12.3 Show that the minimum cation-to-anion radiusratio for a coordination number of 6 is 0.414. (Hint:Use the NaCl crystal structure in Figure 12.2, andassume that anions and cations are just touchingalong cube edges and across face diagonals.) Figure 12.22 Thealuminum oxide-chromiumComposition (mol% Cr203)204060801002300oxide phase diagram.(Adapted from E. N. Bunting,"Phase Equilibria in the SystemCr,O3-Al,O3," Bur. StandardsJ. Research, 6, 1931, p. 948.)2275 + 25°CLiquid40002200Liquid + Solid Solution210038002045 + 5°C2000Al203–Cr203 Solid Solution360020406080100(Al203)(Cr203)Composition (wt% Cr2O3)Temperature (°C)Temperature (°F)

Consider the diagram as shown below with the anion radius R and cation radius r.

12.3 Show that the minimum cation-to-anion radius ratio for a coordination number of 6 is 0.414. (Hint: Use the NaCl crystal structure in Figure 12.2, and assume that anions and cations are just touching along cube edges and across face diagonals.)

12.3 Show that the minimum cation-to-anion radius ratio for a coordination number of 6 is 0.414. (Hint: Use the NaCl crystal structure in Figure 12.2, and assume that anions and cations are just touching along cube edges and across face diagonals.)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Concept explainers

Solidification of metals

The term solidification indicates the conversion of material from the state of liquid to the state of solid. The solid-state is more compact and rigid than liquid, and the solidification indicates the transformation of material from a random state to a more compact and crystalline form. The point at which dendrite formation in liquid starts taking place is referred to as the solidification point.

Question

12.3 Show that the minimum cation-to-anion radius
ratio for a coordination number of 6 is 0.414. (Hint:
Use the NaCl crystal structure in Figure 12.2, and
assume that anions and cations are just touching
along cube edges and across face diagonals.)

Figure 12.22 The
aluminum oxide-chromium
Composition (mol% Cr203)
20
40
60
80
100
2300
oxide phase diagram.
(Adapted from E. N. Bunting,
"Phase Equilibria in the System
Cr,O3-Al,O3," Bur. Standards
J. Research, 6, 1931, p. 948.)
2275 + 25°C
Liquid
4000
2200
Liquid + Solid Solution
2100
3800
2045 + 5°C
2000
Al203–Cr203 Solid Solution
3600
20
40
60
80
100
(Al203)
(Cr203)
Composition (wt% Cr2O3)
Temperature (°C)
Temperature (°F)

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