Electronic structure and bulk properties of MB6 and MB12 borides

Abstract

Ab initio band structure calculations are carried out for the higher borides MB 6 and MB 12 . Highprecision measurements of the elastic constants are performed for the compounds ZrB 12 , HoB 12 , ErB 12 , TmB 12 , LuB 12 , YB 6 and LaB 6 at low temperatures. The bulk properties of the borides are analyzed on the basis of the calculated equations of states and balanced crystal orbital overlap populations. Our calculations indicate that hexaborides with divalent metals, CaB 6 , SrB 6 , BaB 6 , and YbB 6 , are semiconductors with small energy gaps. The metallic MB 6 hexaborides with trivalent M atoms are found to possess larger bulk moduli values. For dodecaborides the bulk moduli are found to be higher for MB 12 with increased filling of the conduction band ͑ZrB 12 , HfB 12 , UB 12 ͒ in comparison with M 3+ B 12 compounds. The total energy calculations for different magnetic configurations in YbB 12 point to the possibility of antiferromagnetic coupling between Yb 3+ ions.

Metal Hexaborides with Sc, Ti or Mn

“…With reference to Figure 2, this suggests that ionic radii 0.80 < r R < 0.85 is a lower limit for an eight-fold coordinated metal. This lower limit is also consistent with published theoretical values of lattice constants for hexaboride structures [33].…”

“…Valence state also influences these properties as divalent hexaborides are commonly insulators or semiconductors and trivalent hexaborides are commonly metallic [5,33,37]. As noted earlier, KB 6 is identified as not a "normal" metal [12] and ThB 6 is a paramagnetic metal [13].…”

“…Theoretical calculations of elastic, electronic and lattice dynamic parameters for metal hexaboride structures are ultimately constrained by geometry or crystal structure [33,34,37]. Valence state also influences these properties as divalent hexaborides are commonly insulators or semiconductors and trivalent hexaborides are commonly metallic [5,33,37].…”

Crystal Structure and Physical Properties of HfB4 via First-Principles Calculations

“…The calculated bulk modulus, shear modulus, Young's modulus, and Poisson's ratio of the Cmcm phase together with the reference materials mentioned above are tabulated in Table 2. As shown in Table 2, the calculated bulk modulus of the Cmcm-HfB4 (243 GPa) is larger than those of HfB [39,40], ZrB12 [63][64][65], and YB4 [8,66] but is comparable to those of HfB2 [43][44][45], HfB12 [48], and other TMB4 (TM= Fe [12,13,67,68], Cr [13,14,69], Mn [11,70], Zr [23], and Ta [27]), indicating its strong ability to resist the volume deformation. Moreover, the bulk modulus (B=243 GPa) for the Cmcm-HfB4 is in consistent with that directly obtained from the fitting results (B0=244 GPa) of the third-order Birch-Murnaghan equation of states, which further demonstrates the good accuracy of our elastic calculations.…”

Аномальные низкочастотные фононы в ZrB-=SUB=-12-=/SUB=-

“…Последние были использова-ны для оценки изотермических параметров Грюнайзена γ T = B 0 (∂ ln(ω)/∂P) для различных компонент спектра. Модули упругости B 0 приняты равными 234 GPa для ZrB 12 и 232 GPa для LuB 12 [28]. Средняя величина γ T = 4.3(4) для трех низкочастотных компонент двухфо-нонного спектра ZrB 12 100 cm −1 близки к ранним оценкам макроскопического коэффициента Грюнайзена γ = 4 [6], что указывает на сильный квазиангармонизм мягких фононов, и служат дополнительным подтверждением предложенной иден-тификации наблюдаемых в ZrB 12 спектров.…”