Question

Which of the following systems (i.e. pair of metals) would you expect to exhibit complete solid solubility? Explain your answers. (i) Cr-V (ii) Mg-Zn (iii) Al-Zr (iv) Ag-Au (v) Pb-Pt

Answer 1

For complete solubility, four Hume-Rothery rules must be satisfied

1. Difference in atomic radii must be less than ± 15%
2. Crystal structures must be the same
3. Electronegativities must be similar
4. Valences should be the same

a) Cr-V system

Metal	Atomic Radius (nm)	Crystal Structure	Electronegativity	Valence
Cr	0.125	BCC	1.6	3
V	0.132	BCC	1.5	+5 ,+3

Here, the percent difference in atomic radii is around 6%, the crystal structure is BCC for both, electronegativity difference is small, and both exist in +3 oxidation state. Therefore, Cr and V are completely soluble in one another.

b) Mg-Zn system

Metal	Atomic Radius (nm)	Crystal Structure	Electronegativity	Valence
Mg	0.16	HCP	1.3	2
Zn	0.133	HCP	1.7	2

Here, the percent difference in atomic radii is around 17%, the crystal structure is HCP for both, electronegativity difference is 0.4, and common valence for both Mg and Zn is +2. Therefore, Mg and Zn are not completely soluble.

(c) Al-Zr system

Metal	Atomic Radius (nm)	Crystal Structure	Electronegativity	Valence
Al	0.143	FCC	1.5	3
Zr	0.159	HCP	1.2	4

Here, the percent difference in atomic radii is around 11%, crystal structures are different, the difference in their electronegativity is 0.3 and the common valences for Al and Zr are different. Therefore, Al and Zr are not completely soluble

(d) Ag-Au system

Metal	Atomic Radius (nm)	Crystal Structure	Electronegativity	Valence
Ag	0.144	FCC	1.4	1
Au	0.144	FCC	1.4	1

Here, atomic radii are the same for both, crystal structures are same, electronegativities are the same, and common valences are also same. Therefore, Ag and Au are completely soluble

(d) Pb-Pt System

Metal	Atomic Radius (nm)	Crystal Structure	Electronegativity	Valence
Pb	0.175	FCC	1.6	2
Pt	0.139	FCC	1.5	2

Here, the percent difference in atomic radii around 20%, crystal structures are same, electronegativities are nearly same, and the most common valence is also same. Therefore, Pb and Pt are not completely soluble because of the large difference in atomic radii.