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Due to the shortage of the 3He gas and its rapidly increasing price, scintillator detectors, the advantages of which are high spatial resolution and capability of detection in real time, become widely used in many neutron instruments. In this work, a position-sensitive neutron detector consisting of a 6LiF/ZnS scintillation screen and a silicon photomultiplier array linked to a capacitive network to detect the positions of incident neutrons, is constructed and tested. To evaluate the detector performance, a series of neutron beam experiments with the detector prototype were performed in the BL20 at the China Spallation Neutron Source. The spatial resolution was measured, and the energy-selective neutron imaging and Bragg edge measurements of a 316L stainless steel sample were performed. A sub-millimeter spatial resolution could be obtained for the detector prototype under study. The detector with such a high spatial resolution is promising for applications in neutron scattering experimental installations, especially for neutron single-crystal diffractometers. [ABSTRACT FROM AUTHOR]