Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Earth science
Reexamination Certificate
2002-07-23
2004-06-08
Barlow, John (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Earth science
C702S023000, C378S070000, C378S071000, C378S073000
Reexamination Certificate
active
06748345
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to a method of analysing crystalline texture.
BACKGROUND TO THE INVENTION
A wide range of materials have a crystalline structure and these include minerals, ceramics, semi-conductors, superconductors, metals and alloys. The vast majority of these materials are polycrystalline, that is composed from a number of component crystals which are often referred to individually as “grains”.
The crystallographic orientations of the crystals in a polycrystalline sample relative to a fixed reference are seldom random. Where there is some preferred orientation of the crystals then the material is said to exhibit a “texture”. Crystalline planes and directions are conventionally represented using Miller indices with {hkl} representing the crystal planes in terms of the normal to the crystal planes, and <uvw> representing the crystal directions within these {hkl} planes. The texture of a sample can therefore be represented by relating these crystalline planes and directions to corresponding physical directions with respect to the sample.
Conventionally a crystalline texture in a plate or thin film sample is represented as {hkl}<uvw>. These planes and directions are parallel to two corresponding orthogonal directions in the sample. In general this is arranged such that {hkl} represents the crystal plane normals which are parallel to the plane normal of the sample, known as the “normal direction” (ND), and <uvw> represents the crystalline directions within these planes that are parallel to a “longitudinal” or “rolling direction” (RD) within the sample. The samples are therefore prepared such that RD lies within the plane of the sample and ND is perpendicular to RD, and normal to the sample surface.
Crystalline texture is important in materials science as a number of material properties are dependent upon the orientations of the crystals. For example, silicon steels have directions of high magnetic permeability along their <100> crystal directions, a fact which is used in the production of transformer cores.
Traditionally the representation of textures in polycrystalline materials has been carried out using pole figure (PF) or Euler angle methods.
A pole figure can be regarded as a scatter plot showing how the respective crystals are oriented relative to an external frame of reference such as that of the sample. A specific direction with respect to the crystal structure is selected, and for each crystal in the sample this direction is plotted as a point on a stereographic projection (showing the intersection of the direction with a surrounding sphere).
The pole figure therefore represents a statistical distribution of a particular crystal direction, for all grains in which the crystallographic orientation is measured and plotted. The pole figure can be obtained by grain-by-grain measurements or collectively by polycrystalline diffraction using x-rays.
There are a number of problems associated with the use of pole figures. One of these is that the appearance of the pole figure is dependent upon the particular crystal direction plotted, due to the crystal symmetry. Considerable expertise and experience in crystallography is required to interpret pole figures, particularly as even a specific texture will have a different appearance depending upon the crystal direction that is plotted in the pole figure.
A further problem is that many of the points within the pole figure are actually related by the crystal symmetry and this makes the interpretation of the pole figures difficult because consideration of the crystal symmetry is also required.
When more than one texture is present within a sample, these textures are superimposed in the pole figures which makes their individual identification problematical. Whereas some common textures in simple crystal systems may be recognisable by an expert, pole figures showing more complicated textures such as those with large index values for {hkl} and/or <uvw>, or for less common crystal systems are much more difficult to interpret.
An alternative to pole figures is to use the Euler method in which consideration is made of the rotations to each crystal that would be required in order to bring each crystal into alignment with a particular orientation in the sample. The crystal orientations relative to the sample can be represented by three consecutive rotations (Euler angles) around selected orthogonal axes attached to the crystal.
These angles are represented as three rotations around orthogonal axes and each individual measurement of the crystal orientation in the sample is plotted as a point located in the resultant three dimensional “Euler angle” space. Using this method, the existence of texture will be marked by clusters of points in the space. As the space is three dimensional, this is usually displayed by a series of slices cut along one of the axes.
In a similar manner to the pole figure method, crystal symmetry makes interpretation of the Euler plot extremely difficult to visualise and understand, particularly with multiple or complicated textures and uncommon crystal systems.
There is therefore a need to simplify crystalline texture analysis such that crystalline texture information can be more readily obtained and interpreted without the high levels of skill and experience often required in known methods.
SUMMARY OF THE INVENTION
In accordance with a first aspect of the present invention we provide a method of analysing crystalline texture from data defining the orientation of crystals in a sample of polycrystalline material, the method comprising:
for each crystal, determining the orientation of a first direction in the sample, with respect to a common reference frame fixed to the crystal structure of each crystal;
selecting a number of crystals sharing a similar orientation of the first direction with respect to the reference frame;
for each selected crystal, determining the orientation of a second direction in the sample with respect to the reference frame;
selecting a number of crystals sharing a similar orientation of the second direction with respect to the reference frame; and
determining and/or representing a crystal texture corresponding to the orientation of the selected crystals with respect to the first and second directions within the sample.
One advantage of the present invention is that it provides a method in which crystal texture can be determined and/or represented in such a manner that it is more easily interpreted. This is enabled by the use of a reference frame attached to the crystal structure rather than to the sample, and the determination of the orientations of first and second directions in the sample with respect to the crystals. Those crystals sharing a common orientation with respect to the sample are therefore selected and the texture may be represented and/or determined accordingly.
The method also enables the automation of the steps of determining the orientation of the crystals with respect to the crystal structure and indeed their selection. This can be performed by a suitably programmed computer.
Preferably the first and second directions are orthogonal, thereby allowing these directions to be related to the directions used by convention in describing crystalline texture.
Although the analysis of the crystal texture could be performed by computation, preferably the orientation of the first and/or second direction with respect to the reference frame, is displayed to a user of the system as an inverse pole figure (IPF). Typically separate IPFs are used for the first direction and second direction.
The use of the common reference frame is convenient for the purposes of presentation to the user in that, unlike the pole figure method, the information displayed is not dependent upon the pre-selection of a particular crystallographic direction. However, the first and second directions are chosen to define the orientation of the sample. Typically one of the first or second directions are arrang
Chou Cheng Tsien
Dicks Keith Graham
Rolland Pierre
Barlow John
Oxford Instruments Analytical Limited
Vo Hien
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