A method for producing or repairing a three-dimensional workpiece made of steel or an Ni, Co, or Fe based superalloy, the method comprising the following steps: - depositing a sequence of layers of a raw material powder onto a substrate; - after depositing a raw material powder layer, irradiating selected areas of said deposited raw material powder layer with an electromagnetic or particle radiation beam in a site selective manner in accordance with an irradiation pattern which corresponds to a geometry of at least part of a layer of the three-dimensional workpiece to be produced, said irradiation pattern comprising a scan pattern, wherein - the substrate has a single-crystalline microstructure or a microstructure wherein grain boundaries extend parallel to each other and the substrate is arranged so that the [0 0 1] orientation matches a build axis of the workpiece, said matching having a tolerance of +/- 15°; - the irradiation is controlled so as to maintain said single-crystalline microstructure and to produce a metallurgical bond between irradiated sites of the raw material powder layer and the substrate and/or a previously deposited raw material powder layer; and - the irradiation is controlled so that at least one of the following conditions is fulfilled: Rz > 0.3 and Rx > 0.3, wherein Rz is a remelting rate along the build axis with Rz = ((D-Iz)/D), Iz being a layer thickness of a presently irradiated raw material powder layer and D being a melt pool depth occurring as a result of the irradiation, and wherein Rx is a remelting rate within the plane of the presently irradiated raw material powder layer with Rx = ((W-dy)/W), W being a melt pool width and dy being a distance between adjacent irradiation sites of the raw material powder layer, the method comprising the further steps of: - defining the scan pattern, so as to be a twodirectional scan pattern, - orienting the scan pattern of a first raw material powder layer such that it extends at an angle of 45° with respect to a predetermined crystal orientation of the substrate, said angle having a tolerance of +/- 15°, wherein said predetermined crystal orientation is one of a [1 0 0] orientation, [0 1 0] orientation, [-1 0 0], and [0 -1 0] orientation, and - choosing a rotation angle of the scan pattern between two subsequently deposited raw material powder layers to be 0° throughout the workpiece, said rotation angle having a tolerance of +/- 15°. - depositing a sequence of layers of a raw material powder onto a substrate; - after depositing a raw material powder layer, irradiating selected areas of said deposited raw material powder layer with an electromagnetic or particle radiation beam in a site selective manner in accordance with an irradiation pattern which corresponds to a geometry of at least part of a layer of the three-dimensional workpiece to be produced, said irradiation pattern comprising a scan pattern, wherein - the substrate has a single-crystalline microstructure or a microstructure wherein grain boundaries extend parallel to each other and the substrate is arranged so that the [0 0 1] orientation matches a build axis of the workpiece, said matching having a tolerance of +/- 15°; - the irradiation is controlled so as to maintain said single-crystalline microstructure and to produce a metallurgical bond between irradiated sites of the raw material powder layer and the substrate and/or a previously deposited raw material powder layer; and - the irradiation is controlled so that at least one of the following conditions is fulfilled: Rz > 0.3 and Rx > 0.3, - defining the scan pattern, so as to be a twodirectional scan pattern, - orienting the scan pattern of a first raw material powder layer such that it extends at an angle of 45° with respect to a predetermined crystal orientation of the substrate, said angle having a tolerance of +/- 15°, wherein said predetermined crystal orientation is one of a [1 0 0] orientation, [0 1 0] orientation, [-1 0 0], and [0 -1 0] orientation, and - choosing a rotation angle of the scan pattern between two subsequently deposited raw material powder layers to be 0° throughout the workpiece, said rotation angle having a tolerance of +/- 15°.