Combined computational and experimentalinvestigation of the La2CuO4–xSx (0 ≤ x ≤ 4)quaternary systemHua Hea, Chuck-Hou Yeeb, Daniel E. McNallyc, Jack W. Simonsond, Shelby Zellmana, Mason Klemma, Plamen Kamenovc,Gayle Geschwindc, Ashley Zebroc, Sanjit Ghosee, Jianming Baie, Eric Dooryheee, Gabriel Kotliarb,and Meigan C. Aronsona,1

aDepartment of Physics and Astronomy, Texas A&M University, College Station, TX 77843; bDepartment of Physics and Astronomy, Rutgers University,Piscataway, NJ 08854; cDepartment of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794; dDepartment of Physics, Farmingdale StateCollege, Farmingdale, NY 11735; and eNational Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY 11973

Edited by Zachary Fisk, University of California, Irvine, CA, and approved June 19, 2018 (received for review January 6, 2018)

The lack of a mechanistic framework for chemical reactions forminginorganic extended solids presents a challenge to acceleratedmaterials discovery. We demonstrate here a combined computa-tional and experimental methodology to tackle this problem, inwhich in situ X-ray diffraction measurements monitor solid-statereactions and deduce reaction pathways, while theoretical compu-tations rationalize reaction energetics. Themethod has been appliedto the La2CuO4−xSx (0 ≤ x ≤ 4) quaternary system, following anearlier prediction that enhanced superconductivity could be foundin these new lanthanum copper(II) oxysulfide compounds. In situdiffraction measurements show that reactants containing Cu(II)and S(2−) ions undergo redox reactions, leaving their ions in oxida-tion states that are incompatible with forming the desired newcompounds. Computations of the reaction energies confirm thatthe observed synthetic pathways are indeed favored over thosethat would hypothetically form the suggested compounds. The con-sistency between computation and experiment in the La2CuO4−xSxsystem suggests a role for predictive theory: to identify and toexplicate new synthetic routes for forming predicted compounds.

Materials by Design | in situ X-ray studies | electronic structure calculations

The discovery of new solid inorganic materials is the primarydriver for advancing our understanding of the formation of

extended solids and their functional properties. While chemicalguidelines like isoelectronic substitution and metathesis reactionhave had some success in guiding exploratory syntheses (1–3),the discovery of new solid inorganic materials so far remainslargely serendipitous. Advancing beyond chemical intuition hasproven difficult. Unlike organic syntheses, in which only specificsites of a molecule are modified in chemical reactions, the syn-thesis of extended solids involves the breakdown and reassemblyof entire atomic lattices, and there is no mechanistic framework todescribe these processes yet (4). The development of a set ofgeneral rules that clarify the essential chemical reactions govern-ing the assembly of atoms in extended solids remains a central goalof materials-inspired research. First-principles calculations such asdensity functional theory (DFT) calculations (5, 6) are becomingincreasingly accurate in computing the energies of differentstructures and their heats of formation, crucial steps toward re-alizing the challenging goal of designing new materials with de-sired functionality without prior knowledge of the crystal structure(7–13). However, these predicted compounds have too ofteneluded experimental discovery, even when they are predicted to bethermodynamically stable. We envisage here a powerful way thatpredictive theory can accelerate the discovery of new compounds,by clarifying the energetics of the different steps of the reactionsthat comprise candidate syntheses, and ultimately using this insightto recommend syntheses that are likely to be viable. Previously, therewas a decided lack of direct information about reactions leadingto the formation of extended solids that could subsequently be

compared with theory. The use of in situ X-ray diffraction (XRD)experiments, where the syntheses are carried out in a high-energyX-ray beam, provides a powerful way to explore these chemicalreactions (14–16). The formation of a crystalline phase can be ob-served in real time, providing a record of the sequence of structuresand phases that occur on heating and cooling. We will show herethat, by using this information, one can deduce the reaction path-ways and rationalize the energetics of the chemical reactions,establishing a step-by-step correspondence between computationsand experiments. The goal is to connect our chemical intuition topredictive theory, and in this way to gain insight into reactionpathways that are central to the formation of extended solids. Anadded benefit is that the exploration of materials phase diagrams, afoundational task for materials-inspired research, is greatly accelera-ted using in situ XRD measurements.Here, we present our investigation of the La2CuO4–xSx (0 ≤ x ≤

4) quaternary system using experimental and computationalmethods in parallel to show the advantages of this combinedmethod. Previously, we have proposed theoretical compoundsLa2CuO3S and La2CuO2S2 (17), which are obtained by replacingone-half or all of the apical oxygen with sulfur in La2CuO4 (Fig. 1),the parent compound of the first high-temperature superconductor

Significance

Discovery of new materials enabling new technologies, fromnovel electronics to better magnets, has so far relied on ser-endipity. Computational advances show promise that newmaterials can be designed in a computer and not in the lab, aproposal called “Materials by Design.” We present here a de-tailed comparison between theory and experiment, carryingout the synthesis of a high-temperature superconductor in anX-ray beam to elucidate the sequence of chemical reactions asthe compound forms. Parallel computations of the stabilities ofpossible compounds that could form from the selected ele-ments accurately predict the observed reactions. Paired withour chemical intuition, this methodology provides understand-ing and potentially control of the essential chemical principlesresponsible for stabilizing virtually any compound.

Author contributions: H.H., G.K., and M.C.A. designed research; H.H., C.-H.Y., D.E.M.,J.W.S., S.Z., S.G., J.B., and E.D. performed research; H.H., C.-H.Y., D.E.M., S.Z., M.K., P.K.,G.G., A.Z., S.G., J.B., E.D., and G.K. contributed new reagents/analytic tools; H.H. and G.K.analyzed data; and H.H., G.K., and M.C.A. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Published under the PNAS license.1To whom correspondence should be addressed. Email: maronson@tamu.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1800284115/-/DCSupplemental.

Published online July 17, 2018.

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discovered within the cuprate family (18). Electronic structurecalculations indicate that sulfur substitution produces large effectson the charge-transfer energy and orbital distillation, providing aconcrete mechanism to distinguish between competing theories ofhigh-Tc superconductivity (17, 19–21). Nevertheless, experimentalrealization of La2CuO2S2 or La2CuO3S has never been reported,nor any related oxysulfide-containing copper(II). Here, we use insitu XRD measurements to examine this La2CuO4–xSx quaternarysystem to determine whether La2CuO3S and La2CuO2S2, whichwere predicted to be locally stable but globally thermodynamicallyunstable (17), actually form, and, if so, by which synthetic route.Our approach is to explicate the range of compounds that arepossible as sulfur is introduced into La2CuO4, to determinewhether S replaces O as a dopant, and at larger levels, whetherLa2CuO3S and La2CuO2S2, or perhaps other compounds, actuallyform experimentally. Establishing a quaternary-phase diagramconnecting La2CuO4 and La2CuS4 is a substantial undertaking, andwe will demonstrate here how effective in situ XRD measurementsare for accelerating this foundational synthetic task. An equallyimportant aspect of the in situ approach is that it allows us tomonitor the progress of the chemical reactions in detail, and todeduce reaction pathways under the actual experimental condi-tions. Combined with theory, this information opens the door to arole for predictive theory in exploratory synthesis. The increasingavailability of databases containing computational results on a widerange of materials, including their heats of formation, allows us theopportunity to compare the stabilities of the proposed targetcompositions against those of known compounds in the La–Cu–O–Schemical system. In this way, we aim to understand the energetics ofthe experimentally observed reactions. Combining the theoreticaland experimental studies, we have been able to explicate the ex-perimental challenges incumbent in synthesizing the theoreticalcompounds La2CuO3S and La2CuO2S2, or in general, copper(II)oxysulfides.

Results and DiscussionWe first conducted the synthesis of the parent compoundLa2CuO4 following the conventional solid-state reaction method(22). The mixture of La2O3 and CuO powders was heated up tohigh temperature while the reaction was monitored using in situXRD (23–25) as shown in Fig. 2. The diffraction patterns atroom temperature suggest that, instead of La2O3, La(OH)3 is pre-sent as the starting material, which is not surprising since La2O3 is

hygroscopic and it readily absorbs moisture from the uncured high-temperature cement, forming La(OH)3. Nevertheless, the presenceof La(OH)3 does not seem to affect the formation of La2CuO4. Atelevated temperature, La(OH)3 gradually loses water, first formingLaOOH, and then turning back to dry La2O3, as shown by thediffraction patterns. The formation of La2CuO4 is observed attemperatures above 860 °C, although raising the temperature above1,000 °C greatly accelerates the growth of La2CuO4, which is mostlikely due to the much faster diffusion of CuO at these temperatures(26). These observations are consistent with literature reports inwhich polycrystalline La2CuO4 powder is usually synthesized byfiring La2O3 and CuO powders at a temperature between 900 °Cand 1,100 °C (27, 28).The energy of formation of La2CuO4 from La2O3 and CuO

(ΔE = Eproducts − Ereactants) has been evaluated from the differenceof their total energies (Table 1). We note that, although mixingLa2O3 and CuO at elevated temperature is a well-establishedmethod for synthesizing La2CuO4, the computed reaction energyis actually positive (17), implying that the product is unstable withrespect to the binary oxides. It is plausible that the formation ofLa2CuO4 is driven by kinetics rather than thermodynamics. On theother hand, the small positive reaction energy, 51 meV/atom, isvery similar to estimates of the standard deviation of the differ-ence between computed and experimental reaction energies, ∼50meV/atom (29, 30). Finite temperature effects, possibly related tovacancies and configurational entropy, could also affect the overallenergies sufficiently to render La2CuO4 thermodynamically stable.While we cannot, for now, calculate these small energy differ-ences, theory and theory agree on the gross energetics of La2CuO4,and it seems likely that it is on the verge of being stable.We employ the same procedures to examine the solid-state

reactions aimed at producing the theoretical compound La2CuO3S.We first investigate the reaction pathway La2O2S + CuO =La2CuO3S, noted as proposal A in Table 1. The diffractionpatterns (Fig. 3A) are unchanged up to ∼760 °C, beyondwhich new diffraction peaks gradually appeared at Q ∼ 1.6 Å−1

(double peaks) and 2.1 Å−1, corresponding to La2O2SO4, andthe peak at Q ∼ 2.58 Å−1 corresponding to Cu2O, concomitantwith the weakening of the CuO and La2O2S peaks. Theweight fractions obtained from Rietveld refinements also in-dicate the gradual increase of La2O2SO4 and Cu2O, and thedecrease of La2O2S and CuO over the same temperaturerange. Above 1,000 °C, additional chemical reactions oc-curred, as new diffraction peaks from LaCuSO and La2O3appeared, while the starting material La2O2S and theintermediate-phase Cu2O were almost depleted. We are nowable to draw a stepwise reaction pathway for the reactions be-tween La2O2S and CuO at high temperature. La2O2S and CuOfirst react at ∼760 °C, forming La2O2SO4 and Cu2O (Table 1). Athigher temperature, the newly formed Cu2O reacts with theremaining La2O2S, forming LaCuSO and La2O3. The computedenergies of these two experimental reactions are both negative,indicating these are thermodynamically favorable reactions.

Fig. 1. Crystal structures of La2CuO4 and La2CuO2S2. (A) Crystal structure ofLa2CuO4 (K2MgF4 type), the parent compound of the first cuprate super-conductor. (B) Crystal structure of the theoretical compound La2CuO2S2,which is derived by replacing the apical oxygen in La2CuO4 with sulfur.Replacing one-half of the apical oxygen produces La2CuO3S.

Fig. 2. Synthesis of La2CuO4 from La2O3 and CuO powders, monitored by insitu powder XRD. At Left is shown the evolution of the diffraction peaks astemperature changes, and at Right is shown the weight fraction of eachphase determined from Rietveld refinements of the diffraction patterns.

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Reaction step 1, where La2O2S + 8 CuO = 4 Cu2O + La2O2SO4,has an especially negative energy, −197 meV/atom, which providesa large thermodynamic driving force for the forward reaction,compared with the proposed reaction La2O2S + CuO = La2CuO3S,which has instead a large positive energy, 182 meV/atom.It is important to point out that the chemical equations

reported here may not represent the entirety of the reactionsthat actually occur, since XRD is only sensitive to crystallinematerials. Reactions producing amorphous products or gases, orreactions involving moisture and/or oxygen that were acciden-tally introduced into the sample container, may not be entirelycaptured and may sometimes need to be deduced. For example,the experiment actually produced slightly more La2O2SO4 andless LaCuSO compared with the amounts that could have beenmade if the equations were strictly followed. This discrepancycould be readily explained if a small amount of La2O2S wasoxidized to La2O2SO4 by O2 in the sample tube, instead of byCuO (SI Appendix, Fig. S2). Nevertheless, the evolution of thediffraction patterns provides a clear and understandable accountof the main reactions in the La2CuO4−xSx system.We then tested the second theoretical reaction, proposal B,

where La2O3 and CuS were combined to form the theoreticalcompound La2CuO3S. As seen from Fig. 3B at temperaturesnear 450 °C, we notice the decomposition of CuS into Cu2S,followed by the appearance of La2O2S and La2O2SO4. Wepropose that S released from the decomposition of CuS reactsimmediately with La2O3, forming La2O2S and La2O2SO4. Thisproposal has been subsequently confirmed by conventionallaboratory-based synthesis where S and La2O3 powders werecombined, showing that the same products formed at hightemperatures. At temperatures above 860 °C, the intermediatephases La2O2S and Cu2S react, forming LaCuSO. The stepwisereaction pathways and the total reaction are summarized inTable 1 together with their computed reaction energies. Bothexperimental steps, 8 CuS + 4 La2O3 = 4 Cu2S + 3 La2O2S +La2O2SO4 and La2O2S + Cu2S = 2 LaCuSO, have negative re-action energies, which provide the driving force. Overall, thetotal reaction energy of this two-step process is negative, incontrast with the positive 266 meV/atom for the direct reactionLa2O3 + CuS = La2CuO3S that was theoretically proposed.Synthesis of the suggested compound La2CuO3S was also

attempted using La2S3 as a sulfur source (proposal C). From Fig.3C, it is clear that, at temperatures between 600 and 760 °C, the

weight fractions of La2S3, La2O3, and CuO drop simultaneously,concomitant with the appearance of the additional phases Cu2O,La2O2S, and La2O2SO4. It is not clear whether La2S3 is oxidizeddirectly by CuO, or if La2S3 first reacts with La2O3 to formLa2O2S, and then La2O2S is subsequently oxidized by CuO, sincethe additional phases appear simultaneously. Nevertheless, thenet reaction is the same for both reaction pathways, and theyboth have large negative reaction energies, as shown in Table 1.Above 760 °C, LaCuSO is formed by the reaction betweenLa2O2S and Cu2O, the same reaction as found in experiment A.Again, the total reaction has large negative reaction energy,−221 meV/atom, in sharp contrast with the positive 79 meV/atominvolved with the theoretical proposed reaction.Our experiments so far indicate that the theoretically pro-

posed syntheses for the formation of La2CuO3S are not realistic,and we have been able to use total energy calculations to explainthe energetically favorable outcomes that are observed in ourexperiments. Consequently, we adopted a broader charge for oursynthesis program, which is the examination of the compositionalspace, La2CuO4−xSx (0 ≤ x ≤ 4), with several aims: (i) if smalleramounts of S could be doped into La2CuO4; (ii) if higher con-centration of S in starting materials would facilitate the forma-tion of the theoretically proposed compounds; (iii) the existenceof any previously unreported ternary or quaternary compound.Eight different compositions (x = 0, 0.25, 0.5, 0.75, 1, 2, 3, and 4)have been screened using the in situ XRD method, and theproducts formed at different temperatures are identified andthen used in the construction of the nonequilibrium phase dia-gram displayed in Fig. 4. In general, no chemical reaction occursat temperatures below ∼600 °C (the light purple region), exceptthe changes among La2O3, La(OH)3, and LaOOH that we de-scribed earlier. As the temperature is raised above 600 °C, thereactions between La2S3 and CuO start, producing Cu2O andLa2O2SO4 as indicated in the yellow region in Fig. 4. The finalproducts produced at higher temperatures depend on the sulfurconcentrations x. In the O-rich region (green region, x < 0.25),the La2CuO4 phase is still among the list of products. However,refinements of the x = 0.25 data suggest that essentially all S hasended up in the product La2O2SO4, leaving none available for S-doping in La2CuO4. The quaternary product LaCuSO prevails inthe region of 0.75 < x < 3 (blue region), and when x is close to 3,additional phases LaCuS2 (31) and La3CuO2S3 (32) appear, andwhen x = 4, LaCuS2 and La2CuS4 (33) phases dominate. Except

Table 1. Comparison of reaction energies of the proposed and the experimental reaction pathways

Reaction Computed energy, meV/atom

Parent compound: La2O3 + CuO = La2CuO4 51 (17)Proposal A

La2O2S + CuO = La2CuO3S 182Experiment A

Step 1 (760–1,000 °C): La2O2S + 8 CuO = 4 Cu2O + La2O2SO4 −197Step 2 (1,000–1,100 °C): 2 La2O2S + Cu2O = 2 LaCuSO + La2O3 −54Total: La2O2S + CuO = 7=8 LaCuSO + 7=16 La2O3 + 1=8 La2O2SO4 + 1=16 Cu2O −118

Proposal BLa2O3 + CuS = La2CuO3S 266

Experiment BStep 1 (450–760 °C): 8 CuS +4 La2O3 = 4 Cu2S + 3 La2O2S + La2O2SO4 −43Step 2 (860–1,000 °C): La2O2S + Cu2S = 2 LaCuSO −22Total: La2O3 + CuS = 1=8 La2O2SO4 + 1=8 Cu2S + 3=4 LaCuSO + 1=2 La2O3 −37

Proposal C2=3 La2O3 + 1=3 La2S3 + CuO = La2CuO3S 79

Experiment CStep 1 (600–760 °C): 2 La2O3 + La2S3 + 24 CuO = 3 La2O2SO4 + 12 Cu2O −231or La2S3 + 2 La2O3 = 3 La2O2S La2O2S + 8 CuO = 4 Cu2O + La2O2SO4 −144

−197Step 2 (760–950 °C): 2 La2O2S + Cu2O = 2 LaCuSO + La2O3 −54Total: 2=3 La2O3 + 1=3 La2S3 + CuO = 1=8 La2O2SO4 + 7=8 LaCuSO + 7=16 La2O3 + 1=16 Cu2O −221

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for these overall observations, side-by-side comparisons of thereactions have also revealed several interesting aspects of thissystem. First, the oxidized product La2O2SO4 does not survivefor the full S range. When the sulfur concentration x < 2,La2O2SO4 grows into a better crystalline product at temperatureabove 800 °C (sharper peaks, as indicated by the peak split at Q ∼1.6 Å), and when x ≥ 2, La2O2SO4 transforms into La2O2S above800 °C. We speculate that the formation of La2O2SO4 involvestwo steps, where in the first step only an intermediate phase forms(noted as La2O2SO4* in Fig. 4) and the bona fide La2O2SO4 formsin the second step, during which the participation of La2O3 isrequired, as indicated by the chemical equations in experimentC. We conclude that the availability of La2O3 at above 800 °Cdetermines whether the final product is La2O2SO4 or La2O2S.The product lists shown in SI Appendix, Table S2 clearly sup-port this argument. Second, a different reaction pathway be-tween La2O2S and Cu2O has been revealed by the experimentwith x = 0.5. Instead of forming LaCuSO, we have observed theformation of Cu and La2O2SO4 from the reaction betweenLa2O2S and Cu2O in this experiment. The two differentchemical equations and their reaction energies are determinedto be the following:

2  La2O2S  +  Cu2O  =   2  LaCuSO 

+   La2O3ðΔE=−54 meV=atomÞ, [1]

La2O2S  + 4  Cu2O  =   8  Cu +   La2O3SO4ðΔE=−223 meV=atomÞ.

[2]

The validation of both reactions has been further corroborated byconventional laboratory syntheses (SI Appendix, Fig. S3). The rel-ative magnitudes of the reaction energies suggest that the secondreaction should always dominate. However, considering a startingcomposition of La2O2S and Cu2O in a 2:1 molar ratio, a largeamount of La2O2S would remain unreacted if the reaction fol-lowed Eq. 2. This will actually alter the reaction energy as follows:

2  La2O2S  +   Cu2O  =   2  Cu+14La2O2SO4  

+  74La2O2SðΔE=−73 meV=atomÞ.

Thus, we see that this reaction energy then is the same as that ofEq. 1, taking into account the accuracy of the DFT computa-tions. This explains the formation of LaCuSO when the molarratio of the starting compositions La2O2S/Cu2O is close or largerthan 2, which is the case for x > 0.75.Although multiple synthetic routes have been tested, it has not

been possible to synthesize the theoretical compound La2CuO3Sor La2CuO2S2, seemingly due to the formation of competingphases, namely, LaCuSO and La2O2SO4. To thoroughly evaluatethe thermodynamic stabilities of the theoretical compounds andthe competing phases, we have obtained the total energies of therelated elements, binary, ternary, and quaternary compounds.From this information, we have constructed the convex hull,which is the locus of formation energies for both known andtheoretical compounds. The thermodynamic stability of a com-pound can be evaluated by its energy relative to the hull, that is,

Fig. 3. Attempted syntheses for La2CuO3S, monitored by in situ powderXRD. (A) Synthesis from La2O2S + CuO. (B) Synthesis from La2O3 + CuS. (C)Synthesis from 2/3 La2O3 + 1/3 La2S3 + CuO. At Left is shown the evolution ofthe diffraction peaks as temperature changes, and at Right is shown theweight fraction of each phase determined from Rietveld refinements of thediffraction patterns. The weight fractions of La2O3, La(OH)3, and LaOOH aresummed and reported as the effective La2O3 weight fraction to make iteasier to track the evolutions of phases of interest. The colors indicate dif-ferent chemical compounds as follows: (B) black (La2O3), blue (CuS), red(Cu2S), yellow (La2O2S), cyan (La2O2SO4), and green (LaCuSO). (C) Black(La2O3), pink (La2S3), blue (CuO), red (Cu2O), cyan (La2O2SO4), yellow(La2O2S), and green (LaCuSO).

Fig. 4. Nonequilibrium phase diagram of La2CuO4−xSx (0 ≤ x ≤ 3). The phasediagram was obtained from identifying the crystalline products whileheating the mixtures of La2O3, La2S3, and CuO to high temperatures. Thereaction temperatures shown in the figure are contingent on the heatingrate ∼20 °C/min, because the systems were most likely not at equilibria withthis relatively fast heating rate. The diffraction data for x = 4 are not in-cluded in the figure, since the starting materials involve CuS, which showsdifferent thermodynamic property from CuO. Further details and the re-action pathways are provided in SI Appendix, Table S2.

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the energy difference between a compound and the set of themost stable compounds with the same averaged chemical com-position (34). A positive energy above the hull indicates that thecompound is unstable, and there is a thermodynamic drivingforce for it to decompose into two or more stable compounds.Conversely, a negative energy below the hull suggests a stablecompound. The blue points in Fig. 5A present the known com-pounds in the La–Cu–O–S quaternary system, which all havenegative energies. The theoretical compounds La2CuO3S andLa2CuO2S2 have large positive energies above the hull, 324 meV/atom(by decomposing into La2O2S, Cu, and La2O2SO4) and 232 meV/atom(by decomposing into La2O2S and CuS), suggesting that both arethermodynamically unstable. As expected, the products thatappear in our syntheses are stable, having a negative energywith respect to the hull (Fig. 5B). While metastable solid phasessuch as La2CuO4 (17) and La8Cu7O19 (35) certainly exist andcan be readily synthesized, these compounds are in generalcomputed to have total energies that are about 50 meV/atomabove the hull energy, in sharp contrast with the large values forLa2CuO3S and La2CuO2S2.The ability to track the reaction pathways that culminate in the

formation of La2CuO4 and LaCuSO at high temperatures, andthe decisive absence of the theoretically proposed compoundsLa2CuO3S and La2CuO2S2, make it very clear that the un-derlying mechanism that controls the reactions is a redox re-action that transforms Cu2+ to Cu1+, or even Cu0, in thepresence of S2−. While the experimental reaction pathwaysshown in Table 1 all have a reaction energy that is negative, theinitial, low-temperature steps of the chemical reactions generally

have particularly large negative reaction energies (−197 meV/atomin experiment A and −231 meV/atom in experiment C), suggestinga large thermodynamic driving force for these reactions. Byexamining these reactions, we notice that these are redox re-actions between Cu2+- and S2−-containing compounds, that is,La2O2S + 8 CuO = 4 Cu2O + La2O2SO4 for experiment A and8 CuS + 4 La2O3 = 4 Cu2S + 3 La2O2S + La2O2SO4 for ex-periment B. At intermediate temperatures (500–760 °C), wellbelow the formation temperature of La2CuO4, the Cu2+-con-taining compound reacts with the S2−-containing compound,changing their oxidation states to Cu1+ and S6+ (as in sulfateSO4

2−), respectively. Note that, for the proposed La2CuO3Sand La2CuO2S2, the oxidation state of Cu is Cu2+ and theoxidation state of sulfur is S2−. The inability to realize these desiredoxidation states seems to be the essential reason why S-dopedLa2CuO4 cannot be made by high-temperature solid-state synthe-sis. This suggests that, low-temperature synthesis, for example,introducing a flux or hydrothermal synthesis, may be a more suc-cessful synthetic route (36, 37) to avoid the redox reaction betweenCu2+ and S2.The overwhelming weight of experimental and theoretical

evidence suggests that the theoretical compounds La2CuO3S andLa2CuO2S2 are unlikely to be realized via conventional solid-state synthesis (22), due to their formidable thermodynamic in-stabilities. It is interesting to note that a similar outcome wasobserved (15) for ternary Cu–S compounds, although in thesecompounds S–S bonding is thought to be the driving force thatproduces monovalent Cu at high temperatures. At the sametime, our experiments demonstrate most eloquently the power ofin situ XRD synthesis as a way to articulate reaction mechanismson a step-by-step basis. Typically, all that is known is the out-come of a reaction, a situation that is particularly unenlighteningif a synthesis experiment does not produce desirable products.The in situ XRD measurements allow us to observe how thereactants break down, how they dissolve in a flux, and how newcompounds form on both heating and cooling. This informationcan be used to tailor syntheses to avoid unwanted intermediatephases that can compete with the desired compound and todevelop alternative synthetic strategies that may be more suc-cessful. It can identify underlying mechanisms, such as the redoxreaction that is central to the stability of CuO and CuS com-pounds that will block certain reaction pathways, informationthat may have more general applicability in related classes ofmaterials. Combining the in situ XRD measurements with cal-culations of the total energies for both the desired products aswell as competing compounds has the potential to take “theory-assisted synthesis” to a new level by connecting realistic synthesisto predictive theory. In the long run, the accumulated knowledgeon chemical reactions obtained from in situ XRD measurementscould also be used as an input in computation for in silico syn-thesis to predict viable synthetic routes.

ConclusionsIn this contribution, we have presented our investigation on theLa2CuO4−xSx quaternary system using combined experimentaland computational methods to test whether the theoreticalcompounds La2CuO3S and La2CuO2S2 could be synthesized.Using in situ XRD measurements, the synthetic obstacle toforming these compounds has been identified, which is the redoxreaction between the Cu2+- and S2−-containing starting materialsthat drives them away from the desired oxidation states. Thisincompatibility of the starting materials has also been well de-scribed by the DFT calculations, which have shown large, neg-ative reaction energies for these redox reactions. Although theattempts to experimentally realize the theoretical compoundsare not successful, this study has shown consistency betweenexperiment and computation. This suggests that one could in-tegrate theory and experiment in a closed loop in exploratorysynthesis, where theory could identify theoretical desired mate-rials that are thermodynamically stable, and in situ XRD syn-thesis could be used to pinpoint the feasible synthetic routes.

Fig. 5. Thermodynamic instability of the theoretical compounds La2CuO2S2and La2CuO3S. (A) Convex hull of the La–Cu–O–S quaternary system. (B)Energy above hull of La2CuO2S2 and La2CuO3S in comparison with thoseoccurring in syntheses. The gray region, ±50 meV/atom, shows the probableinherent uncertainty from computation.

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This approach may have potential to advance our knowledge onreaction mechanisms involving the formation of extended solidsand to accelerate materials discovery.The ultimate aim of Materials by Design schemes is to predict

the existence of a new material with specific properties andfunctionality, with a theoretical accuracy that is high enough toensure that the material exists and has the desired properties (38,39). We have shown here that current theoretical accuracy is notyet sufficient in the prototypical correlated oxide La2CuO4 topredict thermodynamic stability, since the strength of correla-tions, thermal effects, and small structural variations such asvacancies are all comparable to the overall accuracy of the totalenergy calculations. The inverse problem, which is to predict newcompounds based on desired functionality, rests on the de-termination of their global stability, that is, whether a compoundis stable against decomposition into other compounds native tothe compositional phase diagram. This is a question that iscentral to synthesis, namely, if the theoretically proposed com-pound can actually be made. Given that synthesis is very de-manding of time and resources, it would improve the successfulconvergence of the synthesis process if theoretical predictions ofnew compounds were to include possible synthesis routes. In-deed, we point out that there is at present very little, if any, re-search into the synthesis pathways in correlated systems like thecuprates. There is great potential for this type of investigation,and the work reported here shows how the in situ experiments

reveal the details of the reactions, step by step, and by comparingto theory, explicate or potentially establish the associated chemicalrules. When applied to new systems, this development would leadto a much deeper understanding of the principles governingchemical reactions themselves, and how they can be practicallyexploited to accelerate the discovery of new materials.

MethodsThe in situ high-temperature powder XRD experiments were conducted atbeamline 6-ID-D at the Advanced Photon Source (APS), Argonne NationalLaboratory, and at beamline 28-ID-2 at the National Synchrotron Light SourceII (NSLS II), Brookhaven National Laboratory. We performed DFT calculationson our target compounds, using the generalized gradient approximation asimplemented within VASP (40–43) and projector augmented wave potentials(44, 45). More details can be found in SI Appendix.

ACKNOWLEDGMENTS. H.H. thanks the 6-ID-D beamline staff at the APS andthe X-ray powder diffraction beamline staff at the NSLS II for their supportand useful discussion. Work at Texas A&M University was supported byWelch Foundation Grant A-1890-20160319. C.-H.Y. and G.K. were supportedas part of the Center for Emergent Superconductivity [US Department ofEnergy (DOE), Office of Basic Energy Sciences Award DEAC0298CH1088]. Thisresearch used resources of the APS, a US DOE Office of Science User Facilityoperated for the DOE Office of Science by Argonne National Laboratoryunder Contract DE-AC02-06CH11357, and at the NSLS II, a US DOE Officeof Science User Facility operated for the DOE Office of Science by Broo-khaven National Laboratory under Contract DE-SC0012704.

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