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Size Matters

April 5, 2011

Size matters, at least where atoms are involved. The concept of ionic and atomic size has been important to many scientific disciplines. As James Watson and Francis Crick proved in their ball-and-stick modeling of DNA, you can fit differently sized atoms together in just a few ways in which their bond angles make sense.

Metallurgists very early on had a set of heuristics called the Hume Rothery rules that gave guidance as to which metals will form solutions with other metals. One of these rules was that the atomic radius of the solute and solvent atoms should not differ by more than 15%.

Alchemical symbol for iron.

It's not what you think. This is the alchemical symbol for iron. Iron was the last major metal to be smelted, after gold, silver and copper. This progression of metals from noble to base, was thought to be reflected in a deteriorating condition of man on Earth.[1])

I used atomic size quite often in the conduct of my research on the growth of garnet crystals. My source of tabulated radii of metal cations in oxides was the extensive work by R. D. Shannon and C. T. Prewitt.[1-3] These radii told me how much of certain elements I could expect to substitute into the three distinct lattice sites in garnet (12-, 8-, and 4-fold coordinated with oxygen).

The noble gases never were of much interest to chemists, since they don't do much more than occupy a volume. Since these elements, which sit at the far right of the periodic table, have a stable, closed electronic shell, they never bond to anything.

Well, that's not completely true. There have been some tour-de-force examples of noble gas compounds. Xenon tetrafluoride XeF4, the first synthesized binary compound of a noble gas, was synthesized shortly after the English chemist, Neil Bartlett, synthesized the first xenon compound, xenon platinofluoride (XePtF6), in 1962. It's only because of the high electronegativity of fluorine that such compounds can be made.

Because of its large atomic number (54), xenon is rare. However, xenon's rarity is much worse than expected. Its abundance in the Earth's atmosphere, 36 ppb, is just 10% of what it should be based on its presence in other solar system materials, such as meteorites.[5]

Gases will escape from planetary atmospheres, since there's some probability that a gas molecule will be at the planetary escape velocity. Since Xenon is a heavy gas, this mechanism is not very effective, so geologists have been looking for a "xenon sink" somewhere in Earth's crust; namely, xenon dissolved in something, or bonded to something. Of course, the idea of a xenon compound forming naturally is a strange idea.

That's the idea espoused in a recent paper in the Journal of the American Chemical Society. Chemists from McMaster University (Hamilton, Ontario) have reported a synthesis of yellow crystals of XeO2 by hydrolysis of XeF4 in a 2.00 Molar sulfuric acid solution.[6-7] As if this unique synthesis wasn't enough, they propose that Earth's atmospheric deficit of xenon is a result of its being sequestered in silica; specifically, the quartz phase of silica.

Does this make sense? The covalent atomic radius of silicon is 111 pm, while the covalent atomic radius of xenon is estimated as 140±9 pm, or about 25% larger. If we look at bond lengths, the silicon-oxygen bond length in α-quartz is 161 pm, and it's about the same for other forms of silica. The Xe-F bond length in xenon difluoride is about 200 pm, and it's about the same for xenon tetrafluoride. The Xe-F bond would necessarily be smaller than a Xe-O bond because of fluorine's high electronegativity. Conservatively taking 200 pm as the length of the Xe-O bond makes it 25% longer than the Si-O bond.

Based on all the heuristics to which I'm accustomed, xenon is just too big to fit into silica. I'm not the only one who questions whether xenon is hidden in silica.[8] Size really does matter when crystals are involved.


  1. See, for example, Hesiod's Works and Days, ll. 176-179. Greek text from Project Perseus. English Translation by Hugh G. Evelyn-White. Works and Days, Harvard University Press (Cambridge, MA.) and William Heinemann Ltd. (London, 1914).
    "For now truly is a race of iron, and men never rest from labor and sorrow by day, and from perishing by night; and the gods shall lay sore trouble upon them."
    Hesiod's Works and Days, ll. 176-179.
  2. R. D. Shannon and C. T. Prewitt, "Effective ionic radii in oxides and fluorides," Acta Cryst. B25 (1969), pp. 925-946.
  3. R. D. Shannon and C. T. Prewitt, "Revised values of effective ionic radii," Acta Cryst. B26 (1970), pp. 1046-1048.
  4. R. D. Shannon, "Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides," Acta Cryst. A32 (1976), pp. 751-767.
  5. I. N. Tolstikhin and R. K. O'Nions, "The Earth's missing xenon: A combination of early degassing and of rare gas loss from the atmosphere," Chemical Geology, vol. 115, no. 1-2 (July 1, 1994), pp. 1-6.
  6. Research Highlights - Chemistry: Where did the xenon go? Nature, vol. 471, no. 7337 (March 10, 2011), p. 138.
  7. David S. Brock and Gary J. Schrobilgen, "Synthesis of the Missing Oxide of Xenon, XeO2, and Its Implications for Earth’s Missing Xenon," J. Am. Chem. Soc., (Online Publication, February 22, 2011)
  8. Andrew G. Christy, "Re: Xenon Oxide, XeO2, a mineral?" Mindat.com Forum (March 5, 2011)

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Linked Keywords: Atoms; ionic_bond; atomic size; James Watson; Francis Crick; ball-and-stick modeling; DNA; bond angles; metallurgist; heuristic; Hume Rothery rules; metal; solid solution; solute; solvent; iron; gold; silver; copper; Ages of Man; garnet crystal; cation; oxide; coordination number; oxygen; noble gas; chemist; periodic table; electron shell; xenon tetrafluoride; Neil Bartlett; electronegativity; fluorine; atomic number; xenon; solar system; meteorite; atmospheric escape; escape velocity; geologist; Journal of the American Chemical Society; McMaster University; Hamilton, Ontario; hydrolysis; Molar concentration; sulfuric acid; silica; quartz; covalent bond; silicon; xenon; xenon difluoride; Hesiod; Works and Days; R. D. Shannon; C. T. Prewitt.