Neutron-diffraction measurements on ${\mathrm{Er}}_{0.8}{R}_{0.2}{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ $(R=\mathrm{Tb},\mathrm{Lu})$ and $\mathrm{Er}{\mathrm{Ni}}_{1.9}{\mathrm{Co}}_{0.1}{\mathrm{B}}_{2}\mathrm{C}$ have been carried out to investigate the influence of chemical doping on the stability of the modulated states in $\mathrm{Er}{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$. Within the magnetically ordered phase and down to $1.6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ (the lowest measured temperature), the powder diffractograms of Lu and Tb doped compounds are consistent with a transverse sine-modulated (fundamental) mode. A neutron diffraction study on a single-crystal ${\mathrm{Er}}_{0.8}{\mathrm{Lu}}_{0.2}{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ recorded at $1.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ has confirmed the absence of higher order harmonics. In contrast, the low-temperature patterns of the Co doped compound reveal the presence of all the odd-order harmonics up to the fifth-order satellite, reminiscent of the structure of the undoped $\mathrm{Er}{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ below the weak-ferromagnetic transition point ${T}_{\mathit{WF}}=2.1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$: a squared-up, noncompensated long-period antiferromagnetic state. The above-mentioned findings are consistent with the conclusions drawn from our previous specific-heat and magnetization measurements on the same compounds: on lowering the temperature further below ${T}_{N}$, both $\mathrm{Er}{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ and Co doped compounds undergo a spontaneous transition at ${T}_{\mathit{WF}}$. In contrast, for the Lu and Tb doped compounds, no such second magnetic phase transition was observed down to $1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$; eventually the squaring-up of these structures, as required by entropy arguments, should occur but at temperatures lower than $1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.
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