The compositional vanadate system Dy
p
Gd
1-
p
VO
4
(0 ≤
p
≤ 1) displays successive crystallographic and magnetic phase transitions below 14 K. An experimental investigation of these phase changes has been made with thermal expansion methods and Mössbauer spectroscopy. It is found that there is a surprising variation of the compositional dependence of the transition temperatures
T
D
(
p
) and
T
N
(
p
), which cannot be adequately explained by conventional pseudo-spin molecular field and pair model approximations. A detailed formalism has been developed that accounts for the observations in terms of a magneto-strictively induced quadrupole moment on the Gd
3+
ions in the mixed crsytal system and, concomitant quadrupole interactions between the Dy
3+
and Gd
3+
ions. The application of the formalism to the corresponding variation of
T
D
(
p
) in the simple diluent system Dy
p
Y
1-
p
VO
4
(0 ≤ p ≤ 1) is also discussed.