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A study of dust-grain charging plays a very important role in the understanding of complex (dusty) plasma. The dust grains are charged by several different processes (e.g., electron and ion attachments, secondary electron emission, photoemission, and field electron and ion emissions), and their charge significantly influences the surrounding plasma. Our laboratory experiment based on an electrodynamic quadrupole trap allows us to investigate some of these processes on a single isolated dust grain which can be trapped and influenced with different agents for a very long time (days). In this paper, we focused on the determination of the relation between charging conditions and the field-emission mechanism because this emission limits positive charges that dust grains can acquire due to photoemission, secondary emission, or ion attachment. The field-ion-emission process is based on the field ionization of the atoms that crosses a critical distance from the grain surface. We have found that the sources of these atoms are either the surrounding gas or the ions implanted into the grain and leaving it due to diffusion. The diffusion can be described by two time constants differing by an order of magnitude. We used two sets of dust grains: gold and amorphous carbon. The experimental results are confirmed by a simple model.