The following questions are all for CsCl. 4.6.8: what is the radius ratio for th
ID: 819929 • Letter: T
Question
The following questions are all for CsCl.
4.6.8: what is the radius ratio for the two types of atoms?
4.6.9: what type of interstitial site is the cation in?
4.6.10: what type of unit cell do the anions form?
4.6.11: Describe the complete unit cell of CsCl that includes both the anions and cations ?
4.6.12: is your answer to question 4.6.11 the same as a BCC unit cell ? Explain why or why not.
The following questions are all for ZnS.
4.6.13: Determine the complete unit cell for ZnS?
4.6.14: what is the total charge on the unit cell you determined in question 4.6.13?
4.6.15: what do you think the charge should be for an ionic unit cell?why?
4.6.16: if your answers for question 4.6.15 and 4.6.16 do not match; how can you adjust the unit cell to make them match? Note that you can not add new atoms to the unit cell to make them match.
4.6.17: What is the crystal structure for ZnS?
Explanation / Answer
Consider a simple cubic arrangement of anions, with a cation in the center of the cubic cell (as in CsCl, which is (8,8)-coordinate). As the cation decreases in size, it will reach a point when the anions begin to touch, which unfavourable electrostatically, due to the repulsion between like-charged species. At this point, the structure changes so the anions are again separated by oppositely charged cations, an arrangement which is electrostatically favourable, and the (6,6)-coordinate NaCl structure is adopted. as this trend is continued, there will be a switch to the (4,4)-coordinate ZnS structure. Similar arguments hold for structures of stoichiometry AB2, and others.
Therefore, as the radius ratio decreases, there is a trend towards structures of lower coordination numbers. The Radius ratio rules are the prediction of structure adopted by a given set of ions based on the radius ration of those ions.
The radius ratio rules are not universally successful. As the degree of covalency in the bonding increases, the deviation from the ionic model increases and the less reliable the choice of structure based on the radius ratio becomes. The rules are least reliable for simple compounds like alkali metal halides and alkaline earth metal oxides, and are most reliable for complex fluorides and the salt of oxoanions: in general, as the degree of ionicity increases, so does the accuracy of the rules.
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