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I have read that boron, due to the very high sum of its first three ionization energies, it is not able to form its +3 ions, and thus it generally forms only covalent compounds. But in a popular Indian engineering entrance exam: JEE MAINS-2014 19th April paper, this question was asked:

Which of these statements is not true ?

  1. In aqueous solution, the $\ce{Tl+}$ ion is much more stable than Tl (III)

  2. $\ce{LiAlH4}$ is a versatile reducing agent in organic synthesis.

  3. $\ce{NO+}$ is not isoelectronic with $\ce{O2}$

  4. $\ce{B}$ is always covalent in its compounds.

The answer given was 4.

I get that there might be an exception but I'm not able to find it anywhere. If there exists an ionic compound of boron, could someone please mention that to me?

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    $\begingroup$ Ever heard of MgB2? $\endgroup$ – Ivan Neretin Dec 14 '20 at 5:41
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    $\begingroup$ @IvanNeretin The difference in Pauling electronegativities between Mg and B is only 0.7 (for comparison, that's less than the 0.9 between C and O), suggesting that bonding between Mg and B would be polar covalent, rather than ionic, in character. $\endgroup$ – theorist Dec 14 '20 at 5:49
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    $\begingroup$ @IvanNeretin The bonding in MgB2 seems complex. I looked at a few articles, and it appears that it consists of graphene-like covalently bonded sheets of boron itercalated with Mg atoms, where the Mg acts metallically, i.e., that it consists of a combination of covalent and metallic bonds: mdpi.com/2410-3896/4/2/37 (the borons are the small blue spheres, and the blue rods are covalent boron-boron bonds). $\endgroup$ – theorist Dec 14 '20 at 6:21
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    $\begingroup$ Nope, it doesn't justify the claim. These articles are saying the borons are bonded covalently, and the magesiums are interacting metallically. For there to be ionic bonds between the borons and the magnesiums, there would need to be sufficent charge transfer between the borons and the magnesiums for their interaction to be considered ionic, and these articles don't indicate that. I.e., the picture they're painting doesn't seem to be negative borons bonded to positive magnesiums, but rather neutral covalently-bonded borons sitting in a sea of positive magnesium ions and negative electrons. $\endgroup$ – theorist Dec 14 '20 at 6:39
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    $\begingroup$ See: chemistry.stackexchange.com/questions/100419/… $\endgroup$ – Nilay Ghosh Dec 14 '20 at 7:58
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Boron can form ions but there is some fine print. You won't get monatomic cations like the metals below it. Instead, ionic boron structures are formed from clusters where the ionic bonding is driven by the molecular orbital structures in these clusters, not by electronegativity (cf. This answer).

Such clusters are internally held together by covalent bonds between the boron atoms, so in this sense boron is still forming covalent bonds. The ionic bonds would be with atoms of other elements outside the boron cluster. Since the valence shells of a neutral boron atom are less than half filled the clusters will likely have low-energy, bonding orbitals that require electrons from outside atoms. Thus the boron clusters will be anionic and the ionic bonds will be most likely formed with electropositive metals. As suggested in the comments, magnesium diboride, $\ce{MgB2}$, is one of the most widely studied compounds containing such boron clusters. It has drawn much research interest because of its relatively high critical temperature (39 K) for superconductivity, which may be related to the impact of ionic magnesium-boron bonding on the eletronic interactions that lead to superconduction.

Magnesium diboride has a layered structure in which magnesium layers alternate with boron layers. The latter are covalently bonded into a hexagonal honeycomb, resembling a carbon layer in graphite. However, in the boron layers each atom supplies only three electrons per atom instead of four, so the layers may act as electron-accepting structures to form macro-anion having the formula $\ce{B^-}$. An ionic model for the diboride would then have the empirical formula $\ce{Mg^{2+}(B^-)2}$. Here I discuss two references I have examined, in which the bonding is examined and the results may be compared with this model.

De la Mora et al. [1] compare magnesium diboride with other $\ce{MeB2}$ diborides using early transition metals and aluminum (the latter might also be regarded as having early-transition-metal character, as there is no $d$ block separating this element from magnesium). They find that while all the diborides have significant ionic character, this ionicity is enhanced in the magnesium compound. Thereby the magnesium compound has increased electrical-conduction anisotropy as the valence electrons are strongly localized towards the boron layers. Zirconium diboride, with less ionic bonding and less electron localization, is also superconducting, but its critical temperature according to this reference is only 5.5 K versus 39 K for the magnesium compound. The authors also suggest that an isoelectronic, even more strongly ionic $\ce{Li(BC)}$ compound may offer an even further enhancement in superconductivity.

Nishibori et al. [2] found that at room temperature, magnesium is essentially fully ionized to $\ce{Mg^{2+}}$ while the boron remains neutral; the negative charge is associated with the interstitial regions as if to constitute metallic bonds. This still represents two-thirds of the theoretical charge separation for an ionic model and in that sense, the bonding between magnesium and boron may be deemed predominantly ionic. At 15 K the electrons become more localized so the boron now has a significant negative charge and the percentage of theoretical charge separation exceeds 80%.

Thus both references agree that in magnesium diboride, the combination of an electropositive electron source with a favorable molecular structure for electron acceptance leads to strongly ionic bonding between the magnesium and the boron. This applies especially in the low-temperature superconducting state, even as the boron-boron bonding within the boron layers themselves remains covalent.

References

1. Pablo de la Mora, Miguel Castro and Gustavo Tavizonb, "Comparative study of the electronic structure of alkaline-earth borides (MeB2; Me=Mg, Al, Zr, Nb, and Ta) and their normal-state conductivity", Journal of Solid State Chemistry 169 (2002) 168–175, https://doi.org/10.1016/S0022-4596(02)00045-2.

2. Eiji Nishibori, Masaki Takata, Makoto Sakata, Hiroshi Tanaka, Takahiro Muranaka and Jun Akimitsu, "Bonding Nature in MgB2", Journal of the Physical Society of Japan 70:8 (2001), 2252-2254, https://doi.org/10.1143/JPSJ.70.2252.

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