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Abstract Single crystal Ge is a semiconductor that has broad applications, especially in manipulation of infrared light. Diamond machining enables the efficient production of surfaces with tolerances required by the optical industry. During machining of anisotropic single crystals, the cutting direction with respect to the in-plane lattice orientation plays a fundamental role in the final quality of the surface and subsurface. In this study, on-axis face turning experiments were performed on an undoped (111)Ge wafer to investigate the effects of crystal anisotropy and feedrate on the surface and subsurface conditions. Atomic force microscopy and scanning white light interferometry were used to characterize the presence of brittle fracture on the machined surfaces and to evaluate the resultant surface roughness. Raman spectroscopy was performed to evaluate the residual stresses and lattice disorder induced by the tool during machining. Nanoindentation with Berkovich and cube corner indenter tips was performed to evaluate elastic modulus, hardness, and fracture toughness of the machined surfaces and to study their variations with feedrate and cutting direction. Post-indentation studies of selected indentations were also performed to characterize the corresponding quasi-plasticity mechanisms. It was found that an increase of feedrate produced a rotation of the resultant force imparted by the tool indicating a shift from indentation-dominant to cutting-dominant behavior. Fracture increased with the feedrate and showed a higher propensity when the cutting direction belonged to the <112¯> family. 

Abstract This paper presents a novel method to eliminate cosine error in precision concave and convex surface measurement by integrating a displacement probe in a precision spindle. Cosine error in surface profile measurement comes from an angular misalignment between the measurement axis and the axis of motion and negatively affects the measurement accuracy, especially in optical surface measurements. A corrective multiplier can solve this problem for spherical surface measurement, but cosine error cannot be eliminated in the case of complex optical surface measurement because current tools do not measure such surfaces along the direction normal to the measurement plane. Because the displacement probe is placed on the spindle axis, the spindle error motion will affect the shape precision and surface roughness measurement of optical components such as mirrors and lenses, and the displacement probe will measure a combination of the spindle error motion and the geometry of optical surfaces. Here, the one-dimensional concave, convex, and hollow measurement targets were used, and cosine error was fundamentally eliminated by aligning the probe on the spindle always normal to the measured surface, and compensation was made for the aerostatic bearing spindle rotational error obtained by the reversal method. The results show that this proposed measurement method cannot only eliminate cosine error but also scan the large area quickly and conveniently. In addition, measurement uncertainty and further consideration for future work were discussed.