Theoretical and Experimental Investigations into Novel Oxynitride Discovery in the GaN-TiO2 System at High Pressure

We employed ab initio evolutionary algorithm USPEX to speed up the discovery of a novel oxynitride in the binary system of GaN-TiO2 using high-pressure synthesis. A 1:2 mixture of GaN and nanocrystalline TiO2 (anatase) was reacted under 1 GPa of pressure and at 1200 ◦C in a piston cylinder apparatus to produce a mixture of TiO2 (rutile) and an unknown phase. From the initial analysis of high resolution neutron and X-ray diffraction data, it is isomorphic with monoclinic V2GaO5 with a unit cell composition of Ga10Ti8O28N2 with the following parameters: monoclinic, space group C2/m, a = 17.823(1) Å, b = 2.9970(1) Å, c = 9.4205(5) Å, β = 98.446(3)◦; Volume = 497.74(3) Å3. Further, a joint rietveld refinement revealed two distinct regimes—A Ti-rich block and a Ga-rich block. The Ti-rich block consists of four edge-shared octahedra and contains a site which is about 60% occupied by N; this site is bonded to four Ti. The remainder of the block consists of edge linked Ti-octahedral chains linked to the TiN/TiO fragments at octahedral corners partially occupied by nitrogen. The Ga-block contains two symmetry independent octahedral sites, occupied mostly by Ga, and a pure Ga-centered tetrahedral site bonded mostly to oxygen.


Introduction
The search for alternatives to fossil fuels is driven by increasing energy demands, and the desirability of limiting growth in CO 2 in the atmosphere, while retaining the advantages of fuel transportability.In this regard, visible light [1] driven photocatalysis for overall water splitting (OWS) might produce chemical fuels, such as hydrogen, which would address these criteria [2,3].
Traditional OWS photocatalysts, such as titanium dioxide (rutile) are inorganic oxides with large bandgaps and activity only under ultraviolet light.Rutile is a photosensitizer capable of oxidized organic dyes [4], and it was identified as a photocatalyst in 1956 by Mashio et al. [4].Water splitting was observed with TiO 2 a photo-anode and platinum cathode and an external bias in the pioneering work of Honda and Fujishima et al. [5,6].Other oxides identified as capable of OWS include SrTiO 3 perovskite and K 2 La 2 Ti 3 O 10 , a Ruddlesden-Popper phase [7].
Oxynitrides and solid solutions containing nitrogen absorb the majority of solar spectrum [8-11] compared to the traditional inorganic oxide photocatalysts due to their higher N2p valence states and smaller bandgaps.For example, LaTiO 2 N, produced by the ammonolysis of La 2 Ti 2 O 7 , absorbs visible light [12,13].Attempts to introduce nitrogen into Ti based photocatalysts had varied success.Bimetallic oxynitride perovskites, which contain titanium, are common [10,14] while pure titanium oxynitride compounds exist rarely; sometimes as thin films [15,16].
An important recent discovery was a GaN rich solid solution (GaN) x (ZnO) 1−x , reported by Domen et al. [8,17].Members of the solid solution have bandgaps smaller than the GaN and ZnO endmembers.In addition, they achieved overall water splitting at relatively high efficiency of up to 6%.Inspired by these results, we synthesized the complete solid solution (GaN) x (ZnO) 1−x under pressure and demonstrated hydrogen evolution from water without the use of cocatalysts and sacrificial reagents [18].Further, we investigated the possibility of other oxynitride solid solutions that might go beyond currently available efficiencies.We selected GaN-TiO 2 , cognizant of arguments that d 0 and d 10 oxynitrides are likely to lead to OWS catalysts [8].While it is desirable to produce an OWS catalyst at near ambient pressure, our previous high pressure work suggested high pressure synthesis allows for better control over stoichiometry, which is not always available from ammonolysis.Further, recent computational search based on published databases [19] suggests that many novel oxynitrides have high instability indices at ambient pressure, and that high pressure followed by quench recovery may be required for their synthesis.High pressure experiments are difficult, requiring multiple runs for their optimization, and our previous work on Nb 2 O 5 -GaN system [20] used crystal structure prediction methods and in situ high resolution X-ray scattering to mitigate this disadvantage.Here, using state of the art evolutionary algorithm USPEX along with density functional theory calculations, we studied the pressure-driven stability of GaN-TiO 2 system to better understand and evaluate the structures and stability fields of possible Ga-Ti-oxynitride compounds with chemical composition chosen from a mix of GaN and TiO 2 endmembers.

Theoretical Predictions Using USPEX
We constructed the convex hull, which connects the phases that are stable against decomposition into elements or binaries at a given pressure.The convex hulls were obtained from the enthalpies of the most stable structures of compounds at a given pressure.The enthalpy of formation of the lowest enthalpy Ga-Ti-oxynitrides at 0, 5, 10 and 20 GPa are given in Table 1, which simply shows a tendency for structures with 1:1 and 1:2 ratios of GaN:TiO 2 to move to lower formation enthalpy with increasing pressure.This trend suggests their potential stability with increasing pressure.The structures of the predicted ordered GaTiO 2 N and GaTi 2 O 4 N phases are illustrated in Figure 1 and the Crystallographic Information Files (CIF) are described in the appendix (Table A2).Although not all structural aspects of these ordered phases did match with the disordered experimental phase described in Section 2.2, ab initio calculations at 0 K provided a useful guide to target compositions that are within thermodynamically synthesizable range.
Analysis of X-ray and neutron scattering data suggests that the experimentally synthesized new phase has the composition of Ga 10 Ti 8 O 28 N 2 .After obtaining this result, we performed phase stability calculations for Ga 10 Ti 8 O 28 N 2 against the decomposition to oxynitrides and oxide endmembers i.e., Ti 3 O 3 N 2 and Ga 2 TiO 5 , however, the decomposition reaction energies indicate that Ga 10 Ti 8 O 28 N 2 is an entropy-stabilized oxynitride.The decomposition reaction energies are obtained as follow: 15 meV/atom at 10 GPa and 4 meV/atom at 20 GPa, which indicates its stability with increasing pressure.
Entropy can have a significant impact on free energy calculations of disordered structures; however, incorporating entropy is computationally expensive.Entropy is a sum of the electronic entropy (S el ), configurational entropy (S conf ) and vibrational entropy [21].The electronic entropy S el is easy to calculate, but does not have a significant effect on the free energy.On the other hand, vibrational S vib and configurational S conf entropies are very expensive and can have significant effect on free energy.The configurational entropies are calculated based on Boltzmann's formula which relates entropy values to the number of the accessible arrangement of atoms in the lattice [22].
where k is the Boltzmann constant and g(σ) is the number of all possible configurations.The general formula for the configurational entropy can be obtained from: where P j is the probability of a certain configuration j.Configurational entropies are calculated based on the above formula and the stabilizing temperatures are calculated from: where H ordered−disordered is the difference between enthalpies of ordered and disordered structures and S = S con f .Configurational entropies and required temperatures for stabilizing GaTiO 2 N, GaTi 2 O 4 N and Ga 10 Ti 8 O 28 N 2 are listed in Table 2.The experimentally-observed mixed tetrahedral and octahedral coordination of Ga is accurately predicted with USPEX; however, Ti is predicted to exist in a mixture of octahedral and heptahedral coordination while experiments only observe octahedral Ti.In addition, bond valences are calculated according to S i = Σ j exp (R 0 − R ij /B], where B is 0.37 and R 0 is obtained from published tables [23].Bond valences for Ga and Ti of the predicted structures are consistent with the experimental phase.Theoretical and experimental structural studies revealed that the synthesized phase has positional disorder among both the cations and the anions sites.Since oxygen and nitrogen have similar ionic size, electronegativities and coordination number, these anions are usually disordered across anion sites [9], and hence makes it a real challenge for crystal structure prediction methods.Partial ordering have been observed in some oxynitrides [24][25][26], however, ideally ordered oxynitrides are scarce between known oxynitrides e.g., TaON and Si 2 N 2 O [27,28].While incorporating disorder is not practical with crystal structure prediction methods at the current stage of development, the predicted structures give insights into the chemistry of the system, may guide experimental efforts, and contain structural features, such as the separation of Ti and Ga into different structural blocks, which is confirmed in the experimental analysis.In addition, the average bond lengths of the predicted phases, (Figure 1 & Table A3) are in a good agreement with the experimental data.

Crystallographic Characterization
In anticipation of the inability of X-rays to distinguish between O and N in the anion sites, and because of the favorable scattering contrast between Ga and Ti, bN = 7.29 fm and −3.44 fm, respectively, initially only neutron diffraction data, collected on the POWGEN instrument at the Spallation Neutron Source at Oak Ridge National Laboratory, TN, were utilized.Unit cell indexing and structure solution identified the new phase designated presumptively as "Ga-Ti-O-N", is isomorphic with monoclinic V2GaO5, C2/m, Z = 6, a = 17.758(5)Å, b = 2.990(1) Å, c = 9.323(3) Å and β = 98.44(2)° [30].From the crystal structure of V2GaO5 we can construct a solid solution that accounts for the coupled substitution of Ti/N into the full unit cell contents (Z = 6) of V12Ga6O30.The oxide and oxynitride endmembers of this solid solution would then be Ga12Ti6O30 and Ti18O18N12, respectively.More generally, the solid solution is formulated as Ti6+xGa12−xO30−xNx; empirical formula Ti1+xGa2−xO5−xNx.This formulation provided chemical constraints utilized in the latter stages of structure refinement.
An X-ray diffraction pattern was collected on the high resolution powder [31,32] instrument at beamline 11-BM at the Advanced Photon Source, IL, by taking advantage of the mail-in service at this facility [33].The X-ray data provides an independent means of determining the Ga/Ti content; this is particularly important since the presumed unknown phase designated isomorphous to V2GaO5 phase is nonstoichiometric [30].Any sample related variables, such as residual strain, can also be best determined from the high angular resolution X-ray data.Further, the small size of the sample, its multiphase nature, and the relative complexity of the Ga-Ti-O-N phase, is well matched to the high angular resolution at the 11-BM instrument.The initial X-ray refinements were constrained by assuming a pure oxide composition, Ga and Ti distributed randomly over all cation sites consistent with the presumed chemistry derived from V2GaO5, that is Ga2TiO5, and with displacement parameters for all atoms fixed to a common value (Uiso = 0.01Å 2 ).The peak width parameters were fixed to values determined from a LaB6 standard, which also provided the X-ray wavelength, 0.412447(5) Å.The sample on which X-ray data were collected was identical to the one used for neutron-data collection.Because of the superior counting statistics (Figures 2 and 3) a small amount of an unidentified phase was obvious in the XRD pattern.The largest peaks from this phase were around 7.2, 7.5, 9.3, and 14.2° in 2θ and the most intense peak of the unindexed phase match that of rutile and Ga-Ti-O-N phases; the amounts were estimated to be 1% and 2% of those phases, respectively.Those regions containing peaks from the unidentified phase were excluded from refinements utilizing the X-ray data.These peaks were not observed in the neutron data, probably because of insufficient peak-to-background discrimination.

Crystallographic Characterization
In anticipation of the inability of X-rays to distinguish between O and N in the anion sites, and because of the favorable scattering contrast between Ga and Ti, b N = 7.29 fm and −3.An X-ray diffraction pattern was collected on the high resolution powder [31,32] instrument at beamline 11-BM at the Advanced Photon Source, IL, by taking advantage of the mail-in service at this facility [33].The X-ray data provides an independent means of determining the Ga/Ti content; this is particularly important since the presumed unknown phase designated isomorphous to V 2 GaO 5 phase is nonstoichiometric [30].Any sample related variables, such as residual strain, can also be best determined from the high angular resolution X-ray data.Further, the small size of the sample, its multiphase nature, and the relative complexity of the Ga-Ti-O-N phase, is well matched to the high angular resolution at the 11-BM instrument.The initial X-ray refinements were constrained by assuming a pure oxide composition, Ga and Ti distributed randomly over all cation sites consistent with the presumed chemistry derived from V 2 GaO 5 , that is Ga 2 TiO 5 , and with displacement parameters for all atoms fixed to a common value (U iso = 0.01Å 2 ).The peak width parameters were fixed to values determined from a LaB 6 standard, which also provided the X-ray wavelength, 0.412447(5) Å.The sample on which X-ray data were collected was identical to the one used for neutron-data collection.Because of the superior counting statistics (Figures 2 and 3) a small amount of an unidentified phase was obvious in the XRD pattern.The largest peaks from this phase were around 7.2, 7.5, 9.3, and 14.2 • in 2θ and the most intense peak of the unindexed phase match that of rutile and Ga-Ti-O-N phases; the amounts were estimated to be 1% and 2% of those phases, respectively.Those regions containing peaks from the unidentified phase were excluded from refinements utilizing the X-ray data.These peaks were not observed in the neutron data, probably because of insufficient peak-to-background discrimination.Refinement began with background parameters (cosine series, 12 parameters) and scale factor.Following convergence, cell parameters for both rutile and Ga-Ti-O-N phases were added to the refinement.The differences between observed and calculated patterns was dominated by anisotropic broadening of the Ga-Ti-O-N phase.Refinement of a generalized anisotropic broadening model [34,35] for Ga-Ti-O-N, improved the fit considerably as shown in Figure 2, which is a smaller region of the fit.
The question of stoichiometry was addressed by refining positional parameters, followed by refinement of all metal site occupancies with fixed displacement parameters for all atoms (Uiso = 0.005 Å 2 ), the total occupancy of anion sites fixed to one oxygen, and metal sites constrained to be fully occupied.These assumptions were tested further in joint X-ray-neutron refinements discussed below.At this stage, refinement using just the X-ray data suggested some cation sites were partially disordered but that all were preferred by either Ga or Ti, or indeed were fully occupied by one or other of these metals.For example, the tetrahedral site (Figure 3) is occupied exclusively by Ga, while the block of sites at x = 0 and x = ½ are essentially pure Ti, with about 20% Ga-substitution in the   Refinement began with background parameters (cosine series, 12 parameters) and scale factor.Following convergence, cell parameters for both rutile and Ga-Ti-O-N phases were added to the refinement.The differences between observed and calculated patterns was dominated by anisotropic broadening of the Ga-Ti-O-N phase.Refinement of a generalized anisotropic broadening model [34,35] for Ga-Ti-O-N, improved the fit considerably as shown in Figure 2, which is a smaller region of the fit.
The question of stoichiometry was addressed by refining positional parameters, followed by refinement of all metal site occupancies with fixed displacement parameters for all atoms (Uiso = 0.005 Å 2 ), the total occupancy of anion sites fixed to one oxygen, and metal sites constrained to be fully occupied.These assumptions were tested further in joint X-ray-neutron refinements discussed below.At this stage, refinement using just the X-ray data suggested some cation sites were partially disordered but that all were preferred by either Ga or Ti, or indeed were fully occupied by one or other of these metals.For example, the tetrahedral site (Figure 3) is occupied exclusively by Ga, while the block of sites at x = 0 and x = ½ are essentially pure Ti, with about 20% Ga-substitution in the Refinement began with background parameters (cosine series, 12 parameters) and scale factor.Following convergence, cell parameters for both rutile and Ga-Ti-O-N phases were added to the refinement.The differences between observed and calculated patterns was dominated by anisotropic broadening of the Ga-Ti-O-N phase.Refinement of a generalized anisotropic broadening model [34,35] for Ga-Ti-O-N, improved the fit considerably as shown in Figure 2, which is a smaller region of the fit.
The question of stoichiometry was addressed by refining positional parameters, followed by refinement of all metal site occupancies with fixed displacement parameters for all atoms (U iso = 0.005 Å 2 ), the total occupancy of anion sites fixed to one oxygen, and metal sites constrained to be fully occupied.These assumptions were tested further in joint X-ray-neutron refinements discussed below.At this stage, refinement using just the X-ray data suggested some cation sites were partially disordered but that all were preferred by either Ga or Ti, or indeed were fully occupied by one or other of these metals.For example, the tetrahedral site (Figure 3) is occupied exclusively by Ga, while the block of sites at x = 0 and x = 1  2 are essentially pure Ti, with about 20% Ga-substitution in the remaining TiGa sites (Figure 3).The refined Ga/Ti ratio was approximately 1.25, which would correspond to a unit cell composition of Ga 10 Ti 8 O 28 N 2 .
A joint refinement utilizing both X-ray and neutron data was then initiated.The strain parameters for rutile and Ga-Ti-O-N were refined independently (Figure 4) but constrained to be equal for each phase between X-ray and neutron datasets.The neutron data was weighted at 1.5, compared to the X-ray data weighted at 1.0, to emphasize the favorable scattering differences between O/N and Ga/Ti pairs occupying anion and cation sites, respectively.Starting with the unit cell composition consistent with refinement of cation site occupancies from the X-ray data, Ga 10 Ti 8 O 28 N 2 , atoms were distributed randomly over the cation and anion sites.The neutron refinement was initiated by sequentially refining overall parameters, background and scale, for individual data sets, and then sample parameters common to both datasets, strain and unit cell dimensions.To account for slight differences arising due to the temperatures at which neutron data were collected, elastic strain components were refined for both phases for the X-ray data set.The neutron dataset was contaminated by peaks arising from the vanadium sample holder, and this phase was added to account for this.Following convergence of a refinement of the above parameters and the site positional parameters for the Ga-Ti-O-N phase, the anion and cation site occupancies were determined.remaining TiGa sites (Figure 3).The refined Ga/Ti ratio was approximately 1.25, which would correspond to a unit cell composition of Ga10Ti8O28N2.A joint refinement utilizing both X-ray and neutron data was then initiated.The strain parameters for rutile and Ga-Ti-O-N were refined independently (Figure 4) but constrained to be equal for each phase between X-ray and neutron datasets.The neutron data was weighted at 1.5, compared to the X-ray data weighted at 1.0, to emphasize the favorable scattering differences between O/N and Ga/Ti pairs occupying anion and cation sites, respectively.Starting with the unit cell composition consistent with refinement of cation site occupancies from the X-ray data, Ga10Ti8O28N2, atoms were distributed randomly over the cation and anion sites.The neutron refinement was initiated by sequentially refining overall parameters, background and scale, for individual data sets, and then sample parameters common to both datasets, strain and unit cell dimensions.To account for slight differences arising due to the temperatures at which neutron data were collected, elastic strain components were refined for both phases for the X-ray data set.The neutron dataset was contaminated by peaks arising from the vanadium sample holder, and this phase was added to account for this.Following convergence of a refinement of the above parameters and the site positional parameters for the Ga-Ti-O-N phase, the anion and cation site occupancies were determined.Rietveld fit to 11-BM (APS) X-ray profile containing an estimated TiO2 (46 wt %) and the new phase related to V2GaO5 (54 wt %).Note the much larger anisotropic strain, defined in GSAS-II [34] and originally introduced [35] and used by Stephens [36,37].Note the sharper rutile peaks (vertical red markers) compared to those of the V2GaO5-related phase (vertical black markers).
To set a baseline for comparison of the overall fit, all anion sites were filled with oxygen while the Ga-Ti occupancies of cation sites were refined along with overall displacement parameters (U); the value of U for all cation sites were constrained to be equal, as were those of the anion sites.The results of this refinement suggested the following approximate compositions for the five cation sites (see Table A1, which summarizes the final results for Ga-Ti-O-N): site 1, Ga¾Ti¼; site2, Ti; site3, Ga0.8Ti0.2;site 4, Ti; site5, Ga.The fit to the neutron data, summarized by the weighted profile R-value (Rwp) and goodness of fit (GOF) were 5.81% and 3.70, respectively.The fits to the Ga-Ti-O-N phase Bragg intensities, RB(F 2 ), comparable to the usual single crystal discrepancy factor, were 5.27% and 12.86%, for the X-ray and neutron data, respectively.The site occupancies of all metal and anion sites were then varied, with Uiso constrained as above.The results of this refinement were: neutron overall Rwp = 5.34%, GOF = 3.64, and RB(F 2 ) = 5.25% and 10.14%, for the X-ray and neutron data, respectively.Rietveld fit to 11-BM (APS) X-ray profile containing an estimated TiO 2 (46 wt %) and the new phase related to V 2 GaO 5 (54 wt %).Note the much larger anisotropic strain, defined in GSAS-II [34] and originally introduced [35] and used by Stephens [36,37].Note the sharper rutile peaks (vertical red markers) compared to those of the V 2 GaO 5 -related phase (vertical black markers).
To set a baseline for comparison of the overall fit, all anion sites were filled with oxygen while the Ga-Ti occupancies of cation sites were refined along with overall displacement parameters (U); the value of U for all cation sites were constrained to be equal, as were those of the anion sites.The results of this refinement suggested the following approximate compositions for the five cation sites (see Table A1, which summarizes the final results for Ga-Ti-O-N): site 1, Ga 3 4 Ti 1 4 ; site2, Ti; site3, Ga 0.8 Ti 0.2 ; site 4, Ti; site5, Ga.The fit to the neutron data, summarized by the weighted profile R-value (R wp ) and goodness of fit (GOF) were 5.81% and 3.70, respectively.The fits to the Ga-Ti-O-N phase Bragg intensities, R B (F 2 ), comparable to the usual single crystal discrepancy factor, were 5.27% and 12.86%, for the X-ray and neutron data, respectively.The site occupancies of all metal and anion sites were then varied, with U iso constrained as above.The results of this refinement were: neutron overall R wp = 5.34%, GOF = 3.64, and R B (F 2 ) = 5.25% and 10.14%, for the X-ray and neutron data, respectively.Sites that were within the margin of error of full occupancy by Ga, Ti and O were fixed at those compositions; no anion site was fully occupied by nitrogen.A new set of refinements was performed, maintaining restraints on strain and displacement parameters as described above.Trial refinements with displacement parameters refined without constraint did not significantly improve the overall fit.Finally, the chemical composition was constrained to be consistent with the formula derived for the solid solution Ti 6+x Ga 12−x O 30−x N x ; the amount of nitrogen per unit cell distributed over sites occupied by both oxygen and nitrogen, designated as "ON" sites ON1, 2, 4 and 8, was set equal to the amount of titanium in sites GaTi1 and 3 (Table A1).After convergence, the results summarized in Table A1 were obtained.The overall fits to the X-ray and neutron data are given in Figures 2 and 3, respectively.The CIF file for the experimental phase is deposited into Crystallography Open Database (COD entry 3000168) as prepublication data.

Composition
The unit cell contents for the synthesized Ga-Ti-O-N phase were Ga 10 Ti 8 O 28 N 2 , consistent with the solid solution between theoretical endmembers Ti 18 O 18 N 12 and Ti 6 Ga 12 O 30 , Ti 6+x Ga 12−x O 30−x N x .The sites occupied by nitrogen tend to be segregated into those anion sites associated with the pure Ti-octahedral sites in blocks of structure centered at x = 0, 1 2 (Figure 5, Table A1).If all ON sites were fully occupied by nitrogen this would correspond to N 14 per unit cell, more nitrogen rich than the endmember composition, and so probably a composition that would not crystallize in this structure type.Interestingly, the presumptive pure Ti endmember composition, Ti 18 O 18 N 12 or Ti 3 O 3 N 2 , is one predicted to have ideal bandgap properties for overall water splitting [19] albeit with a predicted instability of 31 meV per atom [19] that probably requires high pressure for synthesis.Wu et al.'s prediction is based upon Ti/O coupled substitution into the Ta 3 N 5 structure [19].The structure of Ta 3 N 5 is orthorhombic Cmcm, a =3.8862Å, b = 10.2118Å, c = 10.2624Å and consists of only distorted TaN 6 octahedra [38].The Ta 3 N 5 structure [38] is very different from that of Ga 10 Ti 8 O 28 N 2 reported here (Figures 3 and 4).It would be interesting to attempt the synthesis of the titanium endmember "Ti 3 O 3 N 2 ".Our preliminary attempts to do so using ammonolysis of TiO 2 were not successful.Sites that were within the margin of error of full occupancy by Ga, Ti and O were fixed at those compositions; no anion site was fully occupied by nitrogen.A new set of refinements was performed, maintaining restraints on strain and displacement parameters as described above.Trial refinements with displacement parameters refined without constraint did not significantly improve the overall fit.Finally, the chemical composition was constrained to be consistent with the formula derived for the solid solution Ti6+xGa12−xO30−xNx; the amount of nitrogen per unit cell distributed over sites occupied by both oxygen and nitrogen, designated as "ON" sites ON1, 2, 4 and 8, was set equal to the amount of titanium in sites GaTi1 and 3 (Table A1).After convergence, the results summarized in Table A1 were obtained.The overall fits to the X-ray and neutron data are given in Figures 2 and  3, respectively.The CIF file for the experimental phase is deposited into Crystallography Open Database (COD entry 3000168) as prepublication data.

Composition
The unit cell contents for the synthesized Ga-Ti-O-N phase were Ga10Ti8O28N2, consistent with the solid solution between theoretical endmembers Ti18O18N12 and Ti6Ga12O30, Ti6+xGa12−xO30−xNx.The sites occupied by nitrogen tend to be segregated into those anion sites associated with the pure Tioctahedral sites in blocks of structure centered at x = 0, ½ (Figure 5, Table A1).If all ON sites were fully occupied by nitrogen this would correspond to N14 per unit cell, more nitrogen rich than the endmember composition, and so probably a composition that would not crystallize in this structure type.Interestingly, the presumptive pure Ti endmember composition, Ti18O18N12 or Ti3O3N2, is one predicted to have ideal bandgap properties for overall water splitting [19] albeit with a predicted instability of 31 meV per atom [19] that probably requires high pressure for synthesis.Wu et al.'s prediction is based upon Ti/O coupled substitution into the Ta3N5 structure [19].The structure of Ta3N5 is orthorhombic Cmcm, a =3.8862Å, b = 10.2118Å, c = 10.2624Å and consists of only distorted TaN6 octahedra [38].The Ta3N5 structure [38] is very different from that of Ga10Ti8O28N2 reported here (Figures 3 and 4).It would be interesting to attempt the synthesis of the titanium endmember "Ti3O3N2".Our preliminary attempts to do so using ammonolysis of TiO2 were not successful.

Implications and Future Work
It is evident that state of the art evolutionary algorithm USPEX can be used reliably to find high pressure phases of oxynitrides with enough structural details and that will be utilized to explore several other oxynitride systems.In fact, the results obtained here will act as a feedback to assist us.We are continuing the synthesis work at even higher pressures in a multianvil press to find out if we can synthesize other members of the solid solution.Further, we are developing methods to predict materials with desired bandgaps more efficiently.

Theoretical Prediction Methods
Ab initio variable-composition evolutionary algorithm USPEX [39][40][41][42][43], which simultaneously searches for stable stoichiometries and their corresponding most stable structures, was employed to search for stable oxynitrides at pressures attainable in a large volume press.In this method, all stoichiometric compounds are considered following a constraint on the total number of atoms on the unit cell.We performed calculations at 0, 5, 10 and 20 GPa for systems having up to 48 atoms in the unit cell.Using USPEX, we generate stoichiometric compounds with initial chemical composition randomly chosen from a mix of GaN and TiO 2 and their corresponding structures generated using random symmetric generator.USPEX makes subsequent generations with 20% random structures, and 80% using heredity, soft-mutation, lattice mutation and transmutation operators, in which transmutation and heredity operators change the composition, while lattice mutation and soft-mutation only change the structure within a fixed-composition mechanism.After relaxing the structures, only the best 60% of the structures, ranked by a fitness function, are used to generate the subsequent generations.

High Pressure Synthesis
A 1:1 mixture of GaN, produced from the ammonolysis of powdered Ga 2 O 3 (Alfa Aeser, Thermo Fisher Scientific Chemicals Inc., Ward Hill, MA, USA, 99.99%) and TiO 2 (Aldrich, Sigma-Aldrich, Saint Louis, MO, USA, 99.8% trace metals basis, anatase) was mixed thoroughly for half an hour in a mortar and pestle.About 1 g of this mixture was loaded into a piston-cylinder apparatus with a 19 mm diameter cylindrical talc pressure cell and rapidly heated at ~200 • C min −1 to 1200 • C, at 1 GPa.Details of this instrument was described in the literature [20].The pressure and temperature was selected based on the previous research experience, where we saw that disorder in a system can bring about the stabilization of high pressure phases at even lower pressures than expected [20].A mixture of TiO 2 (rutile) and an unknown phase resulted after the reaction.In an attempt to increase the yield of the unknown phase, the reaction mixture was adjusted to TiO 2 :GaN = 2:1, and a nano form of the TiO 2 polymorph anatase (Nanostructured & Amorphous Materials, Inc., Houston, TX, USA, 99.4%) was used as a reactant along with crystalline GaN.About 50% of the anatase reacted with GaN before converting to the more refractory rutile polymorph.This sample, containing rutile and Ga-Ti-O-N, was used for subsequent determination of crystal structure.

Supplementary Materials:
The COD entry 3000168 contains the supplementary crystallographic data for this paper.These data can be obtained free of charge via http://www.crystallography.net/cod/search.html.The following materials are available online at http://www.mdpi.com/2073-4352/8/2/15/s1.Refinement statistics: combined R wp = 5.57% GOF = 3.69 for joint X-ray neutron data (R wp = for the individual X-ray and Neutron data sets were R X wp = 13.31%(38,714 observations) and R N wp = 2.15% (4035 observations) respectively; the X-ray:neutron data were weighted 1:1.5; the integrated Bragg discrepancy factors, R B (F 2 ), for the Ga-Ti-O-N phase were 5.32% and 10.22%, for the X-ray and neutron data, respectively.= exp((R 0 − R ij )/B) where R ij is the length of a bond between atoms i and j; ΣS ij , the bond valence sum around each atom should be equal to the valence (oxidation state) of that atom.For the values quoted the parameters R 0 and B were taken from tabulations provided at the International Union of Crystallography: https://www.iucr.org/resources/data/datasets/bond-valence-parameters[48].The R 0 and B parameters used were those compiled for Ti 4+ (1.815, 0.37) and Ga 3+ (1.73, 0.37) bonded to O 2− .TiGa sites used T 4+ parameters.

15 Figure 1 .
Figure 1.The lowest enthalpy structures of (a) GaTiO2N and (b) GaTi2O4N predicted at 20 GPa. Green and blue spheres are gallium and titanium atoms, respectively.Oxygen and nitrogen are represented by red and silver spheres, respectively.The unit cells are outlined with black lines.Visualization is done by VESTA [29].

Figure 1 .
Figure 1.The lowest enthalpy structures of (a) GaTiO 2 N and (b) GaTi 2 O 4 N predicted at 20 GPa.Green and blue spheres are gallium and titanium atoms, respectively.Oxygen and nitrogen are represented by red and silver spheres, respectively.The unit cells are outlined with black lines.Visualization is done by VESTA[29].
44 fm, respectively, initially only neutron diffraction data, collected on the POWGEN instrument at the Spallation Neutron Source at Oak Ridge National Laboratory, TN, were utilized.Unit cell indexing and structure solution identified the new phase designated presumptively as "Ga-Ti-O-N", is isomorphic with monoclinic V 2 GaO 5 , C2/m, Z = 6, a = 17.758(5)Å, b = 2.990(1) Å, c = 9.323(3) Å and β = 98.44(2) • [30].From the crystal structure of V 2 GaO 5 we can construct a solid solution that accounts for the coupled substitution of Ti/N into the full unit cell contents (Z = 6) of V 12 Ga 6 O 30 .The oxide and oxynitride endmembers of this solid solution would then be Ga 12 Ti 6 O 30 and Ti 18 O 18 N 12 , respectively.More generally, the solid solution is formulated as Ti 6+x Ga 12−x O 30−x N x ; empirical formula Ti 1+x Ga 2−x O 5−x N x .This formulation provided chemical constraints utilized in the latter stages of structure refinement.

Figure 2 .
Figure 2. Fit to X-ray data; observed and calculated data are red crosses and the continuous blue line, respectively.The dotted and solid black curves represent the background and the difference between observed and calculated data, respectively.

Figure 3 .
Figure 3. Fit to neutron data; observed and calculated data are red crosses and the continuous blue line, respectively.The dotted and solid black curves represent the background and the difference between observed and calculated data, respectively.The vertical black, blue and green lines mark the positions of Bragg reflections from the Ga-Ti-O-N, TiO2 (rutile) and vanadium sample can, respectively.The largest differences between observed and calculated data are in the rutile phase.

Figure 2 .
Figure 2. Fit to X-ray data; observed and calculated data are red crosses and the continuous blue line, respectively.The dotted and solid black curves represent the background and the difference between observed and calculated data, respectively.

Figure 2 .
Figure 2. Fit to X-ray data; observed and calculated data are red crosses and the continuous blue line, respectively.The dotted and solid black curves represent the background and the difference between observed and calculated data, respectively.

Figure 3 .
Figure 3. Fit to neutron data; observed and calculated data are red crosses and the continuous blue line, respectively.The dotted and solid black curves represent the background and the difference between observed and calculated data, respectively.The vertical black, blue and green lines mark the positions of Bragg reflections from the Ga-Ti-O-N, TiO2 (rutile) and vanadium sample can, respectively.The largest differences between observed and calculated data are in the rutile phase.

Figure 3 .
Figure 3. Fit to neutron data; observed and calculated data are red crosses and the continuous blue line, respectively.The dotted and solid black curves represent the background and the difference between observed and calculated data, respectively.The vertical black, blue and green lines mark the positions of Bragg reflections from the Ga-Ti-O-N, TiO 2 (rutile) and vanadium sample can, respectively.The largest differences between observed and calculated data are in the rutile phase.

Figure 4 .
Figure 4.Rietveld fit to 11-BM (APS) X-ray profile containing an estimated TiO2 (46 wt %) and the new phase related to V2GaO5 (54 wt %).Note the much larger anisotropic strain, defined in GSAS-II [34] and originally introduced[35] and used by Stephens[36,37].Note the sharper rutile peaks (vertical red markers) compared to those of the V2GaO5-related phase (vertical black markers).

Figure 4 .
Figure 4.Rietveld fit to 11-BM (APS) X-ray profile containing an estimated TiO 2 (46 wt %) and the new phase related to V 2 GaO 5 (54 wt %).Note the much larger anisotropic strain, defined in GSAS-II [34] and originally introduced[35] and used by Stephens[36,37].Note the sharper rutile peaks (vertical red markers) compared to those of the V 2 GaO 5 -related phase (vertical black markers).

Figure 5 .
Figure 5. Structure of Ga-Ti-O-N, the gallium titanium oxynitride phase.Visualization is done by VESTA [29].Deep blue polyhedra are occupied exclusively by Ti sites, green pure Ga and light blue are mixed Ti/Ga sites.Red balls represent anion sites occupied by oxygen; ON sites occupied mostly by nitrogen and by ~10% nitrogen, are represented by partially red and grey balls.The origin of the unit cell centered on Ti and is in the back top-left-hand corner, with z vertical, x to the right and y out of the page.The sites occupied by nitrogen are separated mostly into sites within blocks of Ti-centered octahedra, while oxide sites occupy mostly blocks occupied by Ga-and mixed TiGa sites.

Figure 5 .
Figure 5. Structure of Ga-Ti-O-N, the gallium titanium oxynitride phase.Visualization is done by VESTA [29].Deep blue polyhedra are occupied exclusively by Ti sites, green pure Ga and light blue are mixed Ti/Ga sites.Red balls represent anion sites occupied by oxygen; ON sites occupied mostly by nitrogen and by ~10% nitrogen, are represented by partially red and grey balls.The origin of the unit cell centered on Ti and is in the back top-left-hand corner, with z vertical, x to the right and y out of the page.The sites occupied by nitrogen are separated mostly into sites within blocks of Ti-centered octahedra, while oxide sites occupy mostly blocks occupied by Ga-and mixed TiGa sites.

Table 2 .
Configurational entropies and calculated temperatures needed to stabilize given compounds.

Table A1 .
Final results from the joint X-ray neutron refinement of the Ga-Ti-O-N phase.
* Bond Valence S ij

Table A3 .
Average bond lengths of the predicted Ga-Ti-O-N structures optimized at 20 GPa.