Phase diagram, structure and properties

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Conceptual design of yttrium oxyhydrides: Phase diagram, structure and properties Aleksandr Pishtshev, Evgenii Strugovshchikov, and Smagul Karazhanov Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b01596 • Publication Date (Web): 11 Apr 2019 Downloaded from http://pubs.acs.org on April 16, 2019

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Crystal Growth & Design

Conceptual design of yttrium oxyhydrides: Phase diagram, structure and properties Aleksandr Pishtshev,∗,† Evgenii Strugovshchikov,† and Smagul Karazhanov‡ †Institute of Physics, University of Tartu, Tartu, Estonia ‡Department for Solar Energy, Institute for Energy Technology, Kjeller, Norway E-mail: [email protected]

Abstract The synthesis of stable yttrium oxyhydride-type compounds raised a principal question regarding the key factors that may be responsible for formation routes and structural features of these attractive materials. For solving this challenge the interplay between chemical composition and crystalline architectures has been theoretically explored via modeling structural transformations caused by the gradual oxidation of the host metal-hydride system. The close combination of group-theory methods, mixedanion chemistry arguments, and relevant DFT calculations provided us with the opportunity to suggest and characterize the candidate models for most probable stoichiometric versions of yttrium oxyhydrides. The predicted chemical compositions along with the crystallization results have been summarized in the phase diagram. It is shown that the cation-ligand interaction governs the structural stability which is achieved by matching favorable crystallographic positions of the oxygen and hydrogen atoms at the metal center.

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Introduction Recently, a strong effect of the reversible switching of optical properties in a response to illumination has been observed in thin films of incompletely oxidized yttrium- 1–6 and several rare-earth- (Gd, Dy, and Er) 7 hydride systems. A crystal chemical classification of the photochromic oxygen-containing hydride films relates them to advanced multianion materials called oxyhydrides 8–11 in which oxide and hydride anions are sharing the common chemical space within the crystal lattice. Further examination of experimental data on yttrium oxyhydrides raised a principal question of which factors of the oxidation process may promote solid-state crystallization, and which variables may manipulate the formation of solid phases with the different chemical compositions. First theoretical work 12 has shown that a reduction of hydrogen content in the oxygen-hydride system leads to changes in structural properties via the modulation of a local configuration of oxide and hydride anions around the metal center. One may therefore conjecture that in collective assembly of a mixed-anion compound, such reconfiguration could offer a certain flexibility in regulation of the H – –O2 – exchange-ability via valence charge states of the metal center. We will consider this feature as playing a main role in the formation of stable stoichiometric versions of oxyhydrides. In context of modeling of the controllable oxidation, without loss of generality, we can further assume that the mixed yttrium-hydrogen-oxygen crystalline superstructure can be chosen as a starting system for the simulation of experimental situations. Theoretical investigation of the chemical evolution of oxygen accommodations in such model has an advantage in the sense that easy reconfigurability and scalability of the system space can allow us to manipulate the formation of several structural frameworks more straightforwardly in terms of cation and anion orderings. Thus, the main aim of the present work is to study from first-principles in which ways the inserted oxygen may govern the spatial separation of the Y – H and Y – O bonding channels to afford a set of stable lattice geometries. Our goal is to determine oxygen-driven trends of structural transformations that could result in a number of ternary systems with the composition depending on the O2 – /H – anion ratio. 2


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Results and discussion The conceptual design and multiscale simulation model used in the present research follow the general scheme of crystal structure prediction developed in previous works of Pishtshev and co-workers. 13–15 The central part of our study was focused on the finding of the stable chemical compositions and lattice geometries on the base of modeling structural transformations caused by anion exchange. The theoretical screening was based on the following design steps: First, by projecting the chemical space onto cubic crystallographic space spanned by yttrium, hydrogen, and oxygen we constructed a high-symmetry (transformation-oriented) prototype superstructure of oxyhydride system. Second, in order to test a range of lattice geometries with different compositions (driven by direct manipulation of the O/H stoichiometric ratio) we employed such features of the proposed superstructure as the discrete topology with regular metric, a variety of empty sites and interstitials, and enhanced reconfiguration/reconnection capabilities. In implementation of predictive/modeling algorithms, the objective was to take into account a maximum feasible number of reducible compositionstructure configurations. Lastly, the subsequent computational simulations provided a set of possible atomic arrangements associated with particular (terminal) points in which the oxidation process is terminated; their preliminary selection was performed by means of an energy-structure analysis. The final choice was made on the base of stability investigations. The main our finding is that by simulating oxygen-mediated structural evolution of the yttrium-hydride model we have predicted a large number of stable crystalline phases for the arbitrary Y – H – O system. Results presented in Figures 1 – 5, and Tables 1 – 5, encompass ten Yl Hm On -type compositions comprising seventeen stoichiometric solid phases which are stable to further oxidation. The datasets on the structural and physical properties of the given yttrium oxyhydrides are summarized in Supporting Information (SI). In particular, the information containing in Table S18 of SI (components of the elasticity tensor), Table S19 of SI (eigenvalues of the elasticity tensor), and Tables S20–S36 of SI (zone-centered harmonic vibrational modes) reflects structural stability of the systems listed in Table 1. To expand 3



Figure 1: The Y – H – O compositional triangle in terms of the Y, H, and O atomic variables. The predicted phase diagram presents the most probable ternary compositions which are marked by and numbered from 1 to 10. The crystallographic description of equilibrium solid phases is given in Tables 1 and 2. The orange dashed lines connect end members Y2 O3 , YO, YH2 , YH3 , Y(OH)3 and YO(OH). Their choice as key nodes reflects the constraints imposed by the +2 and +3 charge states of yttrium. The union of intersections shown as a solid pentagon represents the region of potential stability. The yellow dashed line connecting Y2 O3 and YH3 corresponds to a homologous series Y(2n+m)/3 Hm On (see text). Stoichiometries classified in Table 4 as stable and metastable are outlined by green and red edges, respectively. our examination on the important aspects of the thermodynamic stability we investigated the action of heat on the predicted crystal structures. That is, to test a destabilization role of heating, we evaluated the thermal stability of the crystal phases in terms of thermal motions of ions by means of ab initio molecular dynamics simulations. Shown in Figures S1 - S17 of SI are the PDF profiles of most critical bond connections; their structural evolution has been simulated over the temperature range 5 – 100 K. The overall region of stability depicted in Figure 1 as a solid pentagon presents a wide selection of possible elemental (node) connectivities with which various matching composi-

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Table 1: Overview of the predicted crystal chemical parameters of 17 structural phase in which the Y – H – O system may crystallize. Collation order corresponds to numbering of the compounds presented in Figure 1. In the last column, the quantity ∆E denotes the formation energy which corresponds to energetics of decomposition reaction on the constituting elements. No Chem. 1 2

Space

formula group Y4 H10 O P -43m (215) Y2 H4 O P m (6)

Y2 H3 O

4

Y2 H2 O

5

Y4 H6 O3

6

Y4 H4 O3

7

YHO

O/H

Z

Lattice constants (˚ A)

type cubic

ratio (f.u.) a 0.1 1 5.230

b 5.230

monoclinic

0.25

1

3.677

ortho- 0.25 rhombic

2

3.606

6.453

0.25

3

3.676

0.33

2

0.5

V ˚3

V/Z Density ˚3

∆E

3

c (A ) (A ) (g/cm ) (kJ/mol) 5.230 143.03 143.03 4.43 −1359.0 4.44

−847.4

6.519 151.69 75.85

4.33

−841.2

3.676

18.542 216.99 72.33

4.54

−870.1

5.269

5.269

5.269 146.28 73.14

4.47

−814.8

2

5.300

5.300

5.182 145.56 72.78

4.47

−723.5

0.5

2

12.430

4.42

−2148.1

0.75

1

3.843 6.529 307.71 153.86 (β = 99.37◦ ) 5.248 5.248 5.454 150.21 150.21

4.51

−1978.9

1.00

4

5.292

5.292

5.292 148.20 37.05

4.75

−661.5

P nma (62)

ortho- 1.00 rhombic

4

7.538

3.767

5.328 151.29 37.82

4.65

−660.3

R-3m (166)

trigonal 1.00

6

3.773

3.773

18.596 229.26 38.21

4.60

−656.7

P mn21 (31)

3

Phase

R3m tri(160) gonal P n-3m cubic (224) P 42/nnm tetra(134) gonal Cm mono(8) clinic P -42m tetra(111) gonal F -43m cubic (216)

3.724 5.409 74.00 74.00 (β = 92.35◦ )

P 4/nmm tetra(129) gonal

1.00

2

3.303

3.303

5.972 65.15 32.58

5.40

−652.9

P -43m (215)

cubic

1.00

4

5.385

5.385

5.385 156.16 39.04

4.50

−648.7

tetragonal cubic

1.00

2

7.542

7.542

5.315 302.33 151.16

4.65

−2634.0

1.67

1

5.361

5.361

5.361 154.08 154.08

4.73

−2785.2

tetragonal tetragonal

2.00

1

5.369

5.369

5.184 149.43 149.43

4.69

−2373.0

2.50

1

5.364

5.364

5.319 153.04 153.04

4.75

−2915.0

Y4 H4 O4 P 4/nmm (129) 8 Y4 H3 O5 P -43m (215) 9 Y2 HO2 P -42m (111) 10 Y4 H2 O5 P -42m (111)

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Table 2: Overview of the shortest interatomic distances evaluated for the structures of Table 1. The last column presents a structural check on a total absence of the hydroxide anion. The quantities δ(YO) and δ(YH) measure the differences of Y – O and Y – H equilibrium bond lengths with respect to the characteristic bond distances 2.167 ˚ A for Y2 O3 and 2.271 ˚ A for YH2 , respectively. Their statistics is characterized by the normal distributions shown in panels C and D of Figure 2. The individual bond orders of contact pairs, v(YO) and v(YH), have been calculated according to the bond valence method 16,17 with the standard Ro and B empirical values given in Ref. 18. Chemical formula Y4 H10 O Y2 H4 O Y2 H4 O Y2 H4 O Y2 H3 O Y2 H2 O Y4 H6 O3 Y4 H4 O3 YHO YHO YHO YHO YHO Y4 H4 O4 Y4 H3 O5 Y2 HO2 Y4 H2 O5

Structure

Y – O δ(YO) v(YO) Y – H δ(YH) v(YH) H – H O – H (˚ A) (˚ A) (˚ A) (˚ A) (˚ A) (˚ A) P -43m 2.291 0.124 0.473 2.256 −0.015 0.343 2.135 2.615 Pm 2.244 0.077 0.537 2.165 −0.106 0.439 2.021 2.536 P mn21 2.206 0.039 0.595 2.134 −0.137 0.477 2.069 2.537 R3m 2.272 0.105 0.498 2.166 −0.105 0.437 2.064 2.561 P n-3m 2.282 0.115 – 2.282 0.011 – 2.635 2.635 P 42/nnm 2.278 0.111 – 2.278 0.007 – 2.591 2.650 Cm 2.150 −0.017 0.692 2.240 −0.031 0.356 2.128 2.488 P -42m 2.216 0.049 – 2.277 0.006 – 2.727 2.624 F -43m 2.292 0.125 0.472 2.292 0.021 0.311 3.742 3.742 P nma 2.243 0.076 0.539 2.307 0.036 0.299 2.428 2.679 R-3m 2.245 0.078 0.536 2.305 0.034 0.300 2.532 2.679 P 4/nmm 2.316 0.149 0.442 2.268 −0.003 0.332 2.336 2.673 P -43m 2.174 0.007 0.649 2.389 0.118 0.239 2.693 2.693 P 4/nmm 2.233 0.066 0.553 2.327 0.056 0.283 2.430 2.660 P -43m 2.207 0.040 – 2.362 0.091 – 3.791 2.681 P -42m 2.353 0.078 – 2.340 0.069 – 3.796 2.592 P -42m 2.204 0.037 0.598 2.319 0.048 0.289 3.793 2.660

tions can be assembled. As expected, given the l × m × n ternary assemblage, the condition of electroneutrality affords stoichiometry in terms of the integralness of l, m and n numbers. As discussed in Ref. 12 the metal substructure of yttrium hydride exhibits no chemical resistance to binding with incorporating oxygen. In this case, displacements of H – by oxygen with subsequent abstractions from Y3+ sites can be characterized as a homolytic cleavage process. Accordingly, the incorporation and accommodation of oxygen in the hydride lattice can be considered as a homolytic substitution. That is, the introduction of oxygen results in the formation of partially-oxidated compounds that may be represented in terms of homologous series. In particular, regardless of any integers m and n in the composition Yl Hm On , one can reveal that, depending on the linkage combination of m and n, the most part of 6


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condensed phases described in Figure 1 and Table 1 can be grouped into two homologous series. The points lying along the yellow dashed line in Figure 1 correspond to a range of compositions obeying the chemical formula of a series Y(2n+m)/3 Hm On . The other homologous series given by the formula Y(4n+2m)/5 Hm On comprises the points of Figure 1 numbered 3, 6, and 9. The compound, Y2 H2 O, labeled by 4 in Figure 1, is a member of one more series Y(2n+m)/2 Hm On which represents a compositional assembly based on points of the pentagon longest edge connecting the neighboring pair of vertices YO and YH2 . In the chemical context, one can also emphasize the other remarkable feature of the predicted phase diagram of the Y – H – O system. We note that in Figure 1 the noticeable part of the area of potential compositional stability is limited by the line of oxides-hydroxides. Obviously, this boundary constraint implies that the formation of hydroxide anions will be critical for the synthesis of oxyhydrides. The entry 1 of Table 1, Y4 H10 O, represents the stable stoichiometric version of oxyhydride with the least content of oxygen. It was initially suggested and characterized in our previous work 12 in terms of a defect superstructure. In the present study, the ordered structure has been unambiguously adjusted to noncentrosymmetric space group P -43m, and the main properties of Y4 H10 O have been re-investigated in more detail. Indeed, we made a comparative fitting of the experimental diffraction data for the transparent-semiconducting Y – H – O thin films 2 to the proposed model of the P -43m symmetry. What is noteworthy in the given comparison is that these films may be regarded as having the chemical composition Y4 H10 O and adopting the cubic P -43m structure. That is, this result may serve as an experimental identification of point 1 on the phase diagram of Figure 1. A comprehensive description of macroscopic elastic and plastic properties is presented in Table 3 for a range of compositions determined by O/H ratio. One can see that the mechanical properties and corresponding limitations closely resemble those observed for the microstructure of typical ion-covalent or metallic materials. This not only emphasizes the structural validity of predicted phases for different oxyhydride compositions, but also gives

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us a certain freedom at making accurate evaluations/interpretations of several intrinsic physical and chemical properties in terms of the Gr¨ uneisen parameter, the Debye temperature, and the Vickers hardness. In the context of performance characteristics, this freedom suggests, for instance, that the hardness is especially interesting in analyzing the stress-driven factors that determine wear-resistance behavior. Moreover, regardless of the nearly same level of aggregate characteristics the proposed crystalline structures demonstrate the interesting feature relating to enhanced values of the Gr¨ uneisen parameter which turns out to be especially high for metallic oxyhydrides (Table 3). Obviously, this feature reflects the presence of the characteristic anharmonic interactions caused by fast-changing charge-density fluctuations; they are operative because the amount of incorporated oxygen atoms is not yet sufficient to effectively restrict quantum-mechanical movements of hydrogen. Focusing further on the fact that large values of the Gr¨ uneisen parameter reflect the strong intrinsic anharmonicity, we tested how the microstructure features affect lattice transport properties. The objective was to analyze the level of reduction of the bulk thermal conductivity (due to lowering the phonon mean-free path) in the anharmonic lattice. The effect was simulated in high-temperature limit on the base of two effective medium model approximations. 22,23 The results are presented for insulating systems in Table 3 in terms of minimum thermal conductivity κmin . Depending on the content of oxygen the estimates of κmin range from 1.07 to 1.80 Wm−1 K−1 which may be indicative of slow phonon transport similar to that of the standard thermal barrier material like YSZ ceramic. 24 That is, because of low heat conduction the proposed oxyhydride compositions cannot easily transfer heat at high temperatures. Interestingly, this is one of particular attributes of an engineering material. The examination of standard formation energies (shown in the last column of Table 1) indicates that the proposed structures of ternary combinations are enthalpically stable with respect to their decomposition into the simple elements. The energetics of spontaneous decomposition into binary products is outlined in Table 4. Further, we performed a comparative analysis of compositional representations of the phase diagram in order to recognize

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Table 3: Aggregate properties evaluated for the crystal structures of Table 1. The bulk (B), shear (G), and Young’s (E) moduli are given in the Hill approximation. 19 The relation G/B denotes Pugh’s ratio, and ν is Poisson’s ratio. The values of the Vickers hardness HV have been evaluated from the model relations of Refs. 20,21. The last column contains numerical estimates of the high-temperature phonon thermal conductivity calculated on the base of Clarke model 22 and Cahill model, 23 respectively, and presented for the insulating systems in terms of a minimum value κmin . The abbreviations: ins=insulator, met=metal. Chem formula Y4 H10 O Y2 H4 O Y2 H4 O Y2 H4 O Y2 H3 O Y2 H2 O Y4 H6 O3 Y4 H4 O3 YHO YHO YHO YHO YHO Y4 H4 O4 Y4 H3 O5 Y2 HO2 Y4 H2 O5

Structure

Grnd state P -43m ins Pm ins P mn21 ins R3m ins P n-3m met P 42/nnm met Cm ins P -42m met F -43m ins P nma ins R-3m ins P 42/nnm ins P -43m ins P 42/nnm ins P -43m met P -42m met P -42m ins

E (GPa) 170.6 127.3 136.1 151.7 134.5 117.8 127.6 140.6 187.2 168.1 149.8 226.8 147.7 168.4 146.9 146.5 126.9

B G G/B ν HV γ ΘD κmin (GPa) (GPa) (GPa) (K) (W/mK) 97.8 70.6 0.72 0.21 13.5/12.9 1.83 619 1.65/1.80 78.7 51.7 0.66 0.23 9.3/9.3 2.15 513 1.33/1.45 91.1 54.4 0.60 0.25 8.3/8.7 2.52 529 1.37/1.50 96.1 61.3 0.64 0.24 10.1/10.2 2.26 557 1.46/1.60 101.4 52.6 0.52 0.28 6.4/7.2 3.18 494 – 92.6 45.7 0.49 0.29 5.2/6.2 3.44 435 – 97.8 49.7 0.51 0.28 5.9/6.8 3.29 488 1.24/1.37 99.3 55.6 0.56 0.26 7.6/8.2 2.81 486 – 125.3 74.8 0.60 0.25 10.7/10.9 2.52 567 1.41/1.54 117.5 66.6 0.57 0.26 7.4/8.1 2.74 538 1.33/1.46 110.2 58.8 0.53 0.27 7.4/8.1 3.03 507 1.25/1.38 137.2 92.6 0.68 0.22 14.9/14.5 2.05 616 1.58/1.72 103.9 58.5 0.56 0.26 8.0/8.5 2.78 507 1.24/1.36 120.0 66.5 0.55 0.27 8.7/9.2 2.85 538 1.33/1.47 117.7 56.8 0.48 0.29 6.1/7.0 3.57 492 – 108.5 57.5 0.53 0.27 7.2/7.9 3.07 471 – 99.5 49.3 0.50 0.29 5.6/6.5 3.43 444 1.07/1.19

non-trivial indicators that might be critical to the chemical stability. The key point was to assign the common region of potential stability. By laying out the possible superpositions and intersections of the main decomposition trends we graphically represented this area in Figure 1 as a solid pentagon. It is noteworthy that such configuration of the composition domain, compiled in terms of decomposition constraints has brought together all the chemical formulas derived in this work by virtue of crystal chemical modeling and DFT-based simulations. Clearly, this fact confirms the full consistency of our theoretical results. The next issue stems from the fact that oxygen can be readily incorporated into metalhydride systems in noticeable amounts 1 In Ref. 12, the H–O exchange possibility, and the activation of Y – O bonding were explained by a high selectivity of the dissociated oxygen atoms which is governed by the metal center. In this context, our interest was to investigate 9



Table 4: Table 1.

Decomposition reaction enthalpy ∆H0 calculated for the crystal structures of Chemical formula Y4 H10 O Y2 H4 O Y2 H4 O Y2 H4 O Y2 H3 O Y2 H2 O Y4 H6 O3 Y4 H4 O3 YHO YHO YHO YHO YHO Y4 H4 O4 Y4 H3 O5 Y2 HO2 Y4 H2 O5

Structure

Decomposition ∆H0 products (kJ/mol) P -43m Y2 O3 , YH3 −250.2 Pm Y2 O3 , YH3 −58.9 P mn21 Y2 O3 , YH3 −52.7 R3m Y2 O3 , YH3 −81.7 P n-3m Y2 O3 , YH3 , Y −79.9 P 42/nnm Y2 O3 , YH3 , Y −41.7 Cm Y2 O3 , YH3 −102.7 P -42m Y2 O3 , YH3 , Y −40.7 F -43m Y2 O3 , YH3 −33.1 P nma Y2 O3 , YH3 −31.9 R-3m Y2 O3 , YH3 −28.3 P 4/nmm Y2 O3 , YH3 −24.5 P -43m Y2 O3 , YH3 −20.3 P 4/nmm Y2 O3 , YH3 −120.4 P -43m Y2 O3 , YH3 , H2 +197.1 P -42m Y2 O3 , YH3 , Y +33.8 P -42m Y2 O3 , YH3 +66.4

the effect of modulation of chemical connections caused by Y – O entities. As it appears from Figure 2, the formation of oxyhydride phases is accompanied by the lattice expansion which begins to grow continuously even with low oxygen content. The expansion can be attributed to a tendency observed in a number of stoichiometric compositions for the Y – O separation to increase gradually with the rising O/H ratio (panel A of Figure 2). One can see that incorporation of more oxygen does not destroy the linear behavior of both trends, but by elongating the bond distances makes the Y – O and Y – H bondings weaker (panel B of Figure 2). On the other hand, when considering transformations of the lattice geometry needed to equilibrate the Y – O and Y – H interactions, just the strong effect of symmetrylowering oxygen and hydrogen displacements may be thought of as holding the general patterns of oxyhydride phase structurally stable. We can characterize this fact by a graphical representation of the composition-dependent variations in Y – O and Y – H distances with respect to the parent compounds Y2 O3 and YH2 (panels C and D of Figure 2, and Table 2). The normal character of both distributions implies that the elongation of Y – O distances, 10


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Figure 2: Analysis of the composition-dependent variability of bond distances. The data points are taken from Tables 1 and 2. (A) The Y – O bond length–O/H ratio linear regression (bottom plot in dark green) along with the illustration of the lattice expansion vs O/H ratio shown for cubic phases (top plot in dark blue). The zero point of horizontal axis corresponds to the cubic YH2 with a = 5.203 ˚ A. 25 (B) The v(YO)–δ(YO) (in red) and v(YH)–δ(YH) (in blue) linear dependences. (C)&(D) The normal distribution of histogrammed data for linear changes in the Y – O and Y – H contacts. The histograms are indicated in red and blue, respectively. The distribution characteristics are shown in the top-left corner. and the change of Y – H contacts are well-bounded above and below. Consequently, the bond-lengths renormalization occurred due to partial oxidation of the metal-hydride system does largely have a neutral effect in the proposed compositions and crystal phases. However, at a higher ratio of O/H, due to the increased activity of Y – O connections, Y and O tend to be bound in a way that leads to the formation of pure oxide phases. Accordingly, the overall strengths of the actual binding interactions become weaker, and as indicated in Table 4, the oxyhydride system does lose thermodynamical stability with respect to the solid-phase decomposition. It is also interesting that, although with decrease of hydrogen content the Y/H ratio can

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vary from 0.4 to 2 across the whole range of oxyhydride ternary compositions, just the totally symmetric case of Y/H= 1 is of frequent occurrence in possible routs of crystallization. The effect of sensitivity to H (i.e., the variation of metal-hydrogen bonds upon partial oxidation) correlates directly with the considerable fluctuations of the Y – H bond distances as illustrated in Table 2 and Figure 2 (panels B and D) for the trend of proposed geometries of Table 1. According to the data of Table 4, the crystallization of chemical compositions with the particular Y/H and O/H ratios greater than 1 (i.e., when a stoichiometric formula of yttrium oxyhydride contains more than one Y per H along with more than one O per H), leads to the formation of metastable and mostly soft crystal phases. Therefore, values of these ratios, Y/H and O/H, may be considered as indicators of the composition effect because they characterize the general space of the phase stability of ternary oxyhydride compounds in terms of the following inequalities: Y/H < 4/3 and O/H < 1.31. Illustratively, the stability-metastability sharing scheme is symbolically sketched in Figure 3. Another structural feature of yttrium oxyhydrides is a fairly large interatomic distance between neighboring hydride anions. From a qualitative point of view, the corresponding explanation was given in previous work. 12 The same reasoning is applicable to a more general case. From Table 2, where we compared the length of H – H contacts for a larger number of proposed compounds and crystal structures, one can see that in most cases the H – H separations satisfy Switendicks criterion 26,27 (lH−H > 2.1 ˚ A). One exception is the bonding situation in the hydrogen-rich compound Y2 H4 O with the largest lH−H = 2.069 ˚ A. Here, the contraction of the H – H spacings is associated with the local reconfiguration of coordinating yttrium and neighboring hydrogens and oxygens; that is, as a certain amount of oxygen is accommodated, the difference of metal-hydrogen and metal-oxygen couplings is equilibrated via the spontaneous enhancement of the repulsive character of H – H interactions. Figure 4 presents structural motifs of the proposed compounds in terms of various polyhedral rationalizations of polyanionic units. The distinctive feature of structure types in which the given compositions are crystallizing is that their characteristic building units are more or

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Figure 3: Illustrative separation scheme for yttrium oxyhydrides. The vertical line describes O/H exchange degree. The boundary line of stability corresponding to the critical ratio O/H= 1.31 separates into the stable (below) and metastable (above) compositions. This value has been evaluated by considering energetics of the calculated phase diagram of the Y – H – O system. Polar (pyroelectric) phases are shown in red, the systems without inversion center are shown in blue. less related to a prototype fcc-superstructure. The 3D crystal framework of these compounds ranges through high-symmetry to low-symmetry lattice geometries; however, all of them can be classified within an appropriate layered architecture capable to locate various amounts of oxygen. Depending on the ordering of anionic units, some of the considered structures display more complex solid state constitution distinguishing by such indicative factors as the coordination geometry, polyhedral environment and linkage, layers configuration and a set of stacking sequences. Based on the valence electron counts and DFT calculations one can ascertain that depending on the O/H ratio, the ground state of these structures exhibits either insulating or metallic character. Also, as highlighted in Table 4 and Figure 4, the O/H ratio is responsible for the different levels of stability of the polyhedral framework; in the particular case of oxygen-rich/hydrogen-poor ternary compositions, the architecture of

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Figure 4: Comparison of the layered crystal structures predicted for different yttrium oxyhydride compositions. Y – green, H – blue, and O – red spheres. The three-dimensional framework is rendered in terms of face-, edge-, and corner-sharing linkages of Y – H – O polydedra. All layers are stacked along the c axis. yttrium oxyhydride is thermodynamically unstable with respect to the decomposition to binary compounds Y2 O3 and YH3 . The other peculiarity can be seen by analyzing geometrical representations of equilibrium atomic positions (Tables S1–S17 of SI). One can observe that

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the redistribution of valence electron density caused by the interplay of O2 – and H – affords two distinct patterns in anion ordering. The patterns differ mainly on how a local configuration of oxygen atoms is structured around the metal center in the unit cell of a given crystal structure. In one packing layout, oxygens prefer to occupy the particular Wyckoff positions of the highest possible site symmetry and low multiplicity, while in another one they, along with the other atoms, belong to the crystallographic orbit of the same (not only isomorphic) site symmetry, and of the same multiplicity. The sole exception is both systems of the P 4/nmm structure, YHO and Y4 H4 O4 , in which packing forces do not favor to oxygen sites to hold the highest point symmetry. The other set of questions concerns the composition-structure-property relationships. The key factors which determine the composition-dependent responses to physical and chemical features, including the effects of inversion symmetry breaking, will be investigated in subsequent papers. As a starting step toward this objective, we will outline the following: We note first that an essential feature is rich polymorphism exhibiting by the equiatomic Table 5: Polymorphism of the YHO system: comparison of structure types, energies, and unit cell volumes. The quantity ∆W of the last column denotes the energy differences between phases. F -43m-YHO is a reference system. Structure & symmetry cubic F -43m orthorhombic P nma trigonal R-3m tetragonal P 4/nmm cubic P -43m

Phase ∆Elattice ∆V ∆W type (eV/f.u.) (˚ A3 /f.u.) (meV/f.u.) AgAsMg 28 0 0 0 TiNiSi 29

13.8

0.77

12.4

SmSI 30

78.3

1.16

49.8

Cu2 Sb 31

22.2

−4.47

87.3

BiF3 32

28.7

1.99

131.4

ternary compound YHO. That is, the system may crystallize in four phase modifications exhibiting two cubic (F -43m, and P -43m), the orthorhombic (P nma), the trigonal (R-3m), and the tetragonal (P 4/nmm) geometries. In Table 5, it is indicated how these polymorphic 15



structures differ by phase type, lattice energies and the volume change. Comparison shows that of the five predicted modifications, the cubic F -43m phase of YHO is the most stable. Further, of particular importance is that in a range of these polymorphic phases, yttrium accommodation in a unit cell is characterized by one crystallographic site (orbit) (Tables S9S13). In a such configuration, the behavior of the metal cation can be regarded as a certain leading factor that redetermines chemical connectivities in the equiatomic ternary composition to crystallize in stable geometry. Accordingly, the structural stability of polymorphic modifications in the YHO system can be understood in terms of the interplay between the rigidity of the yttrium sublattice and the structural flexibility of oxygen/hydrogen interstitial displacements. From an energetic point of view, the displacive flexibility of anionic orderings may be responsible for a narrow energy gap (∆W ) between phases with higher (face-centered cubic) and lower symmetries, as in orthorhombic (∆W = 12.4 meV/f.u.) or trigonal, (∆W = 49.8 meV/f.u.) geometries (Table 5). Thus, the effect of rich polymorphism adds an extra space to possible interpretations of experimental situation because variations between polymorphic forms with different crystallographic arrangements correspond to minor changes of the ground-state energy, and are accompanied by small changes of the unit cell volume. In this context of the mixed-anion chemistry, our next interest was to perform a reconciliation analysis in order to examine results of structural investigations presented in Ref. 3 for thin film samples of oxygen-containing yttrium hydride. In Figure 5, the synchrotron X-ray diffraction pattern is compared with the theoretical ones calculated for two cubic structures adopting P -43m and F -43m spase symmetries, respectively. A good match of both results provides a clear conclusion that the material synthesized in Ref. 3 has a chemical composition YHO, and its morphology is apparently determined by a mixture of P -43m and F -43m crystalline phases. This is clearly different from the F m-3m host structure of the bulk YH2 . Thus, the cubic phases of lower symmetry result from structural distortions along the pathway, F m-3m→F -43m or F m-3m→P -43m, which are chosen in the course of evolution of the oxyhydride system to ensure stability of new ordering patterns of the oxide

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Figure 5: Polymorph identification. Comparison of the theoretical calculations of the XRD profiles with the X-ray diffraction measurements (shown in blue) of the thin film samples 3 of oxygen-containing yttrium hydrides: (A) Superposition with XRD pattern (shown in red) for the P -43m crystal structure of the YHO composition; (B) Superposition with XRD pattern (shown in green) for the F -43m crystal structure of the YHO composition. and hydride ions. Another important result emphasized in Figures 3 and 4 is an appearance of noncentrosymmetric systems in the proposed family of yttrium oxyhydrides. Here, we see clearly that our theoretical approach provides a powerful framework for crystal chemical modeling of the multicomponent system because it offers direct control of inversion symmetry in the course of simulations of structural transformations. It is particularly remarkable that the lack of central symmetry at the macroscopic scale in the structural evolution is caused by the interplay between appropriate anionic orderings and the multi-sublattice periodic structure. In other words, the establishment of compositional order that breaks the inversion center through a mismatch of the different H – and O2 – anion sublattice positions becomes energetically favorable. For example, the stable composition Y2 H4 O favors crystallization into three polymorphic modifications associated with polar space groups P m, P mn21 and R3m, respectively. The other fascinating case indicated in Figure 3 relates to the prediction of a novel metallic material containing oxygen Y4 H4 O3 , which crystallizes in the noncentrosymmetric tetragonal P -42m structure. Note that presently the research of metal systems with broken inversion symmetry attracts a lot of attention due to unconventional features caused 17



by the cross-effects of acentric displacements, spin channels and macroscopic metallic properties. 33–36 In summary, the most attractive side of modeling and simulation of a mixed-anion system is the possibility to use the interplay of different anions to expand and modify the functional properties of a simple binary hydride. In this aspect, the difference between hydrogen and oxygen associated with electronegativity values, atom sizes, orbital properties, and the corresponding affinities is of particular importance. In the present work, the predictive potential of the theory-driven modeling has been employed to predict the structure, and to describe the structural properties of yttrium oxyhydrides. First, the central emphasis was placed on the elaboration of the phase diagram because its knowledge allows one to understand the synthesis and crystallization of the most favorable compositions, and to control the phase transformations that may accompany the formation process. Secondly, our description of the possible crystallizations in the Y – H – O system has proved the stabilization role of oxygen in formation of the anionic framework for various lattice geometries. Finally, the practical importance of our work is that we presented the detail information on solid phases and symmetries for the different crystalline forms of yttrium oxyhydrides.

Methods Computational details Periodic electron structure calculations have been performed within density functional theory by using Vienna ab initio simulation package 37,38 (VASP) with the potential projector augmented-wave method 39,40 (PAW). One-electron energies were evaluated on the base of Perdew-Burke-Ernzerhof (PBE) GGA exchange-correlation functional, 41 and the PAW-PBE pseudo-potentials. The plane-wave basis sets corresponded to 4s2 4p6 5s2 4d1 , 2s2 2p4 , and 1s1 valence electron configurations for Y, O, and H elements, respectively. Plane-wave energy cutoffs of 700 eV, and the Brillouin-zone sampling in terms of the 8×8×8 k-point mesh have

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been used to provide well-converged total-energy results with the degree of accuracy below 1 meV/(unit cell). In the crystal structure calculations, the equilibrium lattice parameters and internal atomic positions were fully optimized for all geometries.

Symmetry aspects The use of symmetry is of crucial importance in the design because the symmetry significantly limits the choice of the available degrees of freedom by identifying the constraints and restrictions that could be imposed on the architecture of the possible compositional motifs, structural patterns and layers. Accordingly, assumptions on the different sets of generic composition-lattice configurations can be readily classified within the relevant groupsubgroup schemes based on the symmetry-adapted atomic displacements and permutations.

Structural evolution, compositional optimization, and post-processing analysis Cubic superlattice of the F m3m symmetry was chosen as a crystalline template for modeling of structural evolutions. To account for the activity of atoms in the oxidation process, and to address a compositional optimization governed by oxygen incorporation, a set of packing configurations was subjected to different oxygen distributions. The evolution of structures were performed on the base of the Bärnighausen tree 42,43 for several sequences of lattice transformations. The ways of crystal symmetry lowering were outlined in terms of the group-subgroup relations; the relations were constructed by means of the program tools 44,45 hosted by Bilbao Crystallographic Server. 46–49 The ISOTROPY software suite 50,51 and the VESTA program 52 have been applied for the determination of the probable crystal structures. Visualizations have been also made by means of the VESTA program. The formation energy (the heat of formation at T = 0 K) was estimated in a standard way in terms of the difference between the ground-state energy per formula unit and the sum of the corresponding energies of constituent elements. Evaluation of the elastic properties was performed by means of the ELATE online tool. 53,54

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Acknowledgement A.P. was supported by institutional research funding IUT2-27 of the Estonian Ministry of Education and Research and by the Estonian Research Council grant PRG 347. E.S. was supported by Dora Plus PhD student mobility grant (T1.2). Part of the calculations has been performed by using facilities of the Notur supercomputing center.

Supporting Information Available Theoretical predictions for structural and elastic properties of yttrium oxyhydrides: optimized results of equilibrium atomic positions, components of the elasticity tensor and its eigenvalues, zone-centered harmonic vibrational modes, pair distribution function profiles for the shortest interatomic distances, and images of X-ray diffraction patterns.

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For Table of Contents Only

Conceptual design of yttrium oxyhydrides: Phase diagram, structure and properties Aleksandr Pishtshev, Evgenii Strugovshchikov, and Smagul Karazhanov

Synopsis In the oxidation process of the yttrium-hydride system its metal and hydrogen substructures undergo structural transformations.The result of transformations can be represented via several homologous series; these series correspond to oxyhydride crystalline phases differing by the oxygen content.


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Phase diagram, structure and properties

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