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Microsoft word - goebel
Microstructure Analysis in Materials Science, Freiberg, June 15 – 17, 2005
A new flat Goebel-mirror for the
optimization of the primary beam in
Bragg-Brentano diffraction geometry
1Retired from Siemens AG, Corp. Technology, Munich, Presently with the Lab. Cryst. Ana-
: X-Ray Powder Diffraction, Planar Goebel-Mirror, Selective Wavelength, Bragg-
Brentano Focussing, Linear Position-Sensitive Detector
Graded Multilayer Optics ("Goebel-Mirrors") have proved as very useful beam
conditioners for parallel-beam diffraction, high-resolution-XRD, grazing incidence reflecto-
metry and -diffraction, as well as in focussing devices using capillary- or flat transmission
samples [1, 2, 3]. For these applications their optical figure is either parabolic or elliptical.
With a flat surface and the appropriate grading these mirrors reflect a divergent beam with-
out changing its divergence, so that they provide ideal beam conditions (monochromacy,
high intensity) for the Bragg-Brentano focussing principle. Most commercial powder diffrac-
tometers use this geometry. An outstanding property of the flat mirrors is that they can be
adjusted to any wavelength with minor changes of the primary beam path. This enables a
quick change of wavelengths to optimize the penetration depth for a high signal and to avoid
the excitation of fluorescence radiation for a low background. Especially diffractometers
equipped with linear position-sensitive detectors  become extremely powerful with respect
to data collection speed and quality. Such a system was tested in a series of critical meas-
urements using Cr-, Fe-, Co- and Cu radiation. The applications reach from steel and metal-
lurgy, surface problems, coatings to minerals, catalysts and pigments.
Introduction The Bragg-Brentano focussing principle is still the most widespread in x-ray powder diffrac-
tion. A major improvement of the data collection in this field was achieved in the late 1970’s
by the use of linear Position-Sensitive Detectors (PSPC, [4,5]) A modern solution of this
principle is presently marketed by PANalytical with the name “X’Celerator” indicating the
high gain of data collection efficiency by multi-channel recording. An example with the
above mentioned classical PSPC system of is given in fig. 1: about 1000 angular positions of
0.01° resolution are collected simultaneously without significant loss of resolution due to
defocusing. Scanning the entire angular range has so the potential of an acceleration factor
up to 1000 for the data collection speed or counting statistics compared to the normal step-
File: STATRNG.RAW - stationary detector sections Old file structure - converted Old file structure - converted by EVA V3.30File: FRANS04.RAW - Tetracycline-Hydrochloride 30/mi39-1987 (*) - C22H24N2O8·HCl - Tetracycline hydrochloride
Fig.1: Rapid data collection (30°/min) in X-ray powder diffraction with a linear PSPC. The red section is the angular range (10°) simultaneous accumulated at 0.01° resolution (=1000 digital chan-nels). Test Material: Tetracycline Hydrochloride (sample provided by PANalytical).
Experimental Most existing systems are laid out for Cu-K radiation (E = 8.05 keV, = 0.154 nm) having
a wide range of general purpose applications in powder diffraction and being easy to handle
for most available instrumental attachments. There are, however, many important applica-
tions that require a change to a different wavelength from the following reasons:
high absorption in the sample and production of fluorescence background need to opti-
mize the penetration depth, sample volume, signal-to-background ratio and consequently
optimization of diffraction angle or angular range for the analytical goal, i.e. stress-
analysis, peak resolution/angular dispersion, minimum sample influences on measure-
An ideal powder diffraction system consists therefore of a combination of a position sensi-
tive detector and a selectable wavelength primary beam with high intensity and high wave-
length purity. It should be easily switchable to different wavelengths depending on the ex-
A nearly perfect solution for the Bragg-Brentano focussing principle is offered by
the Planar Goebel-Mirrors
as primary beam monochromators and optics. They are de-
signed as graded multilayer reflectors, where the grading is optimized to the distance to the
tube focus (x) to fulfil the Bragg equation (see fig. 2). The design of such mirrors requires a
gradient d’ of the multilayer period d twice as high as in parabolic Goebel-Mirrors (used in
parallel-beam systems) and an optically flat surface. Although being monochromatized the
beam looks like being reflected like an optical beam (Fig. 3).
A new flat Goebel-mirror for the optimization of the primary beam in Bragg-Brentano
Figure 3: Beam paths for Bragg-Brentano diffrac-
Figure 2: Layout of flat Göbel Mirrors. tometers with primary crystal monochromator (top) Bragg’s Law: d=
λ / 2 sin
Θ with sin
Θ = p/x. and flat Göbel Mirror (bottom). The short lever Multilayer Period d=
λ x / 2p.
arm, high reflectivity (70% and higher) and adjust-
Gradient d’ =
λ / 2p, independent of x.
ability to all wavelengths, together with a position-sensitive detector, form a compact and flexible powder diffraction system.
File: SCHLIFF.RAW - Polierter Schliff
76-1877 (C) - Fe3C - Cementite, syn87-0721 (C) - Fe - Iron
Fig. 4: Sensitive detection of 0.3% Cementite in steel. Measurement 10°/min with CrKα radiation. The maximum of α−Fe at 69° is 105 counts high.
Applications The power and flexibility of the system is demonstrated on industrial problems:
1) Sensitive detection of minor phases in steels (retained austenite, carbides, nitrides and
2) Characterisation and depth profiling of surface layers for steel hardening and protection
3) Stress measurements on γ-iron (Austenitic steel)) using the 311-reflection at 147° 2θ with
1. H. Göbel: 43rd Annual Denver X-Ray Conference (August 1-5, 1994), Paper D-63. 2. M. Schuster and H. Göbel: J. Phys. D: Appl. Phys.28 (1995) A270-275. 3. M. Schuster and H. Göbel: Adv. in X-Ray Analysis 39 (1996) 57-71. 4. H. Göbel: Adv. in X-Ray Analysis 22 (1979) 255-265. 5. H. Göbel: Referate des Berg-und Hüttenmännischen Tags 1983.
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