Parametric Rietveld Refinement Research Articles

Parametrics XRD Rietveld refinements of mechanically activated solid-state reactions in iron-brass alloy

The process of diffusion at the atomic level plays an important role in the formation of new phases. Iron-based Fe9Cu2Zn alloy was investigated by high-energy ball milling of elemental α-Fe powders and Cu7Zn2 brass alloy. The evolutions of structural, microstructural and mechanical properties of the obtained powders were studied by means of X-ray diffraction analysis using the parametric Rietveld refinement method which leads to higher precision of refined parameters. The solid state reaction pathways, occurring after 1 h of milling of (70 wt% α-Fe + 30 wt% Cu7Zn2) powder mixture, take place via demixing of metastable cubic complex γ-Cu5Zn8 in addition to cfc α-Cu7Zn2 and α-Cu25Zn8 phases and subsequently leading to the formation of new stable nanometric phases, namely cubic complex Γ-Fe4Zn9 and trigonal α-Cu3Zn with a stable grain size and good mechanical properties.

Dependence of magnetic properties with structural/microstructural parameters of ball-milled Fe15Co2P3 powder mixture

This research work aims to investigate the mechanical alloying of Fe15Co2P3 powder mixture in terms of phases’ formation, microstructural parameters, and magnetic properties as function of milling time. Parametric Rietveld refinement method, of the obtained X-ray patterns, was performed for qualitative and quantitative phase analysis alongside the determination of structural, microstructural, and mechanical properties. The ball-milled powder mixture crystallized within the face-centered cubic α-Fe(P) solid solution in equilibrium with Co75Fe25 phase. The crystallite size decreases reaching 100 and 200 nm respectively after 3 h of milling. The highest values of the dislocation density, microstrain, and stored energy are registered for the α-Fe(P) solid solution. The studied mechanical properties manifest the brittle nature of the α-Fe(P) solid solution compared to the Co75Fe25 phase. The squareness ratio Mr/Ms and the coercivity values of the milled powders increase with increasing milling time and reach steady state after 2 h. The hysteresis loss energy and maximum permeability reach minimal values of 45 × 10−4 W/m3 and 49 × 10−3 H/m respectively, after 1 h of milling at the opposite of the switching field distribution. The obtained results demonstrate the formation of nanostructured Fe15Co2P3 ternary alloy with optimum characteristics as promising candidate for diverse applications primarily in the biomedical field for diagnostics and therapeutics such as magnetic hyperthermia and vector probes for future imaging technologies.

In-Situ Investigation of the Oxidation Behaviour of Chemical Vapour Deposited Zr(C,N) Hard Coatings Using Synchrotron X-ray Diffraction

The oxidation behaviour of chemical vapour deposited ZrN, ZrC and ZrCN coatings was investigated using in-situ synchrotron X-ray diffraction (XRD). To obtain a precise analysis of the temperature–dependent phase evolution during oxidation, coating powders were annealed in air between 100 °C and 1000 °C. Simultaneously, 2D XRD patterns were recorded in ~2 °C increments, which were subsequently evaluated using parametric Rietveld refinement. The results were correlated with differential scanning calorimetry and thermogravimetric analysis measurements, to further illuminate the oxidation mechanism of each coating system. ZrCN exhibited the highest oxidation onset temperature, followed by ZrC and ZrN. Furthermore, ZrCN was completely oxidised at a temperature of ~720 °C, which was ~50–70 °C higher than for ZrN and ZrC. The in-situ experiments revealed a similar oxidation sequence for all three samples: first, tetragonal and/or cubic (c/t)–ZrO2 is formed, which subsequently transforms into the more stable monoclinic (m)–ZrO2 phase. ZrCN and ZrC showed a higher c/t–ZrO2 fraction than the ZrN sample at 1000 °C. Furthermore, ex-situ Raman and XRD investigations of the oxidised samples revealed the ongoing c/t–ZrO2 → m–ZrO2 phase transformation during cooling.

Revealing phase boundaries by weighted parametric structural refinement.

Parametric Rietveld refinement from powder diffraction data has been utilized in a variety of situations to understand structural phase transitions of materials in situ. However, when analysing data from lower-resolution two-dimensional detectors or from samples with overlapping Bragg peaks, such transitions become difficult to observe. In this study, a weighted parametric method isdemonstrated whereby the scale factor is restrained via an inverse tan function, making the phase boundary composition a refinable parameter. This is demonstrated using compositionally graded samples within the lead-free piezoelectric (BiFeO3)x(Bi0.5K0.5TiO3)y(Bi0.5Na0.5TiO3)1-x-y and (Bi0.5Na0.5TiO3)x(BaTiO3)1-x systems. This has proven to be an effective method for diffraction experiments with relatively low resolution, weak peak splitting or compositionally complex multiphase samples.

The thermoresponsive behaviour of Nasicon-like CuTi2(PO4)3

The synthesis and thermoresponsive behaviour of high purity CuTi2(PO4)3 (CTP) was examined while heating in air and nitrogen at atmospheric pressure. It is known that a spontaneous redox reaction involving the Cu+ cations that are contained in the Ti2(PO4)3− crystal structure converts the CTP phase to the related Cu0.5Ti2(PO4)3 (CTP2) phase when heated in air. However, the extent of this reaction and the effect that it has on the CTP crystal structure has not been established. Using in situ powder X-ray diffraction it was found that during heating in air, the migration of Cu+ cations out of the Ti2(PO4)3− crystal lattice results in the growth of a CuO phase. To quantify the extent of the migration of the Cu+ cations out of the Ti2(PO4)3− crystal lattice, quantitative phase analysis was used to show that the redox reaction converts the CTP phase to the CTP2 phase in the temperature region from 450 to 530 °C. When increasing the temperature above 530 °C it was found that the CTP phase was spontaneously regenerated forming a high temperature form of the parent CTP phase. Previously heat-treated CTP samples were subjected to further heat treatments and produced different quantitative phase behaviour when compared to a fresh CTP sample. Most significantly it was found that the CTP2 phase was prevalent over a broader temperature range. Comparison of the high temperature and parent CTP phases showed differences between the Cu+ site occupancies. Further heat treatment under nitrogen suppressed the redox reaction and stabilized the CTP phase. This allowed the calculation of the coefficients of thermal expansion (CTE) of CTP across a broad temperature range (30–900 °C). Analysis of the CTP lattice constants via Parametric Rietveld refinement showed that the compound exhibited moderate thermal expansion up to 900 °C.

Rietveld analysis of computed tomography and its application to methanol to olefin reactor beds

This article reports the creation of tomographic reconstructions giving three-dimensional data on the distribution of various structural features for SAPO-34 zeolite catalyst beds used in the commercially important methanol to olefin conversion process. The data were processed using parametric Rietveld refinement to treat entire slices of the tomograph as single refined data sets, allowing extraction of real structural parameters from all voxels of the reconstruction. This has the advantage over more traditional methods of X-ray diffraction computed tomography using peak intensities, that the structural parameters are independent of the intensity, meaning that information can still be extracted from poor data sets: an example is shown where part of the sample was no longer in the beam during data collection. Reconstructions using several structural parameters are presented and the results compared. Analysis of the variation of the catalystcaxis (linked to the degree of deactivation in earlier work) shows small but significant three-dimensional variations in the degree of deactivation with patterns which depend on the silicon content of the catalyst. Average data for the tomographic slices compare well with the results of earlieroperandotwo-dimensional reactor scanning experiments.

Parametric Rietveld refinement of coexisting disordered clay minerals

AbstractX-ray diffraction is one of the most effective tools for the characterization of the stacking defects which occur frequently in clay minerals. Modelling of the diffraction patterns of oriented mounts is often used for obtaining structural information about the nature of stacking order. Manual matching of calculated and observed patterns is time consuming and the results are user dependent and especially troublesome if a consistent model of the same mineral measured under different conditions needs to be obtained. It was shown recently that the Rietveld method could be applied successfully for the evaluation of the X-ray patterns of oriented mounts. Nevertheless, this automatic refinement procedure can also lead to inconsistent results if independent refinements are performed that describe the same sample measured under different conditions. One way to solve this problem is the application of parametric Rietveld refinement. For this approach a set of different measurements of the same sample was collected and fitted in one combined refinement by the connection of the structural models via external parameters. These conditions may involve different pre-treatments (e.g. different intercalations), different temperatures or relative humidities and/or different experimental setup (powder or oriented samples). All patterns were fitted in one overall refinement process by the BGMN software.This approach was demonstrated on a mixture of two disordered reference materials and on a set of geological samples. Two different states for each sample were refined independently and parametrically and it was shown that this approach leads to consistent results, saves computation time and may even resolve small structural differences.

Parametric Rietveld refinement applied to dehydration of sodium naproxen

The identification of the hydration and dehydration transformations of drugs is vital to establish stable pharmaceutical components. Our aim is to monitor the kinetics of hydration and dehydration processes in pharmaceutical solids, and to relate these to the molecular-level crystal structures. One of the primary tools to achieve this is parametric Rietveld refinement. The dehydration of two dihydrate polymorphs of the non-steroidal anti-inflammatory drug (NSAID) sodium naproxen was monitored using synchrotron powder X-ray diffraction measurements at Beamline I711, MAX IV Laboratory, Lund University. Diffraction patterns were measured in the range 300-400 K at 1 K increments. Both polymorphs dehydrate to form identical monohydrate then anhydrous phases. Independent Rietveld refinements were initially performed for each unique phase in order to establish initial values for the parametric refinement. The refinements were performed using TOPAS-Academic [1]. The structures are molecular and both dihydrate polymorphs display pseudosymmetry, thereby requiring an extensive set of restraints. One of the key advantages of the parametric Rietveld refinement is the possibility to introduce algebraic equations that describe the evolution of various parameters [2]. The kinetics of the dehydration processes were monitored using a sigmoid function applied to the scale factors of the various phases (see Figure). The evolution of the unit-cell parameters and atomic displacement parameters were also treated parametrically, and the influence of using multiple coordinate sets (one model per temperature) or a single common coordinate set for each phase was examined. One dihydrate polymorph shows a smooth and continuous transition to the monohydrate, whereas the other polymorph shows an abrupt transition. These differences are linked to the existence of topotactic or non-topotactic chemical transformations between the dihydrate polymorphs and the monohydrate phase.

Processing Extremely Large Powder Diffraction Datasets Using The Rietveld Method

Modern in situ synchrotron powder diffraction experiments can produce massive volumes of data which are of suitable quality for real structural information to be extracted. Parametric Rietveld refinement (Stinton, 2007) is an ideal method for dealing with such datasets as a huge number of diffraction patterns can be processed in parallel while the number of refined parameters is reduced by linking between scans. The time saving compared to earlier sequential methods of refinement using batch files is very significant with processing times being reduced from weeks to a few hours. The stability of the parametric method allows not only extraction of information from data with very weak trends but also refinement of entire slices of a tomographic map including the regions with zero diffraction. The power of the technique will be illustrated by examples from reactor scanning experiments with high time resolution (Wragg, 2012, 2013) as well as more conventional in situ powder diffraction and operando experiments combining diffraction with mass spectrometry. The extraction of structural information from complete tomographic datasets and reconstructions with real structural parameters will also be demonstrated. The figure shows time and space resolved c-axis data for the SAPO-34 catalyst during methanol to olefin conversion, together with mass spectrometry data collected during the experiment.

Thermoresponsive studies of porous and non-porous borophosphates.

In this work we present the synthesis and structure-property investigation of anhydrous low porosity borophsophates [1] BPO4 and porous (NH4)0.5M1.25(H2O)2)(BP2O8)(H2O)0.5 M = Co (II), Mn (II) and NH4Fe[BP2O8(OH)] phases. Cristobalite-type BPO4 crystallizes in the tetragonal lattice, space group I-4 (No. 82) [2]. Variable-Temperature Powder X-ray diffraction (VT-PXRD) patterns for these material were analysed by the sequential and parametric Rietveld refinement [3] protocols. Both methods were used to determine the temperature dependency of the lattice parameters and linear thermal expansion coefficient. Whereas the lattice parameters were refined freely in the sequential method, the individual cell parameters were described using an empirically derived function in the parametric method. Both refinement protocols reveal significant anisotropy along the a- and c- axis as a function of temperature, with thermal expansion coefficients of 10.6 x10-6 /0C and 2.83 x10-6 /0C, respectively. Structural changes accompanying this thermoresponsive behaviour will be discussed, including the variation of the interatomic distances and P-O-B (inter-polyhedral angle, figure 1) with temperature. The open framework (NH4)0.5M1.25(H2O)2)(BP2O8)(H2O)0.5 M = Co(II) (1a), Mn(II) (1b) and NH4Fe[BP2O8(OH)] (2) phases were synthesized under mild hydrothermal methods at 1800C. The crystal structure of the isostructural (1a) and (1b) phases were refined in the hexagonal lattice, space group P65 (no. 170) and compound (2) in the monoclinic lattice, space group P21/c (no.14). Both (1a) and (1b) phases consists of NH4+ and H2O molecules located within the helical channels running along the [001] direction with compound (2) consisting exclusively of NH4+ molecules located within the helical channels running along the [100] direction. Thermoresponsive investigation conducted by TGA analysis reveal a five, four and three step mass loss process for compounds (1a), (1b) and (2) respectively, with the final step observed at 500-7000C range. Preliminary VT-PXRD results of these compounds will also be presented.

In situ monitoring of hydration and dehydration in pharmaceutical solids

This talk will describe a multi-technique study of hydration and dehydration in pharmaceutical solids, using sodium naproxen as a case study. The aim of the work is to establish molecular-level structural understanding of the chemical changes that take place in the solid state as a function of temperature and relative humidity. Dynamic vapour sorption (DVS) analysis on the anhydrous compound carried out as a function of temperature provides a preliminary overview of the solid-form landscape and identifies static conditions to obtain four different hydrate forms [1]. Differences in the sorption and desorption cycles indicates the existence of a polymorphic dihydrate, and the two polymorphs show significant differences in their dehydration behaviour. Crystal structures are established for all phases in the system using either single-crystal or powder X-ray diffraction data, supplemented by dispersion-corrected density functional theory (DFT-D) calculations. The hydration and dehydration processes are monitored by powder X-ray diffraction (PXRD), as a function of relative humidity and temperature, and by variable-temperature solid-state 13C and 23Na NMR. Synchrotron PXRD is applied to the two dihydrate polymorphs to monitor the dehydration processes in approximately real time. The kinetic and structural details of dehydration are established by applying parametric Rietveld refinement [2] to the synchrotron data. This approach adds a structural picture to the kinetic processes. The PXRD studies indicate an essentially continuous dehydration pathway from one of the dihydrate polymorphs to the monohydrate, but a stepped dehydration pathway for the other dihydrate polymorph. The different mechanisms are linked to different degrees of structural similarity, and in particular to the existence of topotactic or non-topotactic transformations between the dihydrate polymorphs and the unique monohydrate and anhydrate phases.

Possibilities and limitations of parametric Rietveld refinement on high pressure data: The case study of LaFeO3

Parametric Rietveld refinement is a powerful technique to apply directly physical or empirical equations to the refinement of in situ powder diffraction data. In order to investigate the possibilities and limitations of parametric Rietveld refinements for high pressure data four competitive crystallographic approaches were used to carry out a full structural investigation of the orthoferrite LaFeO3 (Pbnm at ambient conditions) under high pressure up to 47 GPa. Approach A with traditional Rietveld refinement using atomic coordinates, Approach B where the Rietveld refinement was done by using the rigid body method, Approach C where symmetry modes were used and Approach D where the newly developed method of the rotational symmetry mode description for a rigid body was used. For all approaches sequential as well as parametric refinements were carried out, confirming a second order phase transition of LaFeO3 to a higher symmetric phase (space group Ibmm) at around 21.1 GPa and an isostructural first order phase transition at around 38 GPa.

The fast Z-scan method for studying working catalytic reactors with high energy X-ray diffraction: ZSM-5 in the methanol to gasoline process

The methanol to gasoline process over the zeolite catalyst ZSM-5 in a lab-sized reactor bed (4 mm diameter) has been studied in operando with high energy synchrotron X-ray diffraction. The fast z-scan method was used, scanning the reactor repeatedly and at speed through the X-ray beam. The X-ray diffraction data were processed using high throughput parametric Rietveld refinement to obtain real structural parameters. The diffraction data show only very subtle changes during the process and this allows us to demonstrate the combination of very large data volumes with parametric Rietveld methods to study weak features of the data. The different possible data treatment methodologies are discussed in detail and their effects on the results obtained are demonstrated. The trends in unit cell volume, zeolite channel occupancy and crystallite strain indicate that more or larger reaction intermediates are present close to the reactor outlet.

A time-resolved powder diffraction study of in-situ photodimerization kinetics of 9-methylanthracene using a CCD area detector and parametric Rietveld refinement

The [4π + 4π] photodimerization process of the 9-substituted anthracene derivative crystalline 9-methylanthracene (9-MA) was investigated using time-resolved X-ray powder diffraction. The study was carried out in-situ using a CCD area detector. Sequential and parametric Rietveld refinement was applied for quantitative phase analysis. The results of traditional sequential Rietveld refinement showed that the evolution of the dimerization process can be described using the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model. The parameters of the JMAK equation were obtained successfully by parametric Rietveld refinement and suggest that the reaction follows heterogeneous nucleation and one-dimensional growth with a decreasing nucleation rate.

Automated parametric Rietveld refinement: Applications in reaction kinetics and in the extraction of microstructural information

Two applications of parametric Rietveld refinement employing a newly developed robust computer program are presented. The first application focuses on the parametric kinetic analysis of the reactions involving phase transitions of various polymorphic forms of copper phthalocyanine pigments. The second application concerns the parameterization of crystallite size with respect to experimental temperature. XRPD data for nanocrystalline titanium dioxide measured in dependence on temperature are used in this case study. Both the applications were realized with the help of the developed program in combination with the launch mode of topas® software.

Giant Deuteron Migration During the Isosymmetric Phase Transition in Deuterated 3,5‐Pyridinedicarboxylic Acid

Deuterated 3,5-pyridinedicarboxylic acid exhibits reversible temperature-induced deuteron migration of a magnitude unprecedented in this class of compounds. We used a combination of variable-temperature powder and single-crystal neutron diffraction and density functional theory (DFT)-based computational methods to elucidate the origin of this remarkable behaviour. Single-crystal neutron diffraction shows that between 15 and 300 K, the deuteron moves by 0.32(1) Å and the structure changes from a low-temperature N-D···O form to a high-temperature N···D-O form. Variable-temperature powder neutron-diffraction data, which was fitted by using parametric Rietveld refinement, show that this deuteron migration is due to an isosymmetric, first-order phase transition that occurs by growth of the daughter phase in the parent-phase matrix. Similar phase transitions are observed in two selectively deuterated forms of the material. DFT calculations demonstrate the role of phonons and show that vibrational free-energy stabilisation, which plays a key role in the observed structural phase transitions, is more pronounced in the fully deuterated material and proportional to the mass of the molecule, that is, the level of deuteration. This is consistent with our experimental work, for which distinct crystallographic phase transitions were clearly observed for the three deuterated systems, but not for the fully protonated material.

A case study of parameterized Rietveld refinement:The structural phase transition of CuInSe2

Abstract The ferroelastic high temperature structural phase transition of CuInSe2, from tetragonal chalcopyrite to cubic sphalerite structure type has been reinvestigated in detail by sequential and parametric Rietveld refinement using in-situ high energy synchrotron powder diffraction data. For the description of the structural changes, a symmetry mode based approach is used. The temperature dependence of the isotropic displacement parameters and of all symmetry modes influencing lattice parameters, atomic coordinates, and occupancies, has been modeled with a phenomenological power law model according to the Lanädau theory in order to get direct access to the temperature dependence of the order parameter leading to a more detailed understanding of the nature of the phase transition. The results of this study reveal superior statistics and much higher stability of parametric as compared to sequential Rietveld refinement, offering exciting possibilities in the analysis of ferroelastic phase transitions.

Direct Access to the Order Parameter: Parameterized Symmetry Modes and Rigid Body Movements as a Function of Temperature

The first order phase transition of CsFeO2 was investigated using synchrotron powder diffraction data as a function of temperature. Two alternative approaches were used to describe the deviation of the framework crystal structure relative to the high-symmetry parent structure: symmetry (a.k.a. distortion) modes and polyhedral-tilt parameters. In both cases, the relevant parameters were refined as a function of temperature using the method of parametric Rietveld refinement. We demonstrate a semi-automated and generally applicable method for the determination of spontaneous lattice strain variations, order parameters and power-law exponents as derived from Landau theory.

Parametric Rietveld refinement for the evaluation of powder diffraction patterns collected as a function of pressure

Under the assumption that the structural parameters of a crystalline phase change `smoothly' with increasing pressure, the evolution of the parameters can be parameterized as a function of pressure using continuous monotonic functions. Four different approaches to determine the structural evolution of As2O5with increasing pressure from a set of powder diffraction patterns collected over the pressure range from 2.5 to 19.5 GPa have been investigated. Approach (A) was the common sequential refinement of atomic coordinates with restraints on the geometry and was compared with three parameterization approaches. Approach (B) used direct parameterization by low-order polynomials of each crystallographically distinct atomic coordinate, (C) described the atoms of the asymmetric unit as a rigid body and allowed the internal degrees of freedom of the rigid body to vary with the change in pressure using rigid unit modes, and (D) described the crystal structure as a distortion of the higher-symmetry structure of As2O5(which is here also a high-temperature phase) by using symmetry-adapted distortion modes. Approach (D) offers the possibility to directly introduce an order parameter into Rietveld refinement through an empirical power law derived from Landau theory and thus to obtain the value of the critical exponent. In contrast, the rigid-body approach did not fit the data as well. All parameterizations greatly reduce the number of required parameters.

Kinetic analysis of the phase transformation from α- to β-copper phthalocyanine: A case study for sequential and parametric Rietveld refinements

The solid-state phase transformation from α- to β-copper phthalocyanine, using isothermal data obtained at T=250 °C and nonisothermal data obtained in the temperature range of 30 °C≤T≤330 °C with a constant heating rate of 1.67 °/min, was investigated by sequential and parametric full quantitative Rietveld analyses. Results obtained in this study show that the parametric Rietveld refinement technique is most suitable and applicable for kinetic studies of isothermal powder diffraction data. On the other hand, the sequential Rietveld refinement technique can give reliable results for the kinetic analysis of nonisothermal data. The main advantages of the parametric Rietveld refinement over the sequential Rietveld refinement are increased robustness against outliers, low weight fractions, and noisy data and an increase in computational speed.