Since the prediction by Villain in 1975 of moving magnetic domain walls (or solitons) in 1-dimensional Ising-like antiferromagnets, there has been interest in compounds with these properties. Mössbauer spectra of CsCo₀⁠⁡⁢⁣⁤.₉₉Fe₀.₀₁Cl₃ in the magnetically ordered phases below TN₁ = 21.2 K were analysed by Ward et al (1987) assuming that only the two lowest energy electronic states of the ⁵⁷Fe⁲⁺ ion were significantly occupied (the 2-level relaxation model). This assumption is unreliable above approximately 18 K because it was estimated that the third lowest-lying electronic state of Fe⁲⁺ was significantly occupied at those temperatures. Nevertheless, it was found that two relaxation processes were present, one attributed to moving domain walls, and the other to transitions between the low-lying electronic states of the Fe⁲⁺ ion. In this work the 2-level relaxation model was extended to include the third lowest-lying electronic state of the Fe⁲⁺ ion. A further extension, the combined relaxation model, enables Mössbauer spectra to be fitted when both 3-level electronic relaxation and relaxation due to moving domain walls occur with similar rates at the same ⁵⁷Fe⁲⁺ site. The quasi 1-dimensional Ising-like antiferromagnetic salt NH₄CₒCl₃ doped with less than 1 atomic % ⁵⁷Fe⁲⁺ was synthesised, and Mössbauer spectra were taken at temperatures between 1.3 and 250 K. The Mössbauer spectra of both CₛC₀₁₋ₓFeₓCl₃ and NHâ‚„Coâ‚ -â‚“Feâ‚“Cl3 in the magnetically ordered phases were analysed using the 2-level, 3-level and combined relaxation models. Although good fits to the Mössbauer spectra of CₛC₀₁₋ₓFeₓCl₃ and NH₄FeₓCl₃ were obtained using all the relaxation models, the combined relaxation model was the most satisfactory since the assumptions of this model were not invalidated by the parameters obtained from the fits. The soliton relaxation rates obtained were much slower than those predicted theoretically and found from other experiments on CsCoCl3. One reason for this which is examined in this thesis is that the determined rates are unduly affected by the approximations made in the relaxation models. Another possible explanation of the discrepancy is that the presence of iron in the cobalt chains changes the soliton dynamics. In order to study the effect of doping NNH₄FeₓCl₃with Fe⁲⁺, the isomorphous crystal NH₄FeₓCl₃ was grown. The magnetic structure of NH₄FeₓCl₃ is expected to be governed by ferromagnetic intra-chain interactions and weaker antiferromagnetic inter-chain interactions. The linewidth broadening of the Mössbauer spectra of NH₄FeₓCl₃ at temperatures up to 10 K is evidence for the existence of magnetic correlations above the Neel temperature (1.7 K). The 4.2 and 1.3 K spectra show that a distribution of magnetic hyperfine fields B are present, possibly due to incommensurate magnetic ordering. At 4.2 K the main components of the Mössbauer spectrum are approximately 79 % with B = 0 and 21 % with B = 5.32 T. At 1.3 K the main components of the Mössbauer spectrum are approximately 72 % with B = 5.2 T and 28 %with B = 0. The non-magnetic subspectrum at 1.3 K may be caused by cancellation between the different components of the magnetic hyperfine field.