Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N23/00—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
  • G01N23/20—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by using diffraction of the radiation by the materials, e.g. for investigating crystal structure; by using scattering of the radiation by the materials, e.g. for investigating non-crystalline materials; by using reflection of the radiation by the materials
  • G01N23/207—Diffractometry using detectors, e.g. using a probe in a central position and one or more displaceable detectors in circumferential positions
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N23/00—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
  • G01N23/20—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by using diffraction of the radiation by the materials, e.g. for investigating crystal structure; by using scattering of the radiation by the materials, e.g. for investigating non-crystalline materials; by using reflection of the radiation by the materials

Definitions

• This invention relates in general to x-ray diffraction. More particularly, the present invention relates to a technique for x-ray diffraction utilizing fixed sources and detectors, aligned along axes pre-determined according to the properties of the material under measurement.
• X-ray analysis techniques have been some of the most significant developments in twentieth-century science and technology.
• the use of x-ray diffraction, spectroscopy, imaging, and other x-ray analysis techniques has led to a profound increase in knowledge in virtually all scientific fields.
• One existing class of surface analysis is based on diffraction of x-rays directed toward a sample.
• the diffracted radiation can be detected and various physical properties, including crystalline structure and phase, and surface texture, can be algorithmically determined. These measurements can be used for process monitoring in a wide variety of applications, including the manufacture of semiconductors, pharmaceuticals, specialty metals and coatings, building materials, and other crystalline structures.
• the shortcomings of the prior art are overcome and additional advantages are provided through the present invention which in one aspect is an x-ray diffraction technique (apparatus, method and program products) for measuring a known characteristic of a sample of a material in an in-situ state.
• the technique includes using an x-ray source for emitting substantially divergent x-ray radiation - with a collimating optic disposed with respect to the fixed source for producing a substantially parallel beam of x-ray radiation by receiving and redirecting the divergent paths of the divergent x-ray radiation.
• the first x-ray detector collects radiation diffracted from the sample; wherein the source and detector are fixed, during operation thereof, in position relative to each other and in at least one dimension relative to the sample according to a-priori knowledge about the known characteristic of the sample.
• a second x-ray detector may be fixed relative to the first x-ray detector according to the a-priori knowledge about the known characteristic of the sample, especially in a phase monitoring embodiment of the present invention.
• Angular filters can be affixed to the first and/or second x-ray detector for limiting the angles from which the diffracted radiation is collected by the detector. Fixed source/detector pairs can be employed in texture measurement embodiments of the present invention.
• Compact, low power sources can be used, along with collimating polycapillary optics, to enhance the in-situ performance of these techniques.
• FIGs. 2a-b depict top and perspective views of another monitoring, x-ray diffraction system with a source and two detectors fixed in position at 2 different " ⁇ " directions, in accordance with another aspect of the present invention
• Figs. 3a-b depict front and top isometric views of a texture measurement, x-ray diffraction system with two sources and two detectors fixed in position at 2 different " ⁇ " directions, in accordance with another aspect of the present invention
• FIG. 4 depicts an in-situ, x-ray diffraction system with fixed detectors monitoring a moving sample in a production setting;
• FIG. 5 depicts an in-situ, x-ray diffraction system with fixed detectors measuring a sample in a production bypass path;
• Figs 6a-c depict an electron bombardment source, polycapillary collimating optic, and source/optic combination optimized for use in the x-ray diffraction system of the present invention
• Fig. 7 depicts an exemplary, angular filter used in combination with the fixed detector(s) in accordance with another aspect of the present invention.
• FIG. 8 depicts a typical "2 ⁇ " angle scan, and the potential orientation of fixed detectors, in accordance with the present invention. Detailed Description of the Invention
• the present invention is directed to an x-ray system having detectors fixed in position according to certain known, a-priori information about the sample under study and its movement path, in an "in-situ" production environment.
• the term "in- situ” as used herein connotes applications where the sample exists in its own environment, including under active production.
• Examples include an "in-line” system, coupled directly to a production line and analyzing material as it exists (possibly moving) in the production line in a substantially predictable state; or an "at- line” system which is closely associated with the production line, but which analyzes samples removed from their production line with minimal sample preparation prior to measurement; or an "on-site” system which can be portably transported to a site at which the sample resides in a substantially predictable state; but generally exclude “off-line,” fixed laboratory environments.
• production herein connotes active production or transformation of a material in a production facility, including reviewing materials in their native state (i.e., at an ore mine) at the time their initial transformation occurs.
• sample 120 is a material that has some characteristic from which a-priori knowledge can be derived to optimize the XRD system of the present invention.
• certain crystalline structure information might be known, enabling crystalline phase monitoring using two different detectors at different 2-theta angles. This is discussed further below regarding the "steel phase” example.
• crystalline orientation information might be assumed, any changes in which would enable surface texture monitoring using two different source/detector pairs at different phi angles.
• the configuration of Figs, la-b shows a single source 110, and two fixed detectors at the 2-theta angles 2 ⁇ and 2 ⁇ 2 , for phase monitoring. This is discussed further below in the "texture sensing" example.
• Figs, la-b depict front and top perspective views of a phase monitoring, x- ray diffraction (XRD) system 100 in accordance with the present invention including a source 110, a shutter 112, diverging x-rays 114, a collimating optic 116, a parallel beam 118, a sample 120, diffracted beams 121/122, a first angular filter 124, second angular filter 126, a detector 128, a detector 130, a rigid support structure 115 and a computer 132.
• XRD x-ray diffraction
• Source 110 and collimating optic 116 provide x-ray radiation in the form of a parallel beam 118. Particular details of an exemplary source/optic combination in accordance with the present invention are discussed in connection with Figs. 6a-c below.
• Source 110 may be a point source that generates the divergent x-rays 114 from a small spot and emits the divergent x-rays 114 isotropically from that small spot, or may be a large area source that generates x-rays over a relatively large area and emits the divergent x-rays 114 over a range of angles from each position on the source 110.
• the divergent x-rays 114 may be emitted from an x-ray tube resulting from electron bombardment of an anode, with divergent x-rays 114 constantly emitted from the source, such as an Oxford 5011 electron bombardment source.
• the collimating optic 116 is a device capable of producing a beam of sufficient parallelism to generate a usable diffraction pattern. Parallel beams are also less susceptible to sample displacement in the vertical direction - a significant advantage when operating in an in-situ environment.
• Collimating optic 116 may be a soller slit coUimator, which is an array of absorbing plates separated by gaps. However, since a Sollar slit is a blocking method and hence inherently inefficient, a large source may be required. A pinliole coUimator is also possible, but that is also an inefficient technique.
• collimating optics are prefened, i.e., those which receive a wide angle of divergent x-rays and redirect the divergent rays into a parallel beam.
• Such optics include, for example, curved crystal optics (see e.g., X-Ray Optical, Inc. U.S. patent numbers 6,285,506 and 6,317,483 - all of which are incorporated by reference herein in their entirety), multilayer optics, or polycapillary optics.
• the collimating optic 116 may be a polycapillary optic - a bundle of thin, hollow tubes that collects a portion of the diverging x-rays 114 over a significant solid angle, transmits and therefore redirects the photons from their otherwise straight paths via total external reflection inside the channels, and collimates the collected divergent x-rays 114 into a parallel beam 118 directed at the sample 120.
• This enables the use of smaller, low-power sources.
• the optic/source combination optimized for use in the systems herein are discussed in connection with Figures 6a-c below.
• the system 110 may further include a shutter 112, to block the entirety of the parallel beam 118, when desired.
• Angular filters enable more precise control over the diffracted radiation detected by detectors 128 and 130.
• the first angular filter 124 and the second angular filter 126 may be polycapillary optics (see the discussion below regarding Fig. 7) that reject radiation incident outside of a critical angle for total external reflection while efficiently transmitting radiation within the critical angle, towards the detectors 128 and 130, respectively.
• the resolution of the angular filters is determined according to the peak width of the diffraction peak being monitored. By correlating the angular resolution of the angular filter to the peak width, the maximal power from the peak is provided to the detector, while minimizing any background noise from the off-peak areas.
• soller slits may comprise the angular filters 124 and 126.
• One- and two-dimensional variants of these filters may also be used.
• the detectors 128 and 130 are elements that collect the diffraction pattern produced by the diffracted beams 121 and 122 (each along its own respective 2-theta angle chosen according to a-priori knowledge about the sample characteristics under study) respectively and produce output signals that vary with changes in the diffracted x-rays incident upon them and are communicated to the computer 132.
• the detectors 128 and 130 may be scintillation detectors, detectors that consist of a photomultiplier tube facing a region that contains a solid material such as sodium iodide laced with thallium atoms. Alternately, detector 130 could be a semiconductor detector. These types of "point" detectors are preferred. Other detectors are known to those skilled in the art.
• Detectors used in the disclosed in-situ XRD system usually need to be of small size for compact design of the whole system, and have some moderate resolution ( ⁇ lkev) to select the x-ray source Ka radiation. Higher energy resolutions (which may require the detector to be cooled with liquid nitrogen) are usually not needed. The detectors may require high counting efficiency, and the resultant high sensitivities to detect the diffraction beam, which may be weak. A large capture area (combined with a large angular filter) is desired for a larger tolerance of sample position displacement.
• the present invention makes use of small, inexpensive "point detectors" in one embodiment.
• One example includes a detector (used for texture measurement) with 25 mm 2 capture area and ⁇ 200 ev energy resolution.
• a gas proportional counter detector may be used for steel phase monitoring, with 12 x 25 mm 2 capture area and ⁇ 1000 ev energy resolution.
• a rigid support structure 115 supports the source and detectors in fixed position to each other (while measurements are taken) and the entire system is placed in a measurement position relative to the underlying sample 120.
• the system can be fixed with respect to the sample, or can hover over the sample, or the sample can move under the fixed system.
• the system can rotate with respect to the sample.
• the rotational (phi) angle must be fixed.
• at least one dimension must be fixed between the sample and the system to ensure accurate measurements. This dimension is usually the distance between the system and the sample.
• the computer 132 is a data acquisition device that may contain a standard analysis software package.
• the computer serves to analyze, interpret, and display information about the sample 120 from the response of the detectors 128 and 130 to the diffraction patterns at their respective 2-theta angles.
• FIG. la The top view of Fig. la shows the source 110, detector 128 and detector 130 aligned in parallel along the same phi angle, ⁇ .
• the offset between the detectors can be in the theta direction, the phi direction (discussed below in connection with Figs. 2a-b), the chi direction (i.e., the plane formed by the source/detector pair) or any combination of these directions.
• the x-ray diffraction system 100 provides an in-situ system that enables, e.g., phase detection or monitoring and quantitative analysis of the sample 120.
• the x-ray diffraction system 100 is particularly well suited for in-situ phase analysis of a moving media (e.g., moving galvanized steel in a manufacturing environment subsequent to the application of a coating to the sample 120 - see discussions below).
• the low power source 110 emits the diverging x-rays 114, which are collimated into the parallel beam 118 by the collimating optic 116.
• the intensity of the x-rays within the diffracted beams is measured as a function of the diffraction angle 20. This diffraction pattern may be used in this example to identify and monitor the crystalline phases and other structural properties of the sample 120.
• the diffraction pattern detection devices can be placed in fixed positon.
• two detectors 128 and 130, with the angular filters 124 and 126, respectively, are included in the present invention to acquire data from two different diffraction angles, 2Q ⁇ and 2 ⁇ , respectively.
• the detector 130 measures the intensity of x-ray radiation directed to it by the second angular filter 126 within a preselected energy window from an angle 2 ⁇ .
• An algorithm is performed and a ratio is obtained by the signals input from the detectors 128 and 130 to the computer 132 and the amount of a given phase is determined. In the case that none of a given phase is present, the counts in the region of interest for the diffracted beam 122 at an angle 2 ⁇ 2 received at the detector O 2005/031329
• the present invention is especially useful in applications where a single material phase needs to be examined, such as detection of unwanted phase change in steel that has undergone a galvanizing process, and the angular positions of the diffraction peaks are known with some degree of accuracy.
• Using the two fixed detectors 128 and 130 (with the optional angular filters 124 and 126) instead of either a scanning, movable detector significantly reduces the size and complexity of the detector assembly in an x-ray diffraction system. This results in both lower cost and increased reliability, which are especially important for in-situ applications.
• the inclusion of the collimating optic 116 produces the parallel beam 118 of sufficient intensity to accomplish the desired measurements in a time frame that enables immediate feedback while utilizing the low power source 110.
• Conventional x-ray diffraction systems used for crystallinity analysis make use of a focussing geometry called Bragg-Brentano, in which extensive polishing and sample preparation, as well as sample scanning is often necessary.
• the parallel beam 118 utilized in the present invention eliminates the need for significant sample preparation, and scanning during operation. Scanning may be done once, to determine the shape of the scan curves and ultimate angular position of the detectors. Then during operation, no scanning is necessary.
• FIG. 2a-b show an x-ray diffraction system similar to that of Figs, la-b with the angular positions of the fixed detectors at the same 2-theta angle, but varied in the phi direction.
• Figs. 2a-b show an x-ray diffraction system similar to that of Figs, la-b with the angular positions of the fixed detectors at the same 2-theta angle, but varied in the phi direction.
• FIGS. 2a-b depict an x-ray diffraction (XRD) system 200 in accordance with the present invention including a source 210, a shutter 212, diverging x-rays 214, a collimating optic 216, a parallel beam 218, a sample 220, diffracted beams 221/222, a first angular filter 224 (not entirely visible), second angular filter 226, a detector 228, a detector 230, a rigid support structure 215 and a computer 232.
• XRD x-ray diffraction
• Figs, la-b These components can be similar to those discussed above with respect to Figs, la-b, but are simply arranged at different angular positions.
• the position of the detectors can be displaced along the 2-theta position (Figs, la-b), displaced along the phi position (Figs. 2a-b) or a combination of both directions (not shown) depending on the application and the type and quality of the information known a-priori about the potential application.
• Hot dip galvannealed steel sheets have excellent co ⁇ osion resistance, paintability, phosphatability and weldability; and the properties of these steels are therefore in high demand in the automotive industry. It is important for producing galvannealed steel sheets with superior press formability such as drawability and anti-powdering behavior to control the microstructure of galvannealed coatings.
• the coating properties are greatly influenced by the composition and the microstructure of the coating layer that is formed on the steel substrate during the hot dip galvanizing and galvannealing processes.
• a zinc bath modified with aluminum is used for the hot dip galvannealing process.
• a Fe-Al-Zn reaction initially takes place at the interface between the steel substrate and the zinc coating, which obstructs the Zn-Fe reaction. This step is called inhibition.
• To initiate the Zn-Fe reaction it is necessary to remove the interface layer, the thickness of which increases with increasing aluminum content in the Zn-bath.
• a first Fe-Zn alloying reaction occurs during the formation of the intermetallic ⁇ -phase, columnar ⁇ -crystals grow on top of the thin Fe-Al.
• the local formation of ⁇ -phase and of another intermetallic ⁇ -phase in form of polygonal crystals begins on the surface of the steel substrate and then spreads across the entire interface layer.
• solid/liquid reaction step solid Iron, Zn-Fe phases and liquid Zn
• subsequent solid state reactions occur, transformation of ⁇ -phase to ⁇ -phase and growth of T-phase.
• the quality of the Zn-Fe layer is mainly influenced by several parameters: the steel substrate, the iron content, and the optimum distribution of the Zn-Fe phases in the coating.
• the second two parameters are determined mainly by the temperature and holding time in the galvannealing furnace, the Al content in the Zn bath, steel composition and the steel surface conditions.
• galvanneal steel can exhibit powdering or flaking, due to T-phase formation between the steel substrate and the galvanneal surface coating. This causes the loss of coating from the steel surface, which occurs during forming operations.
• Forming processes in the automotive industry set high standards towards the certification of the steel grade.
• the phase formation process in the surface layer is a complex process and producing the right steel grade at a high yield can be challenging.
• the individual steel mills have to certify their products before shipping. Therefore, an in-line monitoring system capable of identifying and monitoring phases will greatly benefit a continuous sheet steel galvannealing line.
• a semi-quantitative analysis will give nearly real-time results on formation trends as the galvannealed steel sheets roll by the diffraction system.
• the phase composition, or the amounts of each iron zinc compound in the coating is a very important component of galvanneal steel and is directly related to the flaking of the coating. This results in a close connection between the alloying degree of the coating and the press formability of the hot dip galvannealed steel sheet. When a thick ⁇ -phase remains on the surface of the coating, this indicates a low alloying degree of coating. The surface dynamic friction of the coating increases resulting in the poor drawability and rupture of steel sheets. Conversely, when the alloying degree goes up and thickness of the T- phase increases the powdering phenomena becomes noticeable. To produce hot dip galvannealed steel sheets with excellent press formability the alloying degree must be controlled to reduce the amount of both residual ⁇ - and T- phases.
• FIGs. 3a-b are schematic front and top isometric views of an embodiment of the present invention optimized for in-situ texture measurements.
• source detector pairs 310/330 and 311/328 are fixed in respective positions generally along the phi circle, and at a given chi angle to the sample 320.
• Texture analysis determines the preferred orientation of the crystallites in polycrystalline aggregates. What is conventionally required is determining the complete orientation distribution of the crystallites. This usually requires systematic changes in the angular orientation of the sample in chi and phi to collect the diffraction data to produce a pole figure plot.
• a pole figure plot is obtained by measuring the diffraction intensity of a specific plane (for example, [111] plane) at various settings of the chi and phi angles. Pole figures are convenient illustrations of the constructive interference formed by the diffraction patterns associated with the phases of interest (here, known a-priori).
• Each constructive interference spot occurs at a specific location on a specific circle (of varying phi angles) of constant 2-theta angle, where different diffracting planes will produce diffraction peaks at different 2-theta angles.
• the diffraction peaks appear as dots.
• the worst case in which all the grains are randomly oriented with respect to one another, the diffraction peaks appear as solid rings that occur along the curves of constant 2 ⁇ -angle.
• diffraction peaks appear as elongated spots.
• tbte present invention fixed sources and detectors are used to make this texture measurement without rotation of the sample in the chi or phi directions.
• the source detector pair 310/330 is fixed at opposing phi angles ⁇ i and ⁇ 3
• the source/detector pair 311/328 is fixed at opposing phi angles ⁇ 2 and ⁇ 4 .
• This configuration is somewhat analogous to the phase monitor embodiments of Figs, la-b and 2a-b, and may also employ the same components (collimating beams, angular filters), however, here there is a source for each detector, and the positions are fixed along the phi direction, though they can also be fixed along the chi and theta directions also.
• fixed source/detector pairs e.g., one pair at the orientation corresponding to the peak, and another at the background, could be used to make a similar measurement, assuming the location of the peak is known a-priori to some reasonable degree of accuracy.
• Fig. 4 depicts an "in-line" version of an in-situ system 400, coupled directly to a production line, and analyzing an area 421 of material 420 as it exists (possibly moving) in the production line, in a substantially predictable state (especially with respect to the theta, phi and chi angles discussed above).
• This type of environment may be applicable to the steel example discussed above, where steel sheets under production are moving along a movement path 430, or a texture measurement example discussed above, where superconductive tape is moving past the in-situ system.
• the system may gather diffraction data through an area of the material, as a function of translation rate and sampling duration, the material could be stopped and discrete points and the measurement made at each point.
• continuous data sampling along an area of the material during continuous movement may be desirable for processing.
• FIG. 5 depicts an "at-line” version of an in-situ XRD system 500, proximate to ("at") a production line, and analyzing a sample 520 of material 520 as it exists (possibly moving) in the production line, in a substantially predictable state (especially with respect to the theta, phi and chi angles discussed above). Minimal sample handling and preparation is performed (530), and the sample exists under measurement by system 500 essentially as it existed in the production line.
• an "on-site” system which can be portably transported to a site at which the sample resides in a substantially predictable state (e.g., an ore mine where certain characteristics of the samples are of interest; or forensic scenes where certain known materials are being sought).
• Fig. 6a the basic elements of a typical compact, electron-bombardment x-ray source 600 are shown. Electron gun/filament 610 is heated (by applying a voltage) to a temperature such that electrons 612 are thermally emitted.
• Electrode 614 which is covered with target material, where they strike within a given surface area of the anode, called the spot size 618.
• Divergent x-rays 620 are emitted from the anode as a result of the collision between the accelerated electrons and the atoms of the target.
• electromagnetic focusing means 622 may be positioned between filament 610 and anode 614. X-ray sources with spot sizes of 2 microns or less are available commercially. However, as the electron spot size decreases, so does the production of x rays.
• the optic 644 comprises a plurality of hollow glass capillaries 648 fused together and shaped into configurations which allow efficient capture of divergent x-ray radiation 620 emerging from x-ray source 600.
• the captured x-ray beam is shaped by the optic into a substantially parallel beam 650.
• the channel openings 652 located at the optic input end 654 are roughly pointing at the x-ray source.
• each individual channel to essentially point at the source is of significant importance for several reasons: 1) it allows the input diameter of the optic to be sufficiently decreased, which in turn leads to the possibility of smaller optic output diameters; and 3) it makes efficient x-ray capture possible for short optic to source focal lengths.
• the diameters of the individual channel openings 652 at the input end of the optic 654 may be smaller than the channel diameters at the output end of the optic 656.
• Fig. 6c illustrates in cross-section an elevational view of one embodiment of an x-ray source/optic assembly particularly suited for the diffraction systems of the present invention.
• X-ray source/optic assembly includes an x-ray source 600' and an output optic 644' - similar to those discussed above with respect to Figs. 6a-b.
• Optic 644' is aligned to x-ray transmission window 2107 of vacuum x-ray tube 2105.
• X-ray tube 2105 houses electron gun/filament 2115 arranged opposite to high voltage anode 2125. When voltage is applied, electron gun 2115 emits electrons in the form of an electron stream 2120 (as described above). HV anode 2125 acts as a target with respect to a source spot upon which the electron stream impinges for producing x-ray radiation 2130 for transmission through window 2107 and collection by optic 644'.
• Anode 2125 may be physically and electrically connected to a base assembly which includes a conductor plate 2155 that is electrically isolated from a base plate 1265' via a dielectric disc 2160.
• a high voltage lead 2170 connects to conductive plate 2155 to provide the desired power level to anode 2125.
• the electron gun 2115, anode 2125, base assembly 2150 and high voltage lead 2170 may be encased by encapsulant 2175 all of which reside within a housing 2710. (However, dielectric disk 2160 functions to remove excess heat from the assembly, in one embodiment negating the need for any special cooling encapsulants).
• Housing 2710 includes an aperture 2712 aligned to x-ray transmission window 2107 of x-ray tube 2105. In operation, x-ray radiation 2130 is collected by optic 644', and in this example, redirected into a substantially parallel beam 650.
• a control system may also be implemented within x-ray source assembly 600'.
• This control system includes, for example, a processor 2715, which is shown embedded within housing 2710, as well as one or more sensors and one or more actuators (such as sensor/actuator 2720 and actuator 2730), which would be coupled to processor 2715.
• This control system within x-ray source assembly 600' includes functionality to compensate for, for example, thermal expansion of HV anode 2125 and base assembly 2150 with changes in anode power level in order to maintain an alignment of x-rays 2130 with respect to optic 2135. This enables the x-ray source assembly 2700 to maintain a spot size 2745 with stable intensity within a range of anode operating levels.
• This parallel beam production and transmission can be effected by the polycapillary collimating optics and optic/source combinations such as those disclosed in commonly assigned, X-Ray Optical Systems, Inc.
• Fig. 7 depicts a typical polycapillary angular filter 700 useful in the present invention fabricated from a large number of small glass capillaries. Since the refractive index of x-rays in glass is slightly less than unity, total reflection occurs when x-rays 702 are incident on a smooth glass surface at a small incident angle. The critical angle for total external reflection is inversely proportional to the x-ray energy and for 30 keV x-rays is about one milliradians (-0.05 degrees). X-rays incident at angles less than the critical angle can then be transmitted 704 through hollow glass capillaries.
• Fig. 8 depicts a sample diffraction curve derived (e.g., in a laboratory) from scanning a source and detector in the 2-theta direction across a representative sample of interest. Though the 2-theta position is shown, similar curves are derived in diff action practices generally, from which fixed detector locations can be derived. Upon derivation of this curve, and in accordance with the present invention, fixed sources and/or detectors can be placed at the noted angular positions 800, 810 and 820 in accordance with the present invention.
• a single peak detector is used, and a single background detector is used, close to the diffraction angle of the peak (to ensure the same general type of diffraction conditions are collected) but far enough into the noise to ensure a distinctive measurement between the peak and noise - thereby providing an accurate peak magnitude measurement.
• three detectors can be used (peak, half peak and noise); or five detectors (peak, half peak - both sides, and noise - both sides); or more detectors; or any desired mix of detectors or source/detector pairs.
• This invention can also be used for other applications like in-situ strain and stress measurements by collecting, in real time, the diffraction peak profiles, using detectors at fixed positions as discussed above. To obtain high quality data for measurement with high precision, linear detector or even area detectors could be used as well for any of the above-described detectors.
• the processing portions of the present invention can be included in an article of manufacture (e.g., one or more computer program products) having, for instance, computer usable media.
• the media has embodied therein, for instance, computer readable program code means for providing and facilitating the capabilities of the present invention.
• the article of manufacture can be included as a part of a computer system or sold separately.
• At least one program storage device readable by a machine embodying at least one program of instructions executable by the machine to perform the capabilities of the present invention can be provided.

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