HW-07%20Solution - #1 12.2 In this problem we are asked to...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
12.2 In this problem we are asked to show that the minimum cation-to-anion radius ratio for a coordination number of four is 0.225. If lines are drawn from the centers of the anions, then a tetrahedron is formed. The tetrahedron may be inscribed within a cube as shown below. The spheres at the apexes of the tetrahedron are drawn at the corners of the cube, and designated as positions A , B , C , and D . (These are reduced in size for the sake of clarity.) The cation resides at the center of the cube, which is designated as point E . Let us now express the cation and anion radii in terms of the cube edge length, designated as a . The spheres located at positions A and B touch each other along the bottom face diagonal. Thus, AB = 2 r A But ( AB ) 2 = a 2 + a 2 = 2 a 2 or AB = a 2 r A And a 2 r A 2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
There will also be an anion located at the corner, point F (not drawn), and the cube diagonal AEF will be related to the ionic radii as AEF = 2 ( r A + r C ) (The line AEF has not been drawn to avoid confusion.) From the triangle ABF ( AB ) 2 + ( FB ) 2 = ( AEF ) 2
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 7

HW-07%20Solution - #1 12.2 In this problem we are asked to...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online