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This seems counter intuitive to me since ionic radius increases with increasing coordination number. Surely the solid doesn't expand under high pressure? Can you explain?

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  • $\begingroup$ If there is a phase transition to another allotrope under increasing pressure, it would only make sense that the phase would become more dense (the PV term of the Gibbs free energy). The denser crystal structure is likely to have a higher coordination number than the less dense phase - to reduce the atomic volume the atom has to be closer to the ones around it, and likely is now closer to more atoms. $\endgroup$ – Jon Custer Mar 23 '15 at 16:41
  • $\begingroup$ But changing from a sodium chloride structure to the cadmium chloride structure means going from a close packed array of anions to a non close packed array. How does that make sense? $\endgroup$ – RobChem Mar 23 '15 at 16:47
  • $\begingroup$ But cadmium chloride has the halogens in a cubic close packed structure. The structures really aren't that different once you look at them (perhaps slightly cross-eyed). $\endgroup$ – Jon Custer Mar 23 '15 at 19:49
  • $\begingroup$ Apologies, I meant caesium chloride (body centered cubic). 8 coordinate $\endgroup$ – RobChem Mar 23 '15 at 19:53
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    $\begingroup$ And high pressures are trying to squeeze it all together more tightly. The PV energy gained by a denser solid from the higher coordination plays off (and pays off) against the ionic unhappiness. $\endgroup$ – Jon Custer Mar 23 '15 at 21:18
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Lets put some numbers on the phase transition of NaCl from the normal NaCl structure (based on fcc, 6-fold coordinated) at atmospheric pressure, to the CsCl (based on bcc, 8-fold coordinated) structure at high pressure. From Compounds and Alloys Under High Pressure: A Handbook, by E. Yu Tonkov (google found it) one gets that the transition occurs at 27-29GPa, with a volume change of 5%.
The density of NaCl, taken from Wikipedia, is 2.165 gm/cc, or about 27cm$^3$/mol, or 27E-6 m$^3$/mol. Multiply on through and you get, very roughly, the PV energy gained by converting from the less dense NaCl structure to the denser CsCl structure is 40kJ/mol - this is not an inconsequential energy gain for the Gibbs free energy. Thus, the PV energy gained by a denser solid with the higher coordination plays off (and pays off) against the ionic unhappiness.

In the literature there are also indications that the CsCl, and/or higher pressure phases, may be metallic in nature, so the assumption of purely ionic bonding may be in jeopardy.

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