Systematic Thermodynamics of Layered Perovskites: Ruddlesden

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Systematic Thermodynamics of Layered Perovskites: Ruddlesden− Popper Phases Leslie Glasser* Nanochemistry Research Institute, Department of Chemistry, Curtin University, Perth 6845, Western Australia, Australia S Supporting Information *

ABSTRACT: Perovskite, CaTiO3, is the prototype of an extensive group of materials. They are capable of considerable chemical modification, with the further capability of undergoing structural modification by the intercalation of thin sheets of intrusive materials (both inorganic and organic) between the cubic perovskite layers, to form a range of “layered” perovskites. These changes bring about alterations in their electronic, structural, and other properties, permitting some “tuning” toward specific ends. This paper collects the limited known thermodynamic data for layered perovskites of various chemical compositions and demonstrates by example that the thermodynamic layer values are substantially additive. This additivity may be exploited by summing properties of the constituent oxides, by adding differences between adjacent compositions within a series, or even by substitution of oxides for one another, thus permitting prediction beyond the known range of compositions. Strict additivity implies full reversibility so that the additive product may be unstable and may undergo structural changes, producing materials with new and potentially useful properties such as ferroelectricity, polarity, giant magnetoresistance, and superconductivity.

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INTRODUCTION

B cations placed alternately in a unit cell which thus has twice the unit cell volume. If intrusive layers form between the infinite slabs of perovskite octahedra, the general formula becomes An+1BnO3n+1, where n represents the thickness of the layers of octahedra with n = 1 implying that the slab is one octahedron thick and n = 2 meaning two octahedra thick, while n = ∞ corresponds to perovskite itself. The first member of the series (n = 1) is often described as having a prototypical K2NiF4 structure.7 Figure 1 displays the structures of the Ruddlesden−Popper (RP) phases Sr2TiO4 (n = 1) and Sr3Ti2O7 (n = 2). In these layers Ti is the B cation and Sr the A cation. The intrusive layer is 2Sr2+ with the perovskite layers offset by a (1/2, 1/2) translation. An alternative chemical description6 is [2A′][An−1BnO3n+1], which emphasizes the nature of the intrusive layer, with [An−1BnO3n+1] being the formula of the perovskite layerscations A and A′ may be identical. Further depictions of the structures of perovskites, of RP phases, and of many other crystal structures may be found at ChemTube3D.7 Using standard high-temperature bulk synthesis methods, phases with n > 3 tend to be unstable, disproportionating into n = ∞ and n = 3 phases,13 but higher members have been synthesized by precipitation from solution (n = 5, with organic intercalates),14 by low temperature layer-by-layer methods (n = 2−5,15 n = 613), and as epitaxial films with n = 10.16

The mineral perovskite, CaTiO3, has the prototypical structure for an extensive group of materials called, in general, “perovskites”.1−3 These materials are of considerable scientific and technological interest because of the possibilities of significant tailoring of their properties such as superconductivity, ferroelectricity, ferromagnetism, and dielectricity and their possible applications in areas such as catalysis, photocatalysis, and electrochemistry. These possibilities occur because of the flexibility of perovskites in permitting a range of chemical modifications as well as accepting structural modifications by intercalation of thin sheets of intrusive materials between twodimensional cubic slabs of perovskite, to form “layered perovskites”. The Ruddlesden−Popper, Dion−Jacobson. and Sillén−Aurivillius phases are examples of such layered perovskites. The purpose of the present paper is to consider, on the basis of experimental data, regularities in the thermodynamics of these phases in order to facilitate prediction of their thermodynamic properties in general4 and to examine structural changes resulting from thermodynamic instability. Perovskite itself is cubic, with space group Pm3̅m (No. 221 of the International Tables5). The general perovskite formula is ABO3, with the structure consisting of BO6 octahedra which share corners in all three crystallographic directions to form a close-packed array. The A cations occur in 12-fold coordination inside the cuboctahedral holes within a group of eight BO6 octahedra.2,3,6 Double perovskites such as Sr2FeMoO6 have two © 2017 American Chemical Society

Received: April 6, 2017 Published: July 24, 2017 8920

DOI: 10.1021/acs.inorgchem.7b00884 Inorg. Chem. 2017, 56, 8920−8925

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Inorganic Chemistry

such as CsBiNb2O7,21 while the RP phases Ca3Ti2O7 (whose thermodynamics is considered below), Ca3Mn2O7, and Ca3Ru2O7 are polar,18 even though their parent materials are not. The RP phase La2SrCr2O7 has recently undergone detailed analysis22 for its unusual structural configuration of rotated CrO6 octahedra together with a randomized distribution of the La and Sr cations over the A sites. It is suggested22 that this combination of distortion and disorder provides chemical tools by which to adjust the physical properties of the material.

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EXPERIMENTAL SECTION

Systematic Thermodynamics of Layered Perovskites. Thermodynamic extensive properties, such as enthalpy, entropy, and heat capacity, by definition have values proportional to the amount of material involved. It is fortunate for predictive purposes that they also exhibit approximately additive properties chemically; for example, the sum of the formation enthalpies of two oxides which react is approximately equal to the formation enthalpy of that product (which, correspondingly, implies that the enthalpy in reacting the two reactants to form the product is close to zero). This equivalence has been thoroughly examined by Yoder and Flora in their “Simple Salt Approximation” (SSA)23,24 and becomes even more general in the “Isomegethic Rule”25 (“equal size” rule), which demonstrates that chemical substitutions of similar ions (with account taken of their volume differences) yield approximate thermodynamic equivalences. The methodology has been further extended to related structures where a common species is added sequentially, such as the Magnéli phases26 where TiO2 is added sequentially in forming TinO2n−1. In this paper, we consider how these relations are observed using experimental data for sequences of layered perovskite phases and how these results can be combined across different sequences of phases, yielding an extensive set of possibilities for thermodynamic prediction within and across species, as well as introducing possibilities for checking published results. These procedures become even more significant when it is recalled that standard synthetic preparation procedures are unsuitable for the higher members of these series with their small Gibbs energies of formation, so that experimental thermodynamic values are unlikely to ever become available. Layer Depths. The volumes of inorganic solids of related composition are additive quantities.26 In Table 1 we see the application of this assertion for a set of RP phases of composition Srn+1TinO3n+1.13 The table contains half the c axis lengths of the corresponding phase, since each phase contains two formula units per unit cell. The difference between successive increases in n yields a reasonably constant value of about 3.90 Å, except for the first of these differences. This first difference corresponds to an intercalated layer of SrO, while the later differences correspond very closely to the c axis length of SrTiO3 itself. We can safely assume that corresponding layerdepth relations will apply within other layered perovskite series. Thermodynamic Sums and Differences. Table S1 in the Supporting Information gives thermodynamic values for the constituent oxides of the materials considered below. The first four rows of Table 2 give literature values of standard thermodynamic values for strontium titanates in their RP phases. The values in the rows labeled “oxides sum” are the corresponding thermodynamic values calculated by summing the values of their component oxides, while the values in the rows labeled “RP sum” are calculated by summing appropriate terms from the literature values for

Figure 1. Layer structures of the Ruddlesden−Popper (RP) phases Sr2TiO4 (left)8 and Sr3Ti2O7 (right),9 both with tetragonal space group I4/mmm, based on .cif files from NIMS AtomWork.10 The TiO6 groups are represented as green octahedra, with red terminal oxygen spheres, and the interlayer Sr2+ ions are represented as blue spheres. The unit cells are outlined to the right rear of each drawing. Drawn with program GDIS.11,12

The Dion−Jacobson phases have the formula [M+]− [An−1BnO3n+1], where M is an alkali metal and the displacement of the perovskite slabs is either (1/2, 0) or (0, 0), depending on the alkali metal: for example KLaNb2O7.6 The Sillén− Aurivillius phases have the general Aurivillius formula [Bi2O2]-[An−1BnO3n+1], with a fluorite [Bi2O2]2+ layer17 and perovskite layers offset by a (1/2, 1/2) translation, with the possible Sillén addition of halide ion sheets supplementing the [Bi2O2]2+ sheets. For example, SrBiTaO9, Bi3TiNbO9, etc. are ferroelectric Aurivillius phases.18 As mentioned above and detailed in the final paragraphs of this paper, successive additions of perovskite layers come at the expense of reduced stability of the product. In response, many layered perovskites undergo reduction in symmetry19 to more stable forms (perhaps accompanying changes of applied pressure or temperature), corresponding to tilting or rotation of the BO6 octahedra of the perovskite layer. This occurs because of the relative rigidity of these octahedra, as also observed in the process of “crumpling” under pressure of minerals containing such octahedra.20 Such structural changes may be accompanied by randomization of some of the accompanying cations. The resulting phases may have new and potentially useful properties, such as being polar or ferroelectric,18 having giant magnetoresistance, or being superconductive. For example, a number of Dion−Jacobson phases are polar and ferroelectric, Table 1. Layer-Depth Relations in the Series Srn+1TinO3n+116 n (c/2)/Å Δ[c/{2(na − na−1)}]/Å formula of difference

SrTiO3

Sr2TiO4

Sr3Ti2O7

Sr4Ti3O10

Sr5Ti4O13

Sr11Ti10O31

∞ 3.91

1 6.30 2.39 Δ(SrO)

2 10.21 3.91 Δ(SrTiO3)

3 14.12 3.92 Δ(SrTiO3)

4 17.94 3.82 Δ(SrTiO3)

10 41.48 3.92 Δ(SrTiO3)

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DOI: 10.1021/acs.inorgchem.7b00884 Inorg. Chem. 2017, 56, 8920−8925

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Table 2. Standard Thermodynamic Properties at 25 °C of Some Strontium Titanates: RP n, number of Ruddlesden−Popper Perovskite Layers; Formation Enthalpy, ΔfH°; Absolute Entropy, S°; Isobaric Heat Capacity, Cp°; Ratio of Heat Capacity and Entropy, Cp°/S°; Debye Temperature, ΘDa,28 RP n

ΔfH°/kJ mol−1

SrTiO3 Sr2TiO4 Sr3Ti2O7 Sr4Ti3O10

∞ 1 2 3

−1672.4 −2287.8 −3969.7 −5648.8

SrTiO3

∞ oxides sum ΔfP°(sum)/ΔfP°(lit.)

Sr2TiO4 oxides sum ΔfP°(sum)/ΔfP°(lit.) RP sum ΔfP°(sum)/ΔfP°(lit.) Sr3Ti2O7 oxides sum ΔfP°(sum)/ΔfP°(lit.) RP sum ΔfP°(sum)/ΔfP°(lit.) Sr4Ti3O10 oxides sum ΔfP°(sum)/ΔfP°(lit.) RP sum ΔfP°(sum)/ΔfP°(lit.) Sr5Ti4O13 oxides sum RP sum Sr6Ti5O16 oxides sum RP sum

S°/J K−1 mol−1

Data Sources27,29,30 108.8 159.0 262.6 365.4 Summed Values

Cp°b/J K−1 mol−1

Cp°/S°

ΘD28/K

98.4 143.7 242.8 341.9

0.90 0.90 0.92 0.94

441 441 457 472

−1536.7 0.92

105.9 0.97

100.2 1.02

0.95

479

−2128.7 0.93 −2264.4 0.99

161.5 1.02 164.4 1.03

145.4 1.01 143.6 1.00

0.90

441

0.87

421

−3665.5 0.92 −3960.2 1.00

267.3 1.02 267.8 1.02

245.6 1.01 242.1 1.00

0.92

457

0.90

441

−5202.2 0.92 −5642.1 1.00

373.2 1.02 371.4 1.02

345.8 1.01 341.2 1.00

0.93

465

0.92

457

−6739.0 −7321.2

479.1 474.2

446.0 440.2

0.93 0.93

465 465

−8275.7 −8993.6

584.9 583.0

546.2 538.6

0.93 0.92

465 457

1

2

3

4

5

a

The cell values in Roman type are literature values; those in bold italic type are calculated additive values using values either from the constituent oxides (“oxide sum”, see Table S1 in the Supporting Information) or by appropriate sums of the RP values (“RP sum”) in the initial four rows of this table. The rows labeled ΔfP°(sum)/ΔfP°(lit.) give the ratio of the summed to literature values of the thermodynamic property P (P may represent H, S, or Cp). bThe formula used for heat capacity in Yokokawa et al.29 is not listed but, by comparison with known ambient values, it corresponds to Cp° = a + 10−3 × bT + 105 × cT2. strontium titanates in the first four rows. For example, the enthalpy “oxide sum” ΔfH°(Sr2TiO4) = 2 × ΔfH°(SrO) + ΔfH°(TiO2) = −2128.7 kJ mol−1, while the entropy “RP sum” S°(Sr3Ti2O7) = S°(SrTiO3) + S°(Sr2TiO4) = 267.8 J K−1 mol−1. The row following each of these calculated sums is the ratio of the above summed value relative to the literature value, ΔfP°(sum)/ΔfP°(lit.), where “P” represents any of the listed thermodynamic quantities. It is a remarkable observation that the ratios for the RP sums are close to unity for each of the thermodynamic quantities, so that RP sums beyond the available literature values (such as for Sr5Ti4O13 and Sr6Ti5O16) may reasonably be relied upon. Correspondingly, the simple oxide sums for entropy and heat capacity seem to be reliable, while the formation enthalpy functions should be decreased by up to 8% to match the corresponding literature values. We may reasonably conclude from these observations that the layering of the RP phases proceeds with little disturbance to the atomic arrangements (hence RP sums, entropy, and heat capacity are additive) but that there is some added interaction among the oxides in the formation of the RP phases (hence the more negative formation enthalpies). This interaction thus implies, for example, that the reaction SrO + TiO2 → SrTiO3 has a nonzero enthalpyindeed, ΔrH = −135.6 kJ mol−1.27 In Table S2 in the Supporting Information we compare the DFTcalculated enthalpies of these materials with their experimental values; there is a very strong correlation of these two sets of values, with ΔfH

(DFT) = 1.0311 × ΔfH − 3.266, R2 = 1.0. The mean difference of the DFT values from the standard literature values is −113 kJ mol−1, which is in the expected range for DFT calculations.31 Table 3 continues the process of examining thermodynamic relations among RP phases with a group of calcium titanates. We observe that the summed formation enthalpies are slightly closer to the experimental values (within 5% for example) than is the case for the strontium titanates. We have included thermodynamic estimates for the unknown calcium titanate, Ca2TiO4, and below discuss reasons for its instability. We also explore thermodynamic difference relations (TDR)4,32 among the various titanates. Thus, the processes

Ca3Ti 2O7 + 3(SrO − CaO) = Sr3Ti 2O7 Ca4Ti3O10 + 4(SrO − CaO) = Sr4Ti3O10 correspond to substitution of Ca by Sr, with thermodynamic quantities of the products within 3% of their experimental value. The results in Table 3 for the more complex substitutions BaSrTiO4 − BaO + SrO = Sr2TiO4

CaZrTi 2O7 + (2CaO − ZrO2 ) = Ca3Ti 2O7 8922

DOI: 10.1021/acs.inorgchem.7b00884 Inorg. Chem. 2017, 56, 8920−8925

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Table 3. Standard Thermodynamic Properties at 25 °C of Some Calcium Titanates: RP n, number of Ruddlesden−Popper Perovskite Layers; Formation Enthalpy, ΔfH°; Absolute Entropy, S°; Isobaric Heat Capacity, Cp°; Ratio of Heat Capacity and Entropy, Cp°/S°; Debye Temperature, ΘDa,28 RP n CaTiO3 oxides sum ΔfP°(sum)/ΔfP°(lit.) Ca2TiO4 oxides sum RP + oxides Δf P°(RP)/Δf P°(oxides) Ca3Ti2O7 oxides sum ΔfP°(sum)/ΔfP°(lit.) RP sum ΔfP°(sum)/ΔfP°(lit.) Ca4Ti3O10 oxides sum ΔfP°(sum)/ΔfP°(lit.) RP sum ΔfP°(sum)/ΔfP°(lit.) Ca3Ti2O7 + 3(SrO - CaO) = Sr3Ti2O7 ΔfP°(sum)/ΔfP°(lit.) Ca4Ti3O10 + 4(SrO - CaO) = Sr4Ti3O10 Sr4Ti3O10 ΔfP°(sum)/ΔfP°(lit.) BaSrTiO4 BaSrTiO4 − BaO + SrO = Sr2TiO4 Sr2TiO4 ΔfP°(sum)/ΔfP°(lit.) CaZrTi2O7 CaZrTi2O7 + (2CaO − ZrO2) = Ca3Ti2O7 Ca3Ti2O7 ΔfP°(sum)/ΔfP°(lit.)

∞

ΔfH°/kJ mol−1

S°/J K−1 mol−1

Cp°/J K−1 mol−1

Cp°/S°

ΘD28/K

93.3 88.4 0.95

98.1 97.0 0.99

1.05 1.10

545 580

-2373.7 -2332.6 0.98

124.0 123.9 1.00

137.3 138.3 1.01

1.11 1.12

587 593

−3950.5 -3794.3 0.96 -3956.5 1.00

234.7 214.9 0.92 224.7 0.96

239.6 236.1 0.99 238.2 0.99

1.02 1.10

524 580

1.06

553

−5671.6 -5373.9 0.95 -5611.3 0.99 -3821.7 0.96 -5499.9 −5648.8 0.97 −2276.1 -2314.3 −2287.8 0.99 −3713.7 -3883.24 −3950.5 0.98

328.4 303.3 0.92 328.0 1.00 287.1 1.09 398.3 365.4 1.09 191.6 176.9 159.0 0.90 196.2 222.01 234.7 0.95

337.8 333.1 0.99 337.7 1.00 249.1 1.03 350.5 341.9 1.03 146.2 144.5 143.7 0.99 211.9 240.14 239.6 1.00

1.03 1.10

531 580

1.03

531

0.87

421

0.88 0.94

429 472

0.76 0.82 0.90

341 384 441

1.08 1.08 1.02

567 567 524

Data Sources27,29,33,34 −1660.8 -1579.7 0.95

1

2

3

2 3 3 1 1 2 2

a

The values in black roman type are literature values; those in bold italic type are calculated additive values using values either from the constituent oxides (“oxide sum”, see Table S1 in the Supporting Information) or by appropriate sums of the RP values (“RP sum”) in the initial rows of this table. The material Ca2TiO4 is known to be unstable;29 the thermodynamic properties in boldface italic type have been estimated additively. The rows labeled ΔfP°(sum)/ΔfP°(lit.) give the ratio of the summed to literature values of the thermodynamic property P (which here may represent H, S, or Cp). are even slightly closer. We tentatively suggest that the closer substitutions are in ionic radius, the closer the thermodynamic relations. In Table S3 in the Supporting Information, we give thermodynamic data for Sr−Zr−O, Sr−V−O, Sr−Ru−O, and La−Ni−O RP phases. These values bear the same relations to other RP phases as outlined above for Table 2, and so the discussion will not be repeated.

tetragonal phases to a more stable I4/mmm phase with reduced c axis length.37 The principal process is a coordination of two Li ions from 2LiO4 to 2LiO6. Limitations of Additive Thermodynamic Relationships. As shown above, it is simple enough to calculate additive thermodynamic relationships, but one must be aware that it may not always be possible to obtain the resulting predicted products for a number of reasons. For example, there may be kinetic barriers to the synthesis of a given material, or it may be unstable, resulting in decomposition into its component materials in a disproportionation reaction. Below, we examine some of the relevant issues. (1) According to Table 3, the RP phase Ca2TiO4 (with postulated K2NiF4 structure) has favorable formation enthalpy and entropy. However, it is observed that Ca2MO4 cannot be prepared using many transition metals, M. Yokokawa et al.29 have undertaken a thorough analysis of the instability of such postulated K2NiF4-structured materials. Consider the decomposition of such a material and its relation to disproportiona-

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RESULTS AND DISCUSSION The declining stability of the phases with increasing n results in difficulty in preparation of the higher n phases. Reznitskii35 has analyzed the thermodynamics of the changes from the metastable initial phases to the final stable phase and found ΔrG298 ≅ −78 kJ mol−1 and ΔrS298 ≅ −20 J K−1 mol−1. Electron microscopy studies36 show that there is an increase in defects and appearance of antiphase boundaries in epitaxial thin films for such higher members of the SrTiO3 series. Indeed, Li-containing layered phases undergo irreversible structural transformations under electron-beam irradiation during high resolution electron microscopy, from various 8923

DOI: 10.1021/acs.inorgchem.7b00884 Inorg. Chem. 2017, 56, 8920−8925

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Inorganic Chemistry Table 4. Reaction Energies and Entropy for the Formation of Successive Ruddlesden−Popper Phasesa n (RP) 0 0 1 1 2 3

ΔrH/kJ mol−1

ΔrG/kJ mol−1

ΔrS/J K−1 mol−1

−135.6 −56.1 −39.8 −23.4 −9.5 −6.7

−136.5 −57.4 −39.6 −21.8 −7.9 −5.0

2.93 4.16 −0.61 −5.40 −5.24 −5.91

SrO + TiO2 → SrTiO3 1/2Sr2TiO4 + 1/2TiO2 → SrTiO3 1/2Sr4Ti3O10 − 1/2TiO2 → Sr2TiO4 SrTiO3 + SrO → Sr2TiO4 SrTiO3 + Sr2TiO4 → Sr3Ti2O7 SrTiO3 + Sr3Ti2O7 → Sr4Ti3O10

The first row represents direct formation from oxides, while subsequent rows represent additive Ruddlesden−Popper relations. The errors in these values, derived from data from multiple sources, are difficult to estimate. Errors in the formation enthalpies for the well-established oxides42 range up to about 4 kJ mol−1, and we can expect considerably larger errors for the more complex materials. The systematic relations in Table 4, however, give confidence that no major errors persist. a

tion to its oxides: A2MO4 → AMO3 + AO. The corresponding Gibbs energy changes in terms of the component oxides will be

to the transition metal within the crystal structure. It is also noted that there may be kinetic barriers to the formation of products or that the products may be unstable, undergoing disproportionation reactions.

Δr G° = Δf,oxideG°(AM O3) − Δf,oxideG°(A 2M O4 )

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(2) Thus, ΔrGo may be positive (and A2MO4 unstable) in some circumstances of the relation between the oxides AMO3 and A2MO4. It is known that Sr2MO4 materials with large transition metal ions M may be prepared while Ca2MO4 materials are absent. This reflects the fact that the larger radius38 of Sr2+ (126 pm) better matches transition metal ion radii for packing purposes than does that of Ca2+ (112 pm). Reznetskii et al.39 have analyzed the thermochemical relations for Ca-containing materials of these types. In an alternative approach, Yokokawa et al.29 have analyzed these relations among materials empirically through use of the Goldschmidt radius tolerance factor for the cation A, tA

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b00884. Thermodynamic properties of some inorganic oxides, comparison of formation thermodynamics of some RP phases from the literature and as calculated by DFT, and thermodynamic properties of some Zr, V, Ru, and Ni RP phases (PDF)

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tA = (rA(IX) + rO)/[ 2 (rM(VI) + rO)]

where rA(IX) is the radius of the nine-coordinate A sites and rM(VI) is the radius of the six-coordinate B sites, presenting the results in the form of a tolerance map (their Figure 10).40 This shows that materials with Ca cations are progressively unstable as the M radius increases, while systems with larger ninecoordinate radii, such as Sr and Ba, are less affected. (3) An important issue of principle is that exact additivity implies zero energetic addition on the reaction by which to stabilize the product so that, correspondingly, there is no thermodynamic barrier to reversal of the process. Thus, the additive reaction product may not even form in such cases, depending on the kinetics and closeness to equilibrium. Table 4 shows that the reaction energies to form successive Ruddlesden−Popper phases are reduced as n increases, with the implication that the phases with increasing n will become progressively less stable and more difficult to synthesize. This proves to be the case, with the higher phases required to be grown epitaxially and with great care required to be taken in the process.41

AUTHOR INFORMATION

Corresponding Author

*L.G.: tel, + 61 8 9848-3334; e-mail, [email protected]. ORCID

Leslie Glasser: 0000-0002-8883-0564 Notes

The author declares no competing financial interest.

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REFERENCES

(1) Wikipedia Perovskites. https://en.wikipedia.org/wiki/Perovskite (accessed March 2017). (2) Borowski, M. Perovskites: structure, properties, and uses. Nova Science Publishers: Hauppauge, NY, 2010. (3) Navrotsky, A. Energetics and Crystal Chemical Systematics among Ilmenite, Lithium Niobate, and Perovskite Structures. Chem. Mater. 1998, 10, 2787−2793. (4) Glasser, L.; Jenkins, H. D. B. Predictive thermodynamics for ionic solids and liquids. Phys. Chem. Chem. Phys. 2016, 18, 21226−21240. (5) Aroyo, M. I.; Hahn, T. International Tables for Crystallography, 6th ed.; Wiley: Hoboken, NJ, 2015; Vol. A, Space-Group Symmetry; http://www.wiley.com/WileyCDA/WileyTitle/productCd0470974230.html (accessed March 2017). (6) Cava Lab Solid State Chemistry Research Group; Perovskite Structure and Derivatives; http://www.princeton.edu/~cavalab/ tutorials/public/structures/perovskites.htmlhttp://www.princeton. edu/~cavalab/tutorials/public/structures/perovskites.html (accessed March 2017). (7) University of Liverpool ChemTube3D; http://www.chemtube3d. com/index.html (accessed May 2017). (8) Blasse, G. Crystallographic data of sodium lanthanide titanates (NaLnTiO4). J. Inorg. Nucl. Chem. 1968, 30, 656−658. (9) Elcombe, M. M.; Kisi, E. H.; Hawkins, K. D.; White, T. J.; Goodman, P.; Matheson, S. Structure determinations for Ca3Ti2O7,

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CONCLUSIONS We have collected the known thermodynamic data for a range of RP layered perovskites and demonstrated that the thermodynamic values are reasonably additive, thus permitting prediction of properties for materials with unknown values. This additivity may be exploited by summing properties of the constituent oxides, by adding differences between adjacent compositions within a series, or even by substituting oxides for one another. Ca2MO4 is generally unstable for large transition metals, M, whereas Sr2MO4 is stable; this difference is attributed to the larger size of the Sr2+ ion being a better fit 8924

DOI: 10.1021/acs.inorgchem.7b00884 Inorg. Chem. 2017, 56, 8920−8925

Article

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DOI: 10.1021/acs.inorgchem.7b00884 Inorg. Chem. 2017, 56, 8920−8925