In LaOF, which has a structure closely related to fluorite, each lanthanum is surrounded by four oxide and four fluoride ions. Although X-ray-diffraction studies cannot easily distinguish oxygen from fluorine, two bond distances are seen in the crystal structure:

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2.42 to one anion and 2.60 to the other anion. (a) Write the crystal-chemical formula (Section 1.3) for LaOF. (b) Given the eight-coordinate La+ radius of 1.30 and the four- coordinate radii for O and F of 1.24 and 1.17 , respectively, assign the two observed distances to La-O and La-F bonds. (c) Determine the ideal valences of the La-F bonds and the La-O bonds. (d) Use the bond valences from part (c) and the bond- valence parameters Ra-F=2.02 and Ra-o-2.17 to estimate the length of La-F and La-O bonds in this structure. Does your assignment of the two bonds based on bond valences agree with the assignment based on ionic radii in part (b)?