Scanning the energy accurately reveals the location of the edge. There is a chemical shift between the un-annealed (red) and the annealed (blue) sample. | The scattering patterns obtained at energies of 17.98keV (red) and 18.05keV (blue) and a temperature of 450^{o}C. |
Since our sample is initially a pressed pellet, its density will change during heating due to the removal of pores and, to a lesser extent, thermal expansion. An indication of the amount of densification can be obtained by an application of Beer's law. An indication of the densification of the sample can be obtained by plotting the product of density and thickness against temperature and measuring the initial and final thickness' of the sample to see by how much the sample thickness has altered. From 450^{o}C to 500^{o}C (just below the Littleton softening point) there is a plateau region in the general increase of density*thickness, indicating no significant change in physical sample dimensions. At 600^{o}C the maximum value of density*thickness has been achieved, and at higher temperatures the density*thickness product starts to decrease again. | The variation of sample density times thickness as the temperature increases during sample heating. |
The scattering pattern obtained at 450^{o}C (blue), fit components (red; A-Guinier and B-Porod), and unified model fit (green). | Guinier plot showing the 375^{o}C, 17.98keV data set and the Guinier fit component. |
The slope analysis of the Porod regime was achieved by weighted least squares regression of the Porod equation (curve B). As a consequence of the high energies used to create the scattering contrast we have a very compressed q scale which does unfortunately give a very short Porod region. The region used for fitting is limited to the linear section and does not extend into the detector range where there would be a high fluorescence contribution. | The Guinier radii were obtained by fitting a unified Guinier exponential/power-law model to the scattering pattern. The unified model, in essence, is a superposition of the Porod and Guinier equations and is an approximate form that describes the complex morphology of the sample over a range of structural levels. A structural level in scattering is described by Guinier's equation (curve A) and a structurally limited power law (Porod eq.), which on a log-log plot is reflected by a knee and a linear region. Displaying the fit over the knee in the log-log plot as a traditional Guinier plot shows the quality of the fit used. |
At higher temperatures, the scattering patterns exhibit a clear maximum in the log-log plot of I(q),
indicating particle-particle interactions are present. This greatly complicates the analysis as most
formalisms are not strictly valid except in the dilute solution limit. With these points in mind, the values
obtained from the Guinier analysis are subject to systematic errors. However, in-situ experiments are
concerned with trends on variation of a parameter, such as temperature, rather than absolute values, and
clear trends emerge from this type of analysis. | The 17.98keV scattering patterns at 350^{o}C (red), 450^{o}C (green), 550^{o}C (blue), 650^{o}C (pink), and 725^{o}C (light blue). |
Guinier radii measured at 17.98kev (stars) and 18.05keV (triangles). A second Guinier radius emerges above 600^{o}C. | Porod slope exponents obtained at 17.98keV (stars) and 18.05keV (triangles). |
At low temperatures the values of R_{g} obtained at the two energies are very close to
each other. Then, at a temperature between 525^{o}C and 550^{o}C, there is a splitting of
the line. This splitting indicates the appearance of a second Guinier region, i.e. the formation of a
second hump in the scattering pattern. The point at which the values of R_{g} split
is attributed to the dilatometric softening point of the glass, which is defined as the temperature at which
the glass deforms under its own weight. The generally quoted associated temperature is known as the
Littleton softening point, i.e. the temperature at which the viscosity is 10^{7.6}dPas. For
our glass composition the theoretical value of the Littleton softening point is 503^{o}C. The splitting of R_{g} is attributed to the growth of agglomerates in the sample. Past the Littleton softening point the glass starts to soften, and the gaps between the glass grains start to change shape. Since the nanocomposite sits in these gaps the nanoparticles start to move and form agglomerates. This also explains the constant R_{g} branch, as this would represent individual primary particles. | The temperature dependence of the slope of the scattering pattern is more complex and requires thought
about the change in morphology of the sample as heating progresses.
In the Debye model the treatment depends on the assumption of atomically smooth boundaries between the
inhomogeneities and the host material. Also, in the limit of large scattering vectors, in the size range
xi < q < r_{0}, where r_{0} is the typical inter-atomic distance,
the Debye model predicts the characteristic q^{-4} Porod power-law behaviour. Again,
this requires that the interfaces are sensed as smooth on an atomic scale. In practice we
observe that none of our data obey this law, though all have a power-law, q^{-n}
dependence, where n(which we call the Porod exponent) is non-integral and less than 4. Non-integral power-law scattering in the Porod region may also be exhibited by systems in which the size distribution of the scattering inhomogeneities is itself a power law, with scattering proportional to q^{-n} arising from a particle (or pore) size distribution proportional to r^{2}. However, particles grown by condensation processes such as sol-gel and vapour deposition techniques are usually subject to a log-normal size distribution because the reaction cross-section depends on the surface to volume ratio of the particles. The most simplistic model which fits the data and our knowledge of the initial microstructure of the sample is that of a combination of surface and mass fractals. It is with this model in mind that we interpret our data. |
The first box in the Figure (350^{o}C) shows the initial morphology of the sample, where the nanoparticles are sitting loosely in the pores and the glass grains have a rough surface. As temperature increases (450^{o}C box) the glass grains start to become less rough on the surface, as the energy necessary for movement on an atomic scale is surpassed. With further heating past the Littleton softening point (550^{o}C box) there is deformation on a much larger scale, causing the pores to collapse. This causes the nanoparticles to be pushed together to form agglomerates. At high temperatures (650^{o}C) the majority of the pores have been removed from the sample leaving the nanoparticles in agglomerates whose shape resembles the initial pore network. | Schematic of the proposed model. |