and phase fractions of the two phases were xed, so that the ratio of the lattice parameters and total number of B-site atoms was maintained between the nuclear and magnetic phases.
As the starting model for the structure renement of Y 1.175 Ba 1.825 Fe 2 MnO 8.04 (5) was the atomic structure from the DFT model as described above, the composition was initially set close to the nominal value at Y 1.16 Ba 1.84 Fe 2 MnO 8 , with the additional Y inserted onto the Ba A-site. As the Rietveld renement progressed, the composition was allowed to rene with the only restraint being that full occupancy was enforced at each metal site. During the Rietveld renement the space group was changed to Pmmm to allow an orthorhombic distortion in the lattice parameters to improve the t of broader reections with hkl values where h s k. The rened orthorhombic distortion is small with a strain (a À b)/(a + b) of 0.04%, and is presumably related to spin-orbit coupling which is not included in the current DFT calculations. The nal Rietveld plots can be found in Fig. 7a and b, the resulting structure is shown in Fig. 8b and the results of the renements are given in Tables 1 and 2, the reduced c 2 was 4.46 for 72 variables.
Renement of the oxygen content was trialled during the structure analysis. No vacancies were observed on the ve oxygen positions and no extra oxygen within the structure could be found. This was trialled by placing an extra oxygen site in plane with the Y site (A1 in Table 1), previously reported as the O4 site in the undoped material. 18 As no additional oxygen or any oxygen vacancies were found, the oxygen content was xed to the nominal value of O 8 in the nal renement, which is in good agreement with the oxygen content observed from iodometry (O 8.04 (5) (5) contains an excess of Y that occupies the A2 site together with Ba (Table 1). When trialled in the renement there was no observed disorder on the A1 site which remained fully occupied by Y. The atomic coordinates of the rened structure show little deviation from those of the DFT structure ( Fig. 8c and Table 1), with the exception of a small orthorhombic distortion and the z positions of O1 and O2 (Table 1). O1 and O2 are no longer related by symmetry due to the orthorhombic distortion away from the calculated tetragonal P4/ mmm structure, and have different heights in the cell such that the basal planes of the square pyramids are slightly buckled.
Ordering between the two B-site geometries in the rened structure was observed to change little from the starting values of Fe 0.8 Mn 0.2 (B1) and Fe 0.4 Mn 0.6 (B2) for the square pyramidal and octahedral sites respectively, which were set to the rened Mössbauer occupancies. The rened site occupancies were Fe 0.762(1) Mn 0.238(1) for the square pyramidal site and Fe 0.437(2) Mn 0.563 (2) for the octahedral site, a 4% difference from values rened using room temperature Mössbauer spectroscopy (Fig. 7c). Note that due to the large contrast in neutron scattering between Fe and Mn (coherent scattering lengths of 9.45 fm and À3.73 fm, respectively 55 ), the renement of the occupation of this site is reliable. The magnetic moments for the B-sites were rened to be 3.41(3) and 2.81(4) m B for the square pyramidal and octahedral sites respectively, consistent with the square pyramidal site hosting more Fe relative to the octahedral site.

Discussion
The initial DFT screening of potential doping onto the Fe site of YBa 2 Fe 3 O 8 was successful in predicting a favourable doping species (Mn) and content (YBa 2 Fe 2 MnO 8 ), which was previously unreported in the 3a p structure. We note, however, that considerable experimental work was still required to obtain a pure doped compound and characterize it, with slight differences in stoichiometry and structure compared to that predicted computationally.
To reduce computational expense, DFT calculations were limited to stoichiometric compositions in which the average oxidation state on the B-site was restricted to 3+, or equivalently, the oxygen content was xed to 8. Experimentally however, the sample composition and atmosphere used during synthesis   (5) , we nd that the calculated unit cell volume is within 3.5% of experiment, with a similar agreement between the reported and calculated cell volumes for the undoped material. One could envision calculating reaction energies for a number of non-stoichiometric compositions. However, for each composition larger super-cells and more congurations would be required in order to determine the most stable cation arrangement. Additional complexity is introduced by the necessity of modelling the inevitably disordered A-sites, as well as potentially disordered B-sites. Hence we suggest that a computational investigation of small changes in stoichiometry is unfeasible at present.
To quantify the level of ordering between Fe and Mn on the B-sites, we dene the parameter F ¼ (3f À 1)/2, where f is the fraction of Mn on the octahedral sites. DFT calculations predicted a complete segregation of Mn to the octahedral sites in YBa 2 Fe 2 MnO 8 (F ¼ 1), in a completely disordered system 1/3 of the octahedral sites would be occupied by Mn (F ¼ 0), and experimentally the fraction of octahedral sites occupied by Mn was rened to 0.563(2) (F ¼ 0.34). To model the expected extent of ordering at nite temperatures based on 0 K DFT energies, a statistical mechanics approach described in the ESI, † 30 was applied to the six congurations used for the DFT calculations at the composition YBa 2 Fe 2 MnO 8 . When the occupations of the B-sites are estimated at the synthesis temperature of 1475 K, there is a preference for Mn in the octahedral site, though substantial mixing of Fe and Mn is predicted, with F ¼ 0.57. At 300 K, however, the structure is predicted to be very close to fully ordered with F ¼ 0.996. Under cooling during synthesis, cation motion will be frozen out at high temperatures, trapping the structure in a state with some site disorder due to congurational entropy. This explains the deviation of the rened value of F ¼ 0.34 away from fully ordered F ¼ 1, but shows that the 0 K DFT calculations had calculated the correct site preference for Mn within the structure.
A small, but signicant difference between the calculated and experimental structure is the slight orthorhombic distortion of the rened nuclear structure. The tetragonal parent material, YBa 2 Fe 3 O 8 , is reported to become orthorhombic upon introduction of oxygen vacancies to form YBa 2 Fe 3 O 8Àd (d $ 0.14). 21 It is possible that the orthorhombic distortion observed in Y 1.175 Ba 1.825 Fe 2 MnO 8.04 (5) is similarly due to oxygen vacancies, however we note that this is not supported by the results of iodometric titration or attempts to rene oxygen contents away from stoichiometry. An alternative explanation is that spinorbit coupling of the antiferromagnetically ordered electronic spins, which necessarily have orthorhombic symmetry, has caused an orthorhombic distortion of the nuclear structure as reported for the mixed valence compound YBaFe 2 O 5 . 56 In both cases, the orthorhombic distortion is accompanied by buckling of the basal planes of the square pyramidal sites, as observed here for Y 1.175 Ba 1.825 Fe 2 MnO 8.04 (5) . Neither effect would be captured in the stoichiometric DFT calculations performed with collinear spin and neglecting spin-orbit interactions. The present experimental data are unable to distinguish between the two potential causes of this orthorhombic distortion.
The rened structure of Y 1.175 Ba 1.825 Fe 2 MnO 8.04 (5) shows that the unit cell distorts upon doping compared to YBa 2 Fe 3 O 8 (ref. 18) by a 0.9% shortening of the a and b axes and a concurrent 1.4% lengthening of the c axis. This results in a 2.3% increase in the average c/a ratio upon doping, and a 0.5% reduction in cell volume. These changes in cell shape can be related to changes in the M-O bonding environments upon doping, seen in the comparison of the M-O bonds of Y 1.175 Ba 1.825 Fe 2 MnO 8.04 (5) and YBa 2 Fe 3 O 8 ( Table 3). As observed in the DFT calculations, experimentally the M Oct -O Axial bond on the octahedral site is seen to lengthen on doping by 4.2% (0.094(3)Å), consistent with the expected Jahn-Teller distortion when accommodating Mn 3+ in an octahedral site. The elongation of the unit cell upon doping is largely due to this Jahn-Teller distortion.
We used the methodology reported by Baur 57 implemented in VESTA 58 to further quantify the distortions of the polyhedra in the 3a p structure by calculation of a distortion parameter according to the following equation: where D is the distortion parameter, n is the number of bonds in the polyhedron, L i is the length of bond i, and L avg is the average bond length in the polyhedron. An undistorted polyhedron  (Table 3), giving rise to a buckling in the basal planes of the square pyramidal sites. It is interesting to note that the undoped compound, YBa 2 Fe 3 O 8 , contains octahedral sites which are already distorted, with two long bonds and four short bonds, even though no Jahn-Teller distortion would be expected for high spin d 5 Fe 3+ . It is possible that this distortion already evident within the 3a p structure leads to the octahedral site being particularly favourable for hosting Jahn-Teller active Mn 3+ ions, and similar sites in other Fe 3+ oxides could be targeted for doping with Mn 3+ . Although this is the rst reported mixed Fe/Mn compound with the 3a p structure, other perovskite based Fe/Mn oxides have been reported, and show similar site preferences. For example, the brownmillerite Ca 2 Fe 2 O 5 has similarly distorted octahedral sites, with D ¼ 0.045. 24 Introduction of Mn into the compound to form Ca 2 Fe 1.039(8) Mn 0.962(8) O 5 (ref. 27) leads to an increase in the distortion of the octahedral sites (D ¼ 0.066), with Mn preferred in these sites. There are, however, many other examples of Mn 3+ doping into perovskite based structures, in which the Mn 3+ is coordinated in octahedral geometry, 27,60 square pyramidal geometry 28 or with B-site disorder. 61,62 By the use of DFT we have been able to clearly predict the correct B-site ordering within a 3a p structure, even though precedents exist for all possible alternatives in known structures.

Conclusions
In summary, we have shown that it is possible to use DFT calculations to obtain reaction enthalpies to form complex oxides from binary oxides; we have then been able to use this method to predict a stable doping level in the YBa 2 Fe 3 O 8 structure, with the Mn doping level of x ¼ 1 and Mn atoms preferentially doping onto the already distorted octahedral site and increasing the level of distortion. We also have rationalised why doping becomes unfavourable when x ¼ 2 and M ¼ Mn; increasing the doping level above 1 forces a larger proportion of Mn atoms into the square pyramidal sites which in turn results in a less distorted octahedral geometry. These calculations have been able to successfully predict the approximate composition, B-site ordering (and distortion of B-sites, Fig. 8c) and accurate atomic coordinates of the doped structure of an oxide where the ordering is between two similar transition metals. The predicted material was then synthesised with only small deviations in the structure and composition.
We have shown that using this methodology, we were able to predict compositions for which the formation of the 3a p structure is favourable or unfavourable, and that these results match subsequent experimental observations. We therefore conclude that the methodology presented here can be used as a powerful tool to guide the synthesis of new materials by chemical substitution and can be used for large and or complex oxides where the systems are too large or complex for existing methods.