US2511151A

US2511151A - X-ray apparatus and method

Info

Publication number: US2511151A
Application number: US775824A
Authority: US
Inventors: Ekstein Hans; Siegel Stanley
Original assignee: Armour Research Foundation
Current assignee: Armour Research Foundation
Priority date: 1947-09-24
Filing date: 1947-09-24
Publication date: 1950-06-13
Anticipated expiration: 1967-06-13

Description

June 13, 1950 H. EKSTEIN ETI'AL 2,511,151

x-RAY' APPARATUS AND METHOD Filed Sept. 24, 1947 fl ms' [A19 72-7 l atented June 13, 1950 UNITED STATES PATENT OFFICE X-RAY APPARATUS AND METHOD Hans Eiistein and Stanley Siegel, Chicago, 111., assignors to Armour Research Foundation of Illinois Institute of Technology, Chicago, 111., a corporation of Illinois Application September 24, 1947, Serial No. 775,824

7 Claims. (Cl. 25053) This invention relates to an improved method and apparatus for facilitating the precision determination of lattice parameters, and particularly to a method and apparatus for effecting the focusing of a beam of X-rays upon an X-ray sensitive indicating medium after diffraction of such beam by a sample to be analyzed.

The desirability of producing a focusing of X-rays to facilitate X-ray analysis of crystalline structure is in itself not a new concept; however, all previous methods utilized were based on geometrical focusing in which supposedly mono chromatic X-rays are brought to a focus. However, at large angles of diffraction, which are particularly desirable in precision lattice determinations, such as in phase studies, stress measurements, etc., the diffraction line becomes inevitably broad because of the finite spectral width of the characteristic radiation and because of the diffraction mechanism.

In contrast, the methods and apparatus constituting this invention are based upon the concept of producing a focusing of X-rays of difierent wavelengths. Hence, the methods and apparatus of this invention permit the determination of lattice parameters with improved accuracy by making the Debye-Scherrer line sharper than is possible by any method heretofore known.

The deficiencies of the presently known methods will be clearly apparent from the following analysis. The limiting factor of the precision possible by conventional focusing methods is the finite spectral width of the characteristic X-ray line. A strictly parallel and monochromatic beam, when striking a crystal aggregate of sufficiently large grains, will give rise to a diffracted beam of negligible angular width. As it is not possible to produce a characteristic X-ray line of a single wave-length, and since such characteristic X-ray line consists of a finite band of wavelengths, it follows that under the usual conditions the resulting diffracted beam cannot give rise to a line any narrower than that corresponding to the spectral width of the initial beam.

It is true that other factors, the geometric conditions and the small size of crystal grains, usually cause a broadening of the line in excess of that due to the spectral impurity of the incident radiation; but at large Bragg angles 0 of the diffraction, where the Bragg angle 0 has the largest sensitivity to changes in lattice parameters, the width caused by thisspecial impurity is predominant when the geometric arrangements are as refined as currently feasible.

In other words, no further refinement of the geometry of the system can produce a line substantially narrower than those currently obtained.

v Accordingly, the methods and apparatus embodied in this invention provide a decided improveinent in the focusing of X-rays through the attainment of an indicating line substantially narrower than those currently obtained, by elimihating the line broadening efiects caused by the spectral impurity. The methods and apparatus of this invention contemplate the utilization of a diverging beam of X-rays including a band of wavelengths and a portion of the rays of each distinct wavelength are caused to pass through a predetermined focal point after diffraction by a polycrystalline sample being analyzed. If an Iii-ray sensitive film or other recording instrument is placed at such focal point, the resulting line indication will be very narrow and hence adaptable for precision X-ray analysis purposes.

Accordingly, it is an object of this invention to provide an improved method and apparatus'for X-ray analysis of crystal structure, and particularly a method and apparatus for producing a sharper focus of X-rays diffracted by a polycrystalline sample than has heretofore been possible of accomplishment.

Another object of this invention is the provision of an improved method and apparatus for focusing of X-rays which does not require a monochromatic beam of X-rays for its successful operation but which will produce a sharp focus of a beam of X-rays of a finite band of wavelengths.

Still another object of this invention is to provide a method and apparatus for focusing of an X-ray beam deflected by a polycrystalline sample wherein large Bragg angles of incidence of the X-rays upon the polycrystalline sample may be employed without reducing the sharpness of the focus achieved.

A particular object of this invention is to provide an improved X-ray tube envelope construce tion particularly adapted for producing a beam of X-rays of such characteristics that the diffraction of such beam by a polycrystalline sample located exteriorly of the tube envelope will automatically produce a focusing of the diffracted beam, and particularly a shielding envelope construction J which may be conveniently adjusted to produce such focusing for any one of a plurality of dis? tinct bands of X-ray wavelengths.

The specific nature of this invention, as well as other objects and advantages thereof, will become apparent to those skilled in the art from the following detailed description taken in conjunction with the annexed sheet of drawings, which, by way of preferred example only, illustrates two embodiments of this invention.

On the drawings: 7

Figure 1 is a schematicview of an X-ray focusing system illustrating the fundamental concept employed in accordance with this invention to ob: tain focusing of an X-ray beam after diffraction 60 by a polycrystalline sample;

Figure 2 is a schematic sectional view illustrating one arrangement of an X-ray tube and shielding jacket for producing X-ray focusing in accordance with this invention;

Figure 3 is a transverse sectional view taken on the plane IIII II of Figure 2 and Figure 4 is a schematic sectional view illustrating a modified construction of an X-ray tube and jacket for producing focusing of X-rays-by the principles of this invention.

As shown on the drawings:

Referring to Figure 1, let it be assumed that at the point P a source of X-rays is located which produces a diverging original beam of X-rays Ill. The beam I preferablycomprises a finite band of wavelengths and this condition will be recognized by'those skilled in the art as particularly easy to fulfill inasmuch as'that is the type of radiation commonly achieved from any particular point on the target of a conventional X-ray tube. In any event, let it be assumed that the central ray ID of the diverging beam ID has a wavelength A.

Now, in accordance with this invention, the divergent, multi-wavelength beam I0 is permitted to strike a plain crystal face such as that provided by a monochromator II. It will be recognized that a diffracted or reflected beam I2 will thereupon be produced. However, the beam I2 will be divergent and will have the further characteristic that every ray in a particular angular portion of the beam I2 will have only one wavelength because it has been diffracted under an angle of diffraction different from any other ray. This phenomenon is readily apparent from consideration of the fundamental law of X-ray diifraction which is commonly set forth in the following equation:

A=2dm sin 0 (1) where A is a particular wavelength diffracted, dm is the atomic spacing in the difiracting material and 0 is the glancing angle of the radiation of wavelength A with respect ,to the crystal producing the diffraction. The angle 0 is commonly referred to as the Bragg angle.

The difiracted beam I2 produced by the monochromator I I .is therefore formedofrays whose angular position with respect to the central ray I2 of wavelength A is a function of the difference in wavelength of each of the particular rays and the central ray I2. Thus the ray I2a at one side of the beam I2 is angularly spaced from the central ray I2 by the angle do, and the wavelength of such ray I2a may be A plus 11A. The ray [21) at the other edge of the beam is angularly spaced from the central ray I2 of wavelength A byan angle of minus d0, and the wavelength of this. ray is A minus dA.

The beam I2 is then permitted to strike thesurface of a polycrystalline sample I3 which is to be analyzed. With such aspatial distribution of the various wavelengths forming the diffracted ray l2, it is obvious that each ray of the beam I2 will be diffracted by the polycrystalline sample only if it meets a crystal grain suitably oriented, this orientation being different for each incident ray. The various oriented crystals for the required diffraction of the central ray I2 as well as the edge rays I2a and |2b are respectively indicated by the lines I3, I3a and I3b. When such diffraction occurs, the resulting diffracted rays, respectively represented by I4, I la and Nb, will no longer be divergent but will be convergent, and under certain circumstances such diffracted rays can be made to intersect approximately at a point F.

Therefore, if an X-ray sensitive film or other recording or indicating instrument is placed at the point F, then the line indication produced on such film will be very sharp, and precise determinations may be made of the lattice parameters of the polycrystalline sample I3.

Geometrical analysis will indicate not only the conditions under which such focusing of the beam diffracted by the polycrystalline sample will occur at the point Fbut also the location of the point F with respect to the point source P and the monochromator I I. The geometrical analysis proceeds as follows:

Still utilizing Figure 1, let P represent the apparent source of the X-ray beam I2 as viewed from the polycrystalline sample I3.

Let dm be the atomic spacing in the monochromator 'I I; (in be-the Bragg angle for the centralray I0 diffracted by the monochromator II; (is be the atomic spacing in the polycrystalline sample I3; and 0s be'the Bragg angle for the central ray I2 of wavelength A diffracted by the polycrystalline sample I3.

Then by Braggs law, the diffraction of the central ray of wavelength A which occurs by the monochromator I I may be represented bythe following equation:

sin gm Likewise, the diffraction of the same ray by the polycrystalline sample I3 at the point E may be represented by:

S1110: Considering aray of slightly different wavelength and diffraction angle, i. e., A+dA and 0+d0, 'we obtain by differentiating (2) and (3) and setting equals against equals rim COS0md0m=ds cos 681108 d,, cos 0,, d9. d0, By geometric analysis, the angle ,HFE=2d0,-|-d0m (5) Let thedistance fromthe .point source ,P to the sample I3 measuredalong the path of the .central ray of wavelength A (which, of course, is the distance PfE) equallL, .and the distance frompoint E onsample I3Vto,focus. point F equal Then from .the geometry ofFigure 1,

1' (angle HFIQ It has therefore been demonstrated that the location of the focusing point F as measured by the distance along the central ray of lavelength A from the polycrystalline sample I3 may be definitely computed for any selected wavelength and Bragg angle relationship of the X-ray beam with respect to the monochromator II and the polycrystalline sample I3.

It should be particularly noted that the most desirable dimensional relationships are obtained at Bragg angle approaching 90.

For values of s approaching 90 and 08 01, it will be observed that the ratio of the total distance between the point source P and the polycrystalline sample I3 traversed by the central ray to the distance of the focusing point F from the sample It as measured along the path traversed by the central ray is equal to 3. Hence-very practical dimensional relationship can be obtained at Bragg angles approaching 90, for if the. distance from the sample I3 to the focal point F is selected as 5 cm., then the distance L traversed by the central ray need only be 15 cm., which is an entirely practical arrangement. For lower Bragg angles 0m it may be readily observed that the ratio of L/f increases rapidly and hence results in less practical spatial positioning of the source of X-rays P with respect to the monochromator II and the sample I3.

Referring now to Figures 2 and 3, there is shown schematically an apparatus for conveniently utilizing the X-ray focusing methods heretofore disclosed. Thus a shielding jacket 20 is provided in surrounding relationship to a focusing X-ray cathode 2| and target anode 22. That portion of the surface of target anode 22 upon which the high velocity electrons impinge may, if desired, have a removable target 23 mounted thereon in conventional fashion. Thus, by selection of the material of the removable target 23, it is'possible to obtain a variety of discrete bands of wavelengths of the resulting X-rays. The monochromator I I is then mounted in any convenient fashion within the shielding jacket 20 and in such position as to receive a beam of X-rays emitted from a point or line P of the target surface at a large Bragg angle of incidence.

The electrons are brought to a focus on the target point P by use of any suitably sharp focusing arrangement. The shape of the focus on the point P may be in the form of a point or line, or any other suitably shaped sharp focus. The electron source is within the cathode 2|. Apparatus is provided to permit the angular position of the monochromator II to be adjusted with respect to the target 23, and such adjustment permits the apparatus to be conveniently adapted to employ any one of a large varietyof wavelength bands of X-rays.

The shielding jacket 20 is provided with a window portion 20a capable of transmitting X-rays therethrough which is disposed opposite the monochromator II and in selected spatial arrangement therewith so that all diifracted beams from the monochromator I I will pass through the window 20a to the exterior of the jacket 20. The polycrystalline sample I3 to be analyzed is disposed exteriorly of the jacket 20 in the path of the diffracted beam from the monochromator II. A focusing of the rays diffracted by the polycrystalline sample I 3 will then be obtained at a point, such as F, exteriorly of the jacket 20 and hence permits conventional X-ray recording and/or indicating equipment (not shown) to be positioned at this point.

In the modified arrangement shown in Figure 4, the shielding jacket 20 is provided with two X-rays transmitting windows 20b and 200, respectively. The monochromator I I is then positioned to the exterior of the jacket 20 and adjacent the X-ray transmitting Window 20b so that an original beam of X-rays produced from a point P on the target 23 will pass through the window 20b and impinge upon the monochromator II. The diffracted beam then passes through the window 20b in the reverse direction and traverses the interior of jacket 20 to pass through the second X-ray transmitting window 200 and then strike the polycrystalline sample I3 again disposed on the exterior of the jacket 20. The diffracted beam from the sample I3 may then be brought to a focal point F exteriorly of the jacket 20.

It should be particularly noted thatin both embodiments of the preferred forms of apparatus for effecting the focusing of X-rays in accordance with this invention, Bragg angles of diffraction approaching are utilized both in the diffraction by the monochromator II and by the polycrystalline sample I3, and further, the focusing of the X-rays is accomplished without interference of the various diffracted beams with each other. Any other beams originating on the target anode will likewise produce very little inter--v ference efiects.

It is therefore apparent that the method and apparatus of this invention provides an unusually simple yet highly precise method of accomplishing the focusing of an X-ray beam including a distinct band of wavelengths and, as a result, the accuracy of X-ray analysis has been substantially improved without requiring apparatus of any greater expense or complexity than that conventionally employed in the known methods to pro duce inferior results.

It will, of course, be understood that various details of construction and application may be modified through a wide range without departing from the principles of this invention, and it is, therefore, not the purpose to limit the patent granted hereon otherwise than necessitated by the scope of the appended claims.

We claim as our invention:

1. The method of X-ray analysis which comprises producing a polychromatic beam of X-rays diverging from a substantially point source and having a central ray of wavelength A, disposing a flat face of a crystal in the path of said beam to produce a reflected beam, whereby the reflected beam is angularly divergent from said central ray but has a frequency distribution proportional to the angular separation from said central ray, disposing a polycrystalline sample in the path of said reflected beam of X-rays, thereby producing a second reflected beam, and locating an X-ray sensitive indicating medium in the path of said second reflected beam and at a predetermined distance from said sample measured along the path of said central ray of wavelength A of said second reflected beam, said predetermined distance being equal to -L cos 20. tan 0, 1+2 tan 0,,

where L equals the sum of the distances from the source of the X-rays to the polycrystalline sample measured alon the path of said central ray of wavelength A, 6111 is the Bragg angle for said central ray of wavelength A difiracted by the crystal, and 05 is the Bragg angle for said central ray of wavelength A difiracted by the polycrys-l talline-sample.

-2. The method of X-ray analysis which comprises producing a polychromatic beam of X-rays from apoin-t source having a central ray of Wave ength A, placing a flat face of a crystal in the path of t e beam, locating a sample to be analyzed in the path of the diffracted beam, and

positioning an X-ray sensitive indicating medium in the path of the X-ray beam diffracted by the sample at a distance from the sample, equal to -L cos 26,

3. The method of focusing a polychromatic beam of X-rays having a central ray of wavelength A which beam is reflected from a polycrystalline sample Which comprises arranging the fiat face of a crystal monochromator intermediately between the source of the polychromatic X-ray beam and. the sample so that the polychromatic X-ray beam incident upon the sample is initially diffracted by said monochromator, and positioning the sample with respect to the monochromator so that the ratio of the total distance traversed by the central. ray of wavelength A from the source to the sample to the distance from. the sample to the desired focal point measured along the path of the central ray of wavelengthA equals tan 0,, 1 tan 0,,,)( cos 20,

where m is the Bragg angle for the central ray of wavelength A reflected by the monochromator; and 05 is the Bragg angle for the central ray of Wavelength A reflected by the sample.

4. The method of focusing a polychromatic beam of X-rays reflected from a polycrystalline sample and having a central ray of wavelength A which comprises arranging a flat face of a crystal immediately between the source of the polychromatic beam of X-rays and the sampleso that the X ray beam impinging onthe sample is initially reflected by said crystal at a Bragg angle approaching 96", and positioning the sample with respect to the said crystal and the source of the X rays so that the ratio of the total distance traversed b the central ray of wavelength A from the source to the sample to the distance from the Sample measured along the path of the central ray of wavelength A at which focusing of the beam is desired, equals tan l9 1 tan 0,, cos 29,

where 0m is the Bragg angle for the central ray of wavelength A reflected by the crystal, and 5s is the Bragg angle for the central ray of wavelength A reflected by the polycrystalline sample.

5. Apparatus for X-ray analysis comprising a.

source of diverging, polychromatic X-rays producing a beam having a central ray of wavelength A, a flat faced, crystal monochromator,

means for adjustably positioning said crystal the pathot; said diverging reflected beam, thereby producing a converging reflected beam of X-rays, and an 'X-ray sensitive indicating medium disposedin the path of said second reflected beam at av predetermined distance from said sample meas-. ured; along the path of said central ray or wavelength A equal to ,L cos 2Q,

where hequals the sum of the distances from the source of X-rays to the sample measured along the path of the central ray of wavelength A, @m is the Bragg angle for the central ray of wavelength A reflected by the monochromator, and 05 is the Bragg angle for the central ray of wavelength A reflected by the polycrystalline 4 9 6, Apparatus for X.-ray analysis comprising a "tube envelope enclosing a source of a. beam. of

polychromatic X-rays, said envelope having. a first X-ray transmitting window therein permitting, abeam of X-rays to pass through said envelope, a. monochrcmator disposed in the path of said polychromatic beam and arranged to pro.- duce a first reflected beam of polychromatic X- rays directed through said first window back into said envelope, said envelope having a second X- .ray transmitting window disposed in the path of said first reflected beam, means for positioning. a polycrystalline sample. exteriorly of said; en- Velope and in the pathof said first reflected beam, thereby producing a second reflected beam, and

,, an X-ray sensitive recording medium locatediin the path of said second reflected medium at a.

predetermineddistance from said sample corresponding to. the location of a focal point of said second reflected beam.

7. Apparatus for X-ray analysis comprising a tube envelope enclosing a source of a beam of polychromatic X-rays having a central ray ofv wavelength, A, said envelope having afirst X-ray transmitting window, therein permitting saidpolychromatic. beam of X-rays to pass through said envelope, amonochromator disposed inv thepath of saidebeamand arranged to produce a first reflected polychromatic beam of X-raysdirected through s id first window into said envelope, said envelope having a second X-ray transmitting window disposed in the path of said first reflected beam, means for positioning a polycrystalline sampleexteriorly of said; envelope and in the path of said first reflected beam, thereby producing a second reflected beam, and an X-ray sensitive recording medium located in the path of. said second reflected medium at a distance from saidsample measured along the path of said central ray of-wavelength A equal to L cos 20,

where 1; equals the sum of the distances fromthe source of the X-rays to the sample and is meas ured along the path of the central ray of. Wavelength A, where .6111 is the Bragg angle for the centralray. of wavelength A reflected by the monochromator and is the Bragg angle for the central ray of wavelength A reflected by the polycrystalline sample.

HANS EKSTEIN.

STANLEY SIEGEL.

' (References on following page).

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 1,626,306 St. John Apr. 26, 1927 2,329,320 Atlee Sept. 14, 1943 2,452,045 Friedman Oct. 26, 1948 OTHER REFERENCES X-Rays and Electrons, by A. H. Compton, pp. 133 and 134, D. Van Nostrand Co., New York, 1926. (Copy in Div. 54.)