We investigate the formation of carbon-enhanced metal-poor (CEMP) stars via the scenario of mass transfer from a carbon-rich asymptotic giant branch (AGB) primary to a low-mass companion in a binary system. We explore the extent to which material accreted from a companion star becomes mixed with that of the recipient, focusing on the effects of thermohaline mixing and gravitational settling. We have created a new set of asymptotic giant branch models in order to determine what the composition of material being accreted in these systems will be. We then model a range of CEMP systems by evolving a grid of models of low-mass stars, varying the amount of material accreted by the star (to mimic systems with different separations) and also the composition of the accreted material (to mimic accretion from primaries of different mass). We find that with thermohaline mixing alone, the accreted material can become mixed with between 16 and 88 per cent of the pristine stellar material of the accretor, depending on the mass accreted and the composition of the material. If we include the effects of gravitational settling, we find that thermohaline mixing can be inhibited and, in the case that only a small quantity of material is accreted, can be suppressed almost completely.
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