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D2 PHASER User Manual

DOC-M88-EXX141 V5 – 01.2015 3

Basics and principle of operation

The operation mode, which is described here in principle, is called the focussing Bragg Brentano

geometry. Radiation from the X-ray tube (e) (fig. 9 and 10) is emitted from the focus (f) and hits the

sample in the goniometer centre (a). The incident beam direction is (b). The primary beam hits the

sample and is diffracted by the crystal lattice of the powder sample.

The diffraction peaks result from the interference of x-ray waves by the periodic 3d-lattice of the

sample, i.e. of all powder microcrystals, which are in diffraction condition. Each powder microcrystal

contributes to a discrete diffraction peak on the diffraction cones. Their peak intensity is a result of the

atomic types and their positions in the unit cell. The diffraction peaks are generated at specific angles

which are directly correlated with the lattice symmetry (14 Bravais lattice symmetries).

The diffracted radiation is detected by an X-ray sensitive detector (k). Angular positions and intensities

of the diffracted radiation peaks are characteristic for the sample’s crystal structure. Additional

qualitative and quantitative information on crystal properties can be found by analyzing diffraction

patterns, for example chemical composition and physical properties such as crystallinity.

The powder sample rotates with a constant angular velocity around axis (j) (fig. 11 for a standard

sample rotation or fig. 146 for a sample changer) in order to bring more crystallites in the X-ray beam

and therefore improves statistics. The axis (j) of this sample rotation is perpendicular to the goniometer

axis (and to the sample surface) and bisects the incident and diffracted beam. Sample rotation can be

switched on or off if required.

During the measurement of the characteristic diffraction pattern of a polycrystalline sample, detector

and tube rotate (fig. 9 and 10) around the goniometer centre (a) each with angle  to the sample

surface (--geometry). The tube focus (f), the goniometer centre (a) and the detector aperture (l)

define a circle ((d) in fig. 9 and fig. 10), the measurement circle, with the goniometer centre as the

circle’s centre.

Another circle is defined by tube focus (f), goniometer centre (a) and detector aperture (l) which lie on

the circumference of the focusing circle ((m) in fig. 9 & 10). The surface of the sample contacts this

circle tangentially. The circle is called focusing circle because all X-rays which leave the tube focus

(point) within a certain divergence angle area are concentrated (focused) again to a point in the centre

of the detector slit. If a 1D-detector is used, X-rays which are not in --condition do not fulfil the

focussing condition perfectly ((m) in fig. 9).

The diameter of the focusing circle changes with --rotation, the diameter of the measurement circle

remains constant. For optimal focusing, the sample should be a segment of the focusing circle. In

practice the sample surface is flat and hence an approximation to this ideal case. The approximation

becomes better when the focusing circle becomes larger in diameter (at smaller diffraction angles 2).

In this case the focusing condition is better fulfilled.

For smaller focusing circles there are deviations from the ideal focusing condition which can be seen

in measured peak profiles and shifts of the peak position (known as flat specimen errors). The

diffraction angle 2 is the angle between the primary beam direction (b) and the diffracted beam

direction. The beam paths and conditions are shown in figures (9) and (10).

Bruker D2 PHASER User Manual

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