Patent Number: 062495666
Section: description

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring to FIG. 1 showing the first embodiment of the invention, a side-by-side composite monochromator 52 is arranged between an X-ray source 32 and a sample 50. The composite monochromator 52 has a first elliptic monochromator 38 and a second elliptic monochromator 40, the both monochromators being so connected that one side of the first monochromator is in contact with one side of the second monochromator. The basic structure of the elliptic monochromator 52 is the same as one shown in FIG. 8B. The first elliptic monochromator 38 has focal axes parallel to the X-axis, while the second elliptic monochromator 40 has focal axes parallel to the Y-axis. The apparent focal spot size D of the X-ray source 32 is 10 micrometers. To obtain the 10-micrometer apparent focal spot size, it is possible as shown in FIG. 2A to form the focal spot 55, whose spot size is 10 micrometers in diameter, on the target 54 of the X-ray tube and to take X-rays with an appropriate take-off angle, for example, 6 degrees. Alternately, it is also possible as shown in FIG. 2B to form the focal spot 55, which has a linear shape of 10 micrometers in width, on the target 54 of the X-ray tube and to take X-rays in the longitudinal direction of the focal spot 55, i.e., the point-take-off from the line focus. Also in the latter method, we can obtain an apparent focal spot size of 10 micrometers. The X-ray tube used in this embodiment has a target whose material is copper and its characteristic X-rays (i.e., CuK.alpha. with the wavelength of 0.154 nanometers) are utilized. It is not necessary in the invention to increase the power of the X-ray tube because the focusing efficiency for X-rays are very good, the power being about 7 Watts with the stationary-anode X-ray tube in the embodiment. There will now be described a concrete shape of the elliptic-arc of the elliptic monochromator. As shown in FIG. 3, the distance L between the two foci F.sub.1 and F.sub.2 is 300 mm. Defining the minimum distance between the focal point F.sub.1 and the ellipse 56 as p/2, the value of p is 0.03 mm. Accordingly, L is 10-thousand times p and therefore the ellipse 56 is extremely compressed. The other elliptic monochromator 40 has the same shape. Referring to FIG. 3 which is seen in the X-direction, an X-ray source is positioned at the focal point F.sub.1, while a sample is to be set at the focal point F.sub.2 (or near that point in the direction of the optical axis). Defining the direction of the line which passes through the foci F.sub.1 and F.sub.2 as the u-direction and the direction perpendicular thereto as the v-direction, the distance L.sub.1 in the u-direction between the focal point F.sub.1 and the elliptic monochromator 38 is 15 mm. The size L.sub.2 in the u-direction of the elliptic monochromator 38 is 40 mm. The distance L.sub.3 in the u-direction between the elliptic monochromator 38 and the focal point F.sub.2 is 245 mm. The distance L.sub.4 the u-direction between the focal point F.sub.1 and the center of the elliptic monochromator 38 is 35 mm, and the distance L.sub.5 in the u-direction between the focal point F.sub.2 and the center of the elliptic monochromator 38 is 265 mm. L.sub.1 +L.sub.2 +L.sub.3 =L.sub.4 +L.sub.5 =L=300 mm. Table 3 indicates numerically the relationship between the coordinates of the elliptic-arc of the elliptic monochromator 38 and the graded-spacing. The coordinates u and v (the unit is mm) of the elliptic-arc are so measured that the origin of the coordinates is positioned at the focal point F.sub.1. The incidence angle .theta. (the unit is degree) of X-rays is so measured that the X-ray source is positioned at the focal point F.sub.1. The unit of the d-spacing is nanometer. TABLE 3 u (mm) v (mm) .theta. (degree) d (nm) 15 0.9251 1.8575 2.3783 20 1.0587 1.6233 2.7213 25 1.1729 1.4652 3.0148 30 1.2731 1.3500 3.2721 35 1.3622 1.2617 3.5011 40 1.4424 1.1915 3.7072 45 1.5151 1.1344 3.8939 50 1.5813 1.0869 4.0640 55 1.6418 1.0469 4.2194 It is understood from Table 3 that both the incidence angle .theta. and the d-spacing vary continuously along the elliptic-arc. The closest point, on the elliptic monochromator 38, to the focal point F.sub.1 has the coordinates of u=15 mm and v=0.9251 mm. The distance L.sub.6 between the closest point and the focal point F1 is calculated by L.sub.6 =(u.sup.2 +v.sup.2).sup.1/2 =15.03 mm. On the closest point, the breadth .DELTA..theta. of the incidence angle is calculated with the equation (4) by .DELTA..theta.=D/L.sub.6 =0.01/15.03=0.00067 radian. This value of .DELTA..theta. is less than the half-value width .epsilon.=0.001 of the monochromator having the synthetic multilayered thin film. At any point farther apart from the focal point F1 than the closest point, the breadth .DELTA..theta. of the incidence angle becomes less than the above value, so we have no problem. Accordingly, all of the X-rays, with the wavelength of interest, impinging on the elliptic monochromator are to be reflected effectively. Next, there will be described the capture of X-rays by the composite monochromator. The divergence angle .alpha. of X-rays which are incident on the elliptic monochromator indicated in Table. 3 is 1.82 degrees as calculated below. The convergence angle .beta. of X-rays is 0.15 degrees. The above value of the divergence angle .alpha. can be converted from the degree unit to the radian unit, i.e., 0.0318 radian. The first elliptic monochromator catches in the YZ-plane the divergence angle .alpha..sub.y =0.0318 radian, while the second elliptic monochromator catches in the ZX-plane the divergence angle .alpha..sub.x =0.0318 radian. The solid angle .OMEGA. of X-rays which are caught by the composite monochromator is .OMEGA.=.alpha..sub.x.alpha..sub.y =0.001 steradian. With the composite monochromator, when the apparent focal spot size D of the X-ray source is 0.01 mm, the spot size of X-rays focused on the sample is 0.2 mm. The sample may be set at the second focal point of the elliptic monochromator (the standard point) or at any necessary point before or behind, on the optical axis, the standard point, depending upon the measuring conditions (i.e., sample size, required intensity, etc.). The synthetic multilayered thin film with the graded d-spacing as shown in Table 3 can be produced popularly by depositing alternating layers of high atomic number, for example, tungsten (W), and low atomic number, for example, silicon(Si), materials. Another combination may be tungsten (W) and boron carbide (B.sub.4 C). The period of the layers is equal to the d-spacing. The thickness ratio of the two kinds of the layers may be selected variously. As seen from Table 3, the incidence angle .theta. of X-rays on the elliptic monochromator is small as about 1 to 2 degrees, and the d-spacing of the synthetic multilayered thin film is about 2 to 4 nanometers. There will now be described a method of calculating the divergence angle .alpha. of X-rays which are incident on the elliptic monochromator. Referring to FIG. 3, the coordinates (u, v) of the elliptic-arc of the monochromator 38 satisfy the following equation (11) which is derived from the equation for ellipse: EQU v=f(u)=[{p(2L+p) (-u.sup.2 +Lu+p(2L+p)/4)}/(L+p).sup.2 ].sup.1/2. (11) Assuming that L1=G and L1+L2=H, the divergence angle .alpha. can be calculated by the following equation (12), in which the above equation (11) should be used for the function f: EQU .alpha.=cos.sup.-1 [(GH+f(G)f(H))/{(G.sup.2 +f(G).sup.2).sup.1/2 (H.sup.2 +f(H).sup.2).sup.1/2 }]. (12) There will now be described the second embodiment of the invention with reference to FIG. 4. Although the basic structure of the second embodiment is the same as that of the first embodiment shown in FIG. 1., the design values of the elliptic monochromator are different. In the second embodiment, the length of the composite monochromator 52a is 60 mm, and the distance between an X-ray source 32 (located on the first focal point) and a sample 50 (located on the second focal point) is 100 mm. The distance between the composite monochromator 52a and the sample 50 is smaller than that of the first embodiment, so that the X-ray spot size on the sample becomes small down to 0.047 mm in case of the same X-ray source as in the first embodiment. Namely, it is possible with the second embodiment to carry out X-ray analysis for very small samples. Explaining the elliptic shape of the second embodiment with the use of the symbols shown in FIG. 3, p=0.022 mm, L=100 mm, L.sub.1 =17 mm, L.sub.2 =60 mm, L.sub.3 =23 mm, L.sub.4 =47 mm, and L.sub.5 =53 mm. In this case, L is 4545 times p. Table 4 indicates numerically the second embodiment, the meaning of the symbols being the same as in Table 3. TABLE 4 u (mm) v (mm) .theta. (degree) d (nm) 17 0.78811 1.5992 2.7624 22 0.86907 1.4503 3.0459 27 0.93136 1.3533 3.2641 32 0.97857 1.2880 3.4295 37 1.01281 1.2445 3.5494 42 1.03536 1.2174 3.6284 47 1.04698 1.2039 3.6691 52 1.04803 1.2027 3.6728 57 1.03854 1.2137 3.6396 62 1.01822 1.2379 3.5684 67 0.98641 1.2778 3.4570 72 0.94193 1.3381 3.3011 77 0.88287 1.4276 3.0943 In the second embodiment, the divergence angle .alpha. of X-rays which are incident on the elliptic monochromator is 2.0 degrees and the convergence angle .beta. of X-rays which are focused on the second focal point is 1.6 degrees. There will next be described the third embodiment. In the third embodiment, using the symbols shown in FIG. 3, p=0.065 mm, L=400 mm, L.sub.1 =40 mm, L.sub.2 =60 mm, L.sub.3 =300 mm, L.sub.4 =70 mm, and L.sub.5 =330 mm. The spot size of the focused X-rays on the second focal point is 0.2 to 0.25 mm. Table 5 indicates numerically the third embodiment, the meaning of the symbols being the same as in Table 3. TABLE 5 u (mm) v (mm) .theta. (degree) d (nm) 40 2.1640 1.7206 2.5675 44 2.2569 1.6498 2.6776 48 2.3440 1.5886 2.7808 52 2.4257 1.5351 2.8777 56 2.5027 1.4879 2.9690 60 2.5754 1.4459 3.0551 64 2.6441 1.4083 3.1366 68 2.7092 1.3745 3.2138 72 2.7708 1.3439 3.2869 76 2.8293 1.3162 3.3562 80 2.8848 1.2909 3.4220 84 2.9375 1.2677 3.4845 88 2.9875 1.2465 3.5437 92 3.0350 1.2270 3.6000 96 3.0801 1.2091 3.6535 100 3.1228 1.1925 3.7041 In the third embodiment, the divergence angle .alpha. of X-rays which are incident on the elliptic monochromator is 1.31 degrees, which is equal to 0.0229 radian. The first elliptic monochromator catches in the YZ-plane the divergence angle .alpha..sub.y =0.0229 radian, while the second elliptic monochromator catches in the ZX-plane the divergence angle .alpha..sub.x =0.0229 radian. The solid angle .OMEGA. of X-rays which are caught by the composite monochromator is .OMEGA.=.alpha..sub.x.alpha..sub.y =0.00052 steradian. Although the elliptic monochromator has been described above, the elliptic monochromator may be altered to a parabolic monochromator. There will now be described another embodiment in which the present invention is applied to the parabolic monochromator. Referring to FIG. 13 illustrating the parabolic shape of the parabolic monochromator, a parabola 62 which defines a parabolic monochromator 60 has one focal point. Defining the minimum distance between the focal point F and the parabola 62 as p/2, the value of p is 0.026 mm. A microfocus X-ray source is positioned at the focal point F. The X-rays reflected by the monochromator become parallel X-rays, so that the intensity of X-rays impinging on a sample is constant even if the sample is set at any position on the optical axis. Defining the u-direction and the v-direction as illustrated in FIG. 13, the distance L.sub.1 in the u-direction between the focal point F and the parabolic monochromator 60 is 15 mm. The size L.sub.2 in the u-direction of the parabolic monochromator 60 is 40 mm. Two parabolic monochromators of such a shape are combined as shown in FIG. 1 to form a composite monochromator. The apparent focal spot size of the used X-ray source is 10 micrometers, and the X-ray spot size on a sample is 0.8 mm in diameter. Table 6 indicates numerically the relationship between the coordinates of the parabolic-arc of the parabolic monochromator 60 and the graded d-spacing. The coordinates u and v (the unit is mm) are so measured that the origin of the coordinates is positioned at the focal point F. The incidence angle .theta. (the unit is degree) of X-rays is so measured that the X-ray source is positioned at the focal point F. The unit of the d-spacing is nanometer. TABLE 6 u (mm) v (mm) .theta. (degree) d (nm) 15 0.8836 1.6855 2.6209 20 1.0201 1.4600 3.0257 25 1.1405 1.3060 3.3824 30 1.2493 1.1923 3.7049 35 1.3493 1.1039 4.0015 40 1.4425 1.0326 4.2776 45 1.5299 0.9736 4.5369 50 1.6123 0.9237 4.7822 55 1.6914 0.8807 5.0155 It should be noted in the invention that the first and second monochromators may be partly translated in the direction shown in FIG. 8A without departing from the spirit of the invention (depending upon the focal spot size of the microfocus X-ray source, the minimum distance between the focal spot of the X-ray source and the monochromator, the solid angle which is caught by the monochromator, etc.). In such a case, the intensity distribution of X-rays reflected by the composite monochromator might be deformed, because the capture solid angle in the YZ-plane is different from that in the ZX-plane. However, it would be possible for the partly-translated composite monochromator to effect the similar advantage to the non-translated composite monochromator as shown in FIG. 8B, depending upon the measurement condition (the size and the position of the sample, the required X-ray intensity, etc.).