THE invention of the scanning tunnelling microscope1 (STM) has stimulated the development of several new forms of probe microscopy2-10. Here we demonstrate the use of a microscope that is capable of measuring chemical-potential variations on an atomic scale - the scanning chemical potential microscope (SCPM). The system is based on a recently developed tunnelling thermometer11, which allows the spatial mapping, on an atomic scale, of thermoelectric potential variations resulting from absorption of light, by scanning a conducting tip within tunnelling range of a conducting (or semiconducting) sample. In the SCPM, we replace the optical pump with an electrical sample heater, to generate a temperature gradient between the sample and the tunnel-current-measuring device. We measure the spatial variations in the thermoelectric voltage across the tip-sample system as the tip is scanned across the sample surface with no external bias. This signal can be shown to be equal to the product of the local gradient of chemical potential with respect to temperature and the temperature differential normal to the surface being imaged. The images obtained in this way show features that are not present in the conventional STM images. © 1990 Nature Publishing Group.