S Mazumder
Articles written in Pramana – Journal of Physics
Volume 63 Issue 1 July 2004 pp 165-173
Characterization of porous materials by small-angle scattering
Characterization of porous materials by small-angle scattering has been extensively pursued for several years now as the pores are often of mesoscopic size and compatible with the length scale accessible by the technique using both neutrons and X-rays as probing radiation. With the availability of ultra small-angle scattering instruments, one can investigate porous materials in the sub-micron length scale. Because of the increased accessible length scale vis-a-vis the multiple scattering effect, conventional data analysis procedures based on single scattering approximation quite often fail. The limitation of conventional data analysis procedures is also pronounced in the case of thick samples and long wavelength of the probing radiation. Effect of multiple scattering is manifested by broadening the scattering profile. Sample thickness for some technologically important materials is often significantly high, as the experimental samples have to replicate all its essential properties in the bulk material. Larger wavelength of the probing radiation is used in some cases to access large length scale and also to minimize the effect of double Bragg reflections.
Volume 63 Issue 2 August 2004 pp 309-314
D Sen T Mahata A K Patra S Mazumder B P Sharma
Effect of porosity and pore size distribution on the low-frequency dielectric response, in the range 0.01–100 kHz, in sintered ZrO_{2}—8 mol% Y_{2}O_{3} ceramic compacts have been investigated. Small-angle neutron scattering (SANS) technique has been employed to obtain the pore characteristics like pore size distribution, specific surface area etc. It has been observed that the real and the imaginary parts of the complex dielectric permittivity, for the specimens, depend not only on the porosity but also on the pore size distribution and pore morphology significantly. Unlike normal Debye relaxation process, where the loss tangent vis-à-vis the imaginary part of the dielectric constant shows a pronounced peak, in the present case the same increases at lower frequency region and an anomalous non-Debye type relaxation process manifests.
Volume 63 Issue 2 August 2004 pp 321-326
D Sen A K Patra S Mazumder J Mittra G K Dey P K De
This paper deals with the small-angle neutron scattering (SANS) investigation on solution-quenched PH13-8 Mo stainless steel. From the nature of the variation of the functionality of the profiles for varying specimen thickness and also from the transmission electron microscopy (TEM), it has been established that the small-angle scattering signal predominantly originates from the block-like metallic carbide precipitates in the specimen. The contribution due to double Bragg reflection is not significant in the present case. The single scattering profile has been extracted from the experimental profiles corresponding to different values of specimen thickness. In order to avoid complexity and non-uniqueness of the multi-parameter minimization for randomly oriented polydisperse block-like precipitate model, the data have been analyzed assuming randomly oriented polydisperse cylindrical particle model with a locked aspect ratio.
Volume 63 Issue 2 August 2004 pp 327-331
SANS investigation on evolution of pore morphology for varying sintering time in porous ceria
A K Patra S Ramanathan D Sen S Mazumder
Precipitates of ceria were synthesized by homogeneous precipitation method using cerium nitrate and hexamethylenetetramine at 80°C. The precipitates were ground to fine particles of average size ∼0.7 μm. Circular disks with 10 mm diameter, 2 and 3 mm thickness were prepared from the green compacts by sintering at 1300° C for three different sintering times. Evolution of the pore structures in these specimens with sintering time was investigated by small-angle neutron scattering (SANS). The results show that the peak of the pore size distribution shifts towards the larger size with increasing sintering time although the extent of porosity decreases. This indicates that finer pores are eliminated from the system at a faster rate than the coarser ones as sintering proceeds and some of the finer pores coalesce to form bigger ones.
Volume 71 Issue 5 November 2008 pp 892-892 Invited talks (Abstracts only)
Dynamical scaling laws – A few unanswered questions
When a system with continuous symmetry is quenched instantly to a broken symmetry state, topological defects appear in an otherwise homogeneous medium of continuous symmetry. Further growth of the topological defects are of continuous nature such that the time evolution of the system can be described by Ginzburg–Landau free energy functionals.
The phenomenon of new phase formation is a representative example of first-order transition. The phenomenon is fundamental and of immense interest as an example of a highly nonlinear process far from equilibrium. The second phase grows with time and in later stages all domain sizes are much larger than all microscopic lengths. In the large time limit, the new phase-forming systems exhibit self-similar growth pattern with dilation symmetry, with time-dependent scale, and scaling phenomenon. The phenomenon is indicative of the emergence of a morphological pattern of the domains at earlier times looking statistically similar to a pattern at later times apart from the global change of scale implied by the growth of time-dependent characteristic length scale 𝐿(𝑡) – a measure of the time-dependent domain size of the new phase.
The scaling hypothesis assumes the existence of a single characteristic length scale 𝐿(𝑡) such that the domain sizes and their spatial correlation are time invariant when the lengths are scaled by 𝐿(𝑡). Quantitatively, for isotropic systems, the equal-time spatio-temporal composition modulation autocorrelation function 𝑔(𝑟, 𝑡), which reflects the way in which the mean density of the medium varies as a function of distance from a given point, should exhibit the scaling form with time-dependent dilation symmetry $$𝑔(𝑟, 𝑡) = 𝑓 (𝑟/𝐿(𝑡))$$.
The scaling function 𝑓 (𝑟/𝐿(𝑡)) is universal in the sense that it is independent of initial conditions and also interactions as long as they are short ranged. However, form of 𝑓 (𝑟/𝐿(𝑡)) depends non-trivially on 𝑛, the number of components in the vector order- parameter field exhibiting the scaling behaviour, and 𝑑, the dimensionality of the system. It is important to note that the scaling hypothesis has not been proved conclusively except for some model systems.
The Fourier transform of 𝑔(𝑟, 𝑡), the structure factor or scattering function 𝑆(𝑞, 𝑡) for a 𝑑 dimensional Euclidean system, obeys simple scaling ansatz at later times, $$𝑆(𝑞, 𝑡) = 𝐿(𝑡) ^{d} 𝐹 (𝑞𝐿(𝑡))$$.
Based on some of our recent observations on phase separation of a multicomponent alloy involving hydration of cementitious material, it is proposed to discuss some unanswered questions pertinent to the validity of dynamical scaling laws addressing some issues like (i) uniqueness of characteristic length 𝐿(𝑡), (ii) the extent of validity of the scaling laws for new phase formation in the case of non-Euclidean fractal systems, (iii) the extent of validity of the scaling laws for multicomponent systems.
The need for investigations examining the extent and the nature of the validity of the scaling laws for confined systems and for systems subjected to random field will also be discussed.
Volume 71 Issue 5 November 2008 pp 959-963 Small Angle Neutron Scattering
Effects of sintering on microstructure and dielectric response in YCrO_{3} nanoceramic
J Bahadur D Sen S Mazumder V K Aswal V Bedekar R Shukla A K Tyagi
Effects of sintering on pore morphology and dielectric response have been investigated. Pore structure has been probed by small angle neutron scattering (SANS). It has been observed that the size distribution becomes less polydisperse with a slight modification in the distribution as sintering temperature is increased. Dielectric response in the frequency range 0.02–1000 kHz is significantly altered by modification of pore structure because of sintering. A transition from non-Debye type to near-Debye type response has been observed as the sintering temperature is increased.
Volume 71 Issue 5 November 2008 pp 965-970 Small Angle Neutron Scattering
J Bahadur D Sen S Mazumder S Ramanathan
Nanocrystalline nickel oxide powders were calcined at 300, 600 and 900°C and pore structure evolution was followed by small angle neutron scattering (SANS). Pore size distributions at two widely separated size ranges have been revealed. Shrinkage of larger-sized pore with reduction in polydispersity has been observed with increasing heat treatment temperature. The pore structures at various heat treatment temperatures do not scale. This has been attributed to the grain boundary diffusion leading to an asymmetric shrinkage of the pores.
Volume 71 Issue 5 November 2008 pp 971-977 Small Angle Neutron Scattering
D Sen K Dasgupta J Bahadur S Mazumder D Sathiyamoorthy
Small angle neutron scattering (SANS) has been utilized to study the morphology of the multi-walled carbon nanotubes prepared by chemical vapour deposition of acetylene. The effects of various synthesis parameters like temperature, catalyst concentration and catalyst support on the size distribution of the nanotubes are investigated. Distribution of nanotube radii in two length scales has been observed. The number density of the smaller diameter tubes was found more in number compared to the bigger one for all the cases studied. No prominent scaling of the structure factor was observed for the different synthesis conditions.
Volume 71 Issue 5 November 2008 pp 979-984 Small Angle Neutron Scattering
D Sen J Bahadur S Mazumder T Mahata M Syambabu P K Sinha
Mesoscopic density fluctuations in liquid phase sintered silicon carbide have been investigated using small angle neutron scattering (SANS). The increase in the additives results in the modification in the pore size distribution and to some extent the total porosity. SANS revealed a mass fractal nature of the agglomerated matrix microstructure. The fractal dimension of the matrix does not change appreciably with the additives although the upper cut-off value of the fractal decreases significantly with the increase in the additives. The liquid phase sintering due to the presence of additives helps to achieve higher level of densification. However, the agglomeration hinders achievement of the fully dense pellets.
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