DIFFRACTOMETER WITH A MOBILE X-RAY TUBE-DETECTOR SYSTEM
B.S. Roshchin, V.E. Asadchikov, A.V. Buzmakov, I.V. Kozhevnikov,
Yu.S. Krivonosov, R.A. Senin, Yu.N. Shilin and V.A. Shishkov
A.V. Shubnikov Institute of Crystallography RAS
Leninskii prospekt 59, Moscow, 119333 Russia
ABSTRACT
An X-ray diffractometer with a mobile X-ray tube–detector system is able to perform various X-ray examinations of a stationary
sample. The design for this instrument is described, along with its operating principles and control programs. Owing to its highprecision angular movement encoders and its two detectors (one of these, a linear position-sensitive detector, has a working
length of 100 mm and a resolution of <0.2 mm), the diffractometer can be used in both traditional and nontraditional
experiments on X-ray reflectivity, scattering, and absorption. Results from using this setup in reflectometry and X-ray
tomography are presented as examples.
Introduction
The diffractometer with a mobile X-ray tube-detector system [1] was designed to achieve the following objectives:
(1) To offer a means for studying the processes of X-ray diffraction and scattering with the sample in a fixed position (this can
be done when the X-ray source and the detector are able to rotate independently of one another);
(2) To attain the highest possible controllable accuracy of all angular displacements;
(3) To allow independent measurements of reflected (or scattered) X-rays from two directions using two different detectors
(one of which is a position-sensitive detector and other is a scintillation detector); as a result, it is possible to detect X-rays over
a wide solid angle simultaneously.
In the present work, we describe both the design for the diffractometer and its new applications, in which it is the above design
features of the instrument that allow the experimental tasks to be performed. The external appearance of the X-ray
diffractometer with a mobile X-ray tube–detector system is shown in Figure 1.
Figure 1. External appearance of the diffractometer with a mobile X-ray tube–detector system.
General description of a design for a setup
The structural diagram of diffractometer is presented in Figure 2. Series-produced X-ray tube 1, monochromator crystal 2, and
collimating system 3 are all fastened to ring support 4; radiation detector 6 having an analyzer crystal are locked on similar
support 5.The tube and the detector can rotate around the vertical axis in the plane of the ring supports, and, together with the
supports, around horizontal axis 7 (the angle of the ring support’s rotation around axis 7 is monitored by angular encoders).
The sample under analysis, 8, is placed on alignment table 9. The table is used for the horizontal displacement of the sample
and its adjusting in two perpendicular directions (the rotation axes lie in the horizontal plane). The vertical displacement of the
sample is also provided for. The table itself (together with the sample) can additionally rotate in the horizontal plane, and its
angular displacement is monitored by an angular encoder.
Figure. 2. Diagram of the diffractometer with a mobile X-ray tube–detector system: (1) X-ray tube; (2) monochromator crystal;
(3, 12) collimating system; (4) ring support for the X-ray tube; (5) ring support for the detector; (6) scintillation detector; (7)
rotation axis of ring supports 4 and 5; (8) test sample; (9) sample holder with the alignment table; (10) X-ray beam; (11)
position-sensitive linear detector; and (13) analyzer crystal.
Apart from a standard scintillation detector, a linear position-sensitive detector is incorporated in the diffractometer’s
construction. Step motors are used to turn the X-ray source, the counter, and the sample under investigation through different
angles. The diffractometer is controlled by a personal computer (PC). The performance characteristics of the diffractometer are
presented below.
Construction of the whole setup allows the rotation of the X-ray tube holder through 90°; the monochromator crystal through
45°; the analyzer crystal through 45°; the scintillation detector through 90°; the X-ray tube in the plane of ring support 4 from –
30° to +30°; the scintillation detector holder in the plane of ring support 5 from –30° to +30°; and the ring supports about the
horizontal axis from 0° to 35°. The rotation encoder for the angular supports has an accuracy of 2''. The alignment table can be
displaced in the vertical plane by 20 ± 0.05 mm. The alignment table, together with the sample, can rotate around the vertical
axis through angles of 0 to 360° with an accuracy of 1'' (this is achieved using the angular encoder).
Note that the instrument, due to the combined rotation of the X-ray tube, the detector, and the central rotary table, may be
considered an integrated five-circle X-ray goniometer.
Note that the advantage of our diffractometer is the involving of angular movement encoders in its construction. The
diffractometer therefore compares favorably to others in which rotation angles are measured by counting the steps of the
control step motors and considering the reduction factor. When such a system is used, the inaccuracy in manufacturing the
moving elements of the transmission mechanisms may give rise to uncontrollable errors in the counting of angular
displacements. The use of angular movement encoders allows these errors to be eliminated.
Two types of encoders are used in our instrument. Those attached to the shafts of the ring supports are inductance-type
reduction selsyns. The distinguishing features of these encoders were detailed in [2]. Their error, measured on a test bench
using an autocollimator, does not exceed 2'' per complete revolution. The dependence of the encoder’s code on the number of
steps of the control step motor, measured during the testing of the diffractometer over a wide range of angles (>12°), shows
that the linear law is obeyed, and the encoder signals in the each following period correspond to one another. On the one
hand, this confirms the good workmanship of the respective rotation gear and, on the other, indicates that the error of
determining angles in this range of displacements falls far short of the measured value (2'').
Another type of angular movement encoder is used in the central alignment (rotary) table of the diffractometer: rotatingmodulator phase converters [2]. In the technical literature, such encoders are frequently called self-generating or modulating
transducers. The induction transducer was used in our instrument. The induction transducer is based on two pairs of gear
wheels separated by an air gap. One such pair of wheels is shown in Figure 3. The inner wheels with outer teeth are in both
pairs rigidly bound to one another and are referred to as a modulator. A mechanical drive sets the modulator into rotary motion
with constant speed ωm.
Figure 3. Diagram of the Induction-type angle data encoder.
One of the outer wheels with inner teeth (called a stator) is mounted on the transducer’s casing. The other wheel (a rotor) is
attached to the input shaft, the angular position of which is measured. Each wheel in the stator and the rotor has a groove cut
into it, into which a ring winding is inserted. Each wheel has z teeth. If the rotor and stator windings are connected to dc
voltage source E through resistor R (Figure 3), rotation of the modulator with speed ωm gives rise to periodic signals with
frequency ω=ωmZ and a shape close to a sine wave. The phase difference φ between the output signals of the induction
transducers is proportional to the angle α being measured. The proportionality coefficient Z is the electric reduction factor. The
phase difference is measured by a phase shift–time interval–code principle. The error in measuring the angle of rotation (as
verified on a test bench) does not exceed ± 0.4'', while the value of the low-order digit is 0.1''.
Investigation of layers on liquid surface
Note that X-ray reflectometry is virtually the only method for obtaining direct information on the structure of near-surface layers
in liquids. As mentioned above, the distinguishing feature of this diffractometer is the horizontal orientation of the sample; this
allows it to be used in such studies.
Acrylate resins (Eudragits) are conventionally used as film coatings in the pharmaceutical industry to mask unpleasant tastes
and to control the release of drugs [3].
Eudragit polymers are soluble in many organic solvents (methanol, ethanol, isopropyl alcohol, acetone, acetoacetate, and
dichloroethane), but are water insoluble. For this reason, it is believed that these polymers can, under certain conditions, form
layers on the water’s surface. To verify this, we prepared solutions of Eudragit RL polymer in methylene chloride, a
volatilizable organic solvent, with concentrations of 1 mg/ml. Using calibrated syringes, these solutions were poured over a
water surface, and the reflectivity of the liquid samples was then measured. A liquid sample was placed into a fluoroplastic cup
such that the surface of the liquid rose above the edges of the cup. To eliminate the vibration of the surface, antivibration
mounts were placed beneath each of the two slabs upon which the diffractometer is rested. To prevent evaporation from the
water’s surface, the fluoroplastic cup with the liquid was enclosed in a sealed vessel that had windows of thin polymer film
practically transparent to X-rays. The measured angular dependences of the reflectivity of the water and the polymer layers
applied to its surface are shown in Figure 4, along with the theoretical curves.
(a)
(b)
Figure. 4. (a) Experimental angular dependences of the reflectivity of the surface of water coated with a layer of polymer; (b)
4
similar dependences plotted in coordinates {R(θ)sin θ}–θ.
We can see that experimental and theoretical reflectivity curves for water are in good agreement. On the other hand for the
reflectivity curves of the solutions we can observe the maximum of intensity on the angle ~ 0.2 degree, which is caused only
by the small surface dimensions of the samples in study.
After the reflectivity of water was measured, different amounts of polymer solutions were poured over the water surface. The
solution was then left to stand for an hour (to ensure the full evaporation of the organic solvent), and the reflectivity curves
were measured once more. At first glance, all of the experimental curves seem to be absolutely smooth (Figure 4a); i.e., no
film differing slightly from the water in density was revealed in the experiment.
To detect the presence of this film, we plotted these curves in coordinates {R(θ)sin4θ}–θ (Figure 4b). In these coordinates, the
peak due to the finite thickness of the layer was expected to be sharper. It turned out that this peak was indeed recognizable
for all of the samples subjected to analysis. Estimates showed that the thickness of a surface layer with a modified density
increased with the surface concentration of the polymer: its respective values were ~5.5, 6.3, and 7.4 nm, depending on the
amount of polymer. Thus, the diffractometer is capable of revealing surface layers that differ only slightly from water in density.
X-ray tomography
Note that the overwhelming majority of X-ray tomographs utilize X-ray bremsstrahlung (as a rule, this radiation is very hard)
with a characteristic wavelength of <0.2 Å (~60 keV). This radiation is suitable only for analyzing structures of strongly
absorbing or extended samples. At the same time, it is better to use more soft X-rays with wavelengths of 0.7–2.3 Å (18–5.4
keV) to examine the structure of light-element samples with characteristic dimensions of ~1 cm, particularly samples of
carbon-containing materials. The use of monochromatic radiation in tomography allows one to dispense with corrections for
the difference in absorption coefficients at different wavelengths. The above characteristics of the diffractometer show that it
can be used in tomographic investigations of carbon-containing materials, including biological samples. In such cases, the
sample dimensions could be of order of several centimeters, and the resolution of these tomograms (i.e., the size of a
resolvable element) can reach taking into account the linear sensitive detector properties the value of 0.15–0.20 mm; this has
been verified on standardized samples (phantoms).
One important factor of tomographic studies is their duration. The possibility of reducing the measurement time is limited, on
the one hand, by the admissible counting rate of the detector and, on the other hand, by the need to obtain statistically
significant data. The linearity of position-sensitive detector counts was therefore checked against calibrated copper filters.
Experiments showed that the linearity of the counting was maintained while the number of X-ray photons per channel detected
4
1
over an exposure time of 30 s varied from 10 to 10 . In these experiments, counts corresponding to one channel were
assumed to be an independent measurement. If one compares the absorption coefficients obtained for each channel and then
determines the rms deviation of the experimental results from one another, one can see that, even in the worst case where
~10 X-ray photons correspond to each channel, the error in measuring the absorption coefficient does not exceed 30%. As a
result, the dynamic range of the detector’s sensitivity is three orders of magnitude or more.
It is noteworthy that the characteristics of the X-rays used in these measurements are such that a sample with characteristic
dimensions of ~1 cm is rather transparent to them, but their absorption in such a sample is nevertheless substantial even for
light biological tissues such as an epithelial integument.
To assess the instrument’s capabilities and obtain useful (to scientists) structural information, we examined a biological sample
of maximum heterogeneity: a one-year-old Salamandrella keyserlingii he-triton. This triton is of interest to biologists in that its
natural habitat stretches even beyond the Polar circle.
As a preliminary analysis of the triton tissues showed, even those organs having the least contrast for X-rays can be
differentiated using X-rays with a wavelength of 1.54 Å (Figure. 5).
Figure. 5. The reconstruction of Salamandrella keyserlingii.
The tomographic investigations were performed under the following conditions: number of goniometer positions, 72 (over the
range 0–180°); number of detector data channels, 250; data acquisition time for each spectrum, 30 s; X-ray source, CuKα
(1.54 Å); dimensions of the focal spot, 1 × 1 mm; sample-to-source distance, 80 cm; and distance of sample from detector, 8
cm.
The beam was collimated in the vertical plane by a system of slits so that its height in the plane of the detector was <0.1 mm.
The tomographic measurements were taken layer by layer; a total of 12 layers of triton tissue were analyzed. In order to
reconstruct these images, we used Filtered Backprojections technique [4].
The spatial pattern of human’s brain epiphysis was investigated also. A reconstruction of human’s brain epiphysis in normal,
morbid affection by Altsgamer and schizophrenia was obtained (Figure 6). In this case MoKα irradiaton was used. For the first
time fact of significant calcium salt content decreasing and absence of calcification regions connectedness in the presence of
pathology was found.
(a)
(b)
(c)
Figure. 6. A reconstruction of human’s brain epiphysis: (a) in normal state;
(b) morbid affection by Altsgamer; (c) schizophrenia.
Reflectometry of multilayer structures
The angular dependences of the X-ray reflectivity provide information on the surface structure, particularly on the number of
layers applied, their thickness and interfacial roughness. These dependences are a useful inspection tool for industrial
engineers responsible for the deposition of multilayer coatings, particularly in the production of X-ray mirrors.
In the framework of VAMAS [5] project “X-ray reflectivity measurements for evaluation of thin films and multilayer thickness”
two samples of GaAs/AlAs multilayer structures were measured. These samples were deposited at the National Metrology
Institute of Japan (NMIJ). Each of the samples consists of 3 bilayers. Five reflectivity spectra from each sample were obtained
and the average curve for one of the samples is shown on Figure 7.
Figure. 7. Angular dependence of the GaAs/AlAs multilayer reflectivity and the result of simulations.
Let's present the experimental data analysis. In order to verify the thickness of the layers we performed a direct calculation of
the reflectivity curve which corresponds to the structure consisting of 3 bilayers with the given thickness. Calculation was
performed according to Parrat’s formula [6]. It should be mentioned that the thicknesses of the layers don’t correspond to
these which was previewed (compare experimental and calculated curves on Figure 7). To determine the real structure which
was deposed we tried to solve the inverse problem of reflectometry. The results we obtained are given in Table 1. One can
see that if we don’t consider interfacial roughness it is impossible to describe experimental curve quantitatively while angular
position of the peaks are described correctly (Simulation 1). So we have to introduce interfacial roughness and moreover we
have to assume the density of layers to be less than that of a bulk (Simulation 2). Only in this case simulated curve is in a good
agreement with experimental one.
Table 1. Previewed data and the result of simulations of the multilayer reflectivity.
Previewed data
Simulation 1
Simulation 2
Thickness, nm:
Top Layer (Oxide)
Layer 1: GaAs
Layer 2: AlAs
Layer 3: GaAs
Layer 4: AlAs
Layer 5: GaAs
Layer 6: AlAs
1.27
9.04
9.43
9.27
9.43
9.26
9.44
Substrate (GaAs)
-
Roughness, nm:
0.00
9.54
9.93
9.77
9.93
9.76
9.94
0.75 ± 0.75
9.40 ± 0.7
9.71 ± 0.2
9.69 ± 0.2
9.67 ± 0.2
9.63 ± 0.2
9.80 ± 0.1
1.4 ± 0.14
1.4 ± 0.14
0.8 ± 0.08
0.7 ± 0.07
0.6 ± 0.06
0.6 ± 0.06
0.5 ± 0.05
-
-
0.1 ± 0.01
3
Density, g/cm :
Top layer (Oxide)
GaAs
AlAs
Substrate (GaAs)
5.32
3.73
5.32
5.32
3.73
5.32
2.0 ± 0.4
4.8 ± 0.05
3.0 ± 0.02
4.9 ± 0.02
We would like to emphasize that an error of sample parameters determination indicated in Table 1 is caused by ambiguity of
the inverse problem solution rather than an error of measurements.
Conclusions
Thus we have shown that the diffractometer we constructed is really multipurpose one. It was applied to study of liquid
surfaces and solid multilayer structures as well. The new results on structure of several biologic and medical specimens were
received using the new X-ray tomography technique.
Acknowledgments
The work was supported, in part, by the ISTC (project #3124).
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