Apparatus for X-ray analysis and apparatus for supplying X-rays

ABSTRACT

Apparatus for X-ray analysis has a combination of a rotating target X-ray tube and a composite monochromator. The composite monochromator has a first and a second elliptic monochromators joined with each other side by side. Each of the elliptic monochromators has a first focal point at which an X-ray focal spot on a target of the X-ray tube is disposed. Each of the elliptic monochromators has a synthetic multilayered thin film whose d-spacing varies continuously along an elliptic-arc. The shortest distance between the X-ray focal spot and the composite monochromator is set to 40 to 100 mm. Under the shortest distance condition, the effective focal spot size on the target is set to 40 to 100 micrometers to obtain the maximum X-ray intensity on a sample to be analyzed.

INFORMATION

DETAILED DESCRIPTION OF THE INVENTION

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIG. 1, a rotating target X-ray tube has a rotating target . An electron gun emits an electron beam which is incident on the peripheral surface of the target to emit an X-ray beam from the electron beam irradiation region (X-ray focal spot). The X-ray beam is taken out through a beryllium window and incident on a composite monochromator . The take-off angle of the X-ray beam is about 6 degrees with respect to the target surface. The X-ray beam is made monochromatic and focused by the composite monochromator and thereafter incident on a small irradiation spot on a sample. The shortest distance between the center of the focal spot on the target and the composite monochromator is represented by L1, and the length of the composite monochromator is represented by L2.

Referring to FIG. 2, a cylindrical target has a peripheral surface on which a long narrow focal spot is formed with a lengthwise direction parallel to the axis of rotation of the target . The composite monochromator is comprised of the first elliptic monochromator and the second elliptic monochromator joined with each other side by side at right angles. Each of the two elliptic monochromators has a reflection surface made of a synthetic multilayered thin film in which layer boundaries, which contribute to diffraction, are parallel to the reflection surface and a period (it corresponds to crystal d-spacing) varies continuously along an elliptic-arc. The shape and the action of such a composite monochromator are disclosed in detail in U.S. Pat. No. 6,249,566.

Referring to FIG. 3, each of the first elliptic monochromator and the second elliptic monochromator has the first focal point F at which the X-ray focal spot on the target is disposed, and the second focal point F at which the X-ray irradiation region on the sample is disposed. The X-ray beam, which is generated at the first focal point F, is reflected first at the first elliptic monochromator and reflected second at the second elliptic monochromator and thereafter incident on the sample which is disposed at the second focal point F. Alternatively, the X-ray beam is reflected first at the second elliptic monochromator and reflected second at the first elliptic monochromator and thereafter incident on the sample. The first and the second elliptic monochromators and have the same shape basically, and therefore only the first elliptic monochromator will be described below.

Referring to FIG. 4, the first elliptic monochromator has a reflection surface made of an elliptic-arc surface which is a trace of an elliptic-arc, i.e., a part of the ellipse , translated in a direction perpendicular to the drawing sheet. The X-ray beam from the first focal point F of the ellipse reaches the first elliptic monochromator with a divergence angle α which represents an angle with which the elliptic monochromator captures the X-ray beam, and thus the angle α is referred to hereafter a capture angle. The larger the capture angel α, the higher the efficiency of the X-ray use. On the other hand, the X-ray beam from the first elliptic monochromator reaches the second focal point F with a convergence angle β which represents variation of the X-ray incidence angle on the sample. Generally a small convergence angle β is preferable in the X-ray analysis for the sample.

Next, the effective focal spot size of the X-ray focal spot on the target will be described. The effective focal spot size is defined by a focal spot size on the target as seen from the X-ray take-off direction, noting that the maximum diametrical size should be the effective focal spot size. For example, assuming that a long narrow focal spot of 1 mm×0.1 mm is formed on the target as shown in FIG. 2 and a line-focus X-ray beam is taken out from it with the take-off angle of about 6 degrees, the apparent focal spot region becomes about 0.1 mm×0.1 mm and the effective focal spot size is 0.1 mm.

Using a combination of the rotating target and the composite monochromator, it is found that there is the optimum focal spot size on the target after consideration of various requirements. That is, it is found that when the maximum focal spot size is selected an X-ray intensity on the sample (i.e., a total intensity of X-rays impinging on the sample) becomes highest. The procedure to obtain the optimum conditions and its optimum result will now be described in detail below. In the first place, the following items (1) to (5) have been considered.

(1) Relationship Between Focal Spot Size on Target and Maximum Input Power

A relationship is well known between a focal spot size t on the rotating target and the possible maximum input power W as shown in a graph of FIG. . The graph is obtained from an equation (1) in FIG. . The equation (1) is to calculate the maximum input power W (i.e., allowable load) and has been established taking into account the allowable thermal load to the target. Assuming that the material of the target is copper, the rotational speed is 6,000 rpm, the target diameter is 10 cm, and the target thickness (the thickness from the outer surface to the water-cooled inner surface) is 0.2 cm, the maximum input power W depends upon the width t of the focal spot on the target (i.e., the effective focal spot size), noting that the length FL of the focal spot is assumed to be ten times the width t. As seen from the graph of FIG. 9, the larger the focal spot size, the higher the maximum input power.

(2) Condition Under Restriction in Manufacturing Synthetic Multilayered Thin Film

The elliptic monochromator or synthetic multilayered thin film mirror is under restriction in manufacturing it, so that the length L2 (see FIG. 1) of the monochromator is set to 80 mm. The d-spacing of the synthetic multilayered thin film, which makes the reflection surface, is determined so that its maximum value, dmax, is less than 5.0 nanometers and its minimum value, dmin, is more than 2.5 nanometers. With the elliptic monochromator having a multilayered thin film whose d-spacing varies continuously along an elliptic-arc, if the d-spacing value is within a range of 2.5 to 5.0 nanometers, this multilayered thin film can be manufactured. On the other hand, the X-ray diffraction occurs at the reflection surface only when an equation (8) in FIG. 16 or Bragg's equation is satisfied, where d is the d-spacing of the synthetic multilayered thin film, λ is the wavelength of X-rays, and θ is the X-ray incidence angle on the reflection surface. Using the rotating target whose material is copper, CuK α rays has a wavelength λ of 0.154 nanometers. The maximum value dmax and the minimum value dmin of the d-spacing of the synthetic multilayered thin film can be converted to the incidence angle θ with the use of the Bragg's equation, the result being equations (9) and (10) in FIG. .

(3) Requirement Regarding Acceptable Receiving Angle of Reflection Surface

The elliptic monochromator has a reflection surface whose reflection property is shown in FIG. . This reflection coefficient curve has a finite width ω of angle (full width at half maximum of the peak, FWHM). If the incidence angle of X-rays becomes within the angle width ω, the X-rays will be reflected by the reflection surface. The angle width ω is referred to hereafter an acceptable receiving angle. If the incidence X-rays have an angle width (i.e., the breadth of the incidence angle) less than the acceptable receiving angle ω, all of the incidence X-rays will be reflected, but if more than the acceptable receiving angle ω, a part of the incidence X-rays will not be reflected. The X-rays from the X-ray source would be captured by the elliptic monochromator with the best efficiency under the condition that the elliptic monochromator is close to the X-ray source so that the incidence X-rays have an angle width (i.e., the breadth of the incidence angle) which equals the acceptable receiving angle ω. Referring to FIG. 5, assuming that the effective focal spot size of the X-ray source is t, the distance between the X-ray source and the reflection point on the monochromator is L3, and the acceptable receiving angle of the monochromator is ω, when an equation of L3=t/ω (where, ω is measured in radian) is satisfied, the angle width of the incidence X-rays will equal the acceptable receiving angle ω. Therefore, it is most efficient that the relationship between L3 and t are selected so as to satisfy the equation mentioned above. For example, with the conditions that ω is 0.05 degrees and the effective focal spot size t is 0.1 mm, L3 should be about 114 mm. If the center of the monochromator is apart from the X-ray source by 114 mm, the front end (i.e., the end closest to the X-ray source) of the monochromator will be apart from the X-ray source by 74 mm, because the length of the monochromator is 80 mm and 114 mm minus 40 mm (half of 80 mm) equals 74 mm.

(4) Relationship Between Shape of and Incidence Angle θ

Referring to FIG. 4, with the X-Y coordinates shown in the figure, the equation of the ellipse becomes an equation (3) in FIG. . The derivative of the equation (3) gives an equation (4) which indicates the slope at each point on the ellipse (i.e., the slope of the tangent to the ellipse). Expressing the slope in degree, the slope at each point on the ellipse becomes an equation (5). On the other hand, the elevation angle (i.e., the angle with respect to the X-ray coordinate) as seen from the focal point F toward each point of the ellipse is expressed by an equation (6) in FIG. 15, where f is, as shown in FIG. 4, the distance between the focal point F and the origin of the coordinates. The X-ray incidence angle θ at each point on the ellipse is calculated by subtracting the slope of the equation (5) from the elevation angle of the equation (6), resulting in an equation (7) FIG. 7 shows curves of the slope of the equation (5), the elevation angle of the equation (6) and the incidence angle θ of the equation (7). Although the horizontal coordinate of FIG. 7 should be expressed strictly as “distance from coordinates' origin” at each point on the ellipse, it may be expressed as “distance from focal point” because the shape of the actual ellipse is extremely compressed with the coordinates' origin which is very close to the focal point F. Therefore, the horizontal coordinate is expressed as “distance from focal point”. The vertical coordinate indicates an angle which is measured in degree. The graph indicates θmax and θmin too, which are determined under the d-spacing restriction of the synthetic multilayered thin film as mentioned above, θmax being obtained from the equation (9) and θmin being obtained from the equation (10) in FIG. . With the ellipse having a certain major axis “a” and a certain minor axis b, if the incidence angle θ at each point on the ellipse becomes between θmax and θmin, as shown in FIG. 7, over the full length L2 of the elliptic monochromator (i.e., the distance from the focal point is within a range of 100 to 180 mm), the restriction of the synthetic multilayered thin film would be satisfied, noting that the graph of FIG. 7 is derived from calculation with the major axis “a” of the ellipse being 280 mm and the minor axis b being 5 mm. The graph of FIG. 8 is an enlarged graph of FIG. 7, showing a region of 100 to 180 mm in the distance from the focal point and indicating the variation of the incidence angle with the minor axis b. That is, when the minor axis b varies as 5.0 mm, 4.5 mm and 4.2 mm, the incidence angle θ varies as shown in FIG. 8, where the incidence angle θ resides between θmax and θmin with any value of the minor axis b.

(5) Relationship Between Irradiation Spot Size on sample and Position of Monochromator

Referring to FIG. 4, the sample is to be disposed at the second focal point F and it is preferable that the X-ray irradiation spot size on the sample is less than 0.3 mm and the convergence angle β is less than 0.2 degrees. Assuming that the distance between the first focal point F and the center of the monochromator is L4 and the distance between the second focal point F and the center of the monochromator is L5, the X-ray irradiation spot size on the sample equals (L5/L4) times “effective focal spot size t” of the X-ray source. For example, when t is 0.1 mm and L5 is three times L4, the X-ray irradiation spot size on the sample becomes 0.3 mm. With the stationary ellipse , the closer to the X-ray source the elliptic monochromator moves along the ellipse , the larger the irradiation spot size on the sample. On the contrary, the farther from the X-ray source the monochromator moves, the smaller the irradiation spot size.

Next, one embodiment of detailed procedure to obtain the maximum focal spot size will be described. The maximum focal spot size is defined as the spot size with which the X-ray intensity on the sample becomes maximum. Referring to FIG. 17, this flow chart indicates the procedure which determines, for one combination of the distance L1 and the focal spot size t, the shape of the ellipse (i.e., the major axis “a” and the minor axis b) so that the maximum capture angle α is expected, the value of the maximum capture angle α being also determined at the same time.

First, the distance L1 in FIG. 1 (i.e., the distance between the X-ray focal point and the front end of the composite monochromator ) must be selected. Since the present invention has an object to realize a higher X-ray intensity on the sample, it is important basically that the composite monochromator is disposed as close as possible to the X-ray source so as to increase the X-ray capture angle α. Therefore, the distance L1 must be less than 100 mm. On the other hand, with the rotating target X-ray tube, the distance between the focal spot on the target and the beryllium window can not be decreased to a value less than a certain limit. As a matter of course, the distance L1 between the focal spot on the target and the front end of the composite monochromator can not be decreased to the certain limit. The minimum value of the distance L1 would be generally 60 mm, and it might be minimized to 40 mm with a special structure of the X-ray source. Therefore, the distance L1 is set within a range of 40 to 100 mm to calculate the optimum focal spot size. Incidentally, as discussed in the above-described “REQUIREMENT REGARDING ACCEPTABLE RECEIVING ANGLE OF REFLECTIION SURFACE”, under the conditions that ω is 0.05 degrees and the effective focal spot size is 0.1 mm, the distance L1 is set to preferably about 74 mm so that the X-rays are captured by the elliptic monochromator with the highest efficiency. Consequently, the distance L1 within the range of 40 to 100 mm would be reasonable in view of the acceptable receiving angle, although it would depend on the focal spot size.

The actual calculation selects, for the distance L1, four values: 100 mm, 80 mm, 60 mm and 40 mm. The following description uses 80 mm for the distance L1 for example. Then, in the flow chart of FIG. 17, the distance L1 is set to 80 mm and the procedure moves to the next step “decide focal spot size t”. The step selects, for the focal spot size t, one of twenty values from 0.01 mm to 0.4 mm (see the column t in the table of FIG. 18) to calculate the maximum capture angle α for each value of the focal spot size. Then, the focal spot size t is set first to 0.01 mm, resulting in a combination of L1 of 80 mm and t of 0.01 mm.

Next, the procedure moves to the step “decide major axis “a” of ellipse”. The major axis “a” of the ellipse should be determined taking in account the irradiation spot size on the sample. As has been described with referring to FIG. 4, it is preferable that the X-ray irradiation spot size on the sample is less than 0.3 mm. With the effective focal spot size t of 0.01 mm, the irradiation spot size less than 0.3 mm is attainable under a condition that L4/L5 is less than {fraction (1/30)}. Then, since L4 equals the sum of L1 and 40 mm and thus equals 120 mm, L5 should be less than 3,600 mm. Since the major axis “a” of the ellipse equals substantially the sum of L4 and L5, “a” must be less than 3,720 mm. In the calculation in this embodiment, “a” is set to 1,860 mm (see the table in FIG. ).

Next, the procedure moves to the step “minor axis b of ellipse is set to 0.1”. The minor axis b of the ellipse is to vary within a range of 0.1 mm to 10 mm in increments of 0.1 mm in the procedure. The capture angle α will be calculated for each value of the minor axis b and it will be determined what is the optimum minor axis b to expect the maximum capture angle α and what is the maximum value of the capture angle α. Now, b is set first to 0.1 mm, resulting in a combination of the major axis “a” and the minor axis b, and we can calculate the curve of the incidence angle θ in the graph of FIG. . Within the range of 80 to 160 mm in the distance from the focal spot (i.e., within the range of the monochromator), if the curve of the incidence angle θ resides between θmax and θmin, the b value passes the incidence angle requirement. Since the position and the shape of the elliptic monochromator have been determined, the capture angle α and the convergence angle β both shown in FIG. 4 can be calculated. If the convergence angle β is less than 0.2 degrees, the b value passes the convergence angle requirement too. If the b value passes both of the incidence angle requirement and the convergence angle requirement, a combination of the calculated capture angle α and the value of the minor axis b is memorized. These actions corresponds to the step “memorize capture angle α if b passes incidence angle requirement and convergence angle requirement”. On the contrary, if the b value does not pass at least one of the two requirements, the calculated capture angle α is not memorized because the b value is not usable.

Next, the procedure moves to the judgement step “b=10?”. If b does not reach 10 mm, then the procedure executes the step “b=b+0.1” and repeats the step “memorize capture angle α if b passes incidence angle requirement and convergence angle requirement”. If b reaches 10 mm, the procedure moves to the step “acquire maximum value of capture angle α” which acquires the maximum value among the memorized capture angles α along with the b value corresponding to the maximum value. When the above-mentioned calculations have been completed, one set of data in a row including t=0.01 in the table of FIG. 18 have been completed. In the table, t, a, b and L4 are measured in millimeter and α squared is measured in steradian. When t=0.01 mm, a set of the major axis “a” of 1,860 mm and the minor axis b of 10 mm gives the maximum capture angle α, the maximum α squared, which is measured in steradian, being 1.18869 times 10 to the negative fourth power. The expression “E-” in the table means “10 to the negative fourth power”. With the use of the composite monochromator, X-rays are reflected by the two elliptic monochromators sequentially as shown in FIG. and thereafter focused on the sample, so that the capture angle α squared would be proportional to the X-ray intensity on the sample. Thus, the table indicates the capture angle α squared. L4 in the table is L4 shown in FIG. and equals the sum of L1 and 40 mm. It is found that when t is more than 0.15 mm L4 exceeds 120 mm, because holding the condition of L1=80 mm does not satisfy other requirements (i.e., the incidence angle requirement and the convergence angle requirement) and thus L1 has been altered.

The values of the capture angle α squared shown in the table of FIG. 18 are expressed as a curve of “capture angle (str)” which is shown in the upper graph of FIG. 11, the vertical coordinate representing the capture angle α squared and the horizontal coordinate representing the focal spot size t. The upper graph of FIG. 11 shows another curve of “input power (W)” which equals the curve of FIG. . The lower graph of FIG. 11 shows a curve which is given by multiplying the capture angle curve by the input power curve both shown in the upper graph. Since the product of the capture angle α squared and the input power would be proportional to the X-ray irradiation intensity on the sample, the product is referred to as an “efficiency”. The efficiency varies with the focal spot size t and it is found that there is the maximum value or the peak value of the curve. In the graph, when L1=80 mm, the focal spot size of 60 micrometers gives the maximum efficiency. Assuming that the region down to 25 percent loss of the maximum efficiency would be usable practically, the highest efficiency would be expected when the focal spot size is within a range of about 40 to 90 micrometers.

Similar graphs for L1=100 mm, 60 mm and 40 mm can be calculated and are shown in FIGS. 10, and . In FIG. 10, when L1=100 mm, the focal spot size of 70 micrometers gives the maximum efficiency and the practical highest efficiency would be expected within a range of about 60 to 100 micrometers. In FIG. 12, when L1=60 mm, the focal spot size of 50 micrometers gives the maximum efficiency and the practical highest efficiency would be expected within a range of about 40 to 80 micrometers. In FIG. 13, when L1=40 mm, the focal spot size of 40 micrometers gives the maximum efficiency and the practical highest efficiency would be expected within a range of about 30 to 70 micrometers.

It is noted that the focal spot size of 30 micrometers gives a good efficiency only when L1=40 mm (this value is very difficult to realize in the rotating target X-ray tube) but does not give a good efficiency when L1=60 to 100 mm. Therefore, it can be said that the focal spot size of 40 to 100 micrometers gives a good efficiency over a range of 40 to 100 mm in L1.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plan view illustrating schematically one embodiment of the apparatus for X-ray analysis according to the invention;

FIG. 2 is a perspective view illustrating a positional relationship between a rotating target and a composite monochromator shown in FIG. 1;

FIG. 3 is a perspective view illustrating the action of the composite monochromator;

FIG. 4 illustrates a principle with which the elliptic monochromator focuses X-rays;

FIG. 5 illustrates an acceptable receiving angle of the reflection surface of the elliptic monochromator;

FIG. 6 is a graph showing a reflection coefficient curve of the reflection surface of the elliptic monochromator;

FIG. 7 is a graph showing variation of the incidence angle with a position on the ellipse;

FIG. 8 is an enlarged view of the graph shown in FIG. 7;

FIG. 9 is a graph showing a relationship between a focal spot size and the maximum input power;

FIG. 10 is a graph showing an efficiency at L1=100 mm;

FIG. 11 is a graph showing an efficiency at L1=80 mm;

FIG. 12 is a graph showing an efficiency at L1=60 mm;

FIG. 13 is a graph showing an efficiency at L1=40 mm;

FIG. 14 shows equations to calculate the maximum input power of the rotating target;

FIG. 15 shows some equations to calculate an elliptic curve, a slope at each position on the ellipse, an elevation angle from the focal point F, and an incidence angle;

FIG. 16 shows the Bragg's equation and equations to calculate incidence angles corresponding to the maximum and the minimum d-spacing of the synthetic multilayered thin film;

FIG. 17 is a flow chart showing the procedure to obtain the maximum capture angle a for each focal spot size; and

FIG. 18 shows a table of the calculation result at L1=80 mm.

CLAIMS

1. Apparatus for X-ray analysis having an X-ray source generating an X-ray beam which is reflected by monochromator means and is to be incident on a sample, characterized in that: (a) said X-ray source is a rotating target X-ray tube having a rotating target which has an effective focal spot size of 40 to 100 micrometers, (b) said monochromator means is a composite monochromator having a first elliptic monochromator and a second elliptic monochromator joined with each other side by side, (c) each of said elliptic monochromators has a first focal point at which an X-ray focal spot on said target is disposed and a second focal point at which said sample is to be disposed, (d) each of said elliptic monochromators has a reflection surface made of a synthetic multilayered thin film in which layer boundaries, which contribute to diffraction, are parallel to said reflection surface and d-spacing varies continuously along an elliptic-arc so as to satisfy a Bragg's equation for X-rays with a predetermined wavelength at any point of said reflection surface, and (e) a shortest distance between said X-ray focal spot on said target and said composite monochromator is 40 to 100 mm.

2. Apparatus for X-ray analysis according to claim 1, wherein said d-spacing of said synthetic multilayered thin film is within a range of 2.5 to 5.0 nanometers.

3. Apparatus for X-ray analysis according to claim 1, wherein an X-ray irradiation spot size on said sample, which is disposed at said second focal point of each of said elliptic monochromators, is less than 0.3 mm.

4. Apparatus for X-ray analysis according to claim 1, wherein an X-ray convergence angle at said second focal point of each of said elliptic monochromators is less than 0.2 degrees.

5. Apparatus for X-ray analysis having an X-ray source generating an X-ray beam which is reflected by monochromator means, characterized in that: (a) said X-ray source is a rotating target X-ray tube having a rotating target which has an effective focal spot size of 40 to 100 micrometers, (b) said monochromator means is a composite monochromator having a first elliptic monochromator and a second elliptic monochromator joined with each other side by side, (c) each of said elliptic monochromators has a first focal point at which an X-ray focal spot on said target is disposed, (d) each of said elliptic monochromators has a reflection surface made of a synthetic multilayered thin film in which layer boundaries, which contribute to diffraction, are parallel to said reflection surface and d-spacing varies continuously along an elliptic-arc so as to satisfy a Bragg's equation for X-rays with a predetermined wavelength at any point of said reflection surface, and (e) a shortest distance between said X-ray focal spot on said target and said composite monochromator is 40 to 100 mm.

6. Apparatus for supplying X-rays according to claim 5, wherein said d-spacing of said synthetic multilayered thin film is within a range of 2.5 to 5.0 nanometers.

7. Apparatus for supplying X-rays according to claim 5, wherein an X-ray irradiation spot size on said sample, which is disposed at said second focal point of each of said elliptic monochromators, is less than 0.3 mm.

8. Apparatus for supplying X-rays according to claim 5, wherein an X-ray convergence angle at said second focal point of each of said elliptic monochromators is less than 0.2 degrees.

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