The fraction of events which occur without phonon emission or absorption increases greatly at low temperatures. Mössbauer experiments are therefore often performed at the temperature of liquid helium. In order to observe this virtually monochromatic gamma radiation, a substance with a high cross section is needed to absorb the emitted photons. Fe, Sn, and Ir are virtually the only atoms with a large enough cross sections. The re-absorption will only occur if the energy of the gamma ray in the frame of the absorber is the same as that in the emitter within a few parts to 1011, so the same species must also be used for both emitter and absorber.
References
Bancroft, G. M. Mössbauer Spectroscopy: An Introduction for Inorganic Chemists and Geochemists. New York: Wiley, 1973.
Weisstein, E. W. "Books about Moessbauer Effect." http://www.ericweisstein.com/encyclopedias/books/MoessbauerEffect.html.
Wertheim, G. K. Mössbauer Effect: Principles and Applications. New York: Academic Press, 1964.