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Directionally solidified Al2O3–Er3Al5O12–ZrO2 eutectic ceramic rods were fabricated by the laser‐assisted float zone method at growth rates from 25 to 1200 mm/h. The microstructure of the eutectic rods was studied as a function of the solidification rate and the three eutectic phases present in the material were identified by X‐ray and electron diffraction. The size of the eutectic phases measured in the plane perpendicular to the growth direction decreased when the growth rate increased. The microstructure showed a geometrical pattern morphology at low growth rates, an irregular faceted and interpenetrating morphology at medium rates, and a nanofibrillar morphology in samples solidified at 1200 mm/h. The fibrous pattern consisted of Al2O3 trifold shaped nano‐fibers surrounded by a jacket of Er‐stabilized ZrO2 (t < 50 nm) and embedded in a matrix of Er3Al5O12 of ~150 nm width. The residual stress in the alumina phase due to the thermal contraction mismatch between phases was determined by piezospectroscopy. It decreased with solidification rate from 262 MPa compressive at room temperature in the sample with the coarsest microstructure to 135 MPa in the sample solidified at 1200 mm/h. A linear behavior of the thermoelastic stresses was found in the 110–370 K temperature range. The stress relief temperature at which the stresses become zero markedly decreased with the interphase spacing. The decrease was attributed to thermal activation of diffusional creep in the nanometric ZrO2 phase.