| The crystallography of proeutectoid α (hcp) precipitates in β (bcc) matrix in a Ti–7.26 wt% Cr alloy has been studied systematically using transmission electron microscope. The orientation relationship (OR), three-dimensional (3D) interfacial structures were examined. The surface relief effect associated with α precipitates were also studied using optic microscope, scanning electron microscope and atomic force microscope. The O-lattice theory and the near coincidence sites (NCS) model which was developed based on the O-lattice theory, were used to explain the experimental results.The OR, interface normal and dislocation direction were measured precisely. The OR was found to deviate slightly from the ideal Burgers OR. The habit plane was found to be normal to a particular set of Δg's. A set of dislocations, about 11 nm apart, were observed on the habit plane of the precipitates. The Burgers vector of the dislocations is [1 –1 1]β/2([2 –1 –1 3]α/6). The dislocation reaction during plastic deformation could be explained by this Burgers vector. Two sets of dislocations, which are parallel to the dislocations on the habit plane, were observed on the side facet. One set of dislocations, about 9.4 nm apart, have a Burgers vector [1 0 0]β([2 –1 –1 0]α/3) which has not been determined by previous investigations. The other set of dislocations, about 1.8 nm apart, have a Burgers vector [1 1 1]β/2([1 1 –2 0]α/3). The dislocations on the habit plane and side facet loop around the α plate and form the network of dislocations on the end face. Another kind of dislocations was observed due to the dislocation reaction between the dislocations on the habit plane and the dislocations on the side facet in larger spacing or in smaller spacing. The Burgers vector of it is [1 1 –1]β/2([2 –1 –1 –3]α/6). Based on the observation, a 3D model of morphology and dislocation structures of α plate was constructed.The observed OR and dislocation structure on the habit plane was explained by an analytical O-line model. Based on the O-line model, NCS model was developed and the positions of NCS clusters were defined quantitatively by Moiré planes. Then the dislocation structure on the side facet could be explained based on the developed NCS model. A step-kink structure of irrational interface on atomic scale was constructed. Then, the step-kink structures of habit plane and side facet were predicted. Based on the NCS model, from the slabs near the interfaces, the atomic step-kink structures were observed and consistent with the prediction. The models and methods developed and used in the present work could be readily extended to analyze the crystallography of other phase transformation system.Single and double tilt surface relives were both observed. The displacement vector for surface relief was determined to be near the invariant line direction using electron back scattering diffraction method. Based on the results of the crystallography, the surface relief effects were analyzed by the model of decomposition of the transformation displacement field. The single tilt surface relief could be explained by this model. However, the double tilt surface relief could not be explained by the existing models.
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