Boron carbide B4C was discovered1 in 1858, and its crystal structure was first established2 in 1934. It belongs to icosahedral boron compounds, a family of crystalline solids with crystal structures based on various arrangements of B12 icosahedra, which are considered to be some kind of B12 “molecules”. In such solids chemical bonding has been rationalized in terms of polycenter bonds on the B12 closo -cluster (boron icosahedron) and two-electron-two-center (2e2c) and two-electron-three-center (2e3c) bonds between the clusters3. According to the Wade-Jemmis rule4,5,6 26 out of 36 valence electrons of a B12 cluster are accommodated in 13 molecular-orbital-like bonding orbitals to form the cluster. This leaves 10 electrons for external bonding using 12 equivalent external bonding orbitals, thus creating an electron deficiency in the B12 cluster. For a long time, this ‘electron deficiency’ of the intraicosahedral bonding relative to the intericosahedral one was expected to make the icosahedra more compressible compared to the unit cell, contrary to what is known for typical molecular solids. For this reason the icosahedral boron-rich solids were understood as “inverted-molecular” solids7. This gave the origin to the problem of the ratio of the rigidity of the B12 closo -cluster and the unit cell and the mechanism of compression in icosahedral boron-rich solids that had to be proven experimentally.

The first work, which aimed to shed light into the mechanism of compression of icosahedral boron-rich solids in general and boron carbide in particular, was a high-pressure powder neutron diffraction study of boron carbide (B4C) to 11 GPa conducted by Nelmes and co-authors8. By the linear fit of the experimental ‘pressure versus volume’ (P-V) data obtained for both the icosahedron and the unit cell of B4C, the bulk moduli of the icosahedron and the entire structure were determined to be 169(6) GPa and 199(7) GPa, respectively. This led to conclusion that the icosahedron is 23(4) % more compressive than the unit cell of boron carbide, which thus behaved as an “inverted-molecular” solid8.

An experimental evidence that icosahedral boron materials on compression may not behave as “inverted-molecular” solids came from the single-crystal X-ray diffraction data to 65 GPa obtained for the high-pressure boron allotrope, γ-B9. The bulk modulus of the B12 icosahedron was determined to be 285(6) GPa, whereas the bulk modulus of the entire γ-B structure was found to be 227(3) GPa9.

A new insight into the situation in boron carbide, compared to the very first measurements8, was given due to a compressibility study of “nearly stoichiometric boron carbide B4C”10. Single crystals of B4C were investigated using synchrotron X-ray diffraction in a diamond anvil cell to 74 GPa. The structure of B4C was understood as consisting of B11C icosahedra interconnected by the C-B-C chains. The parameters of the equation of state (EoS) of boron carbide were K 300 = 243 (6) GPa (K′ = 3.6 (2)) or 236 (8) at fixed K′ = 4 (K 300 is the bulk modulus, and K′ is its pressure derivative; the zero pressure unit cell volume was fixed on the ambient pressure experimental value). Dera et al.10 pointed out that the “icosahedron volume compression did not follow a typical EoS functional behavior” and they did not calculate the bulk modulus of the B11C icosahedron. Nevertheless, they reported that the B11C icosahedron showed a 13% volume reduction, which was smaller than that of the unit cell volume (18%). The general conclusion was that B4C behaves as a molecular solid10 that is in accordance with the results obtained for γ-B9.

Optical properties and evolution of Raman modes of the same B4C samples, which were characterized and studied using single-crystal X-ray diffraction in ref. 10, were also investigated up to 70 GPa by the same research group11. Based on their spectroscopy data, the authors11 reported high-pressure phase transition in boron carbide at 40 GPa, although, according to Dera et al.10, no signatures of structural phase transitions were observed in B4C by high-pressure XRD studies up to 70 GPa10. Verifying these mutually contradictive reports on boron carbide is not only scientifically important on itself, but it is additionally justified in connection to the commercial value of this unique material. Boron carbide is a very hard and, at the same time, lightweight material for applications in personal security (bullet-proof vests)3. It possesses the highest Hugoniot elastic limit of ceramic materials (ca. 17–20 GPa), i.e. the maximum uniaxial dynamic stress that the material can withstand elastically, surpassing all its denser competitors such as silicon carbide and alumina by a factor of 2 (ref. 12). However, it fails just above the Hugoniot elastic limit and the possible source of failure could be clarified through high-pressure experiments. Thus, establishing the mechanism of compression of boron carbide, clarifying its mechanical properties and limits of its stability under loading, are of both scientific and practical interest.

Here we report high-pressure investigations of stoichiometric boron carbide B13C2 using high-pressure single-crystal X-ray diffraction up to 68 GPa. Single crystals of B13C2, which we study here, were characterized in detail in previous work of our group13. It was established that B13C2 is fully ordered and stoichiometric, and carbon atoms occupy a single position (at the ends of the C-B-C chains)13. In the present work we could track all changes of the crystal structure, atomic positions, and bond lengths with the high accuracy up to 68 GPa. This enabled us to establish the equations of state of both the B13C2 crystal and the B12 icosahedron. As the B12 icosahedra in the stoichiometric boron carbide B13C2 do not contain any carbon atoms, contrary to all previously investigated boron carbides8, 10, 14,15,16,17,18,19,20,21,22,23,24, we could compare the compressional behavior of B12 closo-clusters in B13C2 and boron allotropes α-B and γ-B and conclude not only regarding the ratio of the rigidity of the B12 closo-cluster and the unit cell in these materials, but also concerning the mechanism of compression of boron-rich icosahedral solids.


The equations of state of B13C2 and B12 icosahedra

The single-crystal X-ray diffraction data for B13C2 obtained at variable pressure and some experimental details are presented in Table 1. The quality of the data allowed the refinement of both the lattice parameters and atomic coordinates (Supplementary Table S1). The quality of the structural refinement was good up to the highest pressure achieved that gives evidence that in the course of compression the crystals were maintained in quasihydrostatic environment.

Table 1 Crystallographic details of B13C2 at variable pressure. Formula: B13C2; Crystal System: Trigonal; Z = 3; Space group: R \(\mathop{{\boldsymbol{3}}}\limits^{\bar{}}\) m, crystal size 10 × 10 × 15 µm3 (crystal 1) and 20 × 15 × 10 µm3 (crystal 2, designated as “cr2”).

In the structure of boron carbide B12 icosahedra are located in the corners of the rhombohedral cell, and intericosahedral three-atom C-B-C linear chains are oriented along its body diagonal (Fig. 1a, right). As seen in Fig. 1, the structure of B13C2 is very similar to those of α-B and γ-B, which can be described in terms of a cubic closest packing (ccp) of spheres, where B12 icosahedra play the role of “spheres” (Fig. 1a,b). The unit cell parameters of B13C2 in hexagonal setting are a = 5.5962 (3) Å, c = 12.0661 (7) Å, (space group R \(\mathop{3}\limits^{\bar{}}\) m), as determined in ref. 13. Boron atoms in the crystal structure of B13C2 (Fig. 1) occupy three crystallographically independent positions (BP , BE, and BC) and the forth position is occupied by carbon atoms in the C-B-C chains13. In the present paper we adopt the nomenclature introduced by ref. 13: boron atoms forming the boron icosahedra are labeled as BP (polar positions) and BE (equatorial positions), BC designates the boron atom in the center of the C-B-C chain (Fig. 1).

Figure 1
figure 1

Crystal structures of α-B, γ-B and B13C2. (a) Rhombohedral cells of α-B and B13C2 compared to the elemental rhombohedron which can be selected in the structure of γ-B. (b) Single layers of the cubic closest packing (ccp) of icosahedra in the structures of α-B, γ-B. and B13C2. The view is perpendicular to the layers: for α-B and B13C2 the direction of the view coincides with the c-axis of the trigonal unit cell (hexagonal settings), for γ-B it coincides with the direction (see text). (c) The packing of icosahedra shown in projection along the axes of the rhombohedral cells for α-B and B13C2 and along the a-axis for γ-B. (d) Fragments of the structures of α-B, γ-B and B13C2 showing different types of bonds in the corresponding structures (see text for details). In all structure drawings, atoms in crystallographically independent positions are marked in different colors: for α-B and B13C2 BP are blue, BE are green; for B13C2 carbon and boron atoms of the C-B-C chains are BC (violet) and C (red). For γ-B B1 are blue, B2 are green, B3 are purple, B4 are orange, B5 are violet. Different types of bonds are shown in different colors: 2e2c bonds are yellow, 1e2c bonds are magenta, 2e3c bonds are brown triangles, 3e3c bonds are black.

In this study, all observed reflections perfectly match the B13С2 structure up to the highest pressure reached. Our X-ray diffraction data did not reveal any indication of a phase transition. All the unit cell parameters smoothly decrease on compression (Table 1). Figure 2 presents the dependence of the relative unit cell parameters (a/a 0 and c/c 0) and the relative unit cell (V/V 0) volume of B13C2 on pressure up to 68 GPa. As seen (Fig. 2), the structure of B13С2 is slightly more compressible along the c direction.

Figure 2
figure 2

Pressure-dependent evolution of the relative lattice parameters and the relative unit cell and B12 icosahedron volumes for B13C2. Continuous lines show the fit of the corresponding data with the third-order Birch-Murnaghan equation of state.

The whole experimental volume-pressure data set was fitted using the third-order Birch-Murnaghan (3BM) equation of state that gave the following EoS parameters: V 0  = 327.25 (4) Å3, K 300  = 239 (7) GPa and K′ = 3.2 (3) (V 0 is the zero pressure unit cell volume, K 300 is the bulk modulus, and K′ is its pressure derivative) (Table 2). The fit with the fixed K′ = 4 resulted in the bulk modulus of K 300  = 222 (2) GPa, being lower than that with the free K′.

Table 2 Parameters of the equations of state of B13С2, B4C, α-B, and γ-B obtained on the basis of single-crystal XRD in comparison with those of icosahedra. Volume reduction of the unit cells and icosahedra on compression was calculated for the pressure range from ambient to 60 GPa.

The evolution of the relative volume of the B12 icosahedron (V ico /V ico0 ) with pressure is presented in Fig. 2. It is very similar to that of the unit cell volume. The whole experimental data set of the icosahedra volumes versus pressure (Table 3) was fitted using the 3BM EoS. The EoS parameters were obtained as follows: V ico0  = 12.50 (3) Å3, K ico  = 239 (23) GPa, and K ico ′ = 3.8 (8) (V ico0 is the zero pressure icosahedron volume, K ico is the bulk modulus of icosahedra, and K ico is its pressure derivative). The fit with the K ico  = 4 (fixed) results in a very close value of K ico  = 234 (7) GPa. A comparison of the bulk moduli found for the B13С2 crystal and the B12 icosahedron (Table 2) shows that the bulk B13С2 and the icosahedron have the similar rigidity.

Table 3 The B12 icosahedron volume and bond lengths in boron carbide at variable pressure. “cr2” designates crystal 2. BP , BE and BC are designations from Mondal et al.13; b1 through b7 are designations from Dera et al.10.

Evolution of the bond lengths on compression of B13С2

Recent experimental electron-density study using low-temperature high-resolution single-crystal synchrotron X-ray diffraction data13 clarified the bonding situation in the stoichiometric boron carbide B13С2. In the present work, we investigated single crystals from the same batch. For consistency, we adopt here the notations of bonds introduced in ref. 13.

There are seven distinct bonds in the structure of boron carbide (Table 3), which get into three groups13 (see Fig. 1d, bottom, for bonds notations): intra-cluster polycentral bonds (BP–BP , BE–BE, 1BP–BE and 2BP–BE); inter-cluster bonds (BP–BP), which connect atoms in the polar sites (BP) of the neighboring icosahedra; and bonds involving C-B-C chains (C–BE and C– BC).

Single-crystal X-ray diffraction data, collected at eleven pressure points in the interval from 4 GPa to 68 GPa, allowed us to follow changes in the length of each of the seven bonds in the structure of boron carbide B13С2 (Table 3). All bonds gradually shorten under compression (Fig. 3); their pressure-dependent evolution does not show any anomalies (Fig. 3).

Figure 3
figure 3

Pressure-dependent evolution of bonds of B13C2. (a) Intraicosahedral bonds; (b). Intericosahedral bonds. Bonds designations are according to Mondal et al.13, corresponding notations from Dera et al.10 (b1 through b7) are given in brackets to make it easier to compare.


As mentioned in the introduction, bulk compressibility of boron carbide compared to compressibility of icosahedra has been a matter of debate. Nelmes et al.8 reported the crystal structure to be more rigid than the icosahedron cluster, whereas Dera et al.10 observed an opposite relation.

Our results have shown that the rigidity of the crystal structure of stoichiometric boron carbide B13C2 is similar to that of the B12 icosahedron. Within the standard uncertainty, we found the bulk moduli of the bulk material and the icosahedra to be similar: K 300  = 239(7) GPa (K′ = 3.2(3)) versus K ico  = 239(23) (K ico  = 3.8(8)) (with the fixed K′ = 4, K 300  = 222(2) GPa versus K ico  = 234(7) GPa). The volume reduction of the unit cell of B13C2 and the volume reduction of the icosahedron in the pressure interval between ambient and 60 GPa were calculated to be also similar (18.7% versus 18%, respectively); the difference is less than 1% and within the uncertainty. The bulk modulus obtained by Dera and co-authors10 for the crystals of B4C is in a very good agreement with our result: their 3BM EoS parameters are K 300  = 243 (3) GPa, K′ = 3.6(6), and V 0  = 330.59(5) Å3 (V 0 was fixed at experimental value obtained at ambient conditions); with the fixed K′ = 4, they got K = 236(8) GPa10. The volume reduction of the unit cell of B4C (18%)10 matches very well to what we obtained for B13C2. But interestingly, the volume reduction of the icosahedron in B4C in the same pressure interval (between ambient and 60 GPa) in ref. 10 appeared to be different (13%) (see Table 2).

To clarify a reason of the apparent difference in the ratio of the rigidity of the unit cell and icosahedra found for B13C2 and B4C10, we first compared the icosahedron and the unit cell volume evolution with pressure in the stoichiometric boron carbide B13C2 and boron allotropes α-B25 and γ-B9. In the structures of each of these materials, icosahedra (B12) are built of exclusively boron atoms. Table 2 demonstrates a remarkable observation: in the same pressure range (from ambient up to 60 GPa), the unit cell volume reductions for all these materials are similar (ca. 18% within less than 1% deviation). The B4C, containing B11C icosahedra, is not an exception (18%)10. However, the icosahedra volume reductions are all different and reduce in the raw B13C2 (18.1%), γ-B (16.9%), α-B (14.5%), and B4C (13%). This observation is striking enough and desires an explanation through an insight into the compressional behavior of individual bonds in these solids.

To visualize the difference in the rates of changes of the bond length and compare boron carbide B13C2 with α-B and γ-B, experimentally obtained data for the relative changes of the bond lengths (l P /l P0 ) versus pressure was linearly fitted for all the bonds (l P is the length of the bond at pressure P; l P0 is the length of this bond at P0 = 4.0 GPa, the first pressure point available in our experiment in the DAC). We plotted calculated “line slopes” against corresponding interatomic distances l P0 (Fig. 4) at the lowest pressure, similarly to how it was done for characterization of the bond lengths’ change under pressure for various boron-rich compounds26 and α-B25.

Figure 4
figure 4

Relative change of interatomic distances for α-B, γ-B and B13C2 single crystal plotted against their length at lowest pressure as revealed by in situ single-crystal X-ray diffraction. Circles stay for bonds in α-B, triangles for γ-B, and squares for B13C2. Intraicosahedral bonds are outlined by the black rectangular; red, purple and orange symbols correspond to α-B, γ-B and B13C2, respectively. Intericosahedral bonds and those involving B-B dumbbells and C-B-C chains are shown in green, blue, and black colors for α-B, γ-B and B13C2, respectively.

As seen in Fig. 4, all the points corresponding to the inter-cluster bonds (C–BC, C–BE, and BP–BP) in B13C2 (black squares) lie on one line, and the rate of their compression depends on the initial length of the bonds (the C–BC bond between carbon and boron atoms of the C–BC–C chain is the shortest one, see Fig. 1a, right panel; Fig. 1d, bottom panel; Fig. 1b, right panel). Points corresponding to inter-icosahedral bonds in α-B (green circles in Fig. 4) drop on the same line: initially shorter BP–BP bonds contract slower than the initially longer BE–BE contacts. All points corresponding to the intra-cluster B-B contacts, i.e. those involved in formation of the polycentral bonds of the B12 closo-cluster, for both B13C2 and α-B (orange squares and red circles, correspondingly, in Fig. 4) appear in a very compact area in Fig. 4, indicating similar rates of contraction and their similar lengths at ambient conditions. Why then the B12 icosahedra in B13C2 and α-B undergo such a dramatically different volume reduction (18.1 vs 14.5%) when their crystals are compressed to 60 GPa? Purely geometrical consideration is simply not appropriate. One must take into account types of bonding in each of the solids.

As already mentioned, due to recent experimental electron-density studies of boron allotropes and boron carbide13, 27, 28, the validity of the Wade-Jemmis model (see introduction) was demonstrated for α–B27, γ–B28, and B13C2 13. In all these solids, the molecular-orbital-type bonding on the icosahedral clusters leaves for exo-cluster bonding twelve sp hybrid orbitals perpendicular to the surface of the clusters. Thus, in terms of bonding, we can consider B12 closo-clusters to be similar in these three substances. Concerning the inter-cluster bonds, they were found to be very different in α–B27, γ–B28, and B13C2 13. In α–B and B13C2 the BP–BP bonds connecting polar BP atoms (those between neighboring close-packed layers of B12 icosahedra) are strong covalent 2e2c bonds (see Fig. 1a–c, left and right panels; Fig. 1d, top and bottom panels). The BE–BE contacts in α–B27 are very flexible, because they are a part of relatively weak 2e3c BE–BE–BE bonds (shown by brown triangles in Fig. 1). Instead of these weak bonds, in the same positions (octahedral voids of the ccp) B13C2 possesses three strong 2e2c C–BE bonds, which are additionally strengthened by the 3e3c bonds of the C–BC–C chains, which impose supplementary negative pressure upon the surroundings, as described in ref. 13. Now it is clear that the similar contraction of the crystals of α–B and B13C2 (ca. 18%) happens in B13C2 on the expense of the icosahedra, which are set into the very rigid surrounding of strong 2e2c and even stronger 3e3c bonds, but in α–B on the expense of weak 2e3c bonds. This conclusion is justified by the behavior of the unit cell parameters ratio c/a in α–B and B13C2 upon compression: in α–B the c/a ratio increases with pressure, but it decreases in B13C2 (Fig. 5). In the both cases, above ca. 40 GPa a clear tendency to the leveling is observed that reflects the more homogeneous compression in the both directions at further pressure increase.

Figure 5
figure 5

Evolution of the ratios of the unit cell parameters c/a of α-B and B13C2 compared to that of c′/a′ of γ-B. For α-B the data are taken from Chuvashova et al.25 for γ-B from Zarechnaya et al.9.

In the light of the consideration made for α–B and B13C2 above, it is not a surprise now that the volume reduction of B12 icosahedra in γ–B (16.9%) is intermediate between those in α–B and B13C2 in the same pressure range. As shown in ref. 28, in γ–B there is a broad diversity of inter-icosahedral bonds and those involving the boron dumbbell (Fig. 1a–d, middle panels): three different kinds of strong 2e2c bonds (B3-B3, B2-B5, and B5-B5); for consistency, we follow here the atoms and bonds notations introduced for γ–B in refs 9 and 28. Although initially B5-B5 is slightly longer than B3-B3 and B2-B5, it contracts slightly slower than the latter two. The presence of two types (2e3c and 1e2c) of polar-covalent bonds (2e3c B4-B4-B5, involving two boron atoms of one icosahedron and one atom of a dumbbell, and 1e2c B1-B4, involving atoms of neighboring icosahedra at a distance slightly shorter than that between the BE atoms in α–B) makes the rigidity of the inter-icosahedral space in γ–B to be intermediate between those in α–B and B13C2 (see Fig. 1). To compare the pressure evolution of the c/a ratio in α–B and B13C2 with the evolution of the corresponding c′/a′ ratio in the structure of γ–B (c′ is in the direction perpendicular to the close-packed layers and a′ - within the layer), we expressed the c′ and a′ through the a, b and c parameters of the orthorhombic unit cell of γ–B and plotted the c′/a′ ratio vs P in Fig. 5. As seen, the c′/a′ ratio in γ–B, similarly to what is observed in α–B, first slightly increases, then saturates. Supplementary Figure S1 shows the pressure evolution of the normalized c/a ratios for all of these three solids: the c′/a′(P) curve of γ–B indeed takes an intermediate position between the c/a(P) curves of α–B and B13C2. Thus, the compressional behavior of γ–B is likely controlled by the balance between the contraction of icosahedra and the inter-icosahedral bonds. Figure 4 confirms this interpretation: the lengths of intra-icosahedral contacts in γ–B at ambient pressure are quite similar to those of α–B and B13C2 (see positions of purple triangles in Fig. 4), whereas rates of their contraction under pressure vary considerably (see their scatter within the black rectangular outlining the intra-icosahedral bonds in Fig. 4). Some of them are as compliant as inter-icosahedral contacts (B1-B4 and B5-B5), whereas others are almost as stiff as 2e2c bonds inter-icosahedral and dumbbell bonds of γ–B itself and 2e2c bonds of boron carbide.

Coming back to the difference in the compressibility of icosahedra in B4C10 and stoichiometric boron carbide B13C2, one should take into account different chemical composition, i.e. the boron to carbon ratio, of these two carbides. It is established that boron carbide exists as a single-phase material with a wide homogeneity range of carbon content, from ~7 at. % (B14C) to ~20 at. % (B4.3C), realized by the substitution of boron and carbon atoms for one another within both the icosahedra and intericosahedral chains16. Proposed stoichiometries are based on two extreme models, B12 (CBB) on the boron-rich and B11C(CCC) on carbon-rich ends. The location of C atoms in the crystal structure has been a long-standing debate10, 14,15,16,17,18,19,20,21,22,23,24, as it was difficult to clarify on the basis of powder diffraction data, or even single-crystal diffraction data of insufficient quality. Spectroscopic methods cannot directly give the localization of atoms, as the interpretations of spectra depend on models involved, the spectral range considered, and many other factors which introduce uncertainties.

For their “nearly stoichiometric boron carbide B4C” Dera et al.10 suggested the presence of 85 atomic % boron and 15 atomic % carbon in the BP positions in B11C icosahedra. The presence of carbon likely has to lead to an increase of the rigidity of the icosahedron closo-cluster of B4C due to the higher electronegativity of carbon compared to boron. Indeed, the volume reduction of the B11C icosahedron (13%)10 appears to be smallest compared to B12 icosahedra in boron allotropes α–B (14.5%) and γ–B (16.9%) (see Table 2). The stoichiometric boron carbide B13C2 studied in the present work has been proven to contain carbon only in the C-B-C chains13. The refinement of the site occupancies for BC and C atoms at all pressure points (except the point at 4 GPa, where Rint is relatively high and there is no meaning to refine additional structural parameters) gives the value of 1.000 (2). Thus, there is no any sign of vacancies in the C–BC–C triads. An attempt to substitute BP and BE atoms in icosahedra by carbon and refine the amount of C results in a full occupancy of the corresponding positions by boron atoms (within the uncertainty of 0.003). The B12 icosahedra in the studied boron carbide have a proven B12 composition (see also ref. 13 for extended discussion) and appear to be much more compliant than B11C icosahedra (Table 2); moreover, their compliance is similar to that of the whole structure. This observation gives additional evidence that the stoichiometric boron carbide B13C2 is a compound with true covalent bonding: B12 icosahedra do not play a role of “molecules”, their conventional separation is surely convenient for geometric presentation of the structure, but the compressional behavior of the stoichiometric boron carbide is governed by a complex interplay of both intra-cluster and inter-cluster bonds, as well as those involving C–B–C chains.

To conclude, in the present work we have studied the compressional behavior of the stoichiometric boron carbide B13C2 in the pressure interval up to 68 GPa. Our single-crystal synchrotron X-ray diffraction investigations revealed structural stability of the boron carbide in the studied pressure range. A comparison of the unit cell volume reduction with the reduction of the volume of the B12 icosahedron upon compression of B13C2 from ambient pressure to 60 GPa revealed their similarity. This confirms that the stoichiometric boron carbide B13C2 is a true covalent compound and does show neither ‘molecular-like’ nor ‘inversed molecular-like’ solid behavior upon compression, as previously disputed. Our analysis has shown that, in agreement with the modern understanding of bonding in α–B, γ–B, and B13C2 based on the experimental electron-density studies13, 27, 28, the compressional behavior of these boron allotropes and boron carbide depends on the types of bonding involved in the course of compression, so that the ‘effective compressibility’ of B12 icosahedra may vary in a broad range, from ca. 14% in α–B to ca. 18% in B13C2, as compared to ca. 18% of compression of the corresponding crystals.

Methods summary

Synthesis of crystals

Single crystals of B13С2 were synthesized at high pressures (8.5–9 GPa) and high temperatures (1873–2073 K) using the large-volume-press technique. The stoichiometric composition B13C2 was determined by single-crystal X-ray diffraction in agreement with energy-dispersive X-ray (EDX) analysis (B6.51 (12)C)13 and results of Laser Ablation ICP-MS (B6.5(2)C). By LA-ICP-MS boron, carbon, and trace element concentrations in the material were measured using a 193 nm ArF Excimer laser (GeolasPro, Coherent, USA) attached to an Elan DRC-e (Perkin Elmer, Canada) quadrupole mass spectrometer. The presence of impurities exceeding ppm level could be excluded. At ambient conditions the crystals of the stoichiometric boron carbide B13C2 are semitransparent and have a characteristic dark red or maroon color13. This optical property distinguishes them from crystals of non-stoichiometric or disordered boron carbide, which is described as black material.

Diamond-anvil cell experiments

The BX90-type diamond anvil cells (DAC)29 made at Bayerisches Geoinstitut (Bayreuth, Germany) and diamonds with the culet diameters of 250 µm were used in high pressure experiments. Rhenium gaskets were squeezed between the diamonds to make an indentation with the thickness of 30 µm. Then in the center of indentations, round holes of 120 µm in diameter were drilled. The B13С2 crystals were placed into these chambers. Sizes of the crystals were about 10 × 10 × 15 µm3 and 20 × 15 × 10 µm3. Neon was used as a pressure transmitting medium. Ruby balls used for pressure calibration were placed into the pressure chamber.

Single-crystal X-ray diffraction

Crystals with size of about 10 × 10 × 15 µm3 were selected for measurements in a DAC at ID27 at the European Synchrotron Radiation Facility (ESRF). Diffraction data were collected at 293 K using the Perkin Elmer XRD1621 flat panel detector. The monochromatic radiation had the wavelength of 0.37380 Å and the crystal-to-detector distance was 383 mm. Pressure in the cell was increased up to 68 GPa with a step of about 6 GPa. 160 frames in the omega scanning range of −40° to +40° were collected (0.5° scanning step size) with an exposure time of 1 s. Integration of the reflection intensities and absorption corrections were performed using CrysAlisPro software30, 31. The structure was refined in the anisotropic approximation for all atoms by full matrix least-squares using Jana2006 software32.