This article presents a self-diffusion theory, including analyticalexpressions for activation energy, pre-exponential factor, and self-diffusioncoefficient, dependent on temperature, pressure, the concentration of substitutionalatoms, the concentration of interstitial atoms, and strain for substitutional andinterstitial ternary alloys with the FCC structure, based on the statistical momentmethod (SMM). The theoretical results are applied to numerical calculations for theAuCuSi alloy. The SMM numerical results for AuCuSi are compared with thosefor AuSi, AuCu, and Au. The variation of self-diffusion quantities withtemperature and strain in AuCuSi follows the same patterns as in AuCu, AuSi, andAu. The variation with the interstitial atom concentration in AuCuSi follows thesame pattern as in AuSi, while the variation with the substitutional atomconcentration follows the same pattern as in AuCu. The SMM numerical results forAu's self-diffusion quantities agree well with experimental data and othercalculation results. Other SMM numerical results for self-diffusion quantities arenovel and predict future experimental outcomes.This article presents a self-diffusion theory, including analyticalexpressions for activation energy, pre-exponential factor, and self-diffusioncoefficient, dependent on temperature, pressure, the concentration of substitutionalatoms, the concentration of interstitial atoms, and strain for substitutional andinterstitial ternary alloys with the FCC structure, based on the statistical momentmethod (SMM). The theoretical results are applied to numerical calculations for theAuCuSi alloy. The SMM numerical results for AuCuSi are compared with thosefor AuSi, AuCu, and Au. The variation of self-diffusion quantities withtemperature and strain in AuCuSi follows the same patterns as in AuCu, AuSi, andAu. The variation with the interstitial atom concentration in AuCuSi follows thesame pattern as in AuSi, while the variation with the substitutional atomconcentration follows the same pattern as in AuCu. The SMM numerical results forAu's self-diffusion quantities agree well with experimental data and othercalculation results. Other SMM numerical results for self-diffusion quantities arenovel and predict future experimental outcomes.