Walter Kalceff - Academia.edu (original) (raw)

Papers by Walter Kalceff

Research paper thumbnail of Student Attitudes to Learning Business Statistics: Comparison of Online and Traditional Methods

J. Educ. Technol. Soc., 2004

Worldwide, electronic learning (E-learning) has become an important part of the education agenda ... more Worldwide, electronic learning (E-learning) has become an important part of the education agenda in the last decade. The Suan Dusit Rajabhat University (SDRU), Thailand has made significant efforts recently to use Internet technologies to enhance learning opportunities. The results reported here are part of a pioneering study to determine the effectiveness of a new online learning course in the subject “Business Statistics”. This paper compares two groups of students, one studying using a traditional lecture-based approach, and the other studying using e-learning. The comparison is based on students’ attitudes towards statistics measured using a validated questionnaire, both before and after the 16-week course, and for each of the modes of study. Comparisons are also made with students studying by distance, although the numbers in these groups are too small for sensible statistical analysis. The questionnaire data are augmented by material from interviews and other student reports o...

Research paper thumbnail of X-Ray Diffraction Characterisation of Nanoparticle Size and Shape Distributions:— Application to Bimodal Distributions

We present a novel Bayesian/Maximum Entropy method to detect and resolve the modal characteristic... more We present a novel Bayesian/Maximum Entropy method to detect and resolve the modal characteristics of size distributions from x-ray diffraction line profiles. To our knowledge, none of the existing alternative methods are capable of extracting this information from experimental data.

Research paper thumbnail of D-21 Bayesian Characterisation of Nanocrystallites from Line Profile Data

Research paper thumbnail of Size/Strain Broadening Analysis of SRM 676 Candidate Materials

Advances in X-Ray Analysis, 1994

A project was undertaken to compare the Williamson-Hall and Fourier teclrniques for analyzing par... more A project was undertaken to compare the Williamson-Hall and Fourier teclrniques for analyzing particle-size and micro-strain induced x-ray line profile broadening. The four alumina powders analyzed in the study were the candidates from which SRM 676, a quantitative analysis Standard Reference Material, was chosen. SRM 660 (LaB6) was used to determine the instrument profile function, IPF. However, difficulty was encountered in fitting an appropriate mathematical model to the IPF data; this prevented the application of Fourier analysis methods and restricted the number of profiles that could be analyzed with the Williamson-Hall method. The size/stain data compared favorably with other microstructural data collected on these specimens.

Research paper thumbnail of An Evaluation of Deconvolution Techniques in X-Ray Profile Broadening Analysis and the Application of the Maximum Entropy Method to Alumina Data

Advances in X-Ray Analysis, 1995

This paper reviews several procedures for the removal of instrumental contributions from measured... more This paper reviews several procedures for the removal of instrumental contributions from measured x-ray diffraction profiles, including: direct convolution, unconstrained and constrained deconvolution, an iterative technique, and a maximum entropy method (MEM) which we have adapted to x-ray diffraction profile analysis. Decorevolutions using the maximum entropy approach were found to be the most robust with simulated profiles which included Poisson-distributed noise and uncertainties in the instrument profile function (IPF). The MEM procedure is illustrated by application to the analysis for domain size and microstrain carried out on the four calcined α-alumina candidate materials for Standard Reference Material (SRM) 676 (a quantitative analysis standard for I/Ic determinations), along with the certified material. Williamson-Hall plots of these data were problematic with respect to interpretation of the microstrain, indicating that the line profile standard, SRM 660 (LaB6), exhibits a small amount of strain broadening, particularly at high 2θ angle. The domain sizes for all but one of the test materials were much smaller than the crystallite (particle) size; indicating the presence of low angle grain boundaries.

Research paper thumbnail of A Bayesian/Maximum Entropy Method for the Certification of a Nanocrystallite-Size NIST Standard Reference Material

Springer Series in Materials Science, 2004

Research paper thumbnail of Bayesian inference of nanoparticle-broadened X-ray line profiles

Journal of Research of the National Institute of Standards and Technology, 2004

A single and self-contained method for determining the crystallite-size distribution and shape fr... more A single and self-contained method for determining the crystallite-size distribution and shape from experimental x-ray line profile data is presented. We have shown that the crystallite-size distribution can be determined without assuming a functional form for the size distribution, determining instead the size distribution with the least assumptions by applying the Bayesian/MaxEnt method. The Bayesian/MaxEnt method is tested using both simulated and experimental CeO 2 data. The results demonstrate that the proposed method can determine size distributions, while making the least number of assumptions. The comparison of the Bayesian/MaxEnt results from experimental CeO 2 with TEM results is favorable. 1

Research paper thumbnail of Ferrimagnetism and spin excitation in a Ni-Mn partially inverted spinel prepared using a modified polymeric precursor method

Materials Chemistry and Physics, 2014

h i g h l i g h t s NieMn oxide partially-inverted spinel made by modified polymeric precursor me... more h i g h l i g h t s NieMn oxide partially-inverted spinel made by modified polymeric precursor method. Magnetic measurements showed a ferrimagnetic and a parasitic magnetic transition. NPD revealed a magnetic structure consistent with a star-like moment arrangement. INS measurements indicated four distinct temperature-dependent magnetic regimes.

Research paper thumbnail of Bayesian Analysis of Ceria Nanoparticles from Line Profile Data

A Bayesian/Maximum entropy (MaxEnt) method is applied to quantify the broadening of X- ray line p... more A Bayesian/Maximum entropy (MaxEnt) method is applied to quantify the broadening of X- ray line profiles in terms of the nanocrystallite size effects in ceria. The analysis is in general agreement with transmission electron microscopy results, while demonstrating the impor- tance of appropriate a priori information needed in the method. The analysis also identifies other microstructural effects, such as the presence of dislocations and shape anisotropic ef- fects, which may be influencing the size distributions determined from the Bayesian/MaxEnt method.

Research paper thumbnail of X-ray reflectivity study of radio frequency sputtered silicon oxide on silicon

Thin Solid Films, 2005

ABSTRACT An X-ray reflectivity study carried out on 45-450 angstrom films of radio frequency sput... more ABSTRACT An X-ray reflectivity study carried out on 45-450 angstrom films of radio frequency sputtered silicon oxide on silicon, with particular attention given to the interface between film and substrate. In order to model refectivity data it was necessary to include an interface layer for all films. This interface layer had a density approaching that of the substrate but due to differing compositions of the deposited film and substrate it was subject to a variation in scattering and absorption properties. (c) 2005 Elsevier B.V All rights reserved.

Research paper thumbnail of System for measuring the junction temperature of a light emitting diode immersed in liquid nitrogen

Review of Scientific Instruments, 2006

A versatile system has been developed for the measurement under LABVIEW™ control of junction temp... more A versatile system has been developed for the measurement under LABVIEW™ control of junction temperatures in a light emitting diode ͑LED͒. Measurements are reported on a commercially available high-intensity InGaAlP LED immersed in liquid nitrogen and driven by currents in the range of 18.5-204 mA. The measured junction temperature has an expanded uncertainty of ±2 K at the 95% level of confidence for temperatures from 70 to 298 K. Using the measured junction temperatures, the junction-to-case thermal resistance of the LED was established as 440 K / W for devices with intact encapsulation and 307 K / W for partial encapsulation.

Research paper thumbnail of Wide dynamic range current-voltage characterization system for ceramic superconductors

Review of Scientific Instruments, 1992

Transport current-voltage (I-V) characteristics gathered over several orders of magnitude of curr... more Transport current-voltage (I-V) characteristics gathered over several orders of magnitude of current can reveal much about the loss mechanisms in high Tc superconductors. This article describes the design and implementation of a novel, computer-controlled, I-V characterization system which permits a I-V curve spanning five orders of magnitude of current to be captured in 50 ms. The advantages of this system

Research paper thumbnail of Bayesian inference of nanoparticle-broadened x-ray line profiles

A single and self-contained method for determining the crystallite-size distribution and shape fr... more A single and self-contained method for determining the crystallite-size distribution and shape from experimental x-ray line profile data is presented. We have shown that the crystallite-size distribution can be determined without assuming a functional form for the size distribution, determining instead the size distribution with the least assumptions by applying the Bayesian/MaxEnt method. The Bayesian/MaxEnt method is tested using both simulated and experimental CeO$_{2}$ data. The results demonstrate that the proposed method can determine size distributions, while making the least number of assumptions. The comparison of the Bayesian/MaxEnt results from experimental CeO$_2$ with TEM results is favorable

Research paper thumbnail of System for the study of localized heating at current contacts on ceramic superconductors

Measurement Science and Technology, 1992

ABSTRACT The authors present a versatile and sensitive system used to quantify the heating effect... more ABSTRACT The authors present a versatile and sensitive system used to quantify the heating effect when pulsed and ramped transport currents are supplied to contacts made to high-Tc superconductors. Measurements made with the system reveal that modest currents (of the order of amps) applied for under 200 ms can cause a measurable temperature increase (up to 0.2 K) close to contacts with resistance of the order of a few tens of milliohms. Such a temperature increase has consequences for the reliability of transport measurements made under these conditions. The authors compare the effects of using a conventional pulsed current for establishing transport properties with a technique under development which employs an exponentially rising current ramp.

Research paper thumbnail of Inelastic neutron scattering studies of TbNiAlH 1.4 and UNiAlH 2.0 hydrides

Journal of Physics: Condensed Matter, 2003

The optical vibrations of hydrogen in TbNiAlH{sub 1.4} and UNiAlH{sub 2.0} were investigated by m... more The optical vibrations of hydrogen in TbNiAlH{sub 1.4} and UNiAlH{sub 2.0} were investigated by means of inelastic neutron scattering. The experimental data were analysed, including multiphonon neutron scattering contributions, calculated in an isotropic harmonic approximation. At least two fundamental H optical peaks were observed in TbNiAlH{sub 1.4}, and were assigned to the vibrational modes of hydrogen atoms occupying different interstitial sites in the metal sublattice. The high-energy part of the UNiAlH{sub 2.0} spectra is characterized by strong anharmonicity, and a broad fundamental band. The latter can be accounted for by a large dispersion of phonon modes due to the strong H-H interactions, and/or different metal-hydrogen force constants, which may originate from different metal atoms surrounding the H atoms in the unit cell.

Research paper thumbnail of Effect of injection current on the repeatability of laser diode junction voltage-temperature measurements

Journal of Applied Physics, 2007

The junction-voltage temperature relationship of a laser diode is used to determine the temperatu... more The junction-voltage temperature relationship of a laser diode is used to determine the temperature of the device in the range -20 to 120 °C. We consider changes that occur to this relationship when the diode is driven at its nominal operating current and above. It is found that estimates of the parameters that appear in a function fitted to the voltage-temperature data are sensitive to driving currents at and above the nominal operating current. Changes in parameter estimates are attributed to degradation due to surface recombination at facets occurring when the laser diode is overdriven. An indication of this degradation is the change in the ideality factor that occurs as the current to the device is raised. This work indicates that the temperature of the junction can be determined over the range -20 to 120 °C with a standard uncertainty of ~0.5 °C.

Research paper thumbnail of Phase equilibria in the Fe-rich corner of the Nd-Fe-Ti ternary alloy system at 1100 °C

Journal of Applied Physics, 1994

High-temperature phase relations in the Fe-rich corner of the Nd-Fe-Ti ternary alloy system have ... more High-temperature phase relations in the Fe-rich corner of the Nd-Fe-Ti ternary alloy system have been investigated and an equilibrium phase diagram has been constructed at 1100 °C. Arc-melted and annealed alloys of systematically varying compositions were characterized utilizing scanning electron microscopy, an energy dispersive x-ray microanalysis system (EDS), x-ray diffraction, and optical metallography. Three major phases have been identified, the

Research paper thumbnail of A maximum entropy method for determining column-length distributions from size-broadened X-ray diffraction profiles

Journal of Applied Crystallography, 1999

We present a novel application of the maximum entropy (MaxEnt) method for solving the double-inve... more We present a novel application of the maximum entropy (MaxEnt) method for solving the double-inverse problems of removing instrument broadening from X-ray diffraction profiles and calculating the column-length distribution of the crystallites. The MaxEnt approach is shown to have compelling advantages over the conventional methods it replaces: it is stable and robust, incorporates noise anda prioriinformation into the solution, preserves positivity of the solution, and can be applied successively. We also show how uncertainties in the derived profiles and column distributions can be determined and used in subsequent calculations, including integral breadth, Fourier coefficients, column-length distributions and apparent particle sizes. Calculations are performed on simulated X-ray diffraction profiles for a range of particle sizes, with a detailed study of the sensitivity of the results to background-level estimates and the use of an incorrect instrument response function.

Research paper thumbnail of Eigen-System Analysis of X-ray Diffraction Profile Deconvolution Methods Explains Ill-Conditioning

Journal of Applied Crystallography, 1998

Several deconvolution methods common in X-ray diffraction profile studies have been examined usin... more Several deconvolution methods common in X-ray diffraction profile studies have been examined using an eigen-system analysis in which an error-bound function is used to represent the maximum difference between the solution and true specimen profiles. This approach quantifies the sources of misfitting and illconditioning that appear in the solution profile and expresses them as a function of the control parameter for a particular method. A simulation of an instrumentbroadened profile overlaid with random noise and background signals was used to evaluate the errorbound function for the iterative and constrained deconvolution methods, and the properties of the error-bound function were related to the features of the solution profile for each method. This analysis quantifies the terms that contribute to the ill-conditioning of the solution profile. It shows that, even for optimum values of the control parameters, positivity is not preserved and spurious oscillations are present in the solution profile.

Research paper thumbnail of Student Attitudes to Learning Business Statistics: Comparison of Online and Traditional Methods

J. Educ. Technol. Soc., 2004

Worldwide, electronic learning (E-learning) has become an important part of the education agenda ... more Worldwide, electronic learning (E-learning) has become an important part of the education agenda in the last decade. The Suan Dusit Rajabhat University (SDRU), Thailand has made significant efforts recently to use Internet technologies to enhance learning opportunities. The results reported here are part of a pioneering study to determine the effectiveness of a new online learning course in the subject “Business Statistics”. This paper compares two groups of students, one studying using a traditional lecture-based approach, and the other studying using e-learning. The comparison is based on students’ attitudes towards statistics measured using a validated questionnaire, both before and after the 16-week course, and for each of the modes of study. Comparisons are also made with students studying by distance, although the numbers in these groups are too small for sensible statistical analysis. The questionnaire data are augmented by material from interviews and other student reports o...

Research paper thumbnail of X-Ray Diffraction Characterisation of Nanoparticle Size and Shape Distributions:— Application to Bimodal Distributions

We present a novel Bayesian/Maximum Entropy method to detect and resolve the modal characteristic... more We present a novel Bayesian/Maximum Entropy method to detect and resolve the modal characteristics of size distributions from x-ray diffraction line profiles. To our knowledge, none of the existing alternative methods are capable of extracting this information from experimental data.

Research paper thumbnail of D-21 Bayesian Characterisation of Nanocrystallites from Line Profile Data

Research paper thumbnail of Size/Strain Broadening Analysis of SRM 676 Candidate Materials

Advances in X-Ray Analysis, 1994

A project was undertaken to compare the Williamson-Hall and Fourier teclrniques for analyzing par... more A project was undertaken to compare the Williamson-Hall and Fourier teclrniques for analyzing particle-size and micro-strain induced x-ray line profile broadening. The four alumina powders analyzed in the study were the candidates from which SRM 676, a quantitative analysis Standard Reference Material, was chosen. SRM 660 (LaB6) was used to determine the instrument profile function, IPF. However, difficulty was encountered in fitting an appropriate mathematical model to the IPF data; this prevented the application of Fourier analysis methods and restricted the number of profiles that could be analyzed with the Williamson-Hall method. The size/stain data compared favorably with other microstructural data collected on these specimens.

Research paper thumbnail of An Evaluation of Deconvolution Techniques in X-Ray Profile Broadening Analysis and the Application of the Maximum Entropy Method to Alumina Data

Advances in X-Ray Analysis, 1995

This paper reviews several procedures for the removal of instrumental contributions from measured... more This paper reviews several procedures for the removal of instrumental contributions from measured x-ray diffraction profiles, including: direct convolution, unconstrained and constrained deconvolution, an iterative technique, and a maximum entropy method (MEM) which we have adapted to x-ray diffraction profile analysis. Decorevolutions using the maximum entropy approach were found to be the most robust with simulated profiles which included Poisson-distributed noise and uncertainties in the instrument profile function (IPF). The MEM procedure is illustrated by application to the analysis for domain size and microstrain carried out on the four calcined α-alumina candidate materials for Standard Reference Material (SRM) 676 (a quantitative analysis standard for I/Ic determinations), along with the certified material. Williamson-Hall plots of these data were problematic with respect to interpretation of the microstrain, indicating that the line profile standard, SRM 660 (LaB6), exhibits a small amount of strain broadening, particularly at high 2θ angle. The domain sizes for all but one of the test materials were much smaller than the crystallite (particle) size; indicating the presence of low angle grain boundaries.

Research paper thumbnail of A Bayesian/Maximum Entropy Method for the Certification of a Nanocrystallite-Size NIST Standard Reference Material

Springer Series in Materials Science, 2004

Research paper thumbnail of Bayesian inference of nanoparticle-broadened X-ray line profiles

Journal of Research of the National Institute of Standards and Technology, 2004

A single and self-contained method for determining the crystallite-size distribution and shape fr... more A single and self-contained method for determining the crystallite-size distribution and shape from experimental x-ray line profile data is presented. We have shown that the crystallite-size distribution can be determined without assuming a functional form for the size distribution, determining instead the size distribution with the least assumptions by applying the Bayesian/MaxEnt method. The Bayesian/MaxEnt method is tested using both simulated and experimental CeO 2 data. The results demonstrate that the proposed method can determine size distributions, while making the least number of assumptions. The comparison of the Bayesian/MaxEnt results from experimental CeO 2 with TEM results is favorable. 1

Research paper thumbnail of Ferrimagnetism and spin excitation in a Ni-Mn partially inverted spinel prepared using a modified polymeric precursor method

Materials Chemistry and Physics, 2014

h i g h l i g h t s NieMn oxide partially-inverted spinel made by modified polymeric precursor me... more h i g h l i g h t s NieMn oxide partially-inverted spinel made by modified polymeric precursor method. Magnetic measurements showed a ferrimagnetic and a parasitic magnetic transition. NPD revealed a magnetic structure consistent with a star-like moment arrangement. INS measurements indicated four distinct temperature-dependent magnetic regimes.

Research paper thumbnail of Bayesian Analysis of Ceria Nanoparticles from Line Profile Data

A Bayesian/Maximum entropy (MaxEnt) method is applied to quantify the broadening of X- ray line p... more A Bayesian/Maximum entropy (MaxEnt) method is applied to quantify the broadening of X- ray line profiles in terms of the nanocrystallite size effects in ceria. The analysis is in general agreement with transmission electron microscopy results, while demonstrating the impor- tance of appropriate a priori information needed in the method. The analysis also identifies other microstructural effects, such as the presence of dislocations and shape anisotropic ef- fects, which may be influencing the size distributions determined from the Bayesian/MaxEnt method.

Research paper thumbnail of X-ray reflectivity study of radio frequency sputtered silicon oxide on silicon

Thin Solid Films, 2005

ABSTRACT An X-ray reflectivity study carried out on 45-450 angstrom films of radio frequency sput... more ABSTRACT An X-ray reflectivity study carried out on 45-450 angstrom films of radio frequency sputtered silicon oxide on silicon, with particular attention given to the interface between film and substrate. In order to model refectivity data it was necessary to include an interface layer for all films. This interface layer had a density approaching that of the substrate but due to differing compositions of the deposited film and substrate it was subject to a variation in scattering and absorption properties. (c) 2005 Elsevier B.V All rights reserved.

Research paper thumbnail of System for measuring the junction temperature of a light emitting diode immersed in liquid nitrogen

Review of Scientific Instruments, 2006

A versatile system has been developed for the measurement under LABVIEW™ control of junction temp... more A versatile system has been developed for the measurement under LABVIEW™ control of junction temperatures in a light emitting diode ͑LED͒. Measurements are reported on a commercially available high-intensity InGaAlP LED immersed in liquid nitrogen and driven by currents in the range of 18.5-204 mA. The measured junction temperature has an expanded uncertainty of ±2 K at the 95% level of confidence for temperatures from 70 to 298 K. Using the measured junction temperatures, the junction-to-case thermal resistance of the LED was established as 440 K / W for devices with intact encapsulation and 307 K / W for partial encapsulation.

Research paper thumbnail of Wide dynamic range current-voltage characterization system for ceramic superconductors

Review of Scientific Instruments, 1992

Transport current-voltage (I-V) characteristics gathered over several orders of magnitude of curr... more Transport current-voltage (I-V) characteristics gathered over several orders of magnitude of current can reveal much about the loss mechanisms in high Tc superconductors. This article describes the design and implementation of a novel, computer-controlled, I-V characterization system which permits a I-V curve spanning five orders of magnitude of current to be captured in 50 ms. The advantages of this system

Research paper thumbnail of Bayesian inference of nanoparticle-broadened x-ray line profiles

A single and self-contained method for determining the crystallite-size distribution and shape fr... more A single and self-contained method for determining the crystallite-size distribution and shape from experimental x-ray line profile data is presented. We have shown that the crystallite-size distribution can be determined without assuming a functional form for the size distribution, determining instead the size distribution with the least assumptions by applying the Bayesian/MaxEnt method. The Bayesian/MaxEnt method is tested using both simulated and experimental CeO$_{2}$ data. The results demonstrate that the proposed method can determine size distributions, while making the least number of assumptions. The comparison of the Bayesian/MaxEnt results from experimental CeO$_2$ with TEM results is favorable

Research paper thumbnail of System for the study of localized heating at current contacts on ceramic superconductors

Measurement Science and Technology, 1992

ABSTRACT The authors present a versatile and sensitive system used to quantify the heating effect... more ABSTRACT The authors present a versatile and sensitive system used to quantify the heating effect when pulsed and ramped transport currents are supplied to contacts made to high-Tc superconductors. Measurements made with the system reveal that modest currents (of the order of amps) applied for under 200 ms can cause a measurable temperature increase (up to 0.2 K) close to contacts with resistance of the order of a few tens of milliohms. Such a temperature increase has consequences for the reliability of transport measurements made under these conditions. The authors compare the effects of using a conventional pulsed current for establishing transport properties with a technique under development which employs an exponentially rising current ramp.

Research paper thumbnail of Inelastic neutron scattering studies of TbNiAlH 1.4 and UNiAlH 2.0 hydrides

Journal of Physics: Condensed Matter, 2003

The optical vibrations of hydrogen in TbNiAlH{sub 1.4} and UNiAlH{sub 2.0} were investigated by m... more The optical vibrations of hydrogen in TbNiAlH{sub 1.4} and UNiAlH{sub 2.0} were investigated by means of inelastic neutron scattering. The experimental data were analysed, including multiphonon neutron scattering contributions, calculated in an isotropic harmonic approximation. At least two fundamental H optical peaks were observed in TbNiAlH{sub 1.4}, and were assigned to the vibrational modes of hydrogen atoms occupying different interstitial sites in the metal sublattice. The high-energy part of the UNiAlH{sub 2.0} spectra is characterized by strong anharmonicity, and a broad fundamental band. The latter can be accounted for by a large dispersion of phonon modes due to the strong H-H interactions, and/or different metal-hydrogen force constants, which may originate from different metal atoms surrounding the H atoms in the unit cell.

Research paper thumbnail of Effect of injection current on the repeatability of laser diode junction voltage-temperature measurements

Journal of Applied Physics, 2007

The junction-voltage temperature relationship of a laser diode is used to determine the temperatu... more The junction-voltage temperature relationship of a laser diode is used to determine the temperature of the device in the range -20 to 120 °C. We consider changes that occur to this relationship when the diode is driven at its nominal operating current and above. It is found that estimates of the parameters that appear in a function fitted to the voltage-temperature data are sensitive to driving currents at and above the nominal operating current. Changes in parameter estimates are attributed to degradation due to surface recombination at facets occurring when the laser diode is overdriven. An indication of this degradation is the change in the ideality factor that occurs as the current to the device is raised. This work indicates that the temperature of the junction can be determined over the range -20 to 120 °C with a standard uncertainty of ~0.5 °C.

Research paper thumbnail of Phase equilibria in the Fe-rich corner of the Nd-Fe-Ti ternary alloy system at 1100 °C

Journal of Applied Physics, 1994

High-temperature phase relations in the Fe-rich corner of the Nd-Fe-Ti ternary alloy system have ... more High-temperature phase relations in the Fe-rich corner of the Nd-Fe-Ti ternary alloy system have been investigated and an equilibrium phase diagram has been constructed at 1100 °C. Arc-melted and annealed alloys of systematically varying compositions were characterized utilizing scanning electron microscopy, an energy dispersive x-ray microanalysis system (EDS), x-ray diffraction, and optical metallography. Three major phases have been identified, the

Research paper thumbnail of A maximum entropy method for determining column-length distributions from size-broadened X-ray diffraction profiles

Journal of Applied Crystallography, 1999

We present a novel application of the maximum entropy (MaxEnt) method for solving the double-inve... more We present a novel application of the maximum entropy (MaxEnt) method for solving the double-inverse problems of removing instrument broadening from X-ray diffraction profiles and calculating the column-length distribution of the crystallites. The MaxEnt approach is shown to have compelling advantages over the conventional methods it replaces: it is stable and robust, incorporates noise anda prioriinformation into the solution, preserves positivity of the solution, and can be applied successively. We also show how uncertainties in the derived profiles and column distributions can be determined and used in subsequent calculations, including integral breadth, Fourier coefficients, column-length distributions and apparent particle sizes. Calculations are performed on simulated X-ray diffraction profiles for a range of particle sizes, with a detailed study of the sensitivity of the results to background-level estimates and the use of an incorrect instrument response function.

Research paper thumbnail of Eigen-System Analysis of X-ray Diffraction Profile Deconvolution Methods Explains Ill-Conditioning

Journal of Applied Crystallography, 1998

Several deconvolution methods common in X-ray diffraction profile studies have been examined usin... more Several deconvolution methods common in X-ray diffraction profile studies have been examined using an eigen-system analysis in which an error-bound function is used to represent the maximum difference between the solution and true specimen profiles. This approach quantifies the sources of misfitting and illconditioning that appear in the solution profile and expresses them as a function of the control parameter for a particular method. A simulation of an instrumentbroadened profile overlaid with random noise and background signals was used to evaluate the errorbound function for the iterative and constrained deconvolution methods, and the properties of the error-bound function were related to the features of the solution profile for each method. This analysis quantifies the terms that contribute to the ill-conditioning of the solution profile. It shows that, even for optimum values of the control parameters, positivity is not preserved and spurious oscillations are present in the solution profile.