Effect of surface energy on the growth of boron nanocrystals

Abstract

Abstract. The surface energies of α-rhombohedral (α-rh), β-rhombohedral (β-rh), α-tetragonal (α-t), and β-tetragonal (β-t) boron were calculated from first principles to investigate their role in nano-scale crystal growth. Equilibrium shapes of boron crystals were obtained using Wulff's theorem. Our results shows that α-t boron, despite its low cohesive energy, is more stable than the other structures as a result of its low surface energy when the number of atoms is less than about 216. Since the nanowire of α-t boron that was obtained experimentally was larger than this, it was probably in a metastable state. The difference between the surface energy of the abplane and that of the ac-plane explains why the α-t nanowires grow in the c direction.

First-principles study of the crystal and electronic structures of α-tetragonal boron

“…They detected no impurities in the a-t boron obtained; this was inconsistent with the view generally accepted since the experiment by Amberger et al in 1971 [14-16]. We have theoretically proven that a-t boron has so small a surface energy that it could be more stable than the other polymorphs when a crystal is in nanoscale, and we have proposed a model in which the boron nanobelt is grown on the basis of a stable nucleus of a-t structure [26][27][28].…”

“…However, this does not mean that a-t boron is more stable than a-and b-rh boron, since the lattice shapes are different in each case, and besides, b-rh boron could be slightly more stable with defects and interstitial atoms [45][46][47]. In our previous work, we proved that nanosized a-t boron can be synthesized because of its low surface energy, even though it has a lower cohesive energy than a-and a-rh boron [26][27][28]. If a-t boron were to have a structure like that of configuration B, then a-t boron could be produced more easily than we expected.…”

“…The cohesive energy per atom, 5.983 eV, was much higher than that of B 50 (5.913 eV) and was as high as those of a-and b-rh boron (5.979 and 5.976 eV, respectively) calculated by the same method and under the same conditions. Thus the synthesis of a-t boron may be easier than was previously considered [26][27][28]. However, this does not mean that a-t boron is more stable than a-and b-rh boron.…”

Electronic structures and mechanical properties of boron and boron-rich crystals (Part I)

“…Therefore, it is now almost accepted that pure α-tetragonal form cannot exist. However, there is a possibility that pure α-tetragonal boron exists in nanocrystals; see [60] and the references therein. A compound AlB 12 can be also regarded as a crystal whose structure is stabilized by impurity [61][62][63].…”

Wulff Constructions for an Equilibrium MFI-Type Zeolite Shape Modelling under Different Conditions

“…For example, α-tetragonal (α-t) boron has been shown to be more stable than α-rhombohedral (α-rh), βrhombohedral (β-rh), or β-tetragonal (β-t) boron due to its lower surface energy. Then, the equilibrium shapes of the born crystals were determined using Wulff's theorem [21]. Using density functional theory (DFT) calculations, Jiang et al obtained the surface energies of six low-index stoichiometries of TiO 2 .…”