Abstract: An X-ray generator comprises a container (1) for maintaining a high vacuum or low pressure gas atmosphere internally, a hemimorphic crystal (4), temperature raising/lowering means (3, 5-7), and a metal target (8) for generating X-rays. In this X-ray generator the metal target (8) has a pointed protrusion protruding toward the hemimorphic crystal (4). When X-rays are generated by raising/lowering the temperature of the hemimorphic crystal (4) by using the temperature raising/lowering means (3, 5-7), the intensity of an electric field formed between the hemimorphic crystal (4) and the metal target (8) increases at the pointed end of the protrusion and thus the intensity of X-rays generated through collision of electrons against the metal target (8) increases. Consequently, an X-ray generator employing a hemimorphic crystal, which is capable of generating X-rays with practically sufficient intensity can be provided.