Based on the finding with the use of the coincidence Doppler measurements that the nano-sized Cu precipitates are coherently embedded in the Fe-Cu matrix alloy, taking a bee structure and acting as efficient positron traps, we measured 2D-ACARs of carefully grown and heat treated single crystals of Fe-Cu. We found that the precipitates have a Fermi surface with 12 necks touching the {110} Bragg planes of the bee Brillouin zone, which contrasts distinctly with that of the bulk Cu with 8 necks touching the {111} Bragg planes of the fee Brillouin zone. The 3 dimensional momentum reconstruction of the 2D-ACAR data showed that the Fermi surface cutoff of the Cu precipitates is blurred considerably as compared with that of bulk fee Cu, suggesting a marked size effect in the momentum distribution.