Phase Transitions in Boron Carbide

Abstract

The idealized rhombohedral unit cell of boron carbide is formed by a 12-atom icosahedron and a 3-atom linear chain. Phase transitions are second order and caused by the exchange of B and C sites or by vacancies in the structure. Nevertheless, the impact of such minimal structural changes on the properties can be significant. As the X-ray scattering cross sections of B and C isotopes are very similar, the capability of X-ray fine structure investigation is substantially restricted. Phonon spectroscopy helps close this gap as the frequency and strength of phonons sensitively depend on the bonding force and mass of the vibrating atoms concerned. Phase transitions known to date have been identified due to significant changes of properties: (1) The phase transition near the chemical composition B₈C by clear change of the electronic structure; (2) the endothermic temperature-dependent phase transition at 712 K according to the change of specific heat; (3) the high-pressure phase transition at 33.2 GPa by the drastic change of optical appearance from opacity to transparency. These phase transitions affect IR- and Raman-active phonons and other solid-state properties. The phase transitions at B_~8C and 712 K mean that a well-defined distorted structure is converted into another one. In the high-pressure phase transition, an apparently well-defined distorted structure changes into a highly ordered one. In all these cases, the distribution of polar C atoms in the icosahedra plays a crucial role.

Keywords: boron carbide; electronic properties; phase transition; phonons; structural disorder.

Figure 1

Idealized rhombohedral unit cells of α-rhombohedral (structure formula B₁₂) boron and boron carbide (structure formula B₁₂ CBC) [12]. In (B₁₁C) CBC at the carbon-rich limit, the icosahedral C atom occupies one of the B(1) polar sites. Reprinted from Ref. [13] published by Elsevier Masson SAS. All rights reserved.

Figure 2

IR-phonon spectra of B_4.3C boron carbide and α-rhombohedral boron. The abscissas are shifted relative to one another to facilitate the correlation of icosahedral vibrations.

Figure 3

Shares of structure elements in the unit cell of boron carbide [16,22]; (a), B₁₂ and B₁₁C icosahedra, (b), CBC, CBB, and B☐B chains (☐, vacancy). Symbols connected with solid lines, isotope-enriched boron carbide; other symbols, polycrystalline boron carbide. Reprinted from Ref. [22] “© IOP Publishing. Reproduced with permission. All rights reserved”.

Figure 4

Empirical band scheme of boron carbide based on experimental results (see [3,4] and references cited therein).

Figure 5

B_4.3C. (a) Optical absorption edge [3,4,42]. Symbols, polycrystalline material; line, single crystal. (b) X-ray Raman scattering (XRS) spectrum [43]. Symbols selected experimental data for q = 1.05 °A⁻¹; line, site-specific ab initio calculation for the background of icosahedral B atoms. We assume that the composition of this boron carbide corresponds to B_4.3C, the carbon-rich limit of the homogeneity range; the composition B₄C claimed by the authors does not exist (see above).

Figure 6

B_4.3C, photoluminescence spectrum at 290 K [42]. Excitation with the 514.5 nm (2.4 eV) line of an Ar laser; intensity 280 mW mm⁻². Squares, experimental results; thin black lines, averaged experimental results, before and after subtracting the 1.56 eV model fit, respectively; thick colored lines, recombination models of free excitons (1.560 and 1.5695 eV, respectively).

Figure 7

Phase transition near the compound B₈C.

Figure 8

Phonon spectra of ¹¹B_xC at 30K [33,40]. (a), IR-active phonons; (b), Raman-active phonons.

Figure 9

(a). IR-active phonon of ¹¹B_xC near 400 cm⁻¹ (All fits were obtained using the Origin Pro software). (b). Phonon shift depending on C content and comparison between the reduction of phonon strength (components 1 and 2) and relation of the phonon strength of component #1 depending on C content compared with the relative share of CBC chains in the structure (obtained from the IR-active stretching vibration near 1600 cm⁻¹ in Figure 2b).

Figure 10

IR-active phonons near 700 cm⁻¹. (a), ¹¹B_xC at 30 K; (b), ^natB_xC at 160 K, phonon-wavenumbers of ^natB_4.3C and ^natB_10.37C.

Figure 11

IR-active phonons near 700 cm⁻¹. (a) Fits obtained with OriginPro software. (b) Wave numbers of phonon components vs. C content. The results of the high-frequency components of B_8.52C (C content 0.105) are rather uncertain.

Figure 12

IR-active phonons near 950 cm⁻¹. (1) and (2) mark the apparent shift and strength of specific components.

Figure 13

Heavily damped plasma absorption in ¹¹B_xC at 30 K [28].

Figure 14

Raman-active phonons of ¹¹B_xC at 270/320 cm⁻¹.

Figure 15

Specific heat of B_4.3C boron carbide vs. T. Black circles, measured; red dashed line, polynomial fit; blue, difference between measured data and fitted line; purple dotted line, 1st derivative.

Figure 16

IR-active phonon of ^natB_4.3C boron carbide near 400 cm⁻¹. (a) Absorption index k vs. wave number between 100 and 800 K; (b) wave number and phonon strength of the components vs. T. Black, bending mode of the CBC chain; red, icosahedral vibration.

Figure 17

The gap width of boron carbide depending on pressure. Black triangles, gap width, roughly estimated from transient-light photos [35]. Compared with experimental and theoretical results [45,46,60,61]; pink, ordered structure [60]; pink vertical bar, varying configurational disorder [60]; blue filled circles, pressure-dependence [35]. Experimental results: cyan, ambient conditions [62,63]; dash-dotted lines, adapted to relevant gap widths at 0 GPa for distorted and undistorted B_4.3C (Ektarawong’s RNG model), respectively; pressure-dependence according to the calculation for (B₁₂)CCC [61].

Figure 18

Electronic band scheme of B_4.3C boron carbide [17] derived from optical and electrical measurements; DOS calculated by Ektarawong et al. (RNG model) [45] and Rasim et al. [29] for reference (data taken from diagram each). Vertical arrows show absorption (upward) and emission (downward) processes; the visible range is marked. Reprinted from Ref. [17] published by Elsevier Masson SAS. All rights reserved.

Figure 19

IR phonon mode Grüneisen parameters below (▽) and above (△) the phase transition at 33.2 GPa. Insert: an example of determining γ.

Figure 20

Relative shift of phonon frequencies (left ordinate) and unit cell volume (right ordinate) vs. pressure, determining mode γ of typical IR-active phonons of B_4.3C boron carbide [13]. Insert: FT-Raman spectrum of single-crystal B_4.3C boron carbide at ambient conditions. Reprinted from Ref. [13] published by Elsevier Masson SAS. All rights reserved.

Figure 21

Wave numbers of the Raman-active 270/320 cm⁻¹ doublet and ratio of the phonon strengths of both components.