The structural competing and atomic ordering of the full Heusler compounds Fe
2
NiSi and Ni
2
FeSi under uniform and tetragonal strains have been systematically studied by the first-principles calculation. Both Fe
2
NiSi and Ni
2
FeSi have the XA structure in cubic phase and they show metallic band structures and large magnetic moments (greater than 3
μ
B
) at equilibrium condition. Tetragonal distortion can further decrease the total energy, leading to the possible phase transformation. Furthermore, different atom reordering behaviours have been observed: for Fe
2
NiSi, atoms reorder from cubic XA-type to tetragonal L1
0
-type; for Ni
2
FeSi, there is only structural transformation without atom reordering. The total magnetic moments of Fe
2
NiSi and Ni
2
FeSi are mainly contributed by Fe atoms, and Si atom can strongly suppress the moments of Fe atoms when it is present in the nearest neighbours of Fe atoms. With the applied strain, the distance between Fe and Si atoms play an important role for the magnetic moment variation of Fe atom. Moreover, the metallic band nature is maintained for Fe
2
NiSi and Ni
2
FeSi under both uniform and tetragonal strains. This study provides a detailed theoretical analysis about the full Heusler compounds Fe
2
NiSi and Ni
2
FeSi under strain conditions.
Investigation of the structural competing and atomic ordering in Heusler compounds Fe
2
NiSi and Ni
2
FeSi under strain condition
