  The development of long range order in nickel-chromium alloys is of great
technological interest but the kinetics and mechanisms of the transformation
are poorly understood. The present research utilizes a combined computational
and experimental approach to elucidate the mechanism by which phosphorus
accelerates the ordering rate of stoichiometric Ni_2Cr in Ni-Cr alloys. A
series of Ni-33%Cr-x%P samples (in atomic percent) were fabricated with
phosphorus concentrations, x = <0.005-0.1 at.% and aged between 373 and
470{\deg}C for times up to 3000 h. The first-principles modeling considers fcc
Ni with dilute P as a reasonable approximation for the complex Ni-Cr-P alloy
system. Calculation results show a pronounced enhancement of vacancy transport
by vacancy-solute pair diffusion via consecutive exchange and rotation jumps of
vacancies associated with the phosphorus atom. The energy barriers of these two
migration paths are at least 0.35 eV lower than that of vacancy-atom exchange
in pure Ni solvent. The analytical diffusion model predicts enhanced solvent
diffusion by 2 orders of magnitude for 0.1 at.% P at 400-500{\deg}C. The model
prediction is in good agreement with the evolution of micro-hardness. We
characterize the micro-hardness result by a kinetic ordering model, showing a
significant decrease of the activation energy of ordering transformation. These
results help gauge the risk of industrial alloys developing long range order
which increases strength but degrades ductility and toughness. Specifically,
minor alloying additions that bind with excess vacancies and lower the vacancy
migration barrier can greatly accelerate hardening via Ni_2Cr precipitation.
