Lyndon D. Mitchell

Geometrical parameterization of the crystal chemistry of P63/m apatites : comparison with experimental data and ab initio results

Experimental structure refinements and ab initio simulation results for 18 published, fully ordered P6(3)/m (A;{\rm I}_4)(A;{\rm II}_6)(BO4)6X2 apatite end-member compositions have been analyzed in terms of a geometric crystal-chemical model that allows the prediction of unit-cell parameters (a and c) and all atom coordinates. To an accuracy of +/- 0.025 A, the magnitude of c was reproduced from crystal-chemical parameters characterizing chains of ...-A(II)-O3-B-O3-A(II)-... atoms, whereas that of a was determined from those describing (A(I)O6)-(BO4) polyhedral arrangements. The c/a ratio could be predicted to +/-0.2% using multi-variable functions based on geometric crystal-chemical model predictions, but could not be ascribed to the adjustment of a single crystal-chemical parameter. The correlations observed between algebraically independent crystal-chemical parameters representing the main observed polyhedral distortions reveal them as the minimum-energy solution to accommodate misfit components within this flexible structure type. For materials with given composition, good agreement (within +/- 0.5-2.0%) of ab initio crystal-chemical parameters was observed with only those from single-crystal refinements with R </= 4.0%. Agreement with single-crystal work with R > 4.0% was not as good, while the scatter with those from Rietveld refinements was considerable. Accordingly, ab initio cell data, atomic coordinates and crystal-chemical parameters were reported here for the following compositions awaiting experimental work: (Zn,Hg)10(PO4)6(Cl,F)2, (Ca,Cd)10(VO4)6Cl2 and (Ca,Pb,Cd)10(CrO4)6Cl2.

Quantitative Rietveld analysis of hydrated cementitious systems

A study examining the feasibility, and possible necessity, of using transmission data from capillary mounted samples for quantitative analysis of hydrated cement systems was conducted. In order to obtain true quantitative results, the amorphous contents were determined by the addition of an internal standard. The amorphous content of the starting calcium trisilicate was found to be approximately 21-22 wt%, in close agreement with previously published results. The study revealed that the spherical harmonics preferential orientation correction may not be reliable with un-micronized hydrated cement materials in reflection geometry, as chemically unreasonable progressions in portlandite content with time were observed. The data obtained from capillary measurements, however, exhibited little or no preferential orientation, and appeared to produce the progression of phase contents expected from the reaction. The use of capillaries would appear to be justified in some circumstances to obtain reliable quantitative results from hydrated cementitious materials. In this particular system, a significant fraction of calcium carbonate was present as aragonite, as well as the more usual calcite. INTRODUCTION The use of Rietveld refinement for quantitative phase analysis was first described in detail in 1987 (1, 2). Its routine application to the quantification of complex mixtures such as ordinary Portland cement is a much more recent development, largely due to the introduction of innovations such as convolution-based peak synthesis and fundamental parameters into Rietveld software (3). The reduction in the number of parameters required to describe the peaks of each phase makes such an analysis fairly routine with rapid acceptance within the commercial cement community for quality control (4). Rietveld analysis also affords the opportunity to quantify the presence of amorphous materials, both within unhydrated and hydrated cements (5, 6). This is achieved by the addition of a known 345

Geometrical parameterization of the crystal chemistry of P63/m apatite. II. Precision, accuracy and numerical stability of the crystal-chemical Rietveld refinement

A script developed for crystal-chemical Rietveld refinement of P63/m apatite with TOPAS is implemented in parallel with standard structure refinement. Least-squares standard uncertainty (s.u.) values for directly extracted crystalchemical parameters are nearly an order of magnitude lower than those obtained indirectly by analysis of atom coordinates derived by standard Rietveld refinement. This amazing finding originates partly in the reduction of the number of refinement parameters from 21 to 17 and partly in the fact that cell data now derive from crystal-chemical parameters instead of vice versa. Great precision and accuracy otherwise funneled into unit-cell parameters is then more distributed among mostly crystal-chemical distance parameters. The least-squares s.u. values are supported by analysis of numerous refinements of the same experimental data with added artificial intensity noise. Structural parameters from single-crystal results agree better with those extracted by crystal-chemical refinement. On the basis of singular value decomposition analyses performed using the program SVDdiagnostic [Mercier et al. (2006). J. Appl. Cryst. 39, 458‐465], crystal-chemical and standard Rietveld refinements are shown to have similar numerical stability. Crystal-chemical parameters extracted by direct Rietveld refinement, therefore, are more precise than, more accurate than and numerically as reliable as those derived from analysis of regular crystallographic refinement of the same data.

Sucrose synthesis of nanoparticulate alumina

γ -Al2O3 is frequently an unwanted intermediate phase in the conversion of nanoparticulate amorphous alumina into nanoparticulate α-Al2O3. γ -Al2O3 has a relatively disordered structure, but usually requires temperatures in the order of 1100 ◦C to transform completely to the stable α-Al2O3 phase [2]. Dispersion of cations in a polymer matrix has been widely used as a “chimie douce” method for the production of oxide materials at low temperatures. The “Pechini” process, where citric acid and ethylene glycol are co-polymerized to form a resin is a particularly common variant [3]. A highly acidic sucrose solution can self-polymerize or cross-link with polyvinyl alcohol (PVA) to form a heavier and more 3 dimensional resin [4]. The charred polymer also acts as a fuel during calcination, raising the local temperature briefly to much higher temperatures than the equilibrium temperature in the furnace. The extent of cation dispersion in a matrix has been seen to affect phase composition and crystallite size in other systems [3]. Consequently a study was undertaken to ascertain the effect of drastically increasing the dispersion of Al3+ cations in the matrix by increasing the sucrose content. This would be expected to increase the surface area of the material, but as the sucrose : Al3+ molar ratio is greater than 18 : 1, calcining at 600 ◦C should still produce α-Al2O3 according to the hypothesis of Das et al. [1]. The resin was produced by adding 250 ml of 10 M sucrose solution acidified to a pH of approximately 1 with nitric acid, to 3.75 g of Al(NO3)3 · 9H2O. This formulation yielded a 250 : 1 molar ratio. The intimate mixture was caramelized on a hot plate at approximately 250 ◦C to reduce the aqueous solution to a thick syrup. Afterwards, it was placed in an air-circulating oven at 200 ◦C for 18 h resulting in a dehydrated charred resin. The resulting carbon-rich precursor was calcined in a muffle furnace at 600 ◦C for 24 h to produce the aluminum oxide material. Samples of this material were further calcined in a zirconia crucible in air at temperatures of 1050, 1150 and 1250 ◦C to examine the ease of α-Al2O3 formation from this very high surface area γ -Al2O3. X-ray diffraction data were obtained using a Bruker D8 diffractometer equipped with a HISTAR 2dimensional area detector at a sample-detector distance of 15.3 cm. The tube angle was fixed at 10◦ using a 1 mm diameter snout collimator, and frames taken using Cu Kα radiation at detector angles of 15, 30 and 45◦ for 30 min durations. The samples were mounted on a quartz zero background holder. 1-D powder patterns were obtained by integrating the 2-D data across a fixed chi range, and merging the three resulting patterns into one. The instrument broadening function was determined by obtaining frames from the NIST 660a LaB6 standard, and crystallite size obtained by peak fitting with the Bruker TOPAS software [5]. Scanning electron microscope (SEM) micrographs were taken of the alumina using a Cambridge Stereoscan 250. Samples were prepared with carbon adhesives on aluminum stubs, and then sputter-coated with gold. The surface area values of the powders were obtained using BET analysis with nitrogen gas as the absorbate. A Quantachrome Quantasorb system was used for the sorption measurements. After calcination of the charred precursor at 600 ◦C, the material obtained was a white, fluffy powder with a very low density. On examination of this material by SEM, a foil-like microstructure (Fig. 1) was observed. This microstructure probably resulted from preferential growth around the resin pore surfaces. Attempts to resolve the individual particles with a high resolution Field emission gun (FEG) SEM tentatively suggested a particle size of 10–20 nm, however it was not possible to obtain well-resolved images due to charging of the sample. The surface area of the material was found to be approximately 290 m2/g, as opposed to the 194 m2/g reported by Das et al. [1]. Given the greater organic content in this precursor, this increase was not unexpected, but may be of interest given the use of γ -Al2O3 as a catalyst support. X-ray diffraction of the 600 ◦C material yielded a poor crystalline pattern (Fig. 2), which could be assigned as γ -Al2O3. Firing at 1050 ◦C for 30 min yielded a more ordered γ -Al2O3 pattern, while firing for 60 min gave rise to a number of spots corresponding to a few crystallites of α-Al2O3. The significance of spots in a frame is discussed below. Increasing the temperature to 1150 ◦C for 60 min led to the formation of a two phase mixture of γ -Al2O3 and nanocrystalline α-Al2O3 powder with a 17.5 nm crystallite size. Firing at 1250 ◦C for 60 min led to the formation of 25 nm α-Al2O3 with β-Al2O3 present as a minor phase. β-Al2O3 does not exist as a pure alumina polymorph [6], so the presence of β-Al2O3 could be due to trace sodium impurities, producing phases such as NaAl11O17.

The Maturity Approach for Predicting Different Properties of High-Performance Concrete

This paper presents a study of the maturity method for predicting the development of key properties of high-performance concrete, such as compressive strength, splitting tensile strength, modulus of elasticity, and level of cement hydration. The derivation of the maturity method is explained and experimental evidence, collected under different temperature conditions, is presented and discussed. The results were used to study the activation energy, which is a governing parameter of the Arrhenius maturity formulation, for predicting the key properties of high-performance concrete. Recognizing the need for a more accurate determination of activation energy for each concrete property, a new practical approach for calculating the Arrhenius maturity index is proposed.

Problem Solving with the TOPAS Macro Language: Corrections and Constraints in Simulated Annealing and Rietveld Refinement

The TOPAS macro language can be a powerful tool for increasing the capabilities of X-ray powder diffraction analysis. New corrections and constraints can be implemented without altering the programs code, allowing for experimentation with new ideas and approaches. Examples are given, exposing the power and flexibility of the macro language to help solving problems with a few lines of code. The use of simulated annealing for structure solution of an organic material from data exhibiting preferential orientation is one example. Another one is about extraction of useful structural information in Rietveld refinement of natural hydrotalcite-group minerals, a problematic case that would normally be regarded as over-parameterized for the data available.

SVDdiagnostic, a program to diagnose numerical conditioning of Rietveld refinements

Singular value decomposition (SVD) of the matrix of normal equations is used here both passively to assess numerical stability, and actively to troubleshoot problem refinements, singular or not. Such systems can then either be cured by rank reduction or solved with arbitrary-precision arithmetic carrying a number of digits known to be sufficient. SVD analysis provides objective information about such required rank reduction or number of digits. Pre-conditioning of the normal matrix is seen to decrease its condition number by many orders of magnitude in actual cases, illustrating its great practical usefulness. The methods and tools developed here have general applicability to diagnose problems with least squares, in particular ill-conditioned Rietveld refinements. Crystal-chemical and standard refinements described in the work by Mercier et al. [J. Appl. Cryst. (2006), 39. 369-375] are shown to have similar numerical stability. The program SVDdiagnostic is freely available at http://www.tothcanada.com.

D019 SIMULTANEOUS REFINEMENTS WITH COMPLEX COMPOSITIONAL CONSTRAINTS—EXAMPLE OF SINGULAR VALUE DECOMPOSITION TO DIAGNOSE POOR MATRIX CONDITIONING

Modern Rietveld codes afford the opportunity to set up extremely complex refinements with multiple arithmetic constraints. It is sometimes difficult to diagnose when particular variables are causing instability in the refinement, such effects are not always obvious from examining the output ESDs. A new program has been developed called SVDdiagnostic [1,2] that examines the matrix of a Rietveld refinement using Singular Value Decomposition techniques, and outputs two diagnostics for the refinement’s matrix inversion. An example of the use of this approach to diagnose problems in a particularly complex Rietveld refinement is described.