in energetically unstable copper-containing spinels with disordered cation distributions [ 15 , 16 ]. Recently, Voskanyan et al. observed entropy stabilization in pseudobinary TiO 2 -Nb 2 O 5 crystallographic shear (CS) phases, in which positive enthalpies of formation are offset by large positive entropies arising from cation disorder at high temperatures and not from the shear planes per se [ 17 , 18 ]. These results demonstrate that the entropy stabilization of energetically unfavorable materials is possible through the disorder of even two cations instead of five or more. Therefore, the thermodynamic stabilization via configurational entropy is more prevalent than was formerly realized and discoveries of numerous entropically stabilized binary/ternary compounds are pending.

The (Zr,Hf)O 2 -(Nb,Ta) 2 O 5 pseudobinary system forms a fascinating class of materials with wide compositional range [ 19 -29 ]. Among different possible compositions, the single-phase compounds with A 6 B 2 O 17 (A = Zr, Hf; B = Nb, Ta) stoichiometry and orthorhombic crystal structures (space group: Ima2, #46) were the first-born in this family [ 19 , 22 ]. The Zr x Nb 2 O 2x + 5 and Zr x Ta 2 O 2x + 5 phases (5 ≤ x ≤ 8) with α-PbO 2 related superstructures have been described as a (A,B) m O 2m + 1 (A and B are metal and m is multiplicity) homologous series [22] . Subsequently, Thompson et al. showed that at intermediate multiplicities, where molar ratios are no longer rational numbers, a series of incommensurately modulated solid solutions of closely related phases (5.1 ≤ x ≤ 10) form [23] . Although the structure of single crystal Zr 6 Nb 2 O 17 was solved by Galy and Roth in 1973 [22] , the structures of the other three analogs have only been recently solved by McCormack and Kriven [28] . In addition, commensurately modulated Hf 3 Ta 2 O 11 , Zr 5 Nb 2 O 15 , Hf 5 Ta 2 O 15 , and Hf 7 Ta 2 O 19 structures have been also synthesized and successfully refined [ 27 , 29 , 30 ].

Although the structural complexity, compositional diversity, and thermodynamic stability of these compounds are far from being understood completely, the doped hafnium tantalum and niobium zirconium oxides have been extensively utilized in the electronics industry, particularly in metal oxide-semiconductor field-effect transistors (MOSFET) [ 31 -33 ]. In addition, several materials derived from this system have been employed in high-temperature environments as thermal barrier coatings and dielectric films [ 34 , 35 ].

This work reports experimentally measured formation enthalpies of A 6 B 2 O 17 (A = Zr or Hf; B = Nb or Ta) phases from their corresponding binary oxides by employing high temperature oxide melt solution calorimetry (HTOMSC). We found that these pseudobinary modulated structures are entropy stabilized, stable only above a critical temperature, when large positive entropies generated from cation disorder compensate for their positive enthalpies of formation from parent oxides.

Syntheses of Zr [28] . Phase pure Zr 6 Nb 2 O 17 was synthesized by the organic steric entrapment of cations [36] . The zirconium source was zirconium (IV) chloride 99.9% (metal basis) (Alfa Aesar) and the niobium source was niobium(V) chloride, 99.99% (metal basis) (Alfa Aesar). The zirconium (IV) chloride was dissolved in deionized water and the niobium(V) chloride was dissolved in isopropanol. The two solutions were mixed in ratios of Zr:Nb = 6:2 and stirred for one hour. Ethylene glycol (Aldrich) was added in the proportion to maintain a cation valence charge to monomer ratio of four to one. The solution was then heated on a hot plate at 300 ˚C until water and isopropanol were evaporated to allow for gelation. The gel was subsequently dried at 100 ˚C in a box furnace producing a porous mass. It was ground using a zirconia mortar and pestle and calcined at 1050 ˚C for 3 h in a zirconia crucible, at a heating and cooling rate of 10 ˚C min -1 . Then, the powders were pressed into pellets and annealed at 1300 ˚C in a platinum crucible for 10 h. The obtained pellet was crushed, ground and sieved to < 45 μm.

X-ray powder diffraction (XRPD) data were collected for Zr 6 Ta 2 O 17 , Hf 6 Nb 2 O 17 and Hf 6 Ta 2 O 17 at the Synchrotron 11-BM beamline ( λ = 0.041 nm) at the Advanced Photon Source (Argonne National Laboratory, Argonne, IL, USA). Neutron diffraction (ND) data with a flight path of 63.2m were collected at the POWGEN beamline at the Spallation Neutron Source (Oak Ridge National Laboratory, Oak Ridge, TN, USA). Lab source Bruker D50 0 0 diffractometer ( λ = 0.154 nm) was used to analyze the phase purity of Zr 6 Nb 2 O 17 . The PXRD patterns were acquired from 10 to 65 ˚at 1 min -1 and step size of 0.02 ˚. To obtain the thermodynamic properties of A 6 B 2 O 17 compounds, high temperature oxide melt solution calorimetry (HTOMSC) experiments have been performed. Each sample (4-7 mg) was hand-pressed into pellets which were dropped from room temperature (298 K) into 20 g of molten sodium molybdate solvent (3Na 2 O 4MoO 3 ) equilibrated at 1073 K inside a Tian Calvet twin calorimeter (AlexSYS, Setaram, France). Oxygen gas was continuously bubbled through the solvent at 10 mL/min and flushed over the solvent to ensure thorough mixing, complete dissolution, and minimize local saturation in the solvent, as well as to maintain oxidizing conditions. The calibration factor was obtained by dropping corundum ( α-Al 2 O 3 ) pellets. The experimental setup and fundamental details are described elsewhere [37] .

The Zr 6 Ta 2 O 17 , Hf 6 Nb 2 O 17 and Hf 6 Ta 2 O 17 compounds used in this study were from the same batch used by McCormack and Kriven [28] to solve their crystal structure using 11BM synchrotron X-ray and POWGEN neutron diffraction. These diffractograms have been reproduced to highlight the purity of samples for calorimetric studies ( Fig. 1 ). The phase purity of Zr 6 Nb 2 O 17 was only confirmed by powder X-ray diffraction. From Fig. 1 , it is clear that these compounds are isomorphous, have Ima2 symmetry, and are phase pure.

The crystal structure of commensurately modulated A 6 B 2 O 17 is schematically illustrated in Fig. 2 . Unlike CS structures in which reduction of anion content, as required by stoichiometry, is accompanied by condensation of octahedra and formation of shear planes (stacking faults) at different periodicities, the increase in anion content (with respect to parent structure) in A 6 B 2 O 17 is accommodated by distortion of the anionic array, generating new coordination polyhedra. The accommodation of excess anions can also be represented as the transformation of periodic square nets (Schläfli symbol 4 4 ) of anions into denser triangular nets (Schläfli symbol 3 6 ). In the A 6 B 2 O 17 structure, six-coordinated distorted octahedra ( Fig. 2 (E), label 1), seven-coordinated distorted capped trigonal prisms ( Fig. 2 (E), label 2), and eight-coordinated distorted bicapped trigonal prisms ( Fig. 2 (E), label 3) form blocks of equidistant cations that are arranged along the c axis. The six-coordinated octahedra are connected to the capped trigonal prisms via cornersharing and the latter are linked to the eight-coordinated polyhedra via edge-sharing. The distorted bicapped trigonal prisms are connected by both corner and edge sharing. The layers of two substructures with one-atom thickness are assembled alternately along the b direction, generating the commensurately modulated A 6 B 2 O 17 phases with a very long periodic structure. The cation coordination is midway between that in monoclinic H-Nb 2 O 5 and YF 3 . There is a gradual transformation from octahedral coordination to the YF 3 -type (eight-coordinated polyhedra). The sevencoordinated polyhedra (baddeleyite type) possess an intermediate configuration linking the neighboring slabs.

The average enthalpies of drop solution ( H ds ) of (Zr orHf)O 2 -(Nb orTa) 2 O 5 compounds and two standard deviations of the mean obtained via HTOMSC are summarized in Table 2 . Using the measured values, along with previously reported H ds values for constituent oxides ZrO 2 , Ta 2 O 5 , HfO 2 and Nb 2 O 5 , the molar enthalpies of formation ( H f,ox ) per formula unit of each tantalate and niobate from binary oxides, as well as from elements ( H f,el ), were calculated via the thermochemical cycles shown in Table 1

These calorimetric data indicate that the A 6 B 2 O 17 structures, and perhaps the other modulated structures as well, are energetically unstable but apparently stabilized by their entropy and represent a new class of "entropy stabilized oxides." Like CS plane formation in ReO 3 -derived block structures, the structural modulation in A 6 B 2 O 17 is the best option for the system at a given stoichiometry to overcome otherwise unfavorable energetics. To get a negative Gibbs free energy of formation ( G f ) from oxides at a synthesis temperature of (1573 K), the entropy of formation ( S f ) for A 6 B 2 O 17 phases must be significantly positive. However, the differences in vibrational entropies among solid phases are relatively small and thus it is anticipated that they will have a minor contribution to the S f from oxides. As a result, it can be deduced that these modulated structures are thermodynamically stabilized mainly through the configurational entropy, S conf, arising from cation disorder, making these compounds stable only above some minimum temperature. The similar ionic radii of cations in A 6 B 2 O 17 phases and corresponding small bond-length mismatches facilitate near ideal mixing of components. As a rule, the small differences in valence, size, and coordination between two cations located at the same crystallographic site lead to the stabilization of a more disordered structure. We calculated the maximum configurational entropies originating from complete A(Zr,Hf)-B(Ta,Nb) disorder in crystal structures. The statistical mixing of six A atoms with two B atoms results in 37.40 J/mol K (4.50R J/mol K) configurational entropy per formula unit, which is 4.68 J/mol K (0.56R J/mol K) per cation. This configurational entropy per formula unit is ~2.8 times higher than the maximum configurational entropy value of 1.61R for the random mixing of equimolar amounts of five cations in a conventional "high entropy oxide" system. The calculated maximum of S conf can be approximated to the maximum entropy of formation S conf = S conf because constituent binary oxides are not disordered ( Table 2 ). Therefore, the decomposition temperatures for A 6 B 2 O 17 to binary oxides can be calculated using the S conf and measured H f,ox values and the results are listed in Table 2 . The obtained low temperature stability limits calculated using H f,ox / S conf are below the synthesis temperature, indicating that these compounds as synthesized, should have substantial cation disorder, but not necessarily random distribution. Based on this, we also calculated the low temperature stability limits assuming that the A 6 B 2 O 17 was 50 % disordered. The calculated values listed in Table 2 are now higher than the actual synthesis temperature, which immediately implies that these modulated phases must be at least 50 % disordered to be synthesizable at 1573 K. Therefore, one can infer that the energetically metastable A 6 B 2 O 17 (A = Zr, Hf; B = Nb, Ta) phases possess very substantial disorder when synthesized. Once disordering of cations takes place at high temperatures and the compound forms, that disordered configuration gets "frozen -in" kinetically and persists on cooling.

Pronounced cation disorder was observed in Zr 6 Ta 2 O 17 and Hf 6 Nb 2 O 17 by McCormack and Kriven via XRD measurements [28] . Since Zr,Ta and Hf,Nb atomic pairs have different X-ray scattering factors, the ordered and disordered structures were distinguishable by the presence of additional peaks in the difference patterns. It was found that Zr 6 Ta 2 O 17 and Hf 6 Nb 2 O 17 were clearly disordered, as additional high intensity Bragg peaks required for the ordered structure were not present. Thus, successful refinement of the structure was only achieved with a disordered cation sublattice. For Zr 6 Nb 2 O 17 and Hf 6 Ta 2 O 17 , the ordered and disordered structures were indiscernible through XRD analysis because of their almost identical scattering factors. However, based on their isomorphous crystal structures, it was concluded that the Zr 6 Nb 2 O 17 and Hf 6 Ta 2 O 17 are most probably also disordered. Furthermore, the absence of long-range metal ordering in Zr 6 Nb 2 O 17 and Zr 10 Nb 2 O 25 was demonstrated using synchrotron radiation data [ 25 , 26 ]. Moreover, the lack of cation ordering was also observed in Hf 3 Ta 2 O 11 via neutron diffraction experiments [27] .

The homologous series of compounds with a similar cation sublattice is formed by altering the concentration of sevencoordinated polyhedral units in the parent A 6 B 2 O 17 structure as shown in Fig. 3 . The removal of one set of symmetrically equivalent seven-coordinated planar units from A 6 B 2 O 17 leads to the formation of compounds with A 4 B 2 O 13 general formula ( Fig. 3 A), while the addition of one set of symmetrically equivalent planar units to the A 6 B 2 O 17 structure results in A 8 B 2 O 21 stoichiometry ( Fig. 3 C). In other words, by adding or removing a seven-coordinated slab, the series of homologs with different AO 2 mole fractions can be gener- [ 21 , 24 , 25 ]. Hence, our results not only provide thermodynamic properties of individual compositions but can also predict the energetic stability of other homologs in this family. Thus, the logical question arises as to whether there is a class of compounds with A 12 B 2 O 29 stoichiometry waiting to be discovered. While this question remains open, it is apparent that all these different homologs should have positive enthalpies of formation, and as a result, all of them must be entropy stabilized.

We have investigated the enthalpies of formation of A 6 B 2 O 17 (A = Zr or Hf; B = Nb or Ta) commensurately modulated phases via high temperature oxide melt solution calorimetry. We found that all four compounds of this family have endothermic enthalpies of formation from their constituent binary oxides which are neutralized by configurational entropies arising from cation disorder. The configurational entropy per formula unit of A 6 B 2 O 17 is almost 3 times higher than the maximum configurational entropy which can be achieved for an equimolar, five cation containing "high entropy oxide". Therefore, pseudobinary A 6 B 2 O 17 modulated phases, and most likely the other modulated phases of (A,B) m O 2m + 1 homologous series as well, can be considered as new examples of entropy stabilized oxides. These compounds contain an extensive degree of disorder, they are metastable at room temperature, and only stable at elevated temperatures. The generalization is that, although the formation of such homologous series, with commen-surate or incommensurate modulation of structure, is presumably energetically more stable than the formation of completely random structures, such stabilization is not enough to make enthalpies of formation from binary oxides negative, and residual cation disorder, outside the ordered regions, with ensuing large configurational entropy, is essential to stabilizing these structures at high temperatures. Thus, the structures exist through a competition of order and disorder. This work demonstrates that entropy stabilized oxides are not rare, and it opens new horizons for design and discovery of other entropy stabilized oxide systems.