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We present a systematic investigation of the electrical, structural, andantiferromagnetic properties for the series ofBa(Fe$_{1-x-y}$Co$_{x}$Rh$_{y}$)$_{2}$As$_{2}$ compounds with fixed $x \approx$0.027 and $ 0 \leq y \leq 0.035$. We compare our results for the Co-Rh dopedBa(Fe$_{1-x-y}$Co$_{x}$Rh$_{y}$)$_{2}$As$_{2}$ compounds with the Co dopedBa(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ compounds. We demonstrate that theelectrical, structural, antiferromangetic, and superconducting properties ofthe Co-Rh doped compounds are similar to the properties of the Co dopedcompounds. We find that the overall behaviors ofBa(Fe$_{1-x-y}$Co$_{x}$Rh$_{y}$)$_{2}$As$_{2}$ andBa(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ compounds are very similar when the totalnumber of extra electrons per Fe/$TM$ ($TM$ = transition metal) site isconsidered, which is consistent with the rigid band model. Despite thesimilarity, we find that the details of the transitions, for example, thetemperature difference between the structural and antiferromagnetic transitiontemperatures and the incommensurability of the antiferromangetic peaks, aredifferent between Ba(Fe$_{1-x-y}$Co$_{x}$Rh$_{y}$)$_{2}$As$_{2}$ andBa(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ compounds.

Structural and antiferromagnetic properties of Ba(Fe$_{1-x-y}$Co$_x$Rh$_y$)$_2$As$_2$ compounds