The morphology of grains grown by accretion and coagulation is revealed by a new laboratory method of synthesizing cosmic dust analogs. Submicron carbon particles, grown by accretion of carbon atoms from a gas, have a spherical shape with a cauliflower-like surface and an internal micro-structure of radial columns. This shape is probably common for grains grown by accretion at a temperature well below the melting point. Coagulated grains, consisting of spheres that collided to form irregular strings, were also synthesized. Another shape we produced had a bumpy non- spherical morphology, like an interplanetary particle collected in the terrestrial stratosphere. Besides these isolated grains, large spongy aggregates of nanometer-size particles were also found for various experimental conditions. Grains were synthesized using ions to sputter a solid target, producing an atomic vapor at a low temperature. The ions were provided by a plasma, which also provided electrostatic levitation of the grains during their growth. The temporal development of grain growth was studied by extinguishing the plasma after various intervals.