Numerous technological applications of Ni-based Zr and Hf intermetallic alloys promoted comprehensive studies in Zr$_8$Ni$_{21}$ and Hf$_8$Ni$_{21}$ by perturbed angular correlation (PAC) spectroscopy, which were not studied earlier until this report. The different phases produced in the samples have been identified by PAC and X-ray diffraction (XRD) measurements. Using $^{181}$Hf probe, two non-equivalent Zr/Hf sites have been observed in both Zr$_8$Ni$_{21}$ and Hf$_8$Ni$_{21}$ compounds. From present PAC measurements in Zr$_8$Ni$_{21}$, a component due to the production of Zr$_7$Ni$_{10}$ by eutectic reaction from the liquid metals is also observed. The phase Zr$_7$Ni$_{10}$, however, is not found from the XRD measurement. In Zr$_8$Ni$_{21}$, while the results do not change appreciably up to 973 K exhibit drastic changes at 1073 K. In Hf$_8$Ni$_{21}$, similar results for the two non-equivalent sites have been found but site fractions are in reverse order. In this alloy, a different contaminating phase, possibly due to HfNi$_3$, has been found from PAC measurements but is not found from XRD measurement. Density functional theory (DFT) based calculations of electric field gradient (EFG) and asymmetry parameter ($eta$) at the sites of $^{181}$Ta probe nucleus allowed us to assign the observed EFG fractions to the various lattice sites in (Zr/Hf)$_8$Ni$_{21}$ compounds.
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