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Compositionally graded AlGaN buffer layers enable the growth of thicker crack free layers of GaN on (111) Si than is possible with an AlN buffer layer. Using cross sectional transmission electron microscopy and in situ stress measurements, it is shown that a compressive growth stress is incorporated in the GaN layer when the graded AlGaN buffer layer is thick enough to accommodate all microstructural evolution, which is primarily a reduction in threading dislocation density with thickness during growth. Most of the dislocation density reduction is observed to occur when the film is growing under a compressive stress. This compressive stress arises from the changing lattice parameter due to grading and helps to offset the tensile stress generated by microstructural evolution. It also helps to decrease the tensile thermal expansion mismatch stress during cooling and thus reduces film cracking.