Patent Number: 062367102
Section: description

DETAILED DESCRIPTION OF THE INVENTION An x-ray crystal device as shown in FIG. 1 consists of a thin doubly curved crystal lamella 10, a thick bonding layer 12, and a backing plate 14. In this device, the bonding layer 12 having a thickness typically 10 to 50 times the thickness of the crystal constrains and holds the crystal to a preselected geometry. The crystal can be one of a number of crystals used in x-ray diffraction, such as mica, silicon, germanium, quartz, etc. The bonding layer consists of a material that has a high viscosity in its initial state and can be transformed by polymerization, or by a temperature change to a solid. Suitable bonding materials are thermoplastic resins, various thermosetting resins, epoxy, low melting point glass, wax, etc. The most important property of the bonding layer is a viscosity of the order of 10.sup.8 -10.sup.8 Poise (c.g.s. units) before it reaches its final state. A particularly useful epoxy resin called "Torr Seal" is used in one preferred embodiment of the invention. This initially has a paste-like consistency, a viscosity of the order of 10.sup.3 Poise, and a pot life of 30-60 minutes. Furthermore, the low vapor pressure of this material in its cured state is desirable if the crystal device is used in a vacuum environment. Other paste types of epoxy that could be used include "plumber's epoxy" and "Milliput" epoxy putty which have physical properties similar to Torr Seal except for the low vapor pressure. A thin plastic separator sheet 16 between a portion of the surface of the crystal near its edges lies between the crystal 10 and the bonding layer 12. This plastic separator extends 1-3 mm beyond the crystal's edges in order to prevent the bonding material from sticking to the mold or flowing under the crystal during fabrication. Thin plastic strip with pressure sensitive adhesive coating such as "Scotch tape" or "transparent mending tape" which have a thickness of typically 0.05 mm have been successfully used for the said plastic sheet with the adhesive side facing the crystal. Somewhat thinner or thicker plastic sheets could also be used. The plastic separator sheet is omitted in an alternative form of the invention shown in FIG. 2. This form of the invention is simpler than the structure shown in FIG. 1 and is feasible if the epoxy has a sufficiently high viscosity that it cannot flow under the crystal lamella. In this case, the bonding layer 12' does not extend as far beyond the crystal lamella 10', in order to minimize it sticking on the mold. The backing plate 14 in FIG. 1 and 14' in FIG. 2 is selected of a material to which the bonding material adheres, which is dimensionally stable, and which has a coefficient of thermal expansion similar to the crystal. If the crystal to be used is transparent to light (e.g. quartz, alkali halides, etc.) it is desirable to use a transparent material for the backing plate and the bonding material so that optical interferometry can provide a means for quality control. The backing plate can be flat as indicated by reference no. 18 in FIG. 1, or it can have a concave surface as indicated by 19 in FIG. 2. The exact shape of the surface is usually not critical as will be seen in the fabrication method for a preferred embodiment that will be described. It will be noted generally, it is best to use a convex mold for bending the crystals as in U.S. Pat. No. 4,807,268. This allows for the mold to be reused and for the crystal to be conformed directly to the surface of the mold without any intervening layer, yielding high accuracy. In most cases, it is important that the crystal be properly located relative to the mold both in position and in angular orientation. This can be done by using a mold whose size matches the crystal size and using barriers at the exact boundaries of the crystal. This approach can be used for devices like the one in FIG. 2 but is inaccurate when used with ones like FIG. 1. FIG. 3 shows a preferred embodiment in the present invention wherein the crystal lamella 1 has half-circle indentations 2 and 2' accurately made on two opposing faces. This may be done with a special fixture or with an ultrasonic "cookie cutter" and an abrasive slurry. The two indentations engage dowel pins 3 and 3' which slide in cylindrical cavities made in the mold 4 by drilling and reaming. Helical springs such as 5 allow the dowel pins to slide into the mold when the crystal is bent, otherwise, they are essential flush with the top surface of the crystal. This approach to positioning the crystal relative to the mold is compatible with the use of a thick viscous agent for deformation according to the following method: The fabrication method for the crystal device is shown in FIGS. 4A-4D. A convex mold 20 having a surface of the desired shape is prepared by single point machining or by a numerically controlled milling machine. Single point machining (e.g. with a diamond tool) is particularly suited to toroidal surfaces, i.e. surfaces of revolution having one radius of curvature in a plane perpendicular to the axis and a second radius in the plane passing through the axis. The mold surface 22 is polished to a mirror finish; hence, materials such as stainless steel, glass, or hard aluminum alloys may be used. A glass or transparent mold would facilitate the use of interference fringes. After the mold is prepared (by steps that are not shown here), a crystal lamella is prepared. This lamella may be flat as shown by 11 and 13 in FIGS. 5A and 5B, or cylindrical as shown by 15 and 17 in FIGS. 5C and 5D. The thickness of the lamella is critical; it should be no more than .about.1/5,000of the smallest radius of curvature. For mica, the crystal surfaces as cleaved are satisfactory, but for brittle crystals without such pronounced cleavage planes (e.g. quartz and silicon), it is important that the surface be damage free. This may be accomplished by etching or by chemical polishing after cutting and mechanical polishing. After the crystal lamella is prepared, the thin plastic sheet 16 is attached around the edges of crystal 10 as shown in FIG. 4A, and the crystal with plastic sheet is positioned on the convex mold 20. At this stage, it is very important to avoid the presence of dust particles, particularly between the crystal and the mold. If epoxy is used for the bonding agent, a blob of epoxy 7 is placed on top of the crystal 10. The backing plate 14 is attached to a piston 28 by means of a screw 33 which threads into part of the piston and pulls the projecting surface 30 on the back side of the backing plate against a mating surface 31 on the piston. Due to of the slope of the surface 30, the backing plate's surface 40 is pulled snugly against surface 41 of the piston. The piston has a rectangular cross section matching the backing plate and these two components are placed on top of the epoxy as shown in FIG. 4A. The assembly is mounted in the pressing fixture 32 attached to the mold as shown in FIG. 4B. The pressing fixture has a rectangular cavity in which the piston 28 and backing plate 14 are free to slide. In this way, the backing plate is indexed in position relative to the mold via the backing plates's lateral surfaces (e.g. 38 and 40). The assembly is compressed lightly by turning the knob 36 attached to screw 34 to flatten the epoxy and bring the crystal in to better contact with the surface of the mold. As the epoxy begins to polymerize, the pressure on the backing plate 14 is gradually increased by further turning of the screw 34 so as to force the crystal 10 against the mold 20 as shown in FIG. 4B. During this process, if the backing plate and the crystal are transparent, contact between the crystal surface 24 and the mold surface 22 can be monitored by observing interference fringes with illumination by light through the surface 26 of the backing plate 14. Alternatively, such fringes can also be observed by light passing through the mold if it is transparent. Dust particles, or undesirable penetration of the bonding material between the crystal and the mold can be observed in this case, indicating that the plastic sheet 16 failed in its purpose of preventing this penetration. In addition it will be possible to observe cracking of brittle crystals if this happens to occur. However, it should be noted that as long as the pieces of the crystal remain in the proper position, cracking of the crystal will not affect the performance of the device significantly. When the epoxy completely fills the space between the backing plate and crystal with plastic strip as shown in FIG. 4C, the pressure on the backing plate is held constant until the epoxy is completely cured. Then, the device is removed from the mold, from the pressing fixture and from the piston, yielding the result shown in FIG. 4D. In this step, the plastic sheet 16 is important to prevent the bonding material 12 from sticking to the mold 20 so that removal can be accomplished without distorting the bonding material. In this connection, it should be noted that use of parting agents to prevent adhesion of the bonding material to the mold is not desirable because the presence of these agents will reduce the accuracy with which the crystal conforms to the desired shape. However, parting agents may be used to prevent the epoxy from sticking to the pressing fixture. This positioning is less critical and it is recognized that in most cases, the completed device must be aligned relative to the x-ray source after its fabrication is complete (one can only hope to get the least critical alignments correct--the others require in situ adjustments). One of the most important applications of this invention is that of focusing x-rays of a particular wavelength from a source to form an x-ray microprobe. This type of device with point-to-point focusing property is illustrated in FIG. 7A. The crystal in this device has a toroidal shape such that the crystal satisfies either the Johann or Johansson geometry in the plane of the Rowland circle 28 and also has axial symmetry about the line joining the source S and the image I. If a crystal lamella like the one shown in FIG. 5A is used, having crystal planes 21 parallel to the surface 11 and the mold has a radius of 2R.sub.1 in the plane of the focal circle having a radius R.sub.1, the result after bending will be as shown in FIG. 6A and the geometry in the plane of the focal circle after alignment will be the Johann geometry. In this case, the crystal device will be in the usual symmetric position A relative to the Source S and the Image I shown in FIG. 7B. On the other hand, if the crystal lamella of FIG. 5B is used with the crystal planes 23 making an angle with respect to the large surface 13 of the lamella, and the mold has a radius of 2R.sub.1 in the plane of the focal circle of radius R.sub.1, the result after bending will be as shown in FIG. 6B. Then, the geometry in the plane of the focal circle after alignment with respect to the source s and the image I will be similar to the Johann geometry but with the crystal device offset from the symmetric position as shown by position B in FIG. 7B. Two different Johansson geometries are obtained if the crystal slab is curved to a radius 2R.sub.1 as shown in FIG. 5C and FIG. 5D. Like their 2-dimensional analog, Johansson-based point-to-point focussing devices will provide greater solid angle of collection and also more exact focussing than Johann-based devices. They are particularly advantageous when used with crystals having a small rocking curve width. When the crystal planes 25 are parallel to the surface 15 of the crystal at its mid-line as shown in FIG. 5C, the result after bending to a mold with radius R.sub.1 is shown in FIG. 6C. This crystal device when aligned with respect to source s and image I will be in the symmetric position c shown in FIG. 7C. But if the crystal planes 27 make an angle with respect to the surface 17 as shown in FIG. 5D, the result after bending to a mold with radius R.sub.1 would be as shown in FIG. 6D. Then, when the crystal device is properly aligned, it will be asymmetric relative to S and I, as shown by position D in FIG. 7C. The alignment of the crystal devices relative to the Source S and Image I can be accomplished by a device similar to one described in U.S. patent application Ser. No. 09/149,690 (now U.S. Pat. No. . . . ) which is hereby incorporated by reference. For this purpose, it is important to have indexing features on the crystal device so that its position relative to the source and image can be roughly preset and also only adjustments that are absolutely necessary need to be accommodated. The initial positioning is facilitated by the mounting fixture 50 of FIG. 7A having a U shape with the space between the arms of the U configured to match the backing plate. The backing plate with crystal is attached to fixture 50 by screw 33 like it had been previously attached to the piston. A leaf spring 47 maintains contact of surface 38 of the backing plate with surface 39 of 50 before 33 is fully tightened and contact of surface 40 of the backing plate and 41' of 50 is maintained when 33 is fully tightened. Thus, the position of the crystal is now fixed relative to the fixture 50, as it was previously fixed relative to the mold 20. Details of the degrees of freedom for which adjustments might be provided as well as a simple mechanism for adjustment of the others are given in the reference cited. While the asymmetric cases shown in FIGS. 7B and 7D show the crystal device closer to the source than to the image, clearly the opposite situation case could be achieved (i.e. crystal device closer to the image than to the source). The asymmetric cases are sometimes useful to provide additional space in the x-ray source region or image region. DISCUSSION AND RAMIFICATIONS An x-ray crystal device according to this invention provides a doubly bent crystal that accurately conforms to a theoretically optimum shape and provides better performance than similar crystal devices made according to the prior art. Moreover, the methods of fabrication allow for the production of many identical crystal devices from the same mold, thus reducing the cost of the each device. The first monochromatic x-ray microprobe that had sufficient intensity for trace element determination in x-ray fluorescence analysis and was based on a laboratory source was developed using an x-ray crystal device similar to the one described herein (re: papers by Z. W. Chen and D. B. Wittry, "Monochromatic microprobe x-ray fluorescence-- . . . J. Appl. Phys. vol. 84, pp. 1064-73, 1998, and "Microprobe x-ray fluorescence . . . Appl. Phys. Lett. vol. 71, 1997, pp. 1884-6). The device used in the cited work was based on a Johann geometry with focal circle radius of about 125 mm with a mica crystal having an effective area of approximately 8 mm.times.28 mm and produced an x-ray spot size of about 50 .mu.m with an x-ray source of about 20 g .mu.m. An indication of the advantages of some of the features of the present invention can be obtained by comparing the theoretical performance of some examples of specific crystal devices with the Johann-based mica diffractor used by Chen and Wittry. If a silicon (111) crystal were used and the values of the rocking curve width of 8.7.times.10.sup.-5 radian (instead of 30.times.10.sup.-5) and peak reflectivity of 0.7 (instead of 0.2) are assumed, then, with the Johann-based geometry, the broadening of the focal spot due to the crystals rocking curve would be about 8.7 .mu.m instead of 30 .mu.m as it was for the mica crystal. The effective crystal width would be 8.times.(8.7/30).sup.0.5 =4.31 mm for the Johann-based geometry--but we must note that for copper K alpha radiation and Si crystal, the penetration of the rays into the crystal is sufficient that there would be little distinction between this geometry and the Johansson geometry. This distinction becomes more evident if we consider wider crystals, for example 16 mm. The peak reflectivity for the Si crystal is about 3.5 times higher than that of mica, so, if equal widths are considered, the total flux of the focused probe could be the same if the Gaussian image size were smaller by .about.(1/3.5).sup.0.5 =(1/1.87) yielding a spot size of (20/1.87)+8.7=19.4 .mu.m vs (20+30)=50 .mu.m. But, if a Johansson-based crystal were used having a width of 16 mm the corresponding Gaussian image would be 7.6 .mu.m, yielding a spot size of 7.6+8.7=16.3 .mu.m and then the number of photons/sec/cm.sup.2 would be greater than that which was obtained with mica by a factor of approximately (50/16).sup.2 =9.76. In order to make smaller spots, it is important to reduce the broadening due to the rocking curve width. But as this gets smaller, it is no longer possible to utilize all of the characteristic line's natural width. The intensity loss resulting from focusing only part of the characteristic line can be estimated as follows: Bragg's law is: n.lambda.=2d sin.theta. where .theta. is the Bragg angle. Differentiating Bragg's law on both sides and dividing by Bragg's law, we obtain: EQU (.DELTA..lambda./.theta.).sub.B =(1/tan.theta.).DELTA..theta. where .DELTA..THETA. is the rocking curve width. Assuming that the characteristic line has (.DELTA..lambda./.lambda.).sub.L =2.times.10.sup.-4 and assuming values for Cu K radiation and the (111) reflection from silicon, we obtain: EQU (.DELTA..lambda./.lambda.).sub.B /(.DELTA..lambda./.lambda.).sub.L =8.7.times.10.sup.-5 /(tan 14.21).times.2.times.10.sup.-4 =1/1.71 Thus the rocking curve width for the Si (111) crystal would appear to be reasonably well matched to focus nearly all the characteristic X-ray line. One can calculate similarly the results of using a crystal with even narrower rocking curve width e.g. .alpha. quartz (2243) with a rocking curve of about 5.times.10.sup.-6 radian. This would yield image broadening due to the rocking curve width of only about 0.5 .mu.m. Then, the loss of intensity due to not using all of the natural line width is more serious. For this case and copper K radiation we would obtain: EQU (.DELTA.2/.lambda./.lambda.).sub.s /(.DELTA..lambda./.lambda.).sub.L =5.times.10.sup.-6 /(tan 49.64).times.2.times.10.sup.-4 =1/46.8 In order to offset this effect, it is clearly desirable to use the Johansson-based geometry and wider crystals. Also one should use higher voltage for the x-ray source since the intensity of characteristic lines increases as the 1.63 power of the voltage above the critical excitation voltage (for copper K radiation this would be approximately 3.times. if 50 kV instead of 30 kV were used). For this case the total number of photons/sec in a 10 .mu.m spot formed by the quartz crystal would be lower than that obtained in a 16 .mu.m spot with a Si crystal by a factor of (9.5/7.6).sup.2.times.(3/46) 0.1. Thus, by using all available techniques, it should be possible to obtain focal spot sizes significantly less than 10 .mu.m with adequate intensity for x-ray fluorescence analysis, although the detection limits would be lower than those obtained for larger spot sizes. Note that in our calculations we have assumed for simplicity that the number of photons/sec in the Gaussian image is proportional to the square of its diameter, which would be the case for an aperture of fixed size in the electron beam forming the x-ray source. It is well known that if the aperture size is optimized, the current on a spot of diameter d is proportional to d.sup.8/3. We should also note that while it might appear that rocking curves as small as 5.times.10.sup.-6 would make it seem hopeless to align a doubly curved diffractor properly, the natural width of the characteristic x-ray line would in fact allow such an alignment to be done. In any case, it is important that it be possible to preset the position and orientation of the crystal device to as high a degree as possible--otherwise obtaining proper alignment not only requires a costly alignment fixture, but could be like looking for the proverbial "needle in a haystack". The features of the present invention including the possibility of fabricating Johansson-based doubly curved crystal devices and prepositioning them relative to a source and image position are vitally important for future developments in x-ray microprobe technology.