Overview of Technique
X-ray diffraction is an important technique in the field of materials characterization to obtain structural information on an atomic scale from both crystalline and non-crystalline (amorphous) materials. The X-ray diffraction is nondestructive and can be successfully applied to determine crystal structures of metals and alloys, minerals, inorganic compounds, polymers and organic materials as well as to derive such information as crystallite size, lattice strain, surface and interface roughness, chemical composition, and crystal orientation. X-ray diffractometer D8 Advance of Bruker AXS
is a versatile tool for for phase and structural analysis of powders, analysis of liquid samples (capillary and transmission modes) and reflectometry of thin layers. The system includes:
- Vertical Theta-Theta Goniometer with -110^0 < 2Theta < 168^0 goniometer control with stepper motors and optical encoders providing smallest selectable stepsize 0.0001^0.
- New short ceramic Cu X-ray tube with fine long focus.
- Two exchangeable detectors of scattered X-rays: NaI scintillator type detector with low background (0.4 cps) and high dynamic range (up to 2x10^6) and Braun position-sensitive detector.
- Rotation-transmission, capillary and reflectrometry stages.
Basics and Tutorials
X-ray diffractometer Bruker AXS D8 Advance is a multifunctional tool for X-ray diffraction analysis of powders, thin films and bulk materials and X-ray reflectometry of thin layers (crystalline, amorphous or liquid samples).
X-ray powder diffraction (XRD) is an instrumental technique that is usually used to study crystalline materials. The three-dimensional structure of non-amorphous materials is defined by regular, repeating planes of atoms that form a crystal lattice. When a focused X-ray beam interacts with these planes of atoms, part of the beam is transmitted, part is absorbed by the sample, part is refracted and scattered, and part is diffracted. When an X-ray beam hits a sample and is diffracted, we can measure the distances between the planes of the atoms that constitute the sample by applying Bragg's Law. Bragg's Law is nλ=2d sinθ, where the integer n is the order of the diffracted beam, λ is the wavelength of the incident X-ray beam, d is the distance between adjacent planes of atoms (the d-spacings), and θ is the angle of incidence of the X-ray beam. Since we know λ and we can measure θ we can calculate the d-spacings. The characteristic set of d-spacings and theirs intensity generated in a typical X-ray scan provides a unique "fingerprint" of the phases present in the sample. When properly interpreted, by comparison with standard reference patterns and measurements, this "fingerprint" allows for identification of the material. Presence of an amorphous material in the sample can be determined by occurrence of specific wide halo on diffraction pattern. DiffracPlus software for Bruker AXS diffractometer D8 Advance allows carrying out initial processing of diffraction pattern, phase identification of crystalline materials, crystallite size determination and degree of crystallinity calculation. The unit-cell parameters and the crystal structure could be also refined for the identified phases. Powerful modern software (CellRef, FullProf Suite, PowderCell etc.) is applied to solve these problems. Furthermore, modern software (CrysFire, ChekCell, PowderX, Powder-2 etc. ) allow to index diffraction pattern , to define cell parameters and space group even in case of unknown matter. It is a basis for the subsequent full structure solution for new crystalline substance. The diffractometer also allows study of singe-crystalline samples' orientation as well as study of liquid samples (solutions and suspensions). Standard sample holders (diameter-25mm, depth-1.5) or low background quartz and silicon sample holders are used at the analysis of powder specimens. The optimum size of the bulk specimen is 25x25 mm.
XRD methods for crystallite size determination are applicable to crystallites in the range of 2-100 nm. The diffraction peaks are very broad for crystallites below 2-3 nm, while for particles with size above 100 nm the peak broadening is too small. If analyzed crystals are free from microstrains and defects, peak broadening depends only on the crystallite size and diffractometer characteristics. In this case classical Scherrer equation is used for crystallite size determination: d=(Kxl)/(b x cosq) , where d is the crystallite size, l is the X-ray wavelength, b is the width of the peak (full width at half maximum (FWHM) or integral breadth) after correcting for instrumental peak broadening (b expressed in radians), q is the Bragg angle and K is the Scherrer constant. The Scherrer equation gives volume-weighted mean column length. The d value calculated for (hkl) peak should be understood as mean crystallite size in the direction that perpendicular to the (hkl) plane (hkl is Miller indices).
Quantitative XRD phase analysis is a powerful method for determining the quantities of crystalline and amorphous components in multiphase mixtures. Now Rietveld Quantitative Analysis (sometimes called also Multiphase Rietveld Phase Quantification or Rietveld XRD Quantification) is the most-used. The method relies on the simple relationship Wp =Sp(ZMV)p/∑Si(ZMV)i where W is the relative weight fraction of phase p in a mixture of n phases, and S, Z, M, and V are, respectively, the Rietveld scale factor, the number of formula units per cell, the mass of the formula unit (in atomic mass units) and the unit cell volume. Rietveld method can be applied to phase quantification only if structures of all phases are known. At the same time still a direct method, an internal standard method and relative intensity ratio (RIR) method are used. It should be noted that each of the available methods has its intrinsic limitation, so that final choice should be made based on specific task and material to be analyzed.
X-ray reflectometry (XRR) is a non-destructive technique used for estimation of density, thickness and roughness of thin film structures (single layer and multilayers). XRR relies on the interference of X-rays reflected at different interfaces, while X-ray diffraction results from the interference of x-rays diffracted from periodic lattice points. XRR can be used with crystalline, amorphous and liquid samples for typical layer thickness between 5 and 400 nm and surface roughness from 0 to 2 nm. This technique does not work effectively, if there is no difference between the electron density of different layers or layer and substrate. Proper goniometer alignment and selection of the data collection parameters are of crucial importance for a high-quality reflectivity data set. In the elementary case (single layer), the thickness t and density ρ can be obtained from the definition of the fringe spacing Δα and measurement of the critical incident angle αc: t ≈ λ / 2Δα and αc ≈ 1.64×10-3 λ √ρ. In more difficult cases (multilayer) the problem becomes complicated and for its solution is used special software REFSIM (Bruker AXS).
For basic education and principle understanding of XRD and XRR analysis, please, use following web resources:
||Vertical, high precision, two-circle with independent stepper motors and optical encoders
||Theta/Theta convertible to Theta/2Theta
|Maximum usable angular range:
|Smallest selectable stepsize:
||* Solid state NaI dynamic scintillation detector;
* Braun position sensitive detector.
||* Parallel beam with Gobel mirror;
* Focused beam with fixed slits.
||Full Diffracplus package for data acquisition, phase analysis, crystallography and thin film characterization