Dependence of resistivity of solid solution ρ
ss on solute concentration and temperature of measurement was considered. In relatively dilute solid solution, ρ
ss can be approximated by a linear function of solute concentration C. Deviation from Matthiessen's Rule (DMR) defined by change in dρ/dT with C can be replaced by temperature dependence of dρ/dC(≡Δρ), change in ρ with C. Using difference ε = Δρ
T2-Δρ
T1 and ratio η = Δρ
T2/Δρ
T1 of Δρ at two different temperatures T
1 and T
2 (T
1<T
2), following two relations between ρ
SST1 (resistivity of a (b, c) ternary solid solution at T
1K) and resistance ratio
R = ρ
T2/ρ
T1 are obtained.
ρ
SST1=(ρ
PURET2-ρ
PURET1+C
bε
b+C
cε
c)/(R-1)
ρ
SST1=[ρ
PURET2-ρ
PURET1η
b+C
cΔρ
cT1(η
c-η
b)]/(
R-η
b),
where ρ
PURE is ρ of idealy pure solvent metal. For solid solution of high concentration, replacing
C to
f (
X), an appropriate function of atomic fraction
X, and Δρ to Δρ
f(
X) based on the f (
X), similar expressions as above two relations can be obtained. The
R-ρ relations in commercial magnesium alloy AZ91 were investigated comparing with those calculated from reported ρ values. The Δρ of Al in Mg is smaller at 300K than at 77K and DMR is negative, however, Zn in Mg appears to show a positive DMR. As an empirical
R-ρ relation applicable to ρ changes resulted from aging and solution treatment of AZ91 alloy,
52<ρ
77/nΩ•m= [69.1/(
R-0.77)]-13.8<138 is recommended.
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