Triple-axis Diffractometer Research Articles

On the lattice parameters of silicon carbide

The thermal expansion coefficients of the hexagonal SiC polytypes 4H and 6H and with Al and N dopants have been determined for temperatures between 300 and 1770 K. Further, a set of the room temperature lattice parameters in dependence on doping with N, Al, and B has been obtained. Data for the thermal expansion were taken on a triple axis diffractometer for high energy x rays with a photon energy of 60 keV, which allows the use of large single crystals with a volume of at least 6×6×6 mm3 without the need to consider absorption. The room temperature measurements for samples with different dopants have been performed on a four-circle diffractometer. The thermal expansion coefficients along the a- and c-directions, α11 and α33, increase from 3×10−6 K−1 at 300 K to 6×10−6 K−1 at 1750 K. It is found that α11 and α33 are isotropic within 107 K−1. At high temperatures both coefficients for doped samples are ∼0.2×10−6 and 0.3×10−6 K−1 lower than for the undoped material.

Thermal Expansion Coefficients of 6H Silicon Carbide

The thermal expansion of 6H Silicon Carbide with different dopant concentrations of aluminum and nitrogen was determined by lattice parameter measurements at temperatures from 300 K to 1575 K. All samples have a volume of at least 6 x 6 x 6 mm3 to ensure that bulk properties are measured. The measurements were performed with a triple axis diffractometer with high energy x-rays with a photon energy of 60 keV. The values for the thermal expansion coefficients along the a- and c-direction, α11 and α33, are in the range of 3·10-6 K-1 for 300 K and 6·10-6 K-1 for 1550 K. At high temperatures the coefficients for aluminum doped samples are approximately 0.5·10-6 K-1 lower than for the nitrogen doped crystal. α11 and α33 appear to be isotropic.

Early detection of nanoparticle growth from x-ray reciprocal space mapping

The potential for nondestructive in situ detection of the formation of weakly diffracting nanoparticles has been confirmed by a combination of experiment and simulation. A triple axis diffractometer was used to collect two-dimensional reciprocal space maps of diffracted synchrotron x-rays from nanoscale Al2Cu precipitates embedded in a bulk metallic matrix. The appearance and asymmetric profile of the monochromator pseudostreaks are demonstrated to be indicative of the sensitivity of the technique to both the presence and orientation of the nanoparticles. This is a fundamental step toward in situ detection of sparsely dispersed, embedded nanoparticles and to quantitative temporal studies of particle number, scale, and dispersion.

Effective Stresses and Plastic Strain Rates in a Superalloy: a High Temperature In Situ Study by Synchrotron X-Ray TCD

Variations in the lattice parameters of γ and γ' phases perpendicular to the [001] tensile axis were recorded in situ at ~10 minutes intervals using the Triple Axis Diffractometer of the High Energy (ID15) beamline at ESRF. Testing was carried out on an AM1 superalloy specimen with a raft microstructure at high temperature (1072°C) under load steps between 0 MPa and 300 MPa. These data were used to evaluate the Young modulus and the effective (Von Mises) stresses within the γ' rafts and γ corridors, as well the average plastic strain rates of each phase. The recorded stress data scatter was within the MPa range, and should be good enough to probe the elementary mechanisms of plasticity.

A high-energy triple-axis X-ray diffractometer for the study of the structure of bulk crystals

A triple-axis diffractometer for high-energy X-ray diffraction is described. A 450 kV/4.5 kW stationary tungsten X-ray tube serves as the X-ray source. Normally, 220 reflections of thermally annealed Czochralski Si are employed for the monochromator and analyser. Their integrated reflectivity is about ten times higher than the ideal crystal value. With the same material as the sample, and working with the WKα line at 60 keV in symmetric Laue geometry for all axes, the full width at half-maximum (FWHM) values for the longitudinal and transversal resolution are 2.5 × 10−3and 1.1 × 10−4for ΔQ/Q, respectively, and the peak intensity for a non-dispersive setting is 3000 counts s−1. In particular, for a double-axis mode, an energy well above 100 keV from theBremsstrahlungspectrum can be used readily. High-energy X-rays are distinguished by a high penetration power and materials of several centimetre thickness can be analysed. The feasibility of performing experiments with massive sample environments is demonstrated.

Diffractometer for high energy X-rays at the APS

The Basic Energy Sciences Synchrotron Radiation Center (BESSRC) has designed and built a diffractometer specialized for high energy synchrotron radiation ( E>60 keV) at the Advanced Photon Source (APS). The diffractometer, which is installed at the elliptical multipole wiggler, uses linearly polarized light (U. Rütt et al., Proc. SPIE 3348 (1998) 132.). The instrument is a triple-axis diffractometer allowing high resolution measurement in two dimensions of the reciprocal space. As opposed to the other diffractometers for high photon energies at HASYLAB (Germany) and ESRF (France) (R. Bouchard et al., 5 (1998) 90; K.-D. Liss et al., J. Synchrotron Rad. 5 (1998) 82), this diffractometer utilizes the vertical scattering plane to take full advantage of the small vertical divergence of the beam and to allow horizontal focusing of the broad beam from the wiggler without disturbing the resolution of the instrument. The instrument is designed to carry heavy sample equipment up to a weight of 200 kg, while maintaining high resolution and low background. First tests have been done to check the overall performance, stability, background and resolution of the diffractometer.

Accurate structure-factor measurements using high-energy synchrotron radiation: a test on cuprite, Cu2O

Using high-energy synchrotron radiation, structure factors were measured on the triple-axis diffractometer at the HASYLAB beamline BW5. A data set for cuprite, Cu2O, was recorded, and the excellent data quality [internal consistencyRint(F2) = 0.0055] allowed full multipole refinements using the programVALRAY. Extinction was still significant, but small. Using data measured at 75, 100, 125 and 150 keV photon energies, it was possible to determine and separate extinction prior to the refinements. After evaluation and comparison of extinction-affected and extinction-free data, significant differences in the electron densities were found.

Investigation of Bragg surface diffraction in semiconductors and epitaxic structures by reciprocal-space analysis

Bragg surface diffraction (BSD) is a special case of three-beam diffraction, where the secondary beam is scattered in the surface-parallel direction. Under the BSD condition, the surface-detour reflection (secondary plus coupling reflections) transfers some of the secondary-beam intensity into the monitored primary beam. The extinction regime in which such transfer takes place depends on the crystalline perfection of the surface. Based on this fact, the mapping of the BSD profile, in an ω:φ scan technique, has been proposed [Morelhão & Cardoso (1996).J. Appl. Cryst.29, 446–456] as a method to obtain information on the in-plane crystalline quality of the surface. With the X-ray optics for BSD mapping, the diffracting surface thickness that defines the profile could not be measured or compared with those under conventional Bragg diffraction. In this report, the BSD using a triple-axis diffractometer is investigated. Reciprocal-space mapping of the Bragg reflection (primary reflection) was performedinandoutof the BSD condition. It reveals the diffracting surface thickness of BSD in GaAs and Si substrates. The triple axis was also used to investigate the BSD in the SiGe multiple quantum well, and it has demonstrated the existence of effective satellite peaks for such structures.

Triple-axis diffractometry on GaN/Al2O3(001) and AlN/Al2O3(001) using a parabolically curved graded multilayer as analyzer

X-ray Bragg diffraction profiles of epitaxial layers of A1N and GaN grown onc-plane sapphire were measured with a novel triple-axis diffractometer using a parabolically curved, graded multilayer mirror in the diffracted beam instead of an analyzer crystal. In addition, the intensity of the incident beam is enhanced by a parabolically graded multilayer mirror acting as condensor for a Ge(022) channel-cut monochromator. This novel diffractometer configuration provides a clear improvement in intensity at sufficiently high resolution for the study of angular peak broadening and peak shape functions of weak reflections from samples of poor structural quality and from thin layers. For AlN and GaN, the reason for peak broadening of symmetric rocking curves was found to be small coherence lengths parallel to the substrate surface and not distinct out-of-plane misorientations. Additionally, different peak broadenings of asymmetric reflections due to edge dislocations were observed for AlN and GaN.

X-ray diffraction solutions to heteroepitaxial growth problems

Modern X-ray diffraction equipment offers a wide choice of methods for understanding the problems involved in the heteroepitaxial growth of a wide range of materials. The basic double axis rocking curve continues to play a key role in the characterisation of heteroepitaxial strained layer structures. The strength of the technique arises from the ability to accurately simulate the diffraction process using the Takagi-Taupin formulation of dynamic theory. There is an increasing use of diffraction space mapping for the less perfect heteroepitaxial systems with large lattice mismatches and different crystal structures, e.g. superconductors, gallium nitride on sapphire. Detailed studies of the state of relaxation of pseudomorphic systems can be achieved using the triple crystal diffractometer. The triple axis diffractometer can also be used to measure the unit cell distortion in good quality non-pseudomorphic systems. Where layers are less perfect and where layers are very thin lower resolution diffraction space mapping can provide useful information with a large reduction in data collection time.

Fabrication and performance characteristics of a [formula omitted] multilayer grating for hard X-rays

We have fabricated and tested a lamella multilayer grating for the hard X-ray range with a grating period of 0.97 μm and a Ni C multilayer period of 4.0 nm. To obtain large size gratings the fabrication process included holographic lithography and ion-beam etching. The reflectivity measurements obtained using a triple-axis diffractometer have shown that the diffraction efficiency and the relative intensities of the diffracted orders strongly depend on the incident angle. A very encouraging result is the possibility to direct practically all diffracted energy to any one first order with total suppression of the other orders.

High-resolution X-ray characterization of periodically domain-inverted nonlinear optical crystals

A high-resolution triple-axis diffractometer has been used for the structural characterization of periodically domain-inverted nonlinear optical crystals of KTiOPO4 and LiNbO3. Striations have been revealed in high-strain-sensitivity multiple-crystal topographs of the domain-inverted regions of both these samples and these are dominated by orientation contrast. The combination of high-resolution reciprocal-space mapping and topography has shown that the extended diffraction streak in the q(210) direction for the domain-inverted LiNbO3 originates from the 'minutely misoriented structure' which is related to the original configuration of dislocations. The reason for the generation of the structural imperfections via the domain-inversion processing is interpreted in terms of the converse piezoelectric effect.

Diffraction Space Mapping of Heteroepitaxial Layers

Abstract The acceptance angle of the detector of a double axis diffractometer is designed such that all of the diffracted beam is recorded for a rocking curve. When this acceptance angle is reduced, as in the triple axis diffractometer, two dimensional diffraction data can be recorded. In the resulting diffraction space maps each diffraction feature has a shape and a position from which the unit cell dimensions of a heteroepitaxial layer can be derived as well as information about relative tilts, curvature, lattice parameter variations and defect densities. Applications of diffraction space mapping using high and low resolution optics are discussed

New Methods for the Accurate Comparison of Lattice Parameters

AbstractTwo new methods of comparison of lattice parameters are described. The first method uses a double crystal diffractometer, fitted with a specimen rotation stage. Bragg peak positions of a silicon reference and the specimen crystal are recorded for the crystals at 0 and rotated 180° about the diffraction vector. From the mean Bragg positions the lattice parameters can, in principle, be compared to parts in 106. The second method is a variant on the above, using a triple axis diffractometer. It uses a beam conditioner and monochromator to define the incident wavevector ko, and an analyser crystal to define the diffracted wave vector kh. Only the analyser motion must be accurate and stable to the arc second level. We present a detailed error analysis for the case where reference and specimen Bragg angles differ significantly. Peak location to a confidence level of 1 arc second permits absolute, traceable lattice parameter determination to several parts in 106.

A triple-axis Bonse–Hart camera used for high-resolution small-angle scattering

A triple-axis diffractometer has been constructed and optimized in our laboratory. It is used on an X-ray point source, using the principle which was pioneered by Bonse and Hart 25 years ago. A triple-reflection channel-cut Ge crystal is used as monochromator and the same as analyser. The width of the direct beam is about FWHM = 17′′ for Cu Kα radiation. Owing to the low background, the stability of the mechanics and the two triple Ge reflections, a signal-to-noise ratio of 107 has been achieved between the direct beam and the parasitic scattering without sample. These characteristics allow routine measurement of scattering to be performed for Bragg spacings up to 6000 Å for typical colloidal samples in semilinear collimation.

Structural uniformity of multilayered tungsten-carbon Bragg reflectors prepared by rf magnetron sputtering

Large area W-C multilayered films used as Bragg reflectors for SR in soft and hard x-ray regions are fabricated using alternate sputter deposition. The structure uniformity of these films is examined by our newly designed triple-axis diffractometer for large area x-ray diffraction topography using SR. The reflectivity of the films agrees well with the calculations which include film surface roughness and interfacial roughness. The diffraction topograph is almost the same as the image of the incident SR beam. The multilayered film examined is uniform in layer period within 2.6% over the whole 70×60-mm2 area of the multilayered film surface, and the layer period deviation across the substrate is within 0.1 nm.

Test of annealed Czochralski grown silicon crystals as X-ray diffraction elements with 145 keV synchrotron radiation

The X-ray diffraction properties of annealed Czochralski grown silicon single crystals have been studied on a triple axis diffractometer using 145 keV synchrotron radiation from the 30 keV critical energy wiggler at CHESS. The silicon crystals, containing approximately 20 ppm oxygen atoms, were annealed at 1200°C for 8 h in order to create a homogeneous distribution of defects. A 10 mm thick crystal produced a Laue diffraction rocking curve with a 4 arcsec wide plateau at 50% reflectivity, and a full width at half maximum of approximately 8 arcsec. The shape of the rocking curve could be reproduced by calculations based on Darwin's extinction theory, using a mosaic distribution determined from high resolution γ-ray rocking curves measured from the same crystal. The momentum transfer resolution function of the triple axis spectrometer using these deformed crystals as monochromator and analyzer was also measured. It was found to be enlarged by factors of 11 and 18 in the perpendicular and parallel directions, respectively, compared with the resolution using perfect crystals. This enlarged resolution element can be advantageous in diffuse scattering experiments.

Structural studies of Langmuir-Blodgett multilayers by means of soft X-ray diffraction

The specularly reflected intensity from cadmium arachidate multilayers has been measured as a function of incidence angle. The films were prepared by the Langmuir-Blodgett technique and ranged from three to 21 layers in thickness. Monochromatic synchrotron radiation of 1560 eV photon energy (wavelength 7.95 Å) was used in combination with a high vacuum compatible triple-axis diffractometer. The measured diffraction profiles were fitted with a theory based on the exact solution of the Fresnel-Bragg equations for multiple reflections including absorption. The optical parameters for the layers were taken from tabulated values, and the layers were constructed using a formulation similar to that employed previously by Pomerantz and Segmüller. The individual layer spacing as well as the total thickness of the film could be derived to within an accuracy of 1% or 1 Å (whichever is larger).

Investigations of asymptotic-Bragg and kinematical scattering from ion-implanted and other silicon samples using an X-ray triple-axis diffractometer

Investigations of asymptotic-Bragg and kinematical scattering from ion-implanted and other silicon samples using an X-ray triple-axis diffractometer

Lattice dynamics of BaO

The frequency-wave vector dependence of the normal modes of vibration have been measured for BaO at room temperature. A total of 99 phonons were examined in the high symmetry directions using coherent inelastic neutron scattering techniques on the triple axis diffractometer at the Missouri University Research Reactor. Very good fits to the data were possible, both with a normal shell model and with a three body force shell model. The normal shell model produced a slightly better fit but required a total of 15 adjustable parameters; the three body force shell model was fit with 8 adjustable parameters. The phonon density of states was calculated and used to determine the temperature dependence of the Debye Temperature.