Theoretical Design of Yttrium Oxyhydrides: Remarkable ...

doi.org/10.26434/chemrxiv.6950138.v1

Theoretical Design of Yttrium Oxyhydrides: Remarkable Richness ofPhase DiagramAleksandr Pishtshev, Evgenii Strugovshchikov, Smagul Karazhanov

Submitted date: 09/08/2018 • Posted date: 10/08/2018Licence: CC BY-NC-ND 4.0Citation information: Pishtshev, Aleksandr; Strugovshchikov, Evgenii; Karazhanov, Smagul (2018):Theoretical Design of Yttrium Oxyhydrides: Remarkable Richness of Phase Diagram. ChemRxiv. Preprint.

The synthesis of stable yttrium oxyhydride-type compounds raised a question regarding the key factors thatmay be responsible for formation routes and structural features of these attractive materials. For solving thisproblem the interplay of chemical composition and crystalline architectures has been theoretically explored interms of possible structural transformations caused by the gradual oxidation of the host metal-hydride system.The combination of group-theory methods, mixed-anion chemistry arguments, and relevant DFT calculationsprovided us with the opportunity to predict and characterize the candidate models for most probablestoichiometric versions of yttrium oxyhydrides. The predicted chemical compositions along with thecrystallization results have been summarized in the phase diagram. It is shown that structural stability isachieved by matching favorable crystallographic positions of the nearest oxygen and hydrogen atoms at themetal center.

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Theoretical design of yttrium oxyhydrides:

Remarkable richness of phase diagram

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 question re-

garding the key factors that may be responsible for formation routes and structural

features of these attractive materials. For solving this problem the interplay of chemical

composition and crystalline architectures has been theoretically explored in terms of

possible structural transformations caused by the gradual oxidation of the host metal-

hydride system. The combination of group-theory methods, mixed-anion chemistry

arguments, and relevant DFT calculations provided us with the opportunity to predict

and characterize the candidate models for most probable stoichiometric versions of yt-

trium oxyhydrides. The predicted chemical compositions along with the crystallization

results have been summarized in the phase diagram. It is shown that structural stabil-

ity is achieved by matching favorable crystallographic positions of the nearest oxygen

and hydrogen atoms at the metal center.

1

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-1–5 and sev-

eral rare-earth- (Gd, Dy, and Er)6 hydride systems. A crystal chemical classification of the

photochromic oxygen-containing hydride films relates them to advanced multianion materi-

als called oxyhydrides7 in which oxide and hydride anions are sharing the common chemical

space within the crystal lattice. Further examination of experimental data on yttrium oxyhy-

drides raised a question of which factors of the oxidation process may promote a crystalliza-

tion process and which variables may control the formation of solid phases with the different

chemical compositions. One can suggest that the differences between crystallization variables

are caused by the local configuration of oxide and hydride anions around the metal center.

In assembly of a mixed-anion compound, such configuration may offer a certain flexibility of

valence charge states of the metal center in regulation of the H–/O2– exchange-ability. We

will consider this feature as playing a key role in the formation of stoichiometric versions

of oxyhydrides and the emergence of stability. We further assume that there is no loss of

generality in supposing that the mixed yttrium-hydrogen-oxygen crystalline superstructure

can be chosen as a starting periodic system for the simulation of experimental situations.

Theoretical investigation of the oxygen chemical evolution in such system has advantages in

the sense that it allows us to evaluate the formation of several structural frameworks more

straightforwardly in terms of anion orderings. Thus, the main objective of the present work

is to model from first-principles in which way the inserted oxygen may govern the spatial

separation of the Y−H and Y−O bonding channels to afford a set of stable lattice geome-

tries. Our goal is to determine evolutionary structural trend that could generate a number

of ternary systems depending on the O2–/H– anion ratio.

2

Results and discussion

The simulation model of the present work follows the general scheme of crystal structure

prediction developed in previous works8 of Pishtshev and co-workers. To explore anion

exchange routes in terms of evolutionary structural transformations the chemical space was

projected onto a cubic crystallographic space spanned by yttrium, hydrogen, and oxygen.

As a result, a fully functional high-symmetry prototype superstructure has been created.

A lot of sites and interstitials makes its three-dimensional periodic lattice a useful starting

template for the simulation of possible atomic arrangements in the course of model oxidation.

This in turn allows one to directly manipulate the O/H stoichiometric ratio in order to test

a range of lattice configurations with different compositions.

Table 1: Overview of the predicted crystal chemical parameters of 13 structures in whichthe initial Y−H−O system may crystallize. Collation order corresponds to numbering of thecompounds presented in Figure 1. In the last column, the quantity ∆E denotes the forma-tion energy which corresponds to energetics of decomposition reaction on the constitutingelements.

No Chem. Space Phase O/H Z Lattice constants (A) V Density ∆E

formula group type ratio (f.u.) a b c (A3) (g/cm3) (kJ/mol)

1 Y4H10O P -43m (215) cubic 0.1 1 5.230 5.230 5.230 143.03 4.43 −1359.0

2 Y2H4O Pm (6) mono- 0.25 1 3.677 3.724 5.409 74.00 4.44 −847.4clinic (β=92.35◦)

Cm (8) mono- 0.25 2 6.368 3.675 6.537 144.65 4.54 −870.1clinic (β=109.00◦)

3 Y2H3O Pn-3m (224) cubic 0.33 2 5.269 5.269 5.269 146.28 4.47 −814.8

4 Y2H2O P42/nnm (134) tetragonal 0.5 2 5.300 5.300 5.182 145.56 4.47 −723.5

5 Y4H6O3 Cm (8) mono- 0.5 2 12.430 3.843 6.529 307.71 4.42 −2148.1clinic (β=99.37◦)

6 Y4H4O3 P -42m (111) tetragonal 0.75 1 5.248 5.248 5.454 150.21 4.51 −1978.9

7 YHO F -43m (216) cubic 1.00 4 5.292 5.292 5.292 148.20 4.75 −661.5

Pnma (62) ortho- 1.00 4 7.538 3.767 5.328 151.29 4.65 −660.3rhombic

R-3m (166) trigonal 1.00 6 3.773 3.773 18.596 229.26 4.60 −656.7

8 Y4H3O5 P -43m (215) cubic 1.67 1 5.361 5.361 5.361 154.08 4.73 −2785.2

9 Y2HO2 P -42m (111) tetragonal 2.00 2 5.369 5.369 5.184 149.43 4.69 −1186.5

10 Y4H2O5 P -42m (111) tetragonal 2.50 1 5.364 5.364 5.319 153.04 4.75 −2915.0

3

Figure 1: The Y−H−O triangle in terms of the Y, H, and O atomic variables: Phasediagram presenting the most probable equilibrium compositions which are marked by � andnumbered from 1 to 10. The crystallographic description of predicted solid phases is given inTables 1 and 2. The orange dashed lines connect such end members as Y2O3, YO, YH2, YH3,and Y(OH)3. The union of their intersections shown as a solid pentagon represents the regionof potential stability. The yellow dashed line connecting the end members YH3 and Y2O3

corresponds to a homologous series Y(2n+m)/3HmOn (see text). Stoichiometries classified inTable 4 as stable and metastable are outlined by green and red edges, respectively.

The main our finding is that by simulating the oxygen-mediated structural evolution

of the yttrium-hydride model we have predicted a large variety of crystalline phases for

the Y−H−O system. Results presented in Figures 1 – 5, and Tables 1 – 4, encompass

ten YxHyOz-type compositions comprising thirteen stoichiometric solid phases. The other

details and datasets on the structural and physical properties of the predicted compounds

are summarized in Supporting Information (SI). In particular, the information and crite-

ria containing in Table S14 of SI (eigenvalues of the elasticity tensor), Tables S15 - S27 of

SI (components of the elasticity tensor ), and Tables S28 - S40 of SI (zone-centered har-

4

Table 2: Overview of the shortest equilibrium interatomic distances evaluated for the crystalstructures of Table 1. The last column presents a structural check on a total absence of thehydroxide anion.

Chemical Structure Y - O Y - H H - H O - Hformula (A) (A) (A) (A)

Y4H10O P -43m 2.291 2.256 2.135 2.615

Y2H4O Pm 2.244 2.165 2.021 2.536

Y2H4O Cm 2.274 2.163 2.062 2.560

Y2H3O Pn-3m 2.282 2.282 2.635 2.635

Y2H2O P42/nnm 2.278 2.278 2.591 2.650

Y4H6O3 Cm 2.150 2.242 2.128 2.488

Y4H4O3 P -42m 2.216 2.277 2.727 2.624

YHO F -43m 2.292 2.292 3.742 3.742

YHO Pnma 2.243 2.307 2.428 2.679

YHO R-3m 2.245 2.305 2.532 2.679

Y4H3O5 P -43m 2.207 2.362 3.791 2.681

Y2HO2 P -42m 2.353 2.340 3.796 2.592

Y4H2O5 P -42m 2.204 2.319 3.793 2.660

monic vibrational modes) confirm structural stability of the systems listed in Table 1. The

entry No 1, Y4H10O, was suggested and characterized in our previous work.9 Here, its struc-

ture has been adjusted to noncentrosymmetric space group P -43m, and properties have been

re-investigated in more detail. A noteworthy result is that our comparative analysis of ex-

perimental XRD patterns of the transparent-semiconducting Y−H−O thin films2 leads to a

suggestion that these films may be regarded as having the composition Y4H10O and adopting

the cubic P -43m structure.

The comprehensive analysis of macroscopic elastic and plastic properties is presented

in Table 3. One can see that these properties closely resemble those observed for typi-

cal ion-covalent or metallic materials. However, regardless of the similarity of aggregate

characteristics the predicted structures demonstrate the interesting feature relating to the

magnitude of the Gruneisen parameter, which turns out to be markedly high for the oxyhy-

drides with the metal ground state (Table 3). Obviously, this fact reflects the characteristic

anharmonic interactions, which are operative because the amount of incorporated oxygen

atoms is still yet insufficient to shield strong quantum-mechanical movements of hydrogen.

5

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.10 The relation G/Bdenotes Pugh’s ratio, and ν is Poisson’s ratio. The Gruneisen parameter (γ) and the Debyetemperature (ΘD) have been estimated within semi-empirical approaches of Refs. 11 and12, respectively. The values of the Vickers hardness HV have been evaluated from the modelrelations of Refs. 13,14. The abbreviations: ins=insulator, met=metal.

Chemical Structure Ground B E G G/B ν γ ΘD HV

formula state (GPa) (GPa) (GPa) (K) (GPa)

Y4H10O P -43m ins 97.8 170.6 70.6 0.72 0.21 1.83 619 13.5/12.9

Y2H4O Pm ins 78.7 127.3 51.7 0.66 0.23 2.15 513 9.3/9.3

Y2H4O Cm ins 94.1 151.0 61.2 0.65 0.23 2.18 556 10.4/10.4

Y2H3O Pn-3m met 101.4 134.5 52.6 0.52 0.28 3.18 494 6.4/7.2

Y2H2O P42/nnm met 92.6 117.8 45.7 0.49 0.29 3.44 435 5.2/6.2

Y4H6O3 Cm ins 97.8 127.6 49.7 0.51 0.28 3.29 488 5.9/6.8

Y4H4O3 P -42m met 99.3 140.6 55.6 0.56 0.26 2.81 486 7.6/8.2

YHO F -43m ins 125.3 187.2 74.8 0.60 0.25 2.52 567 10.7/10.9

YHO Pnma ins 117.5 168.1 66.6 0.57 0.26 2.74 538 9.0/9.4

YHO R-3m ins 110.2 149.8 58.8 0.53 0.27 3.03 507 7.4/8.1

Y4H3O5 P -43m met 117.7 146.9 56.8 0.48 0.29 3.57 492 6.1/7.0

Y2HO2 P -42m met 108.5 146.5 57.5 0.53 0.27 3.07 471 7.2/7.9

Y4H2O5 P -42m ins 99.5 126.9 49.3 0.50 0.29 3.43 444 5.6/6.5

Table 4: Decomposition reaction enthalpy ∆H0 calculated for the crystal structures ofTable 1.

Chemical Structure Decomposition ∆H0

formula products (kJ/mol)

Y4H10O P -43m Y2O3, YH3 −250.2

Y2H4O Pm Y2O3, YH3 −58.9

Y2H4O Cm Y2O3, YH3 −81.7

Y2H3O Pn-3m Y2O3, YH3, Y −79.9

Y2H2O P42/nnm Y2O3, YH3, Y −41.7

Y4H6O3 Cm Y2O3, YH3 −102.7

Y4H4O3 P -42m Y2O3, YH3, Y −40.7

YHO F -43m Y2O3, YH3 −33.1

YHO Pnma Y2O3, YH3 −31.9

YHO R-3m Y2O3, YH3 −28.3

Y4H3O5 P -43m Y2O3, YH3, H2 +197.1

Y2HO2 P -42m Y2O3, YH3, Y +16.9

Y4H2O5 P -42m Y2O3, YH3 +66.4

The examination of formation energies (shown in the last column of Table 1) indicates

that the structures of ternary oxyhydrides are enthalpically stable with respect to the de-

composition into the simple elements. Further investigation of the energetics of spontaneous

6

decomposition into the binary products is outlined in Table 4. To determine which indica-

tors may be critical to the chemical stability we performed a comparative analysis of the

compositional representations of the phase diagram. First, by laying out the possible su-

perpositions and intersections of the main decomposition trends we assigned the common

area of potential stability which is schematically given by a solid pentagon in Figure 1. It is

noteworthy that such configuration of the composition domain compiled in terms of decom-

position constraints has brought together all the chemical formulas derived in the present

work by means of crystal chemical modeling and DFT-based simulations. Clearly, this fact

confirms the full consistency of our results. Moreover, as it was revealed in Ref. 15, the

yellow dashed line in Figure 1 corresponds to the array of condensed phases with the com-

position range obeying the chemical formula of a homologous series Y(2n+m)/3HmOn, where

n and m are integer numbers.

Secondly, both experiments and theoretical results show that oxygen is readily incorpo-

rated into the metal-hydride system in noticeable amounts. It appears from Figure 2 that

the formation of oxyhydride phases is accompanied by the lattice expansion which begins

to grow continuously already at low oxygen content. This expansion can be attributed to

a tendency observed in a number of compositions for Y−O separation to increase gradu-

ally with the rising O/H ratio (bottom plot of Figure 2). One can see that incorporation

of more oxygen does not destroy the linear behavior of both trends, but makes the Y−O

bonding weaker by elongating the distance between Y and O. Thus, in a simplified picture

of the lattice geometries, just the strong effect of symmetry-lowering oxygen and hydrogen

displacements may be thought of as holding the general patterns of the oxyhydride phase

structurally stable. However, at high oxygen content, the overall strengths of the actual bind-

ing interactions become weaker since the relevant calculations have demonstrated that the

oxyhydride system does become metastable with respect to the solid-phase decomposition.

Thirdly, although with decreasing hydrogen content the Y/H ratio can vary from 0.4 to

2 across the range of the ternary compositions considered, just the case of Y/H= 1 is of

7

Figure 2: The Y−O separation (bottom plot in dark green), and the lattice expansionillustrated for the case of cubic phases (top plot in dark blue) versus the O/H ratio. Thedata points are from Tables 1 and 2. The solid lines represent a linear regression. The zeropoint corresponds to the cubic YH2 with a = 5.203 A.16

frequent occurrence. The effect of sensitivity to H correlates directly with the considerable

elongation of the Y−H bond distances (i.e., weakening of the metal-hydrogen bond upon

oxidation process), as illustrated in Table 2 for the trend of predicted geometries. 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 an extended oxygen content makes a hydrogen

amount in the composition smaller than the relevant amounts of yttrium and oxygen), leads

to the formation of metastable and mostly soft crystal structures. Therefore, these ratios may

be considered as critical indicators of the composition effect which places certain restrictions

on the phase stability of ternary compounds in terms of the following inequalities: Y/H > 1

and 1 < O/H < 5/3. These inequalities determine the area where the upper boundary of

the stability can be found. Illustratively, stability-metastability sharing scheme is shown in

Figure 3.

Another specific correlation is the minimum H−H separation (Table 2) which satisfies

Switendicks criterion17 (> 2.1 A) for the most compositions and crystal structures except

for monoclinic phases of the hydrogen-rich Y2H4O. Evidently, the reason for such shortening

8

Figure 3: Illustrative separation scheme for yttrium oxyhydrides. Pyroelectric phases areshown in blue, the systems without inversion center are shown in green. The light-brown-colored rectangular box separates into the stable (below) and metastable (above) compounds.The box offset is limited to the point O/H=5/3.

of H−H spacings is related to a particular low-symmetry structure in which the equilibrium

local configuration of coordinating yttrium and neighboring hydrogens matches the enhanced

repulsive character of H−H interactions via the enhancement of the metal-hydrogen coupling.

Figure 4 shows the predicted compounds. The crystal structures of these compounds

range through high-symmetry to low-symmetry lattice geometries, and exhibit the different

levels of stability. Some of them demonstrate more complex solid state constitution in terms

of such characteristic factors as coordination of Y−H and Y−O groups, layers configuration,

and stacking sequences. As highlighted in Table 4, hydrogen-poor ternary compositions are

metastable with respect to the decomposition to the binary compounds. On the base of the

valence electron counts and DFT calculations one can verify that depending on the O/H

ratio, the ground state of these structures exhibits either insulating or metallic character.

It is interesting to note the polymorphism feature exhibiting by YHO: its crystallization

enables three different crystalline modifications, namely the cubic AgAsMg-type18 (F -43m),

the orthorhombic TiNiSi-type19 (Pnma), and the trigonal SmSI-type20 (R-3m) forms of the

9

Figure 4: Comparison of the crystal structures predicted for different compositions of yt-trium oxyhydride. Y – green, H – blue, and O – red spheres.

lattice structure. Comparison shows that the cubic F -43m phase of YHO is the most stable.

In the context of the phase diagram, we have made a reconciliation analysis to examine

a structural investigation 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 one calculated for the F -43m crystal structure. A good match of both results

provides a clear conclusion that the synthesized material3 has the chemical formula YHO,

and its crystalline structure perfectly corresponds to the cubic space group F -43m. This is

important indication that a lowering of space group symmetry as compared with the Fm-3m

structure of the bulk YH2 results from the parent structure change which is needed to ensure

stability of new ordering patterns of the oxide and hydride ions in the oxyhydride system.

Another important result emphasized in Figures 3 and 4 is an appearance of noncen-

10

Figure 5: Comparison of the SR-XRD measurement of the thin film samples3 of oxygen-containing yttrium hydride (plotted in blue) with the theoretical calculations of the XRDprofile (shown in red) for the F -43m crystal structure of the YHO composition.

trosymmetric systems in the family of yttrium oxyhydrides. In this context, it is particularly

remarkable that our modeling approach has been so general to offer direct control of inversion

symmetry in the course of structural transformations. Evidently, the lack of central symme-

try at the macroscopic scale is caused by the interplay of the mixed-anion chemistry and the

multilattice periodic structure: that is, when compositional order that destroys the inversion

center through a mismatch of the different H– and O2– anion sublattice positions becomes

energetically favorable. For example, the stable composition Y2H4O favors crystallization

into two polymorphic modifications relating to polar space groups Cm and Pm, respectively.

The other fascinating case indicated in Figure 4 relates to the prediction of the metallic ma-

terial containing oxygen Y4H4O3, which crystallizes in the noncentrosymmetric tetragonal

P -42m structure. Note that metals with broken inversion symmetry attract a lot of atten-

tion due to unconventional features caused by the cross-effect of acentric displacements and

macroscopic metallic properties.21,22

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 the functional properties

11

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

yttrium 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 the various lattice geometries. Finally, the

practical importance 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 the-

ory by using Vienna ab initio simulation package23 (VASP) with the potential projector

augmented-wave method24,25 (PAW). One-electron energies were evaluated on the base of

Perdew-Burke-Ernzerhof (PBE) GGA exchange-correlation functional,26 and the PAW-PBE

pseudo-potentials. The plane-wave basis sets corresponded to 4s24p65s24d1, 2s22p4, 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

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.

12

Structural evolution, compositional optimization, and post-processing analysis

Cubic lattice of the Fm3m symmetry was chosen as a crystalline template for 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 screening of structures were performed

on the base of the Barnighausen tree27 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 tools28 hosted by Bilbao Crystallographic

Server.29,30 The ISOTROPY software suite31,32 and the VESTA program33 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.34

Acknowledgement

A.P. was supported by institutional research funding IUT2-27 of the Estonian Ministry of Ed-

ucation and Research. 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 properties of yttrium oxyhydrides: optimized results

of equilibrium atomic positions, eigenvalues of the stiffness matrix, zone-centered harmonic

vibrational modes, and images of X-ray diffraction patterns.

13

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download fileview on ChemRxivPreprint_yttrium_oxyhydrides_2018_08_09.pdf (2.80 MiB)



Supporting information for:

Theoretical design of yttrium oxyhydrides:

Remarkable richness of phase diagram

Aleksandr Pishtshev1*, Evgenii Strugovshchikov1, and Smagul Karazhanov2

1Institute of Physics, University of Tartu, W.Ostwaldi 1, 50411 Tartu, Estonia

2 Department for Solar Energy, Institute for Energy Technology, Kjeller, Norway

CONTENTS

1. Equilibrium atomic positions predicted for yttrium oxyhydrides 2

2. Eigenvalues (λ) of the elasticity tensor in GPa 5

3. Components of the elasticity tensors in GPa 5

4. Calculated X-ray diffraction patterns 8

5. The squares of zone-centered harmonic vibrational modes 14

1. Equilibrium atomic positions predicted for yttrium oxyhydrides

Supplementary Table S1: Y4H10O

Y4H10O, P-43m (215), a = 5.230 Ǻ

Atom Wyckoff position x y z

Y (1) 4e 0.25287 0.25287 0.25287

O (1) 1a 0.00000 0.00000 0.00000

H (1) 4e 0.67058 0.67058 0.67058

H (2) 3c 0.00000 0.50000 0.50000

H (3) 3d 0.50000 0.00000 0.00000


Y2H4O, Pm (6), a = 3.677 Ǻ, b = 3.724 Ǻ, c = 5.409 Ǻ


Y (1) 1b 0.62218 0.50000 0.91202

Y (2) 1a 0.07531 0.00000 0.42624

O (1) 1b 0.09054 0.50000 0.65809

H (1) 1a 0.55802 0.00000 0.21014

H (2) 1a 0.00000 0.00000 0.00000

H (3) 1b 0.08528 0.50000 0.18920

H (4) 1a 0.58224 0.00000 0.67390


Y2H4O, Cm (8), a = 6.368 Ǻ, b = 3.675 Ǻ, c = 6.537 Ǻ


Y (1) 2a 0.87715 0.00000 0.63474

Y (2) 2a 0.37808 0.00000 0.13595

O (1) 2a 0.25557 0.00000 0.76808

H (1) 2a 0.73537 0.00000 0.20558

H (2) 2a 0.00000 0.00000 0.00000

H (3) 2a 0.11268 0.00000 0.33366

H (4) 2a 0.50132 0.00000 0.50423


Y2H3O, Pn-3m (224), a = 5.629 Ǻ


Y (1) 4b 0.00000 0.00000 0.00000

O (1) 2a 0.25000 0.25000 0.25000

H (1) 6d 0.25000 0.75000 0.75000


Y2H2O, P42/nnm (134), a = 5.300 Ǻ, c = 5.182 Ǻ


Y (1) 4f 0.00000 0.00000 0.00000

O (1) 2a 0.25000 0.75000 0.25000

H (1) 4c 0.25000 0.25000 0.25000

Supplementary Table S6: Y4H6O3

Y4H6O3, Cm (8), a = 12.430 Ǻ, b = 3.843 Ǻ, c = 6.529 Ǻ


Y (1) 2a 0.50513 0.00000 0.46418

Y (2) 2a 0.72606 0.00000 0.22276

Y (3) 2a 0.00000 0.00000 0.00000

Y (4) 2a 0.23751 0.00000 0.71629

O (1) 2a 0.18627 0.00000 0.02760

O (2) 2a 0.68984 0.00000 0.56348

O (3) 2a 0.53704 0.00000 0.14191

H(1) 2a 0.08882 0.00000 0.37957

H(2) 2a 0.31160 0.00000 0.40634

H(3) 2a 0.81739 0.00000 0.92723

H(4) 2a 0.42320 0.00000 0.76434

H(5) 2a 0.91327 0.00000 0.30111

H(6) 2a 0.04095 0.00000 0.67801


Y4H4O3, P-42m (111), a = 5.248 Ǻ, c = 5.454 Ǻ


Y (1) 4n 0.24008 0.24008 0.24170

O (1) 1d 0.50000 0.50000 0.00000

O (2) 1c 0.00000 0.00000 0.50000

O (3) 1a 0.00000 0.00000 0.00000

H (1) 2e 0.50000 0.00000 0.00000

H (2) 2f 0.50000 0.00000 0.50000

Supplementary Table S8: YHO

YHO, F-43m (216), a = 5.292 Ǻ


Y (1) 4c 0.25000 0.25000 0.25000

O (1) 4b 0.50000 0.50000 0.50000

H (1) 4a 0.00000 0.00000 0.00000


YHO, Pnma (62), a = 7.538 Ǻ, b = 3.767 Ǻ, c = 5.328 Ǻ


Y (1) 4c 0.37356 0.25000 0.27784

O (1) 4c 0.14364 0.25000 0.01075

H (1) 4c 0.10127 0.25000 0.51149


YHO, R-3m (166), a = 3.773 Ǻ, c = 18.596 Ǻ


Y (1) 6c 0.00000 0.00000 0.24409

O (1) 6c 0.00000 0.00000 0.11854

H (1) 6c 0.00000 0.00000 0.36805


Y4H3O5, P-43m (215), a = 5.361 Ǻ


Y (1) 4e 0.23763 0.23763 0.23763

O (1) 1b 0.50000 0.50000 0.50000

O (2) 1a 0.00000 0.00000 0.00000

O (3) 3d 0.50000 0.00000 0.00000

H (1) 3c 0.00000 0.50000 0.50000

Supplementary Table S12: Y2HO2

Y2HO2, P-42m (111), a = 5.369 Ǻ, c = 5.184 Ǻ


Y (1) 4n 0.24788 0.24788 0.23610

O (1) 1a 0.00000 0.00000 0.00000

O (2) 1b 0.50000 0.50000 0.50000

O (3) 2e 0.50000 0.00000 0.00000

H (1) 2f 0.50000 0.00000 0.50000


Y4H2O5, P-42m (111), a = 5.364 Ǻ, c = 5.319 Ǻ


Y (1) 4n 0.23199 0.23199 0.24953

O (1) 1d 0.50000 0.50000 0.00000

O (2) 1c 0.00000 0.00000 0.50000

O (3) 1a 0.00000 0.00000 0.00000

O (4) 2f 0.50000 0.00000 0.50000

H (1) 2e 0.50000 0.00000 0.00000

2. Eigenvalues (λ) of the elasticity tensor in GPa

Supplementary table S14: Eigenvalues (λ) of the elasticity tensor in GPa

λ1, GPa λ2, GPa λ3, GPa λ4, GPa λ5, GPa λ6, GPa

Y4H10O 86.235 86.235 86.235 104.57 104.57 293.29

Y2H4O (Pm) 34.386 38.269 78.854 110.83 128.33 271.35

Y2H4O (Cm) 37.276 45.572 83.374 145.9 160.05 294.23

Y2H3O 51.56 51.56 51.56 108.26 108.26 304.32

Y2H2O 45.163 45.222 45.854 84.935 100.65 278.06

Y4H6O3 31.818 50.93 58.355 108.67 116.83 299.84

Y4H4O3 49.822 49.89 51.958 115.29 141.5 299.98

YHO (F-43m) 70.995 70.995 70.995 161.85 161.85 375.97

YHO (Pnma) 56.927 65.647 81.351 117.42 146.94 353.11

YHO (R-3m) 45.515 53.617 72.942 123.84 124.67 338.13

Y4H3O5 50.464 50.464 50.464 135.84 135.84 353.16

Y2HO2 45.532 53.781 53.813 121.9 154.05 328.16

Y4H2O5 27.561 36.931 37.002 146.2 193.32 306.18

3. Components of the elasticity tensors in GPa

Supplementary table S15: Y4H10O

167.5 62.9 62.9 0 0 0

62.9 167.5 62.9 0 0 0

62.9 62.9 167.5 0 0 0

0 0 0 86.2 0 0

0 0 0 0 86.2 0

0 0 0 0 0 86.2

Supplementary table S16: Y2H4O (Pm)

125.9 40.6 39.5 0 -38.4 0

40.6 197.8 63.4 0 3.2 0

39.5 63.4 167.9 0 -8.7 0

0 0 0 75.5 0 -11.1

-38.4 3.2 -8.7 0 53.3 0

0 0 0 -11.1 0 41.6

Supplementary table S17: Y2H4O (Cm)

206.5 71.6 31.1 0 23.2 0

71.6 205.8 31.2 0 -21.8 0

31.1 31.2 176.5 0 1.0 0

0 0 0 54.6 0 -22.3

23.2 -21.8 1.0 0 57.0 0

0 0 0 -22.3 0 66.1


173.6 65.4 65.4 0 0 0

65.4 173.6 65.4 0 0 0

65.4 65.4 173.6 0 0 0

0 0 0 51.6 0 0

0 0 0 0 51.6 0

0 0 0 0 0 51.6


159.3 58.7 63.2 0 0 0

58.7 159.3 63.2 0 0 0

63.2 63.2 145.0 0 0 0

0 0 0 45.2 0 0

0 0 0 0 45.2 0

0 0 0 0 0 45.9

Supplementary table S20: Y4H6O3

155.4 53.7 52.0 0 -2.0 0

53.7 189.0 76.1 0 -2.9 0

52.0 76.1 189.0 0 -0.8 0

0 0 0 43.2 0 -13.1

-2.0 -2.9 -0.8 0 51.0 0

0 0 0 -13.1 0 47.0


174.4 59.1 55.3 0 0 0

59.1 174.4 55.3 0 0 0

55.3 55.3 208.0 0 0 0

0 0 0 49.9 0 0

0 0 0 0 49.8 0

0 0 0 0 0 52.0

Supplementary table S22: YHO (F-43m)

233.2 71.4 71.4 0 0 0

71.4 233.2 71.4 0 0 0

71.4 71.4 233.2 0 0 0

0 0 0 71.0 0 0

0 0 0 0 71.0 0

0 0 0 0 0 71.0

Supplementary table S23: YHO (Pnma)

203.5 87.7 66.4 0 0 0

87.7 206.7 66.3 0 0 0

66.4 66.3 207.2 0 0 0

0 0 0 56.9 0 0

0 0 0 0 65.6 0

0 0 0 0 0 81.4

Supplementary table S24: YHO (R-3m)

205.8 87.8 61.4 13.7 0 0

87.8 205.8 61.4 -13.7 0 0

61.4 61.4 169.3 0 0 0

13.7 -13.7 0 59.5 0 0

0 0 0 0 59.5 13.7

0 0 0 0 13.7 59.0


208.3 72.4 72.4 0 0 0

72.4 208.3 72.4 0 0 0

72.4 72.4 208.3 0 0 0

0 0 0 50.5 0 0

0 0 0 0 50.5 0

0 0 0 0 0 50.5

Supplementary table S26: Y2HO2

214.8 60.7 63.6 0 0 0

60.7 214.8 63.6 0 0 0

63.6 63.6 174.6 0 0 0

0 0 0 53.8 0 0

0 0 0 0 53.8 0

0 0 0 0 0 45.5


235.4 42.1 43.4 0 0 0

42.1 235.4 43.4 0 0 0

43.4 43.4 174.8 0 0 0

0 0 0 36.9 0 0

0 0 0 0 37.0 0

0 0 0 0 0 27.6

4. Calculated X-ray diffraction patterns

The Cu Kα monochromatic beam with wavelength λ=1.5406 Ǻ was set as a parameter of

calculation to determine the theoretical X-ray diffraction patterns.

Supplementary picture S1: X-ray diffraction pattern for the Y4H10O structure

Supplementary picture S2: X-ray diffraction pattern for the Y2H4O (Pm) structure

Supplementary picture S3: X-ray diffraction pattern for the Y2H4O (Cm) structure



Supplementary picture S6: X-ray diffraction pattern for the Y4H6O3 structure


Supplementary picture S8: X-ray diffraction pattern for the YHO (F-43m) structure

Supplementary picture S9: X-ray diffraction pattern for the YHO (Pnma) structure

Supplementary picture S10: X-ray diffraction pattern for the YHO (R-3m) structure


Supplementary picture S12: X-ray diffraction pattern for the Y2HO2 structure


5. The squares of zone-centered harmonic vibrational modes


№ Frequency Atomic displacements

1 1215 cm-1 H(2) – H(3) – H(1) – O(1)

2 1141 cm-1 H(3) – H(2) – H(1) – O(1)

3 1137 cm-1 H(2) – H(1) – H(3)

4 1099 cm-1 H(3) – H(2) – H(1)

5 1033 cm-1 H(1) – H(1)

6 986 cm-1 H(1) – H(2) – H(3) – O(1)

7 980 cm-1 H(3) – H(2)

8 855 cm-1 H(1) – H(1)

9 807 cm-1 H(2) – H(3) – H(1)

10 759 cm-1 H(2) – H(1) – H(3) – O(1) – Y(1)

11 602 cm-1 H(1) – H(2) – H(3)

12 352 cm-1 O(1) – Y(1) – H(3)

13 249 cm-1 Y(1) – Y(1)

14 233 cm-1 Y(1) – H(1)

15 158 cm-1 Y(1) – Y(1)

16 154 cm-1 Y(1) – O(1)

Supplementary Table S29: Y2H4O (Pm)


1 1307 cm-1 H(1) – H(4) – H(2) – Y(2)

2 1181 cm-1 H(3) – H(4) – H(1) – O(1)

3 1156 cm-1 H(3) – H(2)

4 1054 – 1143 cm-1 H(4) – H(3) – H(2) – O(1)

5 1041 cm-1 H(4) – H(1) – H(3) – O(1)

6 975 cm-1 H(2) – H(1) – H(4) – O(1) – Y(2)

7 789 cm-1 H(4) – H(2) – H(1) – O(1) – Y(2) – Y(1)

8 765 cm-1 H(2) – H(3) – O(1) – H(1)

9 673 cm-1 H(3) – H(2) – O(1) – H(4) – H(1)

10 628 cm-1 H(2) – H(3) – H(1) – H(4) – Y(2) – Y(1) – O(1)

11 527 cm-1 H(1) – O(1) – H(2) – H(3) – Y(2)

12 374 cm-1 O(1) – Y(1) – H(2) – H(4)

13 355 cm-1 O(1) – Y(1) – Y(2) – H(3) – H(2)

14 294 cm-1 O(1) – Y(1) – Y(2) – H(3) – H(4) – H(2)

15 240 cm-1 Y(1) – Y(2) – O(1) – H(3)

16 131 cm-1 Y(1) – Y(2) – H(2) – H(1) – O(1)

17 115 cm-1 Y(1) – Y(2) – O(1) – H(1) – H(2) – H(3)

Supplementary Table S30: Y2H4O (Cm)


1 1257 cm-1 H(1) – H(2) – H(3) – H(4) – Y(1)

2 1246 cm-1 H(1) – H(2) – H(3) – H(4)

3 1166 cm-1 H(2) – H(3) – H(4)

4 1074 – 1093 cm-1 H(4) – H(3) – H(2) – H(1) – O(1)

5 948 – 951 cm-1 H(2) – H(1) – H(3) – H(4) – O(1) – Y(2)

6 821 cm-1 H(3) – H(2) – O(1) – H(4) – Y(2) – Y(1)

7 613 cm-1 H(1) – H(3) – O(1) – Y(2) – Y(1)

8 494 cm-1 H(3) – H(1) – O(1) – H(4) – Y(2)

9 485 cm-1 H(3) – H(1) – O(1) – H(4) – Y(2) – Y(1) – H(2)

10 333 cm-1 O(1) – H(3) – H(4) – Y(2) – H(2) – H(1) – Y(1)

11 329 cm-1 O(1) – Y(1) – H(3) – Y(2) – H(4) – H(2) – H(1)

12 185 cm-1 Y(1) – Y(2) – H(1) – H(3) – O(1) – H(2)

13 112 cm-1 Y(2) – Y(1) – O(1) – H(3) – H(1)

14 108 cm-1 Y(2) – Y(1) – O(1) – H(1) – H(3)



1 1162 cm-1 H(1) – O(1)

2 1094 cm-1 H(1) – O(1)

3 1030 cm-1 H(1) – H(1)

4 957 cm-1 H(1) – Y(1)

5 845 cm-1 H(1) – H(1)

6 769 cm-1 H(1) – O(1) – Y(1)

7 314 cm-1 O(1) – H(1)

8 273 cm-1 Y(1) – Y(1)

9 267 cm-1 O(1) – Y(1) – H(1)

10 212 cm-1 Y(1) – Y(1)

11 154 cm-1 Y(1) – O(1)

12 148 cm-1 Y(1) – H(1)



1 1156 cm-1 H(1) – O(1)

2 1089 cm-1 H(1) – O(1)

3 1046 cm-1 H(1) – H(1)

4 952 cm-1 H(1) – Y(1)

5 891 cm-1 H(1) – H(1)

6 843 – 856 cm-1 H(1) – H(1)

7 811 cm-1 H(1) – Y(1)

8 354 cm-1 O(1) – H(1)

9 316 – 320 cm-1 O(1) – Y(1)

10 277 cm-1 O(1) – Y(1) – H(1)

11 267 cm-1 Y(1) – Y(1)

12 215 cm-1 Y(1) – Y(1)

13 150 – 161 cm-1 Y(1) – Y(1)

14 144 cm-1 Y(1) – O(1)

15 135 cm-1 Y(1) – H(1)

16 117 cm-1 Y(1) – Y(1)



1 1201 cm-1 H(1) – H(3) – H(4) – H(6) – H(5)

2 1147 cm-1 H(3) – H(5) – H(4) – H(1) – H(2) – H(6)

3 1133 cm-1 H(5) – H(3) – H(1) – H(6) – H(2) – H(4)

4 1079 cm-1 H(1) – O(2) – O(1) – H(6)

5 1058 cm-1 H(4) – H(6) – H(2) – H(1) – H(3) – O(2)

6 1009 cm-1 H(2) – H(4) – H(5) – H(1) – H(6) – O(1)

7 972 cm-1 H(2) – H(4) – H(1) – H(3)

8 946 cm-1 H(2) – H(5) – H(1) – H(6)

9 899 cm-1 H(3) – H(4) – H(1) – H(6) – O(3)

10 875 cm-1 H(6) – H(4) – H(3) – O(2)

11 863 cm-1 H(1) – H(6) – H(2) – H(5) – H(4) – O(3) – O(2)

12 813 cm-1 H(2) – H(4) – H(1) – O(1) – O(3)

13 784 cm-1 H(3) – H(6) – H(2) – O(1)

14 763 cm-1 H(6) – H(4) – H(1) – H(3) – O(3) – O(1)

15 716 cm-1 H(1) – H(2) – H(5) – O(1) – O(2) – Y(1)

16 689 cm-1 H(1) – O(2) – H(6) – H(5) – O(3)

17 667 cm-1 H(5) – H(2) – H(6) – O(3) – O(2)

18 528 cm-1 O(3) – O(2) – Y(3) – H(4) – H(5) – H(3) – H(6)

19 494 cm-1 H(4) – O(2) – H(3) – H(2) – O(3) – Y(4) – Y(3)

20 473 cm-1 O(3) – O(1) – Y(1) – Y(3) – H(4)

21 417 – 419 cm-1 O(1) – O(2) – O(3) – H(1) – H(3)

22 365 cm-1 O(1) – O(2) – O(3) – Y(4) – Y(1) – H(1)

23 336 cm-1 O(1) – O(3) – O(2) – Y(1) – Y(2) – H(2)

24 314 cm-1 O(3) – O(2) – O(1) – Y(1) – Y(2) – Y(3) – H(5)

25 307 cm-1 O(1) – Y(3) – Y(2) – H(3) – Y(4)

26 283 cm-1 O(2) – O(1) – O(3) – Y(4) – Y(3) – H(2)

27 226 – 228 cm-1 Y(2) – Y(4) – Y(3) – Y(1) – O(3) – O(2)

28 192 cm-1 Y(1) – Y(3) – Y(4) – Y(2) – O(1) – O(3)

29 163 cm-1 Y(1) – Y(3) – Y(4) – Y(2) – O(1) – O(2)

30 146 cm-1 Y(4) – Y(2) – Y(3) – Y(1) – O(3) – O(1) – O(2)

31 123 cm-1 Y(3) – Y(4) – Y(2) – O(3) – O(2)

32 112 cm-1 Y(4) – Y(2) – Y(1) – Y(3) – O(2) – O(3)

33 93 cm-1 Y(1) – Y(2) – O(1)



1 1133 cm-1 H(1) – H(2) – O(1) – O(2) – O(3)

2 1102 cm-1 H(1) – H(2) – O(3)

3 1067 cm-1 H(2) – H(1) – O(1) – O(2)

4 977 cm-1 H(1) – H(2) – O(3) – O(2)

5 934 cm-1 H(2) – H(1)

6 790 cm-1 H(1) – H(2)

7 684 cm-1 H(1) – H(2) – O(1) – O(3) – Y(1) – Y(2)

8 627 cm-1 H(2) – O(3) – H(1)

9 553 cm-1 O(3) – O(2) – O(1) – H(1)

10 362 cm-1 O(3) – O(2) – Y(2) – H(1) – H(2)

11 341 cm-1 O(2) – O(3) – O(1) – Y(1) – Y(2)

12 328 cm-1 O(3) – O(1) – O(2) – H(1) – H(2)

13 266 cm-1 Y(1) – Y(2)

14 246 cm-1 O(1) – O(2) – O(3) – Y(2) – Y(1) – H(1)

15 221 – 233 cm-1 Y(1) – Y(2)

16 215 cm-1 O(1) – O(2) – Y(1) – Y(2) – H(1) – Y(2)

17 152 – 154 cm-1 Y(2) – Y(1) – O(1) – O(3) – O(2)

18 149 cm-1 Y(1) – Y(2)

19 131 cm-1 Y(2) – Y(1) – O(1)

Supplementary Table S35: YHO (F-43m)


1 1109 cm-1 H(1) – O(1)

2 1057 cm-1 H(1) – O(1)

3 1054 cm-1 H(1) – O(1)

4 333 cm-1 O(1) – H(1)

5 322 cm-1 O(1) – Y(1) – H(1)

6 320 cm-1 O(1) – H(1)

7 278 cm-1 Y(1) – Y(1)

8 156 cm-1 O(1) – Y(1)

Supplementary Table S36: YHO (Pnma)


1 1080 cm-1 H(1) – H(1)

2 1067 – 1070 cm-1 H(1) – O(1)

3 1050 – 1052 cm-1 H(1) – H(1)

4 889 – 915 cm-1 H(1) – O(1)

5 826 – 865 cm-1 H(1) – O(1)

6 823 cm-1 H(1) – H(1)

7 786 cm-1 H(1) – O(1)

8 532 cm-1 O(1) – Y(1) – H(1)

9 402 – 408 cm-1 O(1) – Y(1)

10 377 cm-1 O(1) – Y(1) – H(1)

11 351 cm-1 O(1) – Y(1)

12 324 – 339 cm-1 O(1) – Y(1) – H(1)

13 286 – 298 cm-1 O(1) – Y(1) – H(1)

14 264 cm-1 O(1) – Y(1) – H(1)

15 198 – 201 cm-1 Y(1) – O(1)

16 165 – 168 cm-1 Y(1) – O(1)

17 152 cm-1 Y(1) – O(1)

18 124 cm-1 Y(1) – O(1)

19 115 cm-1 Y(1) – O(1)

Supplementary Table S37: YHO (R-3m)


1 1092 cm-1 H(1) – H(1)

2 1044 cm-1 H(1) – O(1)

3 944 cm-1 H(1) – O(1)

4 791 cm-1 H(1) – O(1)

5 440 cm-1 H(1) – O(1)

6 413 cm-1 O(1) – Y(1) – H(1)

7 353 cm-1 O(1) – Y(1) – H(1)

8 338 cm-1 O(1) – Y(1) – H(1)

9 215 cm-1 Y(1) – O(1)

10 126 cm-1 Y(1) – O(1)



1 957 cm-1 H(1) – O(3) – O(1)

2 923 cm-1 H(1) – O(3)

3 880 cm-1 H(1) – O(1)

4 557 cm-1 O(2) – O(3) – H(1)

5 343 cm-1 O(3) – O(2) – O(1) – Y(1) – H(1)

6 303 cm-1 O(3) – Y(1) – H(1)

7 285 cm-1 O(3) – O(2) – O(1) – H(1) – Y(1)

8 246 cm-1 Y(1) – Y(1)

9 197 cm-1 O(1) – O(2) – O(3) – H(1) – Y(1)

10 178 cm-1 Y(1) – Y(1)

11 157 cm-1 Y(1) – O(3)

12 149 cm-1 Y(1) – O(1) – H(1)

Supplementary Table S39: Y2HO2


1 1103 cm-1 H(1) – O(3)

2 1080 cm-1 H(1) – O(3)

3 1037 cm-1 H(1) – O(2)

4 687 cm-1 H(1) – O(3) – O(1) – O(2)

5 566 cm-1 O(1) – O(3) – H(1) – O(2)

6 393 cm-1 O(1) – O(3) – O(2) – Y(1) – H(1)

7 351 cm-1 O(3) – O(1) – O(2) – Y(1)

8 336 cm-1 O(3) – H(1) – Y(1)

9 310 cm-1 O(2) – O(1) – O(3) – Y(1)

10 284 cm-1 O(2) – O(3) – O(1) – Y(1)

11 268 – 277 cm-1 Y(1) – Y(1)

12 250 – 265 cm-1 O(2) – O(1) – O(3) – Y(1) – H(1)

13 155 – 157 cm-1 Y(1) – O(2) – O(3)

14 149 cm-1 Y(1) – O(2)

15 138 cm-1 Y(1) – O(1) – O(3)



1 1051 cm-1 H(1) – O(4)

2 1040 cm-1 H(1) – O(3) – O(1)

3 1022 cm-1 H(1) – O(4)

4 1005 cm-1 H(1) – O(1) – O(3)

5 604 cm-1 O(3) – O(2) – O(1) – H(1)

6 565 cm-1 O(2) – O(4) – O(3) – H(1) – O(1)

7 401 cm-1 O(3) – O(4) – Y(1) – H(1)

8 374 cm-1 O(2) – O(3) – O(4) – Y(1) – O(1)

9 318 cm-1 O(4) – O(1) – O(2) – O(3) – Y(1)

10 309 cm-1 O(4) – Y(1) – H(1)

11 279 – 292 cm-1 Y(1) – Y(1)

12 269 cm-1 O(4) – O(2) – O(3) – H(1) – O(1) – Y(1)

13 262 cm-1 Y(1) – Y(1)

14 236 – 245 cm-1 O(4) – O(1) – O(3) – Y(1) – H(1)

15 208 cm-1 O(1) – Y(1) – O(3) – O(2) – O(4)

16 160 cm-1 Y(1) – O(3)

17 151 cm-1 O(1) – Y(1) – O(3)

18 142 cm-1 Y(1) – O(4)

19 137 cm-1 Y(1) – O(1) – O(2)

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