Roman Pielaszek

Analysis of Short and Long Range Atomic Order in Nanocrystalline Diamonds with Application of Powder Diffractometry

Abstract Fundamental limitations, with respect to nanocrystalline materials, of the traditional elaboration of powder diffraction data like the Rietveld method are discussed. A tentative method of the analysis of powder diffraction patterns of nanocrystals based on the examination of the variation of lattice parameters calculated from individual Bragg lines (named the “apparent lattice parameter”, alp) is introduced. We examine the application of our methodology using theoretical diffraction patterns computed for models of nanocrystals with a perfect crystal lattice and for grains with a two-phase, core-shell structure. We use the method for the analysis of X-ray and neutron experimental diffraction data of nanocrystalline diamond powders of 4, 6 and 12 nm in diameter. The effects of an internal pressure and strain at the grain surface are discussed. The results are based on the dependence of the alp values on the diffraction vector Q and on the PDF analysis. It is shown, that the experimental results lend a strong support to the concept of a two-phase structure of nanocrystalline diamond.

High-pressure high-temperature in situ diffraction studies of nanocrystalline ceramic materials at HASYLAB

Abstract High-pressure in situ diffraction studies were performed up to 8 GPa in a cubic anvil cell MAX80 (Station F2.1) and up to 45 GPa in a Diamond Anvil Cell (DAC-Station F3 at HASYLAB, Hamburg). A series of nanocrystals of SiC with grain sizes ranging from 2 nm to several μm were examined in non-hydrostatic conditions by pressing pure powders. A new method of evaluation of powder diffraction data measured at high pressures is presented. This method is based on quantitative evaluation of asymmetry of Bragg reflections where each peak is described as a combination of two reflections of two similar crystallographic phases having different compressibilities. The measured changes of the lattice parameters calculated for split Bragg reflections were used for determination of the pressure gradient which occurs across the grain boundaries in the compressed materials. A model of the strain induced in compacts of pure powders under high pressures is proposed. The model accounts for the presence of two phases: a volume phase corresponds to cores of individual grains which are surrounded by a surface phase which is formed of free surfaces in loose powders and of grain boundaries in solids. Due to extreme hardening of the boundaries under non-hydrostatic pressure conditions, the effective pressure in the interior of the grains is much lower than the applied external pressure. It is suggested that additional ‘hardening’ of the grain boundaries results from the presence of dislocations which are generated at the surface of the grains. The actual gradient of the pressure depends on the size of the grains, and also on the method of synthesis of the materials.

High Pressure X-Ray Diffraction Studies on Nanocrystalline Materials

Application of the in situ high pressure powder diffraction technique for examination of specific structural properties of nanocrystals based on the experimental data of SiC nanocrystalline powders of 2–30 nm in diameter is presented. Limitations and capabilities of the experimental techniques themselves and methods of diffraction data elaboration applied to nanocrystals with very small dimensions (<30 nm) are discussed. It is shown that a unique value of the lattice parameter cannot be determined for such small crystals using a standard powder diffraction experiment. It is also shown that, due to the complex structure constituting a two-phase, core/surface shell system, no unique compressibility coefficient can satisfactorily describe the behaviour of nanocrystalline powders under pressure. We offer a tentative interpretation of the distribution of macro- and micro-strains in nanoparticles of different grain size.

Effect of pressure on synthesis of Pr-doped zirconia powders produced by microwave-driven hydrothermal reaction

A high-pressure microwave reactor was used to study the hydrothermal synthesis of zirconia powders doped with 1 mol % Pr. The synthesis was performed in the pressure range from 2 to 8 MPa corresponding to a temperature range from 215°C to 305°C. This technology permits a synthesis of nanopowders in short time not limited by thermal inertia of the vessel. Microwave heating permits to avoid contact of the reactants with heating elements, and is thus particularly well suited for synthesis of doped nanopowders in high purity conditions. A mixture of ZrO2 particles with tetragonal and monoclinic crystalline phases, about 15nm in size, was obtained. The p/T threshold of about 5-6MPa/265-280°C was necessary to obtain good quality of zirconia powder. A new method for quantitative description of grain-size distribution was applied, which is based on analysis of the fine structure of the X-ray diffraction line profiles. It permitted to follow separately the effect of synthesis conditions on the grain-size distribution of the monoclinic and tetragonal phases.

Sintering of Compacts from Nanocrystalline Diamonds Without Sintering Agent

Compacts of polycrystalline diamond were made in toroid-type high-pressure camera under the pressure of 8 GPa using temperatures between 800 to 2150°C without the use of additive components. Nanocrystalline commercial DALAN, and microcrystalline ASM diamond powders were used. The compacts were characterized by helium pycnometry, Vickers hardness measurements, X-ray diffraction and SEM methods. The starting and sintered nanocrystalline grain compacts were found to have strongly one-dimensionally disordered cubic modification. The nanocrystalline powder had a bimodal grain size distribution function as determined from X-ray diffraction data and ab initio intensity calculations performed with the use of Debye functions. It was found that neither the grain size nor one-dimensional disordering change under high-pressure high-temperature conditions. There is a general tendency in a decrease of density of compacts with increase in the sintering temperature what resulting partly from graphitization above 1000–1200°C. The main factor which determines the density of the diamond compacts is closed porosity. Typically, the nanocrystalline diamond compacts sintered from 30 sec. to 6 min. have densities around 90% of the theoretical value. Their Vickers microhardness is 24 GPa and less.

Structure analysis of nanocrystalline MgO aerogel prepared by sol-gel method

Wet gel obtained by sol-gel technique was dried in supercritical CO2 to prepare hydrated form of magnesium oxide. Calcination at 723 K under vacuum yielded nanocrystalline MgO aerogel. Structure studies were performed by X-ray diffraction, scanning and transmission electron microcopies. Electron microscopy images reveal rough, unfolded and ramified structure of solid skeleton. Specific surface area SBET was equal to 238 m2/g. X-ray pattern reveals the broadened diffraction lines of periclase, the only crystalline form of magnesium oxide. The gamma crystallite size distribution was determined using FW 5 4 / 5 1 M method proposed by R. Pielaszek. The obtained values of and σ (measure of polydispersity) of particle size parameters are equal to 6.5 nm and 1.8 nm, respectively, whereas the average crystallite size estimated by Williamson-Hall procedure was equal to 6.0 nm. The obtained at Rietveld refinement Rwp, and S fitting parameters equal to 6.62% and 1.77, respectively, seem to be satisfactory due to the nanosize of MgO crystallites and because of the presence of amorphous phase.

Grain Boundary Migration in Nanocrystalline Iron

In this study a series of 3D models for curved [100] grain boundaries (GBs) in pure α-iron have been constructed. Each model consisted of a spherical grain, with an initial size of about 9 nm, surrounded by a large single-crystal. Different orientations have been assigned to the grain and the matrix in order to obtain interfaces with misorientation angles in the range of 5-45 degrees in steps of 5 degrees. The molecular dynamics with Embedded Atom Method (EAM) potential have been performed for investigation of the temporal changes in GB migration and grain rotations at temperature of 1000 K. The relationship between GB misorientation and its mobility has been found. It was also discovered that the density of the material decreases with a reduction of GB area. The effect of a triple junction on the interface motion has been also studied by introducing a bi-crystal matrix instead of a singlecrystal one. The results are discussed in terms of grain growth investigations in nanometals.

Error Estimation in XRD Crystallite Size Measurements

Th effect of diffraction peak broadening is commonly used as a convenient tool for the grain size determination of fine crystalline powders. Quantitative analysis of the peak profile also allows the size distribution to be determined, providing complete Grain Size Distribution (GSD) curve. Among other things, the accuracy of the crystallite size (or GSD) measurements depends on the level of noise present in the experimental diffraction patterns. Particularly, GSD analysis relies on the resolution of two strongly correlated parameters: the average grain size and the dispersion of grain sizes σ. Both influence the diffraction profile being fitted in a similar way. Resolution of these quantities is then a very demanding task in terms of quality of the the experimental data. In this paper possible errors in GSD analysis arising from experimental noise present in diffraction patterns are estimated. It will be shown, that the dispersion of grain sizes a is more sensitive to the noise than the size . Photon flux (X-ray tube/synchrotron) needed for reliable evaluation of GSD will be estimated and a practical directions on optimal experimental setup given. A simple experssion for the standard deviations of the GSD parameters (i.e. dispersion of average grain size and dispersion of dispersion of the grain sizes) will be given as a function of the experimental noise level.

Nanopowder diffraction theory - : Line profile for polydispersive powders

One of the most general diffraction laws, the Debye equation, is rewritten for the special case of a crystalline materials. The Debye formula obtained for crystals has two components: structural and microstructural (diffraction line position and profile). An analytical expression for the diffraction line profile for polydispersive powders (particularly, nanopowders) with a Gamma Grain Size Distribution (GSD) is derived. The expression consists of elementary functions only and can readily replace standard functions, like Gaussian, Lorentzian or Pearson functions for diffraction peak fitting purposes. This allows for direct determination of Grain Size Distribution using standard fitting software.

Preparation of SiC-Diamond Nanocomposites

Compacts of composites SiC-diamond were made by infiltration of Si into nanocrystalline diamond powders in a toroid-type press under the pressure of 7.7 GPa at 1300 °C. In-situ high pressure diffraction studies of these processes were performed in MAX80 cubic anvil press at a pressure of 8.5 GPa in temperatures up to 1800°C in HASYLAB at DESY, Hamburg, Germany. Sintering was performed for (i) pure nanocrystalline diamond powders, (ii) a mixture of nanocrystalline powders of diamond and nanocrystalline SiC, (iii) a mixture of nanocrystalline diamond with microcrystalline Si powders and (iv) compacts of nanocrystalline diamond infiltrated by Si. The SiC-diamond composites obtained by infiltration of Si have best physical properties: hardness similar to conventional diamond compacts (approximately 50 GPa), highest density 3.35 g cm -3 and uniform nanocrystalline microstructure.