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To design tailored materials, it is highly desirable to predict microstructures of alloys without empirical parameter. Phase field models (PFMs) rely on parameters adjusted to match experimental information, while first-principles methods cannot directly treat the typical length scale of 10 mu m. Combining density functional theory, cluster expansion theory and potential renormalization theory, we derive the free energy as a function of compositions and construct a parameter-free PFM, which can predict microstructures in high-temperature regions of alloy phase diagrams. Applying this method to Ni-Al alloys at 1027 degrees C, we succeed in reproducing evolution of microstructures as a function of only compositions without thermodynamic empirical parameter. The resulting patterns including cuboidal shaped precipitations are in excellent agreement with the experimental microstructures in each region of the Ni-Al phase diagram. Our method is in principle applicable to any kind of alloys as a reliable theoretical tool to predict microstructures of new materials.