High pressure phases of different tetraboranes

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This article was downloaded by: [Dalhousie University] On: 09 October 2014, At: 02:48 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK High Pressure Research: An International Journal Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/ghpr20 High pressure phases of different tetraboranes Ainhoa Suarez-Alcubilla ab , Idoia G. Gurtubay ac & Aitor Bergara abc a Materia Kondentsatuaren Fisika Saila, Zientzia eta Teknologia Fakultatea, Euskal Herriko Unibertsitatea, UPV/EHU, 644 Postakutxatila, 48080 Bilbo, Basque Country, Spain b Centro de Fisica de Materiales CSIC-UPV/EHU, 1072 Postakutxatila, E-20080 Donostia, Basque Country, Spain c Donostia International Physics Center (DIPC), Paseo de Manuel Lardizabal, 20018 Donostia, Basque Country, Spain Published online: 02 Oct 2013. To cite this article: Ainhoa Suarez-Alcubilla, Idoia G. Gurtubay & Aitor Bergara (2014) High pressure phases of different tetraboranes, High Pressure Research: An International Journal, 34:1, 59-69, DOI: 10.1080/08957959.2013.843174 To link to this article: http://dx.doi.org/10.1080/08957959.2013.843174 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &

Transcript of High pressure phases of different tetraboranes

Page 1: High pressure phases of different tetraboranes

This article was downloaded by: [Dalhousie University]On: 09 October 2014, At: 02:48Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

High Pressure Research: AnInternational JournalPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/ghpr20

High pressure phases of differenttetraboranesAinhoa Suarez-Alcubillaab, Idoia G. Gurtubayac & Aitor Bergaraabc

a Materia Kondentsatuaren Fisika Saila, Zientzia eta TeknologiaFakultatea, Euskal Herriko Unibertsitatea, UPV/EHU, 644Postakutxatila, 48080 Bilbo, Basque Country, Spainb Centro de Fisica de Materiales CSIC-UPV/EHU, 1072Postakutxatila, E-20080 Donostia, Basque Country, Spainc Donostia International Physics Center (DIPC), Paseo de ManuelLardizabal, 20018 Donostia, Basque Country, SpainPublished online: 02 Oct 2013.

To cite this article: Ainhoa Suarez-Alcubilla, Idoia G. Gurtubay & Aitor Bergara (2014) High pressurephases of different tetraboranes, High Pressure Research: An International Journal, 34:1, 59-69,DOI: 10.1080/08957959.2013.843174

To link to this article: http://dx.doi.org/10.1080/08957959.2013.843174

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.

This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &

Page 2: High pressure phases of different tetraboranes

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High Pressure Research, 2014Vol. 34, No. 1, 59–69, http://dx.doi.org/10.1080/08957959.2013.843174

High pressure phases of different tetraboranes

Ainhoa Suarez-Alcubillaa,b∗ , Idoia G. Gurtubaya,c and Aitor Bergaraa,b,c

aMateria Kondentsatuaren Fisika Saila, Zientzia eta Teknologia Fakultatea, Euskal Herriko Unibertsitatea,UPV/EHU, 644 Postakutxatila, 48080 Bilbo, Basque Country, Spain; bCentro de Fisica de Materiales

CSIC-UPV/EHU, 1072 Postakutxatila, E-20080 Donostia, Basque Country, Spain; cDonostia InternationalPhysics Center (DIPC), Paseo de Manuel Lardizabal, 20018 Donostia, Basque Country, Spain

(Received 24 July 2013; final version received 2 September 2013)

High pressure phases of boron hydrides B4H10, B4H8 and B4H6 and their stability against dissociationinto H and smaller B–H units are reported. Structure predictions based on particle swarm optimizationreveal that all the boron hydrides studied show a tendency to separate into smaller structural units at lowpressure. Under high pressure, the three-dimensional network in all the stoichiometries selected seems tobe the most favourable arrangement. A study of the dissociation of B4H10 reflects an affinity to dissociateinto B4H8 and H2 in all the studied pressure range. Nevertheless, B4H8 does not seem to segregate in thestudied pressure range and B4H6 may dissociate at 150 GPa.

Keywords: high pressure; boron hydrides; crystal structure prediction, dissociation

1. Introduction

During the last years, interest in boron hydrides has increased remarkably. One of the reasons is theuniqueness of its constituent elements. On the one hand, boron, being located between metals andinsulators in the periodic table and with only three valence electrons, shows by itself an exotic andfascinating chemistry. On the other hand, when boron is combined with hydrogen, an extensiveand amazingly diverse family of boron hydrides appears. The recent interest on these systemsstems from the fact that they are hydrogen-rich compounds and the compression of this type ofmaterials may reveal novel routes to achieve a metallic state of hydrogen at high pressure.[1–3]

The simplest boron hydride is diborane, B2H6 (dimer of BH3), known to possess a curious three-centre bond. This singular bonding allows diborane to form a great variety of crystal structures.At ambient pressure, B2H6 crystallizes in the well-known structure of β-diborane, characterizedby Lipscomb.[4]

A recent study has reported several metastable molecules at 1 atm, as well as oligomers of BH3,which, as pressure increases, arrange in molecular dimers, trimers and one-dimensional chainsuntil 100 GPa.[5] Under higher pressure, recent calculations have shown a stable metallic phasewhich adopts the Pbcn phase at 350 GPa.[6] This phase reveals a large density of states at theFermi level and its Tc has been stimated to be 100 K.

∗Corresponding author. Email: [email protected]

© 2013 Taylor & Francis

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60 A. Suarez-Alcubilla et al.

These precedents have motivated us to continue with the study, under compression, of thesmallest arachno-borane, B4H10. The interest on this borane arises from different factors: first,its crystal structure is well characterized at ambient pressure [7]; second B4H10 possesses, afterB2H6, the largest ratio between B and H within the large family of boron hydrides; and finally thenumber of atoms of this binary system allows us do feasible computational calculations.

In our research, we have found that the structure of tetraborane under pressure, from 50 to300 GPa, evolves from a molecular crystal to polymeric chains, as it happens in diborane.[5] Ourresults suggest that these chains are made by structural units smaller than B4H10 and, therefore,we have extended our analysis to other stoichiometries with less H atoms, such as B4H8 and B4H6

in the same pressure range.

2. Computational methods

Stable and most competitive metastable structures of B4H10, B4H8 and B4H6 have been obtainedvia the particle swarm optimization (PSO) technique as implemented in the CALYPSO [8,9] code.This method has been successfully used in the study of other materials at high pressure.[10–14]Structural relaxations were performed in the framework of the frozen core all-electron projectedaugmented wave method,[15] as implemented in Vienna Ab-initio Simulation Package,[16,17]with exchange-correlation functionals as parametrized by Perdew et al.,[18] for the general-ized gradient approximation. A plane-wave cutoff energy of at least 900 eV was used andthe integration over the Brillouin zone was performed on a grid of 12 × 12 × 12 Monkhorst–Pack k-points.[19,20] All necessary convergence tests were performed and total energies wereconverged to less than 0.01 meV/atom.

In the B4H10 calculations, we have performed structure prediction simulations at 50, 150 and300 GPa, with 2 formula units of B2H5 per unit cell. In the case of B4H8 and B4H6, 2 formula unitsof B2H4 and B2H3 per unit cell, respectively, were used at the same pressures. In our evolutionarysimulations, each generation consisted of 30 structures, the first generation being random. Eachsubsequent generation was produced from the lowest enthalpy 60% structures of the precedinggeneration; thus, the most competitive structures always survived into the next generation.

3. Structure searching and enthalpies

We have investigated B4H10, B4H8 and B4H6 at high pressure. The PSO method through theCALYPSO code was first applied to predict the most stable structures of the boron hydridesproposed at certain pressures. Then, we have studied the relative stability of the best three structuresfound at each pressure in a pressure range from 50 to 300 GPa. For the shake of clarity, only thecurves corresponding to structures with competitive enthalpies in the pressure range consideredare shown in subsequent figures.

3.1. B4H10

We have obtained the most stable structures of B4H10 at 50, 150 and 300 GPa, using CALYPSO.After studying the most favourable ones, the lowest enthalphy phases have been selected andwe have calculated the evolution of their enthalpies in a pressure range from 50 to 300 GPa.Figure 1 shows the relative enthalpy curves for the most competitive of the predicted structures ofB4H10, the reference being the best structure predicted at 50 GPa. This structure has been named

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High Pressure Research 61

50 100 150 200 250 300Pressure (GPa)

-0.05

0.00

0.05

0.10

0.15

0.20

H–H

S 50-1

(eV

/ion)

S50-1

(P-1)

S150-1

(P-1)

S150-2

(C2/m)

S300-1

(P-1)

S300-2

(P-1)

Figure 1. (Colour online) Enthalpy per ion as a function of pressure for the most competitive phases found in the structuresearch for B4H10. All enthalpies are related to the best structure predicted at 50 GPa, called S50−1. S150−2 represents,therefore, the second best structure found at 150 GPa. The space group of each structure is shown in parentheses.

S50−1, as it is the best structure predicted at 50 GPa. Following this criterium, S150−2 would bethe second-best structure predicted at 150 GPa.

As it can be seen in the curves (Figure 1), S50−1 is the most stable structure in the pressurerange from 50 to 270 GPa.

In contrast to what is observed at ambient pressure, under extreme conditions molecular B4H10

becomes unstable and, surprisingly, it seems to dissociate between 50 and 210 GPa (Section 4).At 50 GPa, the structure has space group P1̄ and reveals (Figure 2(a)) an arrangement where Batoms form quasi-parallel layers bonded by B atoms. These layers are separated by layers ofhydrogen atoms, and the shortest distance between the H atoms within the layers is 0.74Å. Thisseparation is similar to that of molecular H2 at ambient pressure, which suggests that these atomsmay form hydrogen dimers. At 150 GPa, the most stable is still the P1̄ structure. In Figure 2(b),we can observe an increase in the number of B–B bonds in the quasi-planar B layers revealing adenser phase.

At higher pressure, from 270 to 300 GPa, S300−1 is the most favourable one. This structurehas also P1̄ spatial group but, unlike S50−1, crystallizes forming a three-dimensional network.The parameters given in Table A1 of Appendix 1 reveal that this structure is quasi-hexagonal. At300 GPa (Figure 2(c)), the volume of the cell is 14.88Å3. This represents approximately a 72%volume decrease with respect to the S50−1 structure, whose volume is 53.18Å3. In this three-dimensional network, the B–B bonds found at 50 and 150 GPa, which linked the quasi-parallellayers of B atoms, have disappeared. These layers, instead, are bonded by H atoms with a bondlength of 1.71Å(between hydrogens).

In order to determine the insulating or metallic character of S300−1, the only B4H10 structurewhich does not seem to dissociate, a study of the density of states was carried out around theFermi level. As it can be seen in Figure 3, B4H10 is metallic at 300 GPa.

The possible dissociation of B4H10 at 50 and 150 GPa has motivated the analysis of other stoi-chiometries with fewer atoms of hydrogen. Therefore, we have studied B4H8 and B4H6 followingthe same methodology as in B4H10.

3.2. B4H8

As in the previous case, first we have searched the most favourable structures for B4H8 using theevolutionary algorithm at 50, 150 and 300 GPa. In order to obtain the relative stability of thesestructures in the range from 50 to 300 GPa, we have calculated the enthalpies of these structures

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62 A. Suarez-Alcubilla et al.

a b

c

Figure 2. The most stable structures found of B4H10 at 50 GPa (a), 150 GPa (b) and 300 GPa (c). The unit cell isindicated, B and H atoms are shown with large blue and small green spheres respectively. The cell parameters and atomicpositions of these structures can be found in Table A1 of Appendix 1.

-25 -20 -15 -10 -5 0 5 10 15 20E – E

Fermi(eV)

0

0.5

1

1.5

2

DO

S (s

tate

s/ce

ll)

Figure 3. The density of states of the most stable structure of B4H10 at 300 GPa shows no gap around the Fermi level.

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High Pressure Research 63

50 100 150 200 250 300Pressure (GPa)

-0.05

0.00

0.05

0.10

0.15

H –

HS 50

-1(e

V/io

n)

S50-1

(P1)

S150-1

(P21)

S300-1

(P2)

S300-2

(C2/c)

Figure 4. (Colour online) Enthalpy per ion as a function of pressure for B4H8. The legend reads as in Figure 1.

relative to the enthalpy of the best structure predicted at 50 GPa (S50−1) (Figure 4). As before,only the curves for competitive structures are shown.

In the low pressure range (from 50 to 75 GPa), the most stable structure of B4H8 shows symmetryP1. This structure is formed by units of B4H8 linked by B atoms along the c-axis, with a bondlength distance of 1.71Å(Figure 5(a)).

Above 75 GPa the P1̄ structure undergoes a significant change; the molecular units of B4H8

get closer resulting in a layered arrangement with symmetry P21 (Figure 5(b)). This orderinginduced by the pressure increase causes the reorganization along the axis direction. The P21

structure remains stable up to 220 GPa.For pressures higher than 220 GPa, the most favourable structure has space group P2. This

structure forms a three-dimensional network similar to that of B4H10 under high pressure. Boronatoms form semi-infinite layers along the c-axis linked by hydrogen atoms along a and b directions(Figure 5(c)). This is a quasi-orthorhombic structure (Table A2 in Appendix 1).

The total electronic charge density of the P2 phase at 300 GPa is illustrated in Figure 6. As itcan be observed, since the distances between the boron atoms contained in the ac plane are thesame along the infinite layer, the charge density is uniform.

The density of states per unit cell of the most stable structures found for B4H8 are shown atselected pressures in Figure 7. While this analysis reveals no contribution at E = EFermi at 50 GPa,the structures at higher pressures begin to show a metallic behaviour, being more significant forthe P2 phase (Figure 7 dotted line).

In contrast to the B4H10 borane, all the predicted structures for B4H8 tend to form bigger struc-ture units, chains or even polymeric layers. We have found no evidence of a possible dissociationinto smaller units and molecular hydrogen as in B4H10.

3.3. B4H6

The last boron hydride we have investigated is B4H6. Figure 8 shows the relative enthalpy curvesof the various structures predicted with CALYPSO at 50, 150 and 300 GPa. As in Figures 1 and 4,the enthalpy of the most stable structure found at 50 GPa is used as a reference.

Between 50 and 75 GPa, the most favourable structure is the S50−1 (Figure 9(a)). This structurehas P1 symmetry and shows a layered arrangement of B4H6 units, where each B atom is bondedto two B atoms of the next unit.

This phase evolves, between 75 and 125 GPa, in a structure with C2/m space group(Figure 9(b)). This structure also shows a layered arrangement of B4H6 units, where the B atoms

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64 A. Suarez-Alcubilla et al.

(a) (b)

(c) (d)

Figure 5. The most stable structures of B4H8 at 50 GPa (a), 150 GPa (b) and 300 GPa (c) and (d). Several unit cells areshown. B and H atoms are shown with large blue and small green spheres, respectively.

Figure 6. Charge density for the P2 phase at 300 GPa in the semi-infinite plane ac which contains the B atoms (Figure 5).

form a quasi-planar structure. In this case, the pressure increase has formed an extra intra-unitB−B bond.

Between 125 and about 240 GPa, the S150−1 structure with C2/m symmetry is the mostfavourable one. This structure shows again a layered arrangement on the bc plane (Figure 9(c)).

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High Pressure Research 65

-15 -10 -5 0 5 10 15E – E

Fermi(eV)

0

0.5

1

1.5

2

2.5

DO

S (s

tate

s/ce

ll)

50GPa150GPa300GPa

Figure 7. The density of states for the most stable structures of B4H8 at 50, 150 and 300 GPa shown in Figure 5.

50 100 150 200 250 300

Pressure (GPa)

-0.20

-0.10

0.00

0.10

H–H

S 50-1

(ev

/ion)

S50-1

(P1)

S150-1

(C2/m)

S150-2

(C2/m)

S300-1

(Fmmm)

Figure 8. (Colour online) Enthalpy per ion as a function of pressure for the low enthalpy phases found for B4H6. Thelegend reads as in Figure 1.

However, in this case, the layers are formed by B4H4 units separated by hydrogen molecules,where the H–H bond length is 0.75Å. Those H atoms, which at lower pressures where bondedto B atoms, can now form a molecule because, an extra B–B appears within the B4H4 unit. Thisway, B atoms form quasi-hexagonal buckling rings perpendicular to the a-axis.

At higher pressures (P ≥ 240 GPa), the most competitive structure has a Fmmm space group,where B and H atoms sit on intercalated layers perpendicular to the long axis. The bucklinghexagonal rings formed by B atoms found at lower pressure become planar when pressure isincreased.

We have performed the analysis of the density of states of the B4H6 structures that do notdissociate (Figure 10). This figure shows an insulating character at 50 GPa, but the structures athigher pressures begin to show a metallic behaviour, being more significant for the Fmmm phase(Figure 10 dotted line).

4. Dissociation of B4H10

As mentioned in Section 3.1, B4H10 exhibits a tendency to dissociate at high pressures, resultingin what seems to be molecular hydrogen and smaller boron hydride units. To determine whether

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66 A. Suarez-Alcubilla et al.

(a) (b)

(c)(d)

Figure 9. The most stable structures of B4H6 at 50 GPa (a), 100 GPa (b), 150 GPa (c) and 300 GPa (d).

an affinity to segregation really takes place, a partial analysis has been done following the nextpossible dissociation paths:

B4H10 −→ B4H8 + H2,

B4H10 −→ B4H6 + 2H2.

This study is based on the reagent and compounds’ enthalpies previously analysed at differentpressures. In the case of H2, the enthalpy has been calculated for the structure with space groupC2/c.[21] In the case of B4H8 and B4H6, the enthalpies of H2 and 2H2 have been added, respec-tively, so all structures have 4 B atoms and 10 H atoms. This way, their enthalpies are comparable.The interaction between B4H8 (B4H6) and H2 (2H2) has not been taken into account; in any case,the atom rearrangement due to this interaction, would reduce even more the sum of the enthalpies.Figure 11 shows the enthalpy curves for the possible dissociation paths mentioned above usingthe different structures and stoichiometries found at different pressures (those that did not showpossible dissociation).

The results reveal that B4H10, the only boron hydride studied with crystal structure known atambient conditions, shows a tendency to dissociation into units of B4H8 and one H2 molecule allover the studied pressure range.

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High Pressure Research 67

-15 -10 -5 0 5 10E – E

Fermi(eV)

0

0.5

1

1.5

2

2.5

DO

S (s

tate

s/ce

ll)

50GPa100GPa300GPa

Figure 10. The density of states of the most favourable sructures of B4H6 at 50, 100 and 300 GPa shown in Figure 9.

50 100 150 200 250 300Pressure (GPa)

-0.10

0.00

0.10

0.20

H –

HB

4H10

S 50-1

(eV

/ion)

B4H

10S

50-1

B4H

8S

50-1 +H

2

B4H

8S

150-1+H

2

B4H

8S

300-1+H

2

B4H

6S

50-1+2H

2

B4H

6S

150-2+2H

2

B4H

6S

300-1+2H

2

Figure 11. (Colour online) Enthalpies of B4H10, B4H8 + H2 and B4H6 + 2H2 as a function of pressure. The curvesshow the lowest enthalpies of Figures 1, 4 and 8 to which we have added the H2 enthalpy to complete the 4 atoms ofboron and 10 atoms of hydrogen per unit cell.

5. Conclusions

In summary, the phases of B4H10, B4H8 and B4H6 have been investigated at high pressure usingan evolutionary algorithm implemented in the CALYPSO code and using the density functionaltheory.

The structural analysis of the different studied stoichiometries reveals that B4H10 tends toseparate into smaller structural units: B4H8 and H2 from 50 to 300 GPa. The studied structures,in spite of having very low symmetry, tend to adopt an organization in chains which evolves intoa layered arrangement to finally turn into a three-dimensional network with increasing pressure,except for the B4H6 stoichiometry. This boron hydride, having a fewer number of hydrogen atoms,shows more open structures which evolve from a chain disposition to layered arrangements underhigh pressures.

Acknowledgements

A. Bergara, I. G. Gurtubay and A. Suarez-Alcubilla are grateful to the Department of Education, Universities andResearch of the Basque Government, UPV/EHU (Grant No. IT756-13) and the Spanish Ministry of Science and Innova-tion (Grant No. FIS2010-19609-C02-01) for financial support. A. Suarez-Alcubilla also acknowledges support from theCSIC-JaePredoc program, co-financed by ESF.

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3868.[19] Pack JD, Monkhorst HJ. Special points for Brillouin-zone integrations. Phys Rev B. 1976;13:5188–5192.[20] Pack JD, Monkhorst HJ. Special points for Brillouin-zone integrations—a reply. Phys Rev B. 1977;16:1748–1749.[21] Pickard CJ, Needs RJ. Structure of phase III of solid hydrogen. Nature. 2007;3:473–476.

Appendix 1

Table A1. Structural parameters for the most stable structures of B4H10 at 50, 150 and 300 GPa of Figure 2.

B4H10

P (GPa) Space group Lattice parameters (Å, ◦) Atomic coordinates Wyck. pos.

a = 2.98 b = 3.25 c = 5.62 B1 .09077 .34000 .59248 2iα = 96.6 β = 83.6 γ = 82.5 B2 .60977 .04028 .62482 2i

H1 .16918 .74871 .23930 2i50 P1̄ H2 .49080 .11693 .20420 2i

V = 53.17Å3 H3 .59675 .56230 .00318 2iH4 .10116 .05603 −.00299 2iH5 .19862 .55059 .75552 2i

a = 2.77 b = 2.87 c = 5.01 B1 .09481 .35576 .60907 2iα = 96.6 β = 82.7 γ = 82.5 B2 .62161 .04101 .63256 2i

H1 .15726 .74504 .20383 2i150 P1̄ H2 .48293 .11191 .17129 2i

V = 38.76Å3 H3 .59634 .58208 .00491 2iH4 .07419 .09885 .01092 2iH5 .21592 .60784 .77113 2i

a = 1.59 b = 6.69 c = 1.59 B1 .00287 .67524 .53999 2iα = 92.8 β = 117.9 γ = 88.4 H1 .37808 −.06335 −.02367 2i

300 P1̄ H2 −.06171 .86616 .53308 2iV = 14.88Å3 H3 .00000 .50000 .50000 1g

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Page 13: High pressure phases of different tetraboranes

High Pressure Research 69

Table A2. Structural parameters for the most stable structures of B4H8 at 50, 150 and 300 GPa of Figure 5.

B4H8

P (GPa) Space group Lattice parameters (Å, ◦) Atomic coordinates Wyck. pos.

a = 5 b = 3.45 c = 2.88 B1 .40972 .08074 .16619 1aα = 90 β = 90.7 γ = 109.3 B2 −.40418 .33366 −.36007 1a

B3 .24145 .12818 −.34049 1aB4 −.22137 .24582 .12686 1aH1 .04053 −.16085 −.31888 1a

50 P1 H2 .38663 −.26934 .16218 1aV = 46.84Å3 H3 −.35366 −.31619 −.34140 1a

H4 −.21062 .16435 −.29882 1aH5 −.04318 −.43252 .18246 1aH6 .18356 .44229 −.19305 1aH7 .16602 .42657 −.49750 1aH8 −.14603 −.03726 .18489 1a

a = 4.48 b = 2.69 c = 3.03 B1 −.22067 −.25045 −.43595 2aα = 90 β = 109.5 γ = 90 B2 .39584 −.25029 .37161 2a

150 P21 H1 .00353 .24977 .10769 2aV = 34.54Å3 H2 .17423 .41334 −.22163 2a

H3 .13806 .08481 −.25338 2aH4 .060996 .25822 .00588 2a

a = 7.11 b = 2.37 c = 1.60 B1 .20676 .08813 −.31336 2aα = 90 β = 92.8 γ = 90 B2 .40079 .08464 .23161 2a

300 P2 H1 −.19919 −.41392 .31558 2aV = 26.99Å3 H2 .40204 −.41528 .23168 2a

H3 −.03449 −.42166 .15960 2aH4 .06304 .07361 .30193 2a

Table A3. Structural parameters for the most stable structures of B4H6 at 50, 100, 150 and 300 GPa shown in Figure 9.

B4H6

P (GPa) Space group Lattice parameters (Å, ◦) Atomic coordinates Wyck. pos.

a = 3.32 b = 3.15 c = 4.10 B1 .34127 .47025 −.42356 1aα = 81.11 β = 100.27 γ = 93.93 B2 −.46136 .27772 .28858 1a

B3 .42375 −.36311 −.04437 1aB4 .21919 .12186 −.06268 1aH1 −.33266 −.36327 −.28777 1a

50 P1 H2 −.13433 .10207 −.09060 1aV = 41.69Å3 H3 .08164 −.29744 .44748 1a

H4 −.23722 −.41425 .15985 1aH5 −.19958 .04013 .37904 1aH6 .30959 .07090 −.35050 1a

a = 7.38 b = 2.80 c = 3.44 B1 .10796 .00000 .62482 4iα = 90 β = 105.96 γ = 90 B2 .67933 .00000 .46635 4i

100 C2/m H1 .86588 .16735 .03645 4iV = 68.53Å3 H2 .57833 .00000 .14029 8j

a = 7.17 b = 2.80 c = 3.12 B1 .31150 .00000 .65620 4iα = 90 β = 106.9 γ = 90 B2 .77877 .00000 −.09963 4i

150 C2/m H1 .52269 .00000 .26302 4iV = 20, 28Å3 H2 −.05544 .00000 .06718 4i

H3 .00000 .86645 .50000 4h

a = 2.71 b = 1.68 c = 10.520 B1 .00000 .00000 .61083 8iα = 90 β = 90 γ = 90 H1 .00000 .00000 .50000 4b

300 Fmmm V = 47.96Å3 H2 .00000 .00000 .72972 8i

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