Handbook of Modern Coating Technologies

Powder diffractometer geometry

As said earlier, a materials scientist is often dealing with characterization of polycrystalline materials, which facilitates the application of powder method. Furthermore the transmitted patterns are generally too weak, especially in case of metallic specimens thicker than a few tens of micrometers. Accordingly most of the diffraction studies in materials science are based on back-scattered radiation. As a consequence of enhancement in complexity and pre­cision of X-ray equipment over time, the techniques have progressed from the most basic scan for bulk material to more sophisticated analysis techniques capable of characterizing thin films. Before attempting to learn different diffraction techniques, it is important to understand a few terms regarding geometry of the diffraction equipment.

Various rotational and translational degrees of freedom in modern diffractometers facili­tate irradiation of sample from the desired direction and detection of beams diffracted in dif­ferent directions. Fig. 3—24 identifies different axes of a diffractometer using Eulerian cradle. As an aid to visualization, Fig. 3—25 shows some axes overlayed on a picture of Panalytical X'Pert Pro MRD. The main axes in the XRD equipment are meant for coaxial rotation of sam­ple and detector in the plane of incident and scattered beams. Detector rotation is controlled by the 26 axis, while sample rotation in the plane of diffraction is controlled by the w-axis. 26 signifies angle between incident and diffracted beams (refer Figs. 3—16 and 3—25), while w refers to the angle between specimen surface and the incident beam of X-rays. In the most basic equipment, which can only perform 26/6 scan, w is same as 6 (i.e., always half of 26). The resulting scan shows diffraction peaks from the lattice planes oriented parallel to the specimen surface. Practically as the beam is not fully collimated, all those lattice planes, whose orientations with respect to the specimen surface lie within the divergence angle of the incident beam, will contribute toward diffraction peaks.

For equipment permitting independent control of w and 26 axes, it becomes possible to record diffraction peaks for those lattice planes, which are inclined at a given angle to the specimen's surface. The angle between normal to specimen's planar surface (vector Z) and normal to lattice planes producing the diffracted beam (vector N) is denoted by ф (psi). Apparently the incident beam, diffracted beam and normal N all lie in one plane and the angle between incident and diffracted beams is bisected by the normal N, while the normal to specimen surface, Z would be oriented differently. Furthermore it should be obvious that for equipment permitting only 26/6 scan, vectors N and Z would be collinear and hence, the tilt angle ф would always be zero in such a geometry. The ability of diffraction equipment to record diffraction pattern for different ф angles allows estimation of residual stress.

Sample stage

Specimens mounted in aluminium holder

X-ray source

Detector

X-axis

FIGURE 3-25 Diffraction geometry of Panalytical X'Pert Pro MRD.

More advanced diffractometers permit additional rotational and translational degrees of free­dom through Eulerian cradle (refer Fig. 3—25), Kappa goniometer or Universal Motion Concept (namely, Bruker AXS). The x (chi) axis controls rotation in a plane normal to the plane of dif­fraction (which contains ш and 26 angles). The in-plane rotation of sample about its surface nor­mal (i.e., azimuth angle about vector Z in Figs. 3—24 and 3—25) is controlled by ф axis.

Translation along X and Y (T_X and T_Y) permits bringing the specimen's area of interest into the path of X-ray beam, while translation along Z (T_Z) allows precise location of speci­men surface at the intersection of incident beam and ш axis. Rotation about X and Y (i.e., R_X and R_y) on the specimen stage helps control precession by aligning specimen's normal (Z) with rotation axis ф.

To summarize, the degrees of freedom ш, x, Ф, T_x T_Y, T_Z, R_X, and R_Y are meant for locat­ing and orienting the specimen in the path of the incident beam, while 26 controls the angu­lar position of detector. To facilitate measurements that are noncoplanar with the plane of diffraction (i.e., measurement in-plane with specimen surface) two additional degrees of freedom are provided to the detector. One is translation (T₂₆) in the radial direction along 26, while the other is rotation (26x) about the in-plane rotation axis (namely, Rigaku

SuperLab diffractometer). The in-plane rotation axis lies in the diffraction plane and is perpendicular to the 26 direction.