Breakdown of Matthiessen's rule in aluminium alloys

Measurements of the electrical resistivity of aluminium alloys containing a small amount of a variety of impurities show severe breakdown of Matthiesen's rule at low temperatures. The temperature- dependent part ( rho T- rho 0) of the alloy resistivity is a function of the residual resistivity rho 0 but does not depend on the nature of the impurity; above approximately=20K a 'pure' limit rho T pure can be discerned, beyond this limit the data fit the empirical relation rho T= rho 0+ rho T pure +AT 3 ln rho 0; rho T pure itself varies, as T 5 below approximately=50 K. For even the purest material now available the breakdown term is larger than rho T pure below approximately= 10 K.