The anisotropic part A(an) of the material constant A = partial derivative-lambda/partial derivative-sigma, where lambda is the magnetostriction and sigma is an applied tensile stress, is separated as the difference of the results on A for perpendicular and longitudinal field annealing. We find that A(an) has a maximum which is dependent on the temperature of measurement. The two-ion character of this maximum is confirmed by some model arguments, which are valid at low temperatures.