Predict the ratio of the Young’s moduli for NaCl and MgO, both of which have the rock salt structure. The radii of the ions Na^+ and Cl^− are 0.097 and 0.181 nm, respectively, and the radii of Mg^+2 and O^−2 are 0.066 and 0.140 nm, respectively.

Question

Predict the ratio of the Young’s moduli for NaCl and MgO, both of which have the rock salt structure. The radii of the ions [latex] Na^{+} [/latex] and [latex] Cl^{-} [/latex] are 0.097 and 0.181 nm, respectively, and the radii of [latex] Mg^{+2} [/latex] and [latex] O^{-2} [/latex] are 0.066 and 0.140 nm, respectively.

Accepted Answer

Because both have the same structure, α is the same for both, so [latex] E_{NaCl}/E_{MgO} [/latex]= [|(+1)(−1)|/(0.097 + 0.181)²]/[|(+2)(−2)|/(0.066 + 0.140)²] = 0.138. The experimental values of the moduli are 36 GPa for NaCl and 305 GPa for MgO, so the ratio is 36/305 = 0.12, which is reasonably close to the prediction.

Table 19.1. Young’s moduli for some ceramics
Material	Young’s modulus
Material	GPa	( $10^{6}$ psi)
$Al_{2}O_{3}$	400	58
$B_{4}C$	445	65
$CaF_{2}$	110	16
$CsCl$	25	3.6
diamond	1000	145
$Fe_{3}O_{4}$	200	29
$LiF$	103	15
$MgO$	305	44
$NaCl$	36	5.2
$SiC$	450	65
soda-lime glass	75	11
$SiO_{2}$	96	14
$TiC$	437	63
$ZnS$	86	12.5
$ZrO_{2}$	200	29

Question 19.1: Predict the ratio of the Young’s moduli for NaCl and MgO, bo......

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