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Computer simulations within the framework of density functional theory are performed to study the electronic, dynamic, elastic, magnetic, and thermoelectric properties of a newly synthesized FeRhCrGe alloy and a theoretically predicted FeRhCrSi alloy. From the electronic structure simulations, both FeRhCrZ (Z= Si and Ge) alloys at their equilibrium lattice constants exhibit half-metallic ferromagnetism, which is established from the total magnetic moment of 3.00 μB, and that the spin moment of FeRhCrGe is close to the experimental value (2.90 μB). Their strength and stability with respect to external pressures are determined by simulated elastic constants. The Debye temperatures of FeRhCrSi and FeRhCrGe alloys are predicted to be 438 K and 640 K, respectively, based on elastic and thermal studies. The large power factors (PFs) of the two investigated alloys are in contour with those of the previously reported …