Yb:S-FAP [Yb3+:Sr-5(PO4)(3)F] crystals are an important gain medium for diode-pumped laser applications. Growth of 7.0 cm diameter Yb:S-FAP crystals utilizing the Czochralski (CZ) method from SrF2-rich melts often encounters cracks during the post-growth cool-down stage. To suppress cracking during cool-down, a numerical simulation of the growth system was used to understand the correlation between the furnace power during cool-down and the radial temperature differences within the crystal. The critical radial temperature difference, above which the crystal cracks, has been determined by benchmarking the simulation results against experimental observations. Based on this comparison, an optimal three-stage ramp-down profile was implemented, which produced high-quality, crack-free Yb:s-FAP crystals. (C) 2008 Elsevier B.V. All rights reserved.