Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

Flexural behaviour and design of cold-formed steel beams with rectangular hollow flanges

Until recently, the hot-rolled steel members have been recognized as the most popular and widely used steel group, but in recent times, the use of cold-formed high strength steel members has rapidly increased. However, the structural behavior of light gauge high strength cold-formed steel members characterized by various buckling modes is not yet fully understood. The current cold-formed steel sections such as C- and Z-sections are commonly used because of their simple forming procedures and easy connections, but they suffer from certain buckling modes. It is therefore important that these buckling modes are either delayed or eliminated to increase the ultimate capacity of these members. This research is therefore aimed at developing a new cold-formed steel beam with two torsionally rigid rectangular hollow flanges and a slender web formed using intermittent screw fastening to enhance the flexural capacity while maintaining a minimum fabrication cost. This thesis describes a detailed investigation into the structural behavior of this new Rectangular Hollow Flange Beam (RHFB), subjected to flexural action The first phase of this research included experimental investigations using thirty full scale lateral buckling tests and twenty two section moment capacity tests using specially designed test rigs to simulate the required loading and support conditions. A detailed description of the experimental methods, RHFB failure modes including local, lateral distortional and lateral torsional buckling modes, and moment capacity results is presented. A comparison of experimental results with the predictions from the current design rules and other design methods is also given. The second phase of this research involved a methodical and comprehensive investigation aimed at widening the scope of finite element analysis to investigate the buckling and ultimate failure behaviours of RHFBs subjected to flexural actions. Accurate finite element models simulating the physical conditions of both lateral buckling and section moment capacity tests were developed. Comparison of experimental and finite element analysis results showed that the buckling and ultimate failure behaviour of RHFBs can be simulated well using appropriate finite element models. Finite element models simulating ideal simply supported boundary conditions and a uniform moment loading were also developed in order to use in a detailed parametric study. The parametric study results were used to review the current design rules and to develop new design formulae for RHFBs subjected to local, lateral distortional and lateral torsional buckling effects. Finite element analysis results indicate that the discontinuity due to screw fastening has a noticeable influence only for members in the intermediate slenderness region. Investigations into different combinations of thicknesses in the flange and web indicate that increasing the flange thickness is more effective than web thickness in enhancing the flexural capacity of RHFBs. The current steel design standards, AS 4100 (1998) and AS/NZS 4600 (1996) are found sufficient to predict the section moment capacity of RHFBs. However, the results indicate that the AS/NZS 4600 is more accurate for slender sections whereas AS 4100 is more accurate for compact sections. The finite element analysis results further indicate that the current design rules given in AS/NZS 4600 is adequate in predicting the member moment capacity of RHFBs subject to lateral torsional buckling effects. However, they were inadequate in predicting the capacities of RHFBs subject to lateral distortional buckling effects. This thesis has therefore developed a new design formula to predict the lateral distortional buckling strength of RHFBs. Overall, this thesis has demonstrated that the innovative RHFB sections can perform well as economically and structurally efficient flexural members. Structural engineers and designers should make use of the new design rules and the validated existing design rules to design the most optimum RHFB sections depending on the type of applications. Intermittent screw fastening method has also been shown to be structurally adequate that also minimises the fabrication cost. Product manufacturers and builders should be able to make use of this in their applications.

A shameful spectacle

The linguistics of violence in film and on television is a hotly debated topic, especially whenever outrageously violent crimes are committed in the community. The debate tends to proceed thus: was the perpetrator addicted to watching violent films and videos, and if so, did the language of mediated violence translate into the language of everyday action, blurring the boundaries between fantasy and reality? The cause—effect relationship between fantasies enacted on screen and horrific real-life crimes has never been proven scientifically, despite endless governmental inquiries and many attempts by academics to discover a causation formula. I will not be looking so much at the vexed question of the relationship between stylized violence on celluloid and real violence in a community. Rather, I wish to explore the nature of a particular form of mediated, gendered violence through an analysis of the language of several key films made in the past decade focusing on the violent crime of rape: Hollywood films The Accused (1988), Casualties of War (1989), Thelma and Louise (1991), Strange Days (1996), and the Australian films Shame (1988) and The Boys (1998). In this way, I wish to show how rape is depicted linguistically in film, and how such films may actually give solutions to this abhorrent kind of violence rather than thrill the viewer vicariously, or, in a worst case scenario, stimulate people to further violence.

Raman spectroscopic study of the phosphate mineral Churchite-(Y) YPO4.2H2O

Raman spectroscopy has been used to study the rare earth mineral churchite-(Y) of formula (Y,REE)(PO4) •2H2O. The mineral contains yttrium and depending on the locality, a range of rare earth metals. The Raman spectra of two churchite-(Y) mineral samples from Jáchymov and Medvědín in the Czech Republic were compared with the Raman spectra of churchite-(Y) downloaded from the RRUFF data base. The Raman spectra of churchite-(Y) are characterized by an intense sharp band at 975 cm-1 assigned to the ν1 (PO4)3- symmetric stretching mode. A lower intensity band observed at around 1065 cm-1 is attributed to the ν3 (PO43-) antisymmetric stretching mode. The (PO43-) bending modes are observed at 497 cm-1 (ν2) and 563 cm-1(ν4). Some small differences in the band positions between the four churchite-(Y) samples from four different localities were found. These differences are possible to explain as different compositions of the churchite-(Y) minerals.

Raman spectroscopic study of the antimonate mineral lewisite (Ca,Fe,Na)2(Sb,Ti)2O6(O,OH)7

The mineral lewisite, (Ca,Fe,Na)2(Sb,Ti)2O6(O,OH)7 an antimony bearing mineral has been studied by Raman spectroscopy. A comparison is made with the Raman spectra of other minerals including bindheimite, stibiconite and roméite. The mineral lewisite is characterised by an intense sharp band at 517 cm-1 with a shoulder at 507 cm-1 assigned to SbO stretching modes. Raman bands of medium intensity for lewisite are observed at 300, 356 and 400 cm-1. These bands are attributed to OSbO bending vibrations. Raman bands in the OH stretching region are observed at 3200, 3328, 3471 cm-1 with a distinct shoulder at 3542 cm-1. The latter is assigned to the stretching vibration of OH units. The first three bands are attributed to water stretching vibrations. The observation of bands in the 3200 to 3500 cm-1 region suggests that water is involved in the lewisite structure. If this is the case then the formula may be better written as Ca, Fe2+, Na)2(Sb, Ti)2(O,OH)7 •xH2O.

Using samples to estimate the sensitivity and specificity of a surveillance process

Determining sensitivity and specificity of a postoperative infection surveillance process is a difficult undertaking. Because postoperative infections are rare, vast numbers of negative results exist, and it is often not reasonable to assess them all. This study gives a methodological framework for estimating sensitivity and specificity by taking only a small sample of the number of patients who test negative and comparing their findings to the reference or “gold standard” rather than comparing the findings of all patients to the gold standard. It provides a formula for deriving confidence intervals for these estimates and a guide to minimum requirements for sampling results.

Factors associated with recurrence of venous leg ulcers : a survey and retrospective chart review

Background: Chronic venous leg ulcers have a significant impact on older individuals’ well-being and health care resources. Unfortunately after healing, up to 70% recur. ----- Objective: To examine the relationships between leg ulcer recurrence and physical activity, compression, nutrition, health, psychosocial indicators and self-care activities in order to provide information for preventive strategies. ----- Design: Survey and retrospective chart review Settings: Two metropolitan hospital and three community-based leg ulcer clinics. ----- Subjects: A sample of 122 community living patients with leg ulcer of venous aetiology which had healed between 12 and 36 months prior to the survey. ---- Methods: Data were collected from medical records on demographics, medical history and previous ulcer history and treatments; and from self-report questionnaires on physical activity, nutrition, psychosocial measures, ulcer recurrences and history, compression and other self-care activities. All variables significantly associated with recurrence at the bivariate level were entered into a logistic regression model to determine their independent influences on recurrence. ----- Results: Median follow-up time was 24 months (range 12–40 months). Sixty-eight percent of participants had recurred. Bivariate analysis found recurrence was positively associated with ulcer duration, cardiac disease, a Body Mass Index ≤20, scoring as at-risk of malnutrition and depression; and negatively associated with increased physical activity, leg elevation, wearing Class 2 (20–25mmHg) or Class 3 (30–40mmHg) compression hosiery, and higher self-efficacy scores. After adjusting for all variables, an hour/day of leg elevation (OR=0.04, 95% CI=0.01–0.17), days/week in Class 2 or 3 compression hosiery (OR=0.53, 95% CI=0.34–0.81), Yale Physical Activity Survey score (OR=0.95, 95% CI=0.92–0.98), cardiac disease (OR=5.03, 95% CI=1.01–24.93) and General Self-Efficacy scores (OR=0.83, 95% CI=0.72–0.94) remained significantly associated (p<0.05) with recurrence. ----- Conclusions: Results indicate a history of cardiac disease is a risk factor for recurrence; while leg elevation, physical activity, compression hosiery and strategies to improve self-efficacy are likely to prevent recurrence.

Year 8, 9 and 10 students’ understanding and access of percent knowledge

This paper reports on Years 8, 9 and 10 students’ knowledge of percent problem types, use of diagrams, and type of solution strategy. Non- and semi-proficient students displayed the expected inflexible formula approach to solution but proficient students used a flexible mixture of estimation, number sense and trial and error instead of expected schema based methods.

The structure of the copper(II) complex with 4,5-dichlorophthalic acid: The 1:1 complex 'adduct' salt trans-tetraaqua(2-carboxy-4,5-dichlorobenzoato)(4,5-dichlorobenzene-1,2-dicarboxylic acid)copper(II) 2-carboxy-4,5-dichlorobenzoate

The unusual (1:1) complex ‘adduct’ salt of copper(II) with 4,5-dichlorophthalic acid (H2DCPA), having formula [Cu(H2O)4(C8H3Cl2O4) (C8H4Cl2O4)] . (C8H3Cl2O4) has been synthesized and characterized using single-crystal X-ray diffraction. Crystals are monoclinic, space group P21/c, with Z = 4 in a cell with dimensions a = 20.1376(7), b =12.8408(4) c = 12.1910(4) Å, β = 105.509(4)o. The complex is based on discrete tetragonally distorted octahedral [CuO6] coordination centres with the four water ligands occupying the square planar sites [Cu-O, 1.962(4)-1.987(4) Å] and the monodentate carboxyl-O donors of two DCPA ligand species in the axial sites. The first of these bonds [Cu-O, 2.341(4) Å] is with an oxygen of a HDCPA monoanion, the second with an oxygen of a H2DCPA acid species [Cu-O, 2.418(4) Å]. The un-coordinated ‘adduct’ molecule is a HDCPA counter anion which is strongly hydrogen-bonded to the coordinated H2DCPA ligand [O… O, 2.503(6) Å] while a number of peripheral intra- and intermolecular hydrogen-bonding interactions give a two-dimensional network structure.

Novel ruthenium bipyridyl dyes with s-donor ligands and their application in dye-sensitized solar cells

Two series of novel ruthenium bipyridyl dyes incorporating sulfur-donor bidentate ligands with general formula \[Ru(R-bpy)2C2N2S2] and \[Ru(R-bpy)2(S2COEt)]\[NO3] (where R =H, CO2Et, CO2H; C2N2S2 = cyanodithioimidocarbonate and S2COEt = ethyl xanthogenate) have been synthesized and characterized spectroscopically, electrochemically and computationally. The acid derivatives in both series (C2N2S2 3 and S2COEt 6) were used as a photosensitizer in a dye-sensitized solar cell (DSSC) and the incident photo-to-current conversion efficiency (IPCE), overall efficiency (_) and kinetics of the dye/TiO2 system were investigated. It was found that 6 gave a higher efficiency cell than 3 despite the latter dye’s more favorable electronic properties, such as greater absorption range, higher molar extinction coefficient and large degree of delocalization of the HOMO. The transient absorption spectroscopy studies revealed that the recombination kinetics of 3 were unexpectedly fast, which was attributed to the terminal CN on the ligand binding to the TiO2, as evidenced by an absorption study of R =H and CO2Et dyes sensitized on TiO2, and hence leading to a lower efficiency DSSC.

Raman spectroscopic study of the antimony containing mineral partzite Cu2Sb2(O,OH)7

Raman spectroscopy of the mineral partzite Cu2Sb2(O,OH)7 complimented with infrared spectroscopy were studied and related to the structure of the mineral. The Raman spectrum shows some considerable complexity with a number of overlapping bands observed at 479, 520, 594, 607 and 620 cm-1 with additional low intensity bands found at 675, 730, 777 and 837 cm-1. Raman bands of partzite in the spectral region 590 to 675 cm-1 are attributable the ν1 symmetric stretching modes. The Raman bands at 479 and 520 cm-1 are assigned to the ν3 antisymmetric stretching modes. Raman bands at 1396 and 1455 cm-1 are attributed to SbOH deformation modes. A complex pattern resulting from the overlapping band of the water and OH units is found. Raman bands are observed at 3266, 3376, 3407, 3563, 3586 and 3622 cm-1. The first three bands are assigned to water stretching vibrations. The three higher wavenumber bands are assigned to the stretching vibrations of the OH units. It is proposed that based upon observation of the Raman spectra that water is involved in the structure of partzite. Thus the formula Cu2Sb2(O,OH)7 may be better written as Cu2Sb2(O,OH)7 •xH2O

Raman spectroscopic study of the multi-anion mineral dixenite CuMn2+14Fe3+(AsO3)5(SiO4)2(AsO4)(OH)6

The mixed anion mineral dixenite has been studied by Raman spectroscopy, complimented with infrared spectroscopy. The Raman spectrum of dixenite shows bands at 839 and 813 cm-1 assigned to the (AsO3)3- symmetric and antisymmetric stretching modes. The most intense Raman band of dixenite is the band at 526 cm-1 and is assigned to the ν2 AsO33- bending mode. DFT calculations enabled the position of AsO22- symmetric stretching mode at 839 cm-1, the antisymmetric stretching mode at 813 cm-1, and the deformation mode at 449 cm-1 to be calculated. Raman bands at 1026 and 1057 cm-1 are assigned to the SiO42- symmetric stretching vibrations and at 1349 and 1386 cm-1 to the SiO42- antisymmetric stretching vibrations. Both Raman and infrared spectra indicate the presence of water in the structure of dixenite. This brings into question the commonly accepted formula of dixenite as CuMn2+14Fe3+(AsO3)5(SiO4)2(AsO4)(OH)6. The formula may be better written as CuMn2+14Fe3+(AsO3)5(SiO4)2(AsO4)(OH)6•xH2O.

Synthesis and modifications of metal oxide nanostructures and their applications

Transition metal oxides are functional materials that have advanced applications in many areas, because of their diverse properties (optical, electrical, magnetic, etc.), hardness, thermal stability and chemical resistance. Novel applications of the nanostructures of these oxides are attracting significant interest as new synthesis methods are developed and new structures are reported. Hydrothermal synthesis is an effective process to prepare various delicate structures of metal oxides on the scales from a few to tens of nanometres, specifically, the highly dispersed intermediate structures which are hardly obtained through pyro-synthesis. In this thesis, a range of new metal oxide (stable and metastable titanate, niobate) nanostructures, namely nanotubes and nanofibres, were synthesised via a hydrothermal process. Further structure modifications were conducted and potential applications in catalysis, photocatalysis, adsorption and construction of ceramic membrane were studied. The morphology evolution during the hydrothermal reaction between Nb2O5 particles and concentrated NaOH was monitored. The study demonstrates that by optimising the reaction parameters (temperature, amount of reactants), one can obtain a variety of nanostructured solids, from intermediate phases niobate bars and fibres to the stable phase cubes. Trititanate (Na2Ti3O7) nanofibres and nanotubes were obtained by the hydrothermal reaction between TiO2 powders or a titanium compound (e.g. TiOSO4·xH2O) and concentrated NaOH solution by controlling the reaction temperature and NaOH concentration. The trititanate possesses a layered structure, and the Na ions that exist between the negative charged titanate layers are exchangeable with other metal ions or H+ ions. The ion-exchange has crucial influence on the phase transition of the exchanged products. The exchange of the sodium ions in the titanate with H+ ions yields protonated titanate (H-titanate) and subsequent phase transformation of the H-titanate enable various TiO2 structures with retained morphology. H-titanate, either nanofibres or tubes, can be converted to pure TiO2(B), pure anatase, mixed TiO2(B) and anatase phases by controlled calcination and by a two-step process of acid-treatment and subsequent calcination. While the controlled calcination of the sodium titanate yield new titanate structures (metastable titanate with formula Na1.5H0.5Ti3O7, with retained fibril morphology) that can be used for removal of radioactive ions and heavy metal ions from water. The structures and morphologies of the metal oxides were characterised by advanced techniques. Titania nanofibres of mixed anatase and TiO2(B) phases, pure anatase and pure TiO2(B) were obtained by calcining H-titanate nanofibres at different temperatures between 300 and 700 °C. The fibril morphology was retained after calcination, which is suitable for transmission electron microscopy (TEM) analysis. It has been found by TEM analysis that in mixed-phase structure the interfaces between anatase and TiO2(B) phases are not random contacts between the engaged crystals of the two phases, but form from the well matched lattice planes of the two phases. For instance, (101) planes in anatase and (101) planes of TiO2(B) are similar in d spaces (~0.18 nm), and they join together to form a stable interface. The interfaces between the two phases act as an one-way valve that permit the transfer of photogenerated charge from anatase to TiO2(B). This reduces the recombination of photogenerated electrons and holes in anatase, enhancing the activity for photocatalytic oxidation. Therefore, the mixed-phase nanofibres exhibited higher photocatalytic activity for degradation of sulforhodamine B (SRB) dye under ultraviolet (UV) light than the nanofibres of either pure phase alone, or the mechanical mixtures (which have no interfaces) of the two pure phase nanofibres with a similar phase composition. This verifies the theory that the difference between the conduction band edges of the two phases may result in charge transfer from one phase to the other, which results in effectively the photogenerated charge separation and thus facilitates the redox reaction involving these charges. Such an interface structure facilitates charge transfer crossing the interfaces. The knowledge acquired in this study is important not only for design of efficient TiO2 photocatalysts but also for understanding the photocatalysis process. Moreover, the fibril titania photocatalysts are of great advantage when they are separated from a liquid for reuse by filtration, sedimentation, or centrifugation, compared to nanoparticles of the same scale. The surface structure of TiO2 also plays a significant role in catalysis and photocatalysis. Four types of large surface area TiO2 nanotubes with different phase compositions (labelled as NTA, NTBA, NTMA and NTM) were synthesised from calcination and acid treatment of the H-titanate nanotubes. Using the in situ FTIR emission spectrescopy (IES), desorption and re-adsorption process of surface OH-groups on oxide surface can be trailed. In this work, the surface OH-group regeneration ability of the TiO2 nanotubes was investigated. The ability of the four samples distinctively different, having the order: NTA > NTBA > NTMA > NTM. The same order was observed for the catalytic when the samples served as photocatalysts for the decomposition of synthetic dye SRB under UV light, as the supports of gold (Au) catalysts (where gold particles were loaded by a colloid-based method) for photodecomposition of formaldehyde under visible light and for catalytic oxidation of CO at low temperatures. Therefore, the ability of TiO2 nanotubes to generate surface OH-groups is an indicator of the catalytic activity. The reason behind the correlation is that the oxygen vacancies at bridging O2- sites of TiO2 surface can generate surface OH-groups and these groups facilitate adsorption and activation of O2 molecules, which is the key step of the oxidation reactions. The structure of the oxygen vacancies at bridging O2- sites is proposed. Also a new mechanism for the photocatalytic formaldehyde decomposition with the Au-TiO2 catalysts is proposed: The visible light absorbed by the gold nanoparticles, due to surface plasmon resonance effect, induces transition of the 6sp electrons of gold to high energy levels. These energetic electrons can migrate to the conduction band of TiO2 and are seized by oxygen molecules. Meanwhile, the gold nanoparticles capture electrons from the formaldehyde molecules adsorbed on them because of gold’s high electronegativity. O2 adsorbed on the TiO2 supports surface are the major electron acceptor. The more O2 adsorbed, the higher the oxidation activity of the photocatalyst will exhibit. The last part of this thesis demonstrates two innovative applications of the titanate nanostructures. Firstly, trititanate and metastable titanate (Na1.5H0.5Ti3O7) nanofibres are used as intelligent absorbents for removal of radioactive cations and heavy metal ions, utilizing the properties of the ion exchange ability, deformable layered structure, and fibril morphology. Environmental contamination with radioactive ions and heavy metal ions can cause a serious threat to the health of a large part of the population. Treatment of the wastes is needed to produce a waste product suitable for long-term storage and disposal. The ion-exchange ability of layered titanate structure permitted adsorption of bivalence toxic cations (Sr2+, Ra2+, Pb2+) from aqueous solution. More importantly, the adsorption is irreversible, due to the deformation of the structure induced by the strong interaction between the adsorbed bivalent cations and negatively charged TiO6 octahedra, and results in permanent entrapment of the toxic bivalent cations in the fibres so that the toxic ions can be safely deposited. Compared to conventional clay and zeolite sorbents, the fibril absorbents are of great advantage as they can be readily dispersed into and separated from a liquid. Secondly, new generation membranes were constructed by using large titanate and small ã-alumina nanofibres as intermediate and top layers, respectively, on a porous alumina substrate via a spin-coating process. Compared to conventional ceramic membranes constructed by spherical particles, the ceramic membrane constructed by the fibres permits high flux because of the large porosity of their separation layers. The voids in the separation layer determine the selectivity and flux of a separation membrane. When the sizes of the voids are similar (which means a similar selectivity of the separation layer), the flux passing through the membrane increases with the volume of the voids which are filtration passages. For the ideal and simplest texture, a mesh constructed with the nanofibres 10 nm thick and having a uniform pore size of 60 nm, the porosity is greater than 73.5 %. In contrast, the porosity of the separation layer that possesses the same pore size but is constructed with metal oxide spherical particles, as in conventional ceramic membranes, is 36% or less. The membrane constructed by titanate nanofibres and a layer of randomly oriented alumina nanofibres was able to filter out 96.8% of latex spheres of 60 nm size, while maintaining a high flux rate between 600 and 900 Lm–2 h–1, more than 15 times higher than the conventional membrane reported in the most recent study.

Impact and energy absorption of empty and foam-filled conical tubes

Foam-filled conical tubes have recently emerged as efficient energy absorbing devices to mitigate the adverse effects of impacts. The primary aim of this thesis was to generate research and design information on the impact and energy absorption response of empty and foam-filled conical tubes, and to facilitate their application in energy absorbing systems under axial and oblique loading conditions representative of those typically encountered in crashworthiness and impact applications. Finite element techniques supported by experiments and existing results were used in the investigation. Major findings show that the energy absorption response can be effectively controlled by varying geometry and material parameters. A useful empirical formula was developed for providing engineering designers with an initial estimate of the load ratio and hence energy absorption performances of these devices. It was evident that foam-filled conical tubes enhance the energy absorption capacity and stabilise the crush response for both axial and oblique impact loading without a significant increase in the initial peak load. This is practically beneficial when higher kinetic energy needs to be absorbed, thus reducing the impact force transmitted to the protected structure and occupants. Such tubes also increase and maintain the energy absorption capacity under global bending as well as minimise the reduction of energy absorption capacity with increasing load angle. Furthermore, the results also highlight the feasibility of adding a foam-filled conical tube as a supplementary device in energy absorbing systems, since the overall energy absorption performance of such systems can be favourably enhanced by only including a relatively small energy absorbing device. Above all, the results demonstrate the superior performance of foam-filled conical tube for mitigating impact energy in impact and crashworthiness applications.

Thermoanalytical studies of natural potassium, sodium and ammonium alunites

Dynamic and controlled rate thermal analysis (CRTA) has been used to characterise alunites of formula [M(Al)3(SO4)2(OH)6 ] where M+ is the cations K+, Na+ or NH4+. Thermal decomposition occurs in a series of steps. (a) dehydration, (b) well defined dehydroxylation and (c) desulphation. CRTA offers a better resolution and a more detailed interpretation of water formation processes via approaching equilibrium conditions of decomposition through the elimination of the slow transfer of heat to the sample as a controlling parameter on the process of decomposition. Constant-rate decomposition processes of water formation reveal the subtle nature of dehydration and dehydroxylation.