Section 2.3.1.2. Transmission specimen, θ–2θ scan

Transmission-specimen methods are not as widely used as reflection methods but they provide important supplemental data and have advantages in a number of applications. Reflections occur from lattice planes oriented normal to the specimen surface rather than parallel. Reflection and transmission patterns can be compared to determine texture and preferred-orientation effects. The transmission method is better suited to the measurement of large d's. Smaller specimen volumes are required. The surface `roughness' which may cause large intensity errors due to the microabsorption in reflection specimens is largely reduced.

The same basic diffractometer is used for both methods but the geometry is different because the diffracted beam continues to diverge after it passes through the specimen and the monochromator is required to refocus the beam, on the detector as shown in Fig. 2.3.1.12 (de Wolff, 1968b; Parrish, 1958). The monochromator can be placed before or after the specimen and the position has different effects on the pattern. Using the monochromator in the diffracted beam, the intensity and width of the profiles are determined by the X-ray focal line width and the quality of the bent monochromator rather than the receiving slit which serves as an antiscatter slit. This geometrical arrangement places the virtual image VI of the focal line at the intersection of the focusing circles. After reflection from the specimen, the divergent beam is again reflected by the focusing crystal M and converges on the detector. The pattern is recorded with θ–2θ scanning with the monochromator and detector both mounted on a rigid arm rotating around the diffractometer axis. A beam stop MS can be translated and moved in and out near the crossover point to prevent the primary beam from entering the detector at small 2θ's. To avoid long radii, the crystal surface is cut at an angle σ (about 3°) to the reflecting lattice plane. The distances are related by where is the Bragg angle of the monochromator for the selected wavelength and the l's are shown in Fig. 2.3.1.12(a).

Figure 2.3.1.12| top | pdf | X-ray optics of the transmission specimen with asymmetric focusing monochromator and θ–2θ scanning. (a) Monochromator in diffracted beam. θM Bragg angle of monochromator with surface cut at angle σ to reflecting plane, MS adjustable beam stop, I1, I2, and I3 defined in text and other symbols listed in Fig. 2.3.1.3. (b) Monochromator in incident beam, equivalent to Guinier focusing camera.

Because the profile shape and the intensity are determined by the monochromator, the crystal quality and the accuracy of the bending are crucial factors in determining the quality of the pattern. A flat thin quartz (101) wafer bent with a special device to approximate a section of a logarithmic spiral has been successfully used (de Wolff, 1968b). The curvature can be varied to obtain the sharpest focus. Thin silicon crystals that can be bent are now available, and Johann and Johannsen asymmetric crystals may be used. Pyrolytic graphite monochromators are not applicable; the radii would be longer because graphite is too soft to be cut at an angle, and a receiving slit would be necessary to define the diffracted beam because the monochromator produces a broad reflection.

A polarization factor is introduced by the monochromator, where for mosaic crystals and for perfect crystals. The value of k is strongly dependent on the surface finish of the crystal and the crystal should be measured to determine the effect. A specimen with accurately known structure factors such as silicon can be used to calibrate the intensities.

The Kα-doublet separation is zero at the 2θ angle at which the dispersion of the specimen compensates that of the monochromator, i.e. the 2θ at which the monochromator is aligned and also depends on the distances. The Kα₁ and Kα₂ peaks are superposed and appear as a single peak over a small range of 2θ's. The Kα₂ peak gradually separates with increasing 2θ but the separation is less than calculated from the wavelengths and the intensity ratio may not be 2:1 until higher angles are reached as shown in Fig. 2.3.1.8.

A larger angular aperture α_T can be used for transmission than for reflection α_R because the specimen is more nearly normal to than parallel to the primary beam: where the diffractometer radius R_D = l₁. For R_D = 170 mm, specimen length = 20 mm and l₂ = 65 mm; α_T could be 4.7 times larger than α_R but the monochromator length usually limits it to about 3°. The smallest reflection angle that can be measured is Using α_T = 0.5°, 2θ_min = 1.75° and d = 50 Å for Cu Kα radiation.

Specimen preparation is not difficult and the preparation can be easily tested and changed. The specimen must be X-ray transparent and can be a free-standing film or foil, or a powder cemented to a thin substrate. The substrate selection is important because its pattern is included. If both transmission and reflection patterns are to be compared, the substrate should be selected to have a minimal contribution to both. For example, Mylar is a good substrate for transmission but has a strong reflection pattern, and although rolled Be foil has a few reflections it is often satisfactory for both.

The absorption factor is where t is the powder thickness and s is the sum of the products of the absorption coefficients and thicknesses of the powder and the substrate. The optimum specimen thickness to give the highest intensity is μt = 1, i.e. the specimen should transmit about 38% of the incident Kα intensity. The transmission can be easily measured with a standard specimen set to reflect the Kα and the specimen to be measured inserted normal to the diffracted beam in front of the detector. It is not critical to achieve the exact value and a range of ±15–20% of the transmission can be tolerated. This minimizes the effect of the absorption change with 2θ, and corrections of the relative intensities are required only when accurate values are required.

The intensity of the incident beam can be measured at 0° in the same geometry and used to scale the relative intensities to `absolute' values. The flat specimen, transparency, and specimen surface displacement aberrations are similar to those in reflection specimen geometry except that they vary as rather than . This is an important factor in the measurement of large-d-spacing reflections. The flat-specimen effect is smaller because the irradiated specimen length is usually smaller. The transparency error is also usually smaller because thin specimens are used.

An important advantage of the method is that the specimen displacement can be directly determined by measuring the peak in the normal position and again after rotating the specimen holder 180°. The correct peak position is at one-half the angle between the two values. The axial divergence has the same effect as in reflection. The limitations are that only the forward-reflection region is accessible, and the intensity is about one-half of the reflection method (except at small angles) because smaller specimen volumes are used.

An alternative arrangement for the transmission specimen mode is to use an incident-beam monochromator as shown in Fig. 2.3.1.12(b). This is similar to the geometry used in the Guinier powder camera with the detector replacing the film. A high-quality focusing crystal is required. Wölfel (1981) used a symmetrical focusing monochromator with 260 mm focal length for quantitative analysis. Göbel (1982) used an asymmetric monochromator with a position-sensitive detector for high-speed scanning, see §2.3.5.4.1. By proper selection of the source size and distances, the Kα₂ can be eliminated and the pattern contains only the Kα₁ peaks (Guinier & Sébilleau, 1952). This geometry can have high resolution with the FWHM typically about 0.05 to 0.07°. The profile widths are narrower for the subtractive setting of the monochromator than for the additive setting.

The pattern is recorded with θ–2θ scanning. The 0° position can be determined by measuring 4θ, i.e. peaks above and below 0°, or calibration can be made with a standard specimen. A slit after the monochromator limits the size of the beam striking the specimen. The width and intensity of the powder reflections are limited by the receiving-slit width. A parallel slit is used between the specimen and detector to limit axial divergence.

The full spectrum from the X-ray tube strikes the monochromator and only the monochromatic beam reaches the specimen, so that it is preferred for radiation-sensitive materials. On the other hand, the radiation reaching the specimen may cause fluorescence (though considerably less than the full spectrum) which adds to the background.