Inverse pole figure

A pole figure is inverse pole figure graphical representation of the orientation of objects in space. For example, pole figures in the form of stereographic projections are used to represent the orientation distribution of crystallographic lattice planes in crystallography and texture analysis in materials science.

This sections explains how to colorize orientation maps. The mathematics behind the default MTEX color key is explained in detail in the paper Orientations - perfectly colored. In order to illustrate the orientations of the olivine crystals we first define the habitus of a olivine crystal. Next we represent the orientation of each grain by an appropriately rotated crystal. This is done by the following commands. The idea of inverse pole figure color coding of orientation maps is to visualize the orientation of a grain by the color of the crystal face pointing towards you. In the case Olivine habitus this would lead to six different colors.

Inverse pole figure

A pole figure is simply a stereogram with its axes defined by an external frame of reference with particular hkl poles plotted onto it from all of the crystallites in the polycrystal. Typically, the external frame is defined by the normal direction, the rolling direction, and the transverse direction in a sheet ND, RD and TD respectively. Occasionally, CD meaning cross direction is used instead of TD. Drag an atom in the green sphere to reorientate the unit cell of the grain under consideration. This will alter the projections of the [], [] and [] directions on the stereogram inside the rectangle. Press 'Add grain' to add the [], [] and [] directions of another grain, up to a maximum of two additional grains. Try altering their orientations so that all three are similar and then different, and notice how the positions of the poles change. A pole figure for a polycrystalline aggregate, which shows completely random orientation, does not necessarily appear as might naively be expected. Angular distortions inherent in the stereographic projection result in the accumulation of points close to the centre of the pole figure as shown in the image below. If the material shows a degree of texture, the resultant pole figure will show the accumulation of poles about specific directions. A single crystal can be plotted on the pole figure and there is no ambiguity regarding its orientation. However, as more crystallite poles are plotted onto the pole figure, the specific orientation of a particular crystallite can no longer be defined.

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A pole figure is simply a stereogram with its axes defined by an external frame of reference with particular hkl poles plotted onto it from all of the crystallites in the polycrystal. Typically, the external frame is defined by the normal direction, the rolling direction, and the transverse direction in a sheet ND, RD and TD respectively. Occasionally, CD meaning cross direction is used instead of TD. Drag an atom in the green sphere to reorientate the unit cell of the grain under consideration. This will alter the projections of the [], [] and [] directions on the stereogram inside the rectangle. Press 'Add grain' to add the [], [] and [] directions of another grain, up to a maximum of two additional grains. Try altering their orientations so that all three are similar and then different, and notice how the positions of the poles change. A pole figure for a polycrystalline aggregate, which shows completely random orientation, does not necessarily appear as might naively be expected. Angular distortions inherent in the stereographic projection result in the accumulation of points close to the centre of the pole figure as shown in the image below. If the material shows a degree of texture, the resultant pole figure will show the accumulation of poles about specific directions.

Inverse pole figure

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Instead of colorizing which crystal axis is pointing out of the specimen surface we may also colorizing which crystal axis is pointing towards the rolling or folliation direction or any other specimen fixed direction. Consider the x , y plane of the reference basis; its trace on the sphere is the equator of the sphere. Inverse pole figures Instead of plotting crystal orientations with respect to an external frame of reference, inverse pole figures can be produced which show the rolling, transverse, and normal directions RD, TD and ND respectively with respect to the crystallographic axes. Drag an atom in the green sphere to reorientate the unit cell of the grain under consideration. Article Talk. We can overcome this restriction by replacing the colored crystal shape by a colored ball. This is done by the following commands. The interpetation of the colors becomes more simple if we plot the colored ball in stereographic projection and mark the crystallographic axes. The position of the spots is determined by the Bragg's law. Wikimedia Commons. Angular distortions inherent in the stereographic projection result in the accumulation of points close to the centre of the pole figure as shown in the image below. Try altering their orientations so that all three are similar and then different, and notice how the positions of the poles change. In other projects. Way of visually representing the orientation of objects in 3D space.

A pole figure is a graphical representation of the orientation of objects in space. For example, pole figures in the form of stereographic projections are used to represent the orientation distribution of crystallographic lattice planes in crystallography and texture analysis in materials science.

The interpetation of the colors becomes more simple if we plot the colored ball in stereographic projection and mark the crystallographic axes. Typically, the external frame is defined by the normal direction, the rolling direction, and the transverse direction in a sheet ND, RD and TD respectively. Instead of colorizing which crystal axis is pointing out of the specimen surface we may also colorizing which crystal axis is pointing towards the rolling or folliation direction or any other specimen fixed direction. Inverse pole figures Instead of plotting crystal orientations with respect to an external frame of reference, inverse pole figures can be produced which show the rolling, transverse, and normal directions RD, TD and ND respectively with respect to the crystallographic axes. The upper sphere is projected on a plane using the stereographic projection. A single pole is not enough to fully determine the orientation of an object: the pole stays the same if we apply a rotation around the normal line. Then, the poles of the other planes are placed on the figure, with the Miller indices for each pole. A pole figure is a graphical representation of the orientation of objects in space. If the parameters of the optics are known especially the distance between the crystal and the photographic film , it is possible to build the stereographic diagram from the diffraction diagram, i. For this reason it is entirely justified to consider for the ipf map proper symmetries only. The Wulff net is arcs corresponding to planes that share a common axis in the x , y plane. Accordingly, we can associate to each grain a specific point in the color key.