X-Ray diffraction method and apparatus

X-ray diffraction method and apparatus, especially for studying polycrystalline and liquid substances, are disclosed which employ monochromator focussing on a goniometer circle along whose periphery detector means are movable at twice the angular speed with which a specimen is rotatable in the goniometer center, around the same axis. The specimen is always in the monochromatic convergent beam. The goniometer circle is arranged such that its periphery intersects the longitudinal monochromator center where a pivot may be provided. By selecting the distance between the X-ray source (line focus) and the monochromator center to equal the circle diameter, symmetric focussing is possible. Precision diaphragm means serve to narrow the convergent beams for combined transmission and back-reflection scans that may be quickly effected for intensity and profile evaluation. Special sample holders permit fast exchange of preadjusted specimens and rotation of flat samples parallel to their surface plane for ascertaining preferred orientations (if any).

BACKGROUND OF THE INVENTION 
The present invention relates to improvements in X-ray diffractometry. The 
known methods and apparatuses for struture analysis of crystalline and 
liquid substances by means of X-rays are based on the considerations and 
insights of Laue and Bragg; a qualified survey is offered in the book by 
H. P. Klug and L. E. Alexander, "X-Ray Diffraction Procedures", New York, 
2nd edition, 1974. 
For investigating single crystals, an X-ray goniometer as described in 
DE-PS No. 20 41 031 is advantageous in that it is possible to obtain from 
the adjusted crystal diffraction patterns according to both the de Jong - 
Bouman method and the Buerger precession method, which was a remarkable 
advance over the prior art which required two different apparatuses. 
In order to study polycrystalline substances, it is customary to employ 
diffractometers based on a fundamental method of Debye-Scherrer. Using 
monochromators, detailed structural analyses become feasible with modern 
automatic diffractometers working on the Bragg - Brentano principle. In 
special cases, the modified methods of Seemann - Bohlin, Guinier and 
others are applied. 
The schematic view of FIG. 1 shows the Bragg - Brentano modification. A 
divergent X-ray beam 12 issues either from an X-ray tube ine focus 10 or, 
less commonly, from the focal line 16 of a (primary) monochromator 14. A 
specimen 22, usually in the shape of a slab of compressed powder material, 
is arranged at the center of the so-called goniometer circle 24 so as to 
be rotatable around an axis that is parallel to the focal line 16 and 
perpendicular to the circle plane. While the specimen 22 is rotated at a 
constant angle speed .theta., a unit comprising a slit 26 and a detector 
28 is swivelled at exactly double speed (2.multidot..theta.). As the 
specimen slab 22 is always at a symmetric position relative to the 
incident and reflected beams, it produces a para-focussing effect which, 
however, will weaken with increasing angles of .theta. in a wide primary 
beam. This is due to the fact that the focussing circles, which intersect 
the focal lines as well as the center of the goniometer circle 24, shrink 
in size so that conformity of focussing arc and tangent plane (=specimen 
22) becomes coarser and finally ceases altogether. Owing to the divergent 
X-ray beam, the diffractometer circles can be zeroed in only by complex 
adjustments involving tedious effort. Another drawback is that the 
para-focussing effect necessitates comparatively large slabs 22 wherein 
preferred orientations of particles are almost inevitable and, moreover, 
quite difficult to ascertain exactly. 
The Seemann - Bohlin principle is elucidated with the aid of FIGS. 2a and 
2b wherein a divergent X-ray beam 12 is seen to be focussed by a 
monochromator 14 onto a specimen 22 that may be curved or flat. The 
specimen or sample 22 is arranged at the periphery of the goniometer 
circle 24, either in a reflection set-up (FIG. 2a) or in a transmission 
set-up (FIG. 2b); altering the measuring mode thus requires the specimen 
and the reflex focussing circle to be rearranged, and the reflex profiles 
differ sharply according to the angular range picked up. For this reason 
and owing to the inconstancy of the spacing between specimen 22 and 
detector 28--which latter, therefore, must be moved along the focussing 
circle by rather intricate kinematic means--this method is more 
appropriate for film cameras than for automatic diffractometers that are 
actually intended for measuring the reflexes in a non-stop fashion under 
conditions as nearly identical as ever possible. 
In the arrangements shown in FIGS. 2a and 2b, a primary monochromator 14 
will normally be indispensable. By contrast, the set-up of FIG. 1 
generally lacks, for reasons of intensity, a primary monochromator but 
preferably includes a secondary one between detector 28 and specimen 22 in 
order to eliminate the latter's undesirable radiation such as fluorescent, 
Compton or radioactive rays the entrance of which into the counter tube 
commonly used as the detector 28 must be prevented. 
By DE-AS No. 1 245 164, a diffraction goniometer has been proposed which 
aims at using both modes of focussing (FIGS. 2a, 2b) in a single 
instrument. It provides an auxiliary arm that is rotatable around an axis 
situated on the goniometer circle and that comprises engaging means for 
the detector. By arranging the detector such that it is both radially 
displaceable and coupled to the auxiliary arm's motion, the detector will 
move on the Seemann-Bohlin focussing circle. However, the instrument 
affords relatively complex mechanical means due to the coupling and 
uncoupling of rotatory and translatory motions involved; furthermore, 
there may be adjustment problems. 
OBJECTS OF THE INVENTION 
It is an object of this invention to improve on focussing diffractometry in 
a simple and economical way and, at the same time, to increase measuring 
accuracy and versatility of the methods and apparatuses employed. 
It is another object of the invention to do away with the need to rearrange 
instrument set-ups when switching from the reflection mode to the 
transmission mode and vice-versa in the course of structure analysis 
measurements. 
The invention also aims at obtaining accurate focussing of the X-ray 
beam(s) along the entire goniometer circle. 
A further object of the invention consists in enlarging the angular range 
of the reflexes that can be measured in any single diffraction scan, 
without sacrificing resolution. 
Moreover, the invention contemplates improving on the diffraction resolving 
power, in particular for investigating specimens that are prone to be 
affected by air or other environmental factors. 
It is yet another object of the invention to enable exploitation of the 
para-focussing effect in the reflection mode of measurements. 
SUMMARY OF THE INVENTION 
Basically, the objects are attained by providing in an X-ray diffraction 
method for determining the structure especially of polycrystalline and 
liquid substances, using an X-ray beam which is focussed by monochromator 
means onto the periphery of a circle and which is adapted to be diffracted 
by a sample specimen arranged in the center of the circle so as to be 
rotatable around an axis perpendicular to the circle plane, and further 
using detector means arranged at the periphery of the circle for measuring 
structure-dependent angles and intensities of the diffracted X-rays, the 
improvement wherein said circle is arranged such that its periphery 
intersects the center of said monochromator means. 
Thus the unique opportunity is offered of combining, with a minimum of 
effort, the known methods in a single arrangement enabling scans through 
the entire 2.multidot..theta. range, with maximum resolution both for the 
transmission mode and the reflection mode; at the same time, there is no 
need for cumbersome rearrangement of set-ups which was inevitable with the 
conventional techniques. The sample specimen to be studied is always in 
the center of the goniometer circle at the periphery of which the 
monochromator means and the detector means are located. Also, the specimen 
is--in contrast to the Bragg-Brentano method, cf, FIG. 1--in the 
convergent primary beam at any time, which fact leads to advantages and 
marginal conditions to be set out below. The comprehensive scanning 
rendered possible by the invention permits accurate comparison of reflex 
intensities which is very important for quantitative evaluation and 
determination of preferred orientations in the specimen. 
SPECIALIZATIONS OF THE INVENTION 
By selecting the spacing between the X-ray source, or its line focus, and 
the center of the monochromator means to equal the diameter of the 
goniometer circle, it is possible to arrange for symmetric focussing and, 
consequently, to employ pyrolytic graphite monochromators which will not 
lend themselves to asymmetric treatment. On the other hand, the invention 
also provides for the use of asymmetrically ground silicon monochromators 
which yield short distances from the X-ray source to the monochromator 
center, thus offering more space for accessories to be attached to the 
goniometer. At any rate, the constantly focussed beam permits to rapidly 
and conveniently determine the zero point of the 2.multidot..theta. scale 
that is fully available. 
Where specimens of larger surfaces are to be studied by symmetric 
reflection, despite the para-focussing effect counteracting the 
monochromator's convergence action, the invention features means for 
precisely narrowing the focussed X-ray beam, parallel to the goniometer 
axis, between the monochromator means and the specimen. A special 
diaphragm which may comprise a twin slit array will, if accurately 
adjusted to the specimen center, allow of transmission and reflection 
scans in a trice, without any displacement of the specimen or even of the 
goniometer itself, as was necessary according to the prior art. It is also 
of great advantage that one and the same specimen holder can be used for 
both the transmission and reflection modes. Samples of powder or liquids 
can be investigated with excellent resolution. No extra set-up is required 
for small-angle measurements. 
By providing, in an embodiment of the invention, a pivot to the goniometer 
circle at its point of intersection with the monochromator center, it is 
easily possible to exchange monochromators so that, in particular, silicon 
monochromators that feature high angular resolution or graphite 
monochromators which yield high intensity can be used selectively without 
affecting the basic set-up of the diffractometer. 
Futher features of the invention, especially as stated in the claims, 
contribute to facilitating the actual measurement work and the instrument 
operation. The adjustments required are relatively simple and can be 
performed quickly. Specimen holders as designed according to the invention 
are adapted to readily receive the various sample shapes and to be rapidly 
exchanged, in preadjusted positions; specimen slabs may be rotated in 
their planes during measurements so that preferred orientations may be 
detected and evaluated or their absence may be established definitely.

DESCRIPTION 
In the arrangement of FIG. 3, an X-ray tube--preferably of the horizontal 
type--is used to generate by a line focus 30 a divergent X-ray beam 32 
laterally limited from a diaphragm 34. A soller slit unit 36 limits the 
beam in vertical directions. The beam 32 thus defined impinges on a curved 
monochromator 38, e.g. made of graphite or silicon, which focusses a 
monochromatic convergent beam 42 onto the periphery of a goniometer circle 
46. In the latter's center there is, parallel to the goniometer axis 48, 
the sample or specimen 44; in FIG. 3, it is shown to be plate-shaped. 
Inasmuch as it will not disturb the focussing condition, the present 
diffractometer's favorable properties can be exploited through the entire 
2.multidot..theta. range. 
The distance D between line focus 30 and monochromator 38 on the one hand 
and between the latter a detector 52 with slit 50 arranged at the 
periphery of goniometer circle 46 on the other hand may be selected to be, 
say, 10" (or roughly 260 mm). This fairly large dimension provides for 
excellent angular resolution with sufficient intensity and for enough 
space on the goniometer tray to accomodate accessories, if such are 
desired. The goniometer ensemble is adapted to be pivoted around an axis 
40 that is located in the longitudinal center of monochromator 38. This 
feature permits easy exchange of monochromators without detracting from 
the convenient adjustment of the means defining the convergent beam 42 or 
of the slit and detector set-ups. 
In the diffractometer of the type described, the focussing conditions are 
satisfied if either narrow Debye-Scherrer capillaries or specimen tubes 78 
(FIG. 5) or thin specimen disks or slabs (44 in FIGS. 3 and 4; 84 in FIGS. 
6 and 8) or foils (not shown) that are coated with powder on either face 
are adjusted so as to be aligned with the goniometer axis 48. Under these 
circumstances, the angular resolution will not depend on the width of 
convergent beam 42 which, therefore, may have a large cross section for 
whatever sort of transmission scans. 
Adequate focussing is, however, also obtained where monochromators designed 
for a certain radiation such as Cu-K.sub..alpha. will be used with another 
radiation of slightly different wavelength, e.g. with Cu-K.sub..beta., or 
if a secondary monochromator (70 in FIG. 4) is inserted between sample 44 
and detector 52. 
But where the reflection mode is used to study specimens of larger 
surfaces, such as thin foils or compacted slabs, these may seriously 
disturb the focussing conditions. Such trouble is removed despite the 
sample being in the goniometer center if an array of diaphragms and slits 
is provided as shown in FIGS. 3 and 4 where edge 56 opposite the center of 
monochromator 38 forms a diaphragm (indicated by phantom lines) that is 
supplemented by a precision diaphragm 58 and a scatter slot 60. This array 
serves to reduce the width of convergent beam 42 to a narrow line 
accurately parallel to goniometer axis 48. A maximum line width of, say, 
0.2 mm (7.9 mil) may be adjusted so as to warrant both high angular 
resolution for reflection scans and sufficient intensity for transmission 
scans. 
In order to achieve a sufficiently narrow beam 42, the diaphragm and slit 
array according to the invention is equipped with precision adjustment 
means such as micrometer screws. Edge 56 may be guided for parallel 
displacement in its plane relative to the longitudinal center of 
monochromator 38. The following diaphragm 58 may comprise movable wall 
sections of a cylindrical casing (not shown) that encompasses 
monochromator 38. A twin slit array will generally be required in the 
small-angle range, i.e. with .theta. equalling 0.5 to 2 degrees. When 
working in the reflection mode or for combined reflection-transmission 
scans, a precision diaphragm should be placed as close to the sample or 
specimen 44 as ever possible. 
The goniometer circle 46 is scanned by the detector unit that is movable 
along its periphery and that may comprise slit 50, a counter tube 52 and a 
counter tube arm 54. The invention contemplates also to encompass large 
portions of the 2.multidot..theta. range or all of it by a locally 
sensitive detector, in particular by a curved wire chamber of the type 
disclosed by V. Perez-Mendez et al. in Nuclear Instruments and Methods 
vol. 156 (1978), pp. 53 to 56. 
FIG. 4 shows an embodiment including a swivel mount 66 (indicated by broken 
lines) which can be moved along an inner circle (also shown by broken 
lines) concentric to goniometer circle 46. Swivel mount 66 support a slit 
68 as well as a secondary monochromator 70 in order to remove undesirable 
radiation issuing from sample 44. For correct X-ray optics, arm 54 and 
swivel mount 66 may comprise suitable guide means such as dovetail 
mechanisms and adjusting screws as well as locking means (not shown). 
FIGS. 5 to 10 show various means for holding the samples or specimens for 
use in the diffractometer according to FIGS. 3 or 4. Sample holders 72 
(FIG. 5) and 79 (FIGS. 6 and 7) are preferred for quick exchange and 
adjustment of samples 44 that may be rod-shaped, as in the example of FIG. 
5, or may be plane by way of foils or slabs of moderate wall thickness 
which are suited for both back-reflection and transmission scans, whereas 
thick slabs will lend themselves to back-reflection diagrams only. 
Sample holder 72 (FIG. 5) includes a support disk 74 having a wheel and 
disk drive 75 for a rotatable goniometer head 76 onto which Debye-Scherrer 
capillaries or specimen tubes 78 may be fixed in customary manner, e.g. by 
means of stick-on wax, sealing wax, piceine, Canada balsam, etc. Specimen 
tube 78 may be optically aligned by using the cross wires of a microscope 
(not shown) and adjusting the goniometer head 76 in all its degrees of 
freedom; for aligning the axis of specimen tube 78 with the goniometer 
axis 48, base disk 74 may comprise a setting device such as a conventional 
compound slide (not shown). A plug-in shaft 96 of base disk 74 can be 
fitted into a corresponding seat (not shown) of the goniometer tray. 
Selectively, the same seat of goniometer tray (46) may receive an identical 
plug-in shaft 96 of sample holder 79 (FIGS. 6 and 7) that may be likewise 
pre-adjusted. As will be seen from FIG. 6, base disk 92 of this embodiment 
is stepped in the fashion of a half-cylinder to provide a vertical step 
face 94 to which a plane plate 80 may be secured verticaly. A round recess 
82 in plate 80 (see also FIG. 7) serves to seat a round base 85 for a 
specimen disk 84 which is inserted into base 85 in axial direction unto a 
stop 87 and locked in this position by means of a socket ring 86 (shown in 
FIG. 8, too). The periphery of base 85 forms a friction rim 88 gripped by 
rollers 89, 91 which are rotatably supported by plate 80. In the 
embodiment shown, two rollers 89 may idle while a third roller 91 serves 
as a friction drive powered by motor 90 for rotating the unit of base 85 
and sample 84 in the plane of plate 80. 
Whilst sample 84 may be a compacted powder slab which, if rather thick, 
permits X-ray diffraction only in the back-reflection mode, foils and thin 
slabs 100 that are also suitable for transmission scans may be supported 
by a similar base 101 (FIGS. 9 and 10) to be selectively seated in sample 
holder 79. Once foil or slab 100 has been placed on a holding ring 103, 
magnets 102 (e.g. in the shape of strips or ledges seen in FIG. 10) may 
act to pull ring 103 to a stop 104 in base 101, which latter also 
comprises a friction rim 88 to be gripped and driven by rollers 89, 91 of 
sample holder 79. 
It will now be evident that these devices allow accurate adjustment of 
whatever sample sort in the center of the goniometer. Thus the 
2.multidot..theta. range can be fully utilized with all the exactitude 
warranted by focussing according to the invention. Zeroing-in is performed 
by 2.multidot..theta. steps of 0.005 degrees (=0.3 arc minutes) or less, 
as the mechanical accuracy of the gear drive used (not shown) may be even 
better. Two step motors may be provided for effecting angular increments 
of 0.0025 degrees (=0.15 angular minutes) indicated by an electronic angle 
display (not shown). A miniature computer (likewise not shown) may be 
provided for motion control, e.g. a twin-diskette system of the type 28KW 
LSI-11 supplied by Digital Equipment Corporation. 
Even in routine work, angular resolutions of 0.135 degrees (=8.1 arc 
minutes) by use of a graphite monochromator and 0.09 degrees with a 
silicon monochromator, respectively, can be attained normally, these data 
to indicate the full width at half-maximum (FWHM) of the SiO.sub.2 triplet 
122/203/301 with Cu-K.sub..alpha. radiation. It depends on the particular 
type of measurement undertaken whether maximum angular resolution or 
maximum intensity are to be aimed at; using graphite monochromators, the 
integrated intensities available are about five times as large as by the 
use of silicon monochromators. 
Comparing FWHM values of Debye-Scherrer reflexes with those of 
back-reflection diagrams, differences of up to 0.04 degrees (=2.4 arc 
minutes) in favor of the reflection scans are found. By means of modified 
Lorentz functions, the reflex profiles can be established for all types of 
diagrams or scans to satisfactory approximation. 
It will be realized that by the invention, convergent focussing of a 
monochromatic primary beam 42 is directed onto the sample 44 as is also 
the case with the Seemann-Bohlin method (FIG. 2b). But unlike the latter, 
the invention provides for locating both the curved monochromator 38 and 
the detector array 50, 52, 54 on the periphery of goniometer circle 46. 
In addition, it will be seen that by the invention, the sample 44 is in the 
center of goniometer circle 46 as according to the Bragg-Brentano method 
(FIG. 1), and the focussing circle radii also decrease with growing Bragg 
angles .theta.. But in contrast to this prior art, the sample 44 is 
irradiated by the convergent beam 42 which is accurately focussed on 
goniometer circle 46 along which the detector array 50, 52, 54 is moved, 
and the diaphragm and slit array 56, 58, 60 provides the additional 
possibility of defining a narrowed beam 42 permitting symmetric reflection 
scans even with specimens of larger surfaces despite their para-focussing 
countereffect. 
Apart from the adjustments necessary, a full measuring program includes the 
following procedures: testing operation readiness for the various 
diffracting modes; quick peak search; automatic data measurement with real 
time diagrams; error compensation and profile fit; indexing unknown powder 
diagrams and associating the measured data to stored data of known 
structures; computing the theoretical powder diagrams and refining the 
analysis by powder data. It is to be emphasized that combined scans in the 
reflection and transmission modes allow of accurate intensity comparison, 
enabling detection of even small fractions of preferred orientation in the 
polycrystalline or liquid samples studied; moreover, quantitative 
evaluation of intensity differences between transmission and reflection 
scans--which appear to be averaged in the Debye-Scherrer diagrams--serves 
to establish and verify exact structures. 
While preferred embodiments have been illustrated and explained 
hereinabove, it should be understood that numerous variations and 
modifications will be apparent to one skilled in the art without departing 
from the principles of the invention which, therefore, is not to be 
construed as being limited to the specific forms described.