We report resonant ultrasound spectroscopy (RUS), dilatometry/magnetostriction, magnetotransport, magnetization, specific heat, and $^{119}$Sn Mossbauer spectroscopy measurements on SnTe and Sn$_{0.995}$Cr$_{0.005}$Te. Hall measurements at $T=77$ K i
ndicate that our Bridgman-grown single crystals have a $p$-type carrier concentration of $3.4 times 10^{19}$ cm$^{-3}$ and that our Cr-doped crystals have an $n$-type concentration of $5.8 times 10^{22}$ cm$^{-3}$. Although our SnTe crystals are diamagnetic over the temperature range $2, text{K} leq T leq 1100, text{K}$, the Cr-doped crystals are room temperature ferromagnets with a Curie temperature of 294 K. For each sample type, three-terminal capacitive dilatometry measurements detect a subtle 0.5 micron distortion at $T_c approx 85$ K. Whereas our RUS measurements on SnTe show elastic hardening near the structural transition, pointing to co-elastic behavior, similar measurements on Sn$_{0.995}$Cr$_{0.005}$Te show a pronounced softening, pointing to ferroelastic behavior. Effective Debye temperature, $theta_D$, values of SnTe obtained from $^{119}$Sn Mossbauer studies show a hardening of phonons in the range 60--115K ($theta_D$ = 162K) as compared with the 100--300K range ($theta_D$ = 150K). In addition, a precursor softening extending over approximately 100 K anticipates this collapse at the critical temperature, and quantitative analysis over three decades of its reduced modulus finds $Delta C_{44}/C_{44}=A|(T-T_0)/T_0|^{-kappa}$ with $kappa = 0.50 pm 0.02 $, a value indicating a three-dimensional softening of phonon branches at a temperature $T_0 sim 75$ K, considerably below $T_c$. We suggest that the differences in these two types of elastic behaviors lie in the absence of elastic domain wall motion in the one case and their nucleation in the other.
