$MgFe_2O_4$ has been studied with X-ray diffraction, M ssbauer spectroscopy and vibration sample magnetometer (VSM). The crystal structure of the sample is found to have a cubic spinel structure with a lattice constant of $a_0=8.390$pm$0.005$AA$.$</TEX> The iron ions at both A (tetrahedral) and B (octahedral)sites are found to be in ferric high-spin states. Its Neel temperature TN is found to be 710$pm$3 K. The Debye temperature for the A and B sites found to be 417$pm$5 K and 331$pm$5 K., respectively. Atomic migation from the A to the B sites starts near 425 K and increases rapidly with increasing temperature to such a degree that 31% of the ferric ions at the A sites have moved over to the B sites by 600 K.