Scherrer Equation, L=Kλ/β.cosθ, was developed in 1918, to calculate the nano crystallite size (L) by XRD radiation of wavelength λ (nm) from measuring full width at half maximum of peaks (β) in radian located at ...Scherrer Equation, L=Kλ/β.cosθ, was developed in 1918, to calculate the nano crystallite size (L) by XRD radiation of wavelength λ (nm) from measuring full width at half maximum of peaks (β) in radian located at any 2θ in the pattern. Shape factor of K can be 0.62 - 2.08 and is usually taken as about 0.89. But, if all of the peaks of a pattern are going to give a similar value of L, then β.cosθ must be identical. This means that for a typical 5nm crystallite size and λ Cukα1 = 0.15405 nm the peak at 2θ = 170° must be more than ten times wide with respect to the peak at 2θ = 10°, which is never observed. The purpose of modified Scherrer equation given in this paper is to provide a new approach to the kind of using Scherrer equation, so that a least squares technique can be applied to minimize the sources of errors. Modified Scherrer equation plots lnβ against ln(1/cosθ) and obtains the intercept of a least squares line regression, ln=Kλ/L, from which a single value of L is obtained through all of the available peaks. This novel technique is used for a natural Hydroxyapatite (HA) of bovine bone fired at 600°C, 700°C, 900°C and 1100°C from which nano crystallite sizes of 22.8, 35.5, 37.3 and 38.1 nm were respectively obtained and 900°C was selected for biomaterials purposes. These results show that modified Scherrer equation method is promising in nano materials applications and can distinguish between 37.3 and 38.1 nm by using the data from all of the available peaks.展开更多
High-energy synchrotron diffraction offers great potential for experimental study of recrystallization kinetics. An experimental design to study the recrystallization mechanism of interstitial-free （IF） steel was im...High-energy synchrotron diffraction offers great potential for experimental study of recrystallization kinetics. An experimental design to study the recrystallization mechanism of interstitial-free （IF） steel was implemented. The whole annealing process of cold-rolled IF steel with 80% reduction was observed in situ using high-energy X-ray diffraction （HEXRD）. The results show how the main texture component of IF steel change, i.e. the α [∥rolling direction （RD）] fiber texture decreases and the γ [∥normal direction （ND）] fiber texture increases. The important part of the α fiber texture is that both the {100} and {112} texture decrease at the beginning of recrystallization. The γ fiber texture increases at the early stage of recrystallization which stems from the increase of {111}. Nevertheless, the {111} does not change after recrystallization. The dynamic evolution of the main texture components {100}, {112}, {111} and {111} is given by in-situ HEXRD.展开更多
Surface modification of γ-Fe2O3 nanoparticles synthesized by a chemically induced transition has been attempted by adding ZnCl2 during synthesis. The structure of the modified particles was studied using X-ray diffra...Surface modification of γ-Fe2O3 nanoparticles synthesized by a chemically induced transition has been attempted by adding ZnCl2 during synthesis. The structure of the modified particles was studied using X-ray diffraction (XRD) and transmission electron microscopy (TEM). The experimental results showed that ZnFe2O4 grew epitaxially on the γ- Fe2O3 crystallites to form composite nanoparticles with the spinel structure, on which FeCl3 might be adsorbed. The apparent grain size dc estimated by XRD using the Scherrer equation was larger rather than smaller than the average particle size measured by TEM. This paradox can be explained by the effect of absorption in the coating heterolayer.展开更多
High-temperature superconductivity in ceramic oxides is a new technology in which advances are occurring at a rapid pace. Here, the author describes some properties of a new nano crystalline ceramic Type II supercondu...High-temperature superconductivity in ceramic oxides is a new technology in which advances are occurring at a rapid pace. Here, the author describes some properties of a new nano crystalline ceramic Type II superconductor, PbSrCaCuO. Type II superconductors are usually made of metal alloys or complex oxide ceramics. The PSCCO perovskite phase structure was prepared by the conventional solid state reaction technique. In order to show the viability of the proposed method, super-conducting powder was prepared in special furnace. The sample was analyzed by X-ray Diffraction (XRD), Particle size determination, SEM and EDX. The comparison of XRD results with JCPDS files confirmed the orthorhombic structure of the sample with a ≠ b ≠ c and α = β = γ = 90°. Scanning electron microscopy (SEM) studies revealed that its particle size is in the nanometer range. It also confirmed the calculated value of particle size from Debye Scherrer’s formula. EDX spectrum shows the elements of the sample. X-ray instrumental peak broadening analysis was used to evaluate the size and lattice strain by the Williamson-Hall Plot method.展开更多
Fabrication of PVDF films has been making using Hot Roll Press. Preparation of samples carried out for nine different temperatures. This condition is carried out to see the effect of temperature fabrication on electri...Fabrication of PVDF films has been making using Hot Roll Press. Preparation of samples carried out for nine different temperatures. This condition is carried out to see the effect of temperature fabrication on electrical properties and crystallite size of PVDF films. The electrical properties like as surface resistivity are discussion focus in this paper. Surface resistivity properties of PVDF can be improved by mechanical treatment on the varying film thickness and the temperature. To obtain the diffraction pattern of sample characterization is performed using X-Ray Diffraction. Crystallite size of PVDF films calculate from broadening pattern of X-Ray Diffraction. Furthermore, from the diffraction pattern calculated β fraction and crystallite size, for calculation to determine the crystallite size of the sample by using the Scherrer equation. Has been obtained an increase piezoelectric properties of PVDF films that characterized by increasing β fraction. Have been obtained β fraction increased from 25.4% up to 44% for temperatures of 130°C up to 170°C, respectively. Resistivity value has been obtained at temperature 130°C up to 170°C, decreased from 1.23 × 104 Wm up to 0.21 × 104 Wm respectively. From the experimental results and the calculation of crystallite sizes obtained for the samples with temperature 130°C up to 170°C respectively are increased from 7.2 nm up to 20.54 nm. These results indicate that mechanical treatment caused increase β fraction and decrease surface resistivity. Increasing temperatures will also increase the size of the crystallite of the sample. This happens because with the increasing temperature causes the higher the degree of crystallization of PVDF film sample is formed, so that the crystallite size also increases.展开更多
Samples of chromium doped ZnO were synthesized using co-precipitation technique at room temperature. Structural and optical properties of Cr doped ZnO samples were investigated by X-ray diffraction technique (XRD and ...Samples of chromium doped ZnO were synthesized using co-precipitation technique at room temperature. Structural and optical properties of Cr doped ZnO samples were investigated by X-ray diffraction technique (XRD and UV-Visible spectroscopy (UV-Vis) respectively. X-ray diffraction (XRD) patterns confirm that the samples have hexagonal (wurtzite) structure with no additional peak which suggests that Cr ions go to the regular Zn sites in the ZnO crystal structure. The lattice constants were calculated using X-ray diffraction data and it is found that lattice parameters decrease with increasing Cr content. The average grain size was calculated using Scherrer’s formula for pure and Cr doped ZnO samples and it is observed that grain size is in the range 11 to17 nm. Band gap of Zn1–xCrxO samples has been evaluated using UV-Vis spectrometer. It is found that the band gap decreases as Cr increases;it is attributed to the s-d and p interactions and the smaller average grain size. It indicates that incorporation of Cr ions into the ZnO matrix. The chemical species of the grown crystals were identified by Fourier transform infrared spectroscopy (FTIR). From FTIR spectra it is observed that IR peaks corresponding to the Zn-O bands. Such results are presented in this paper quantitatively and qualitatively.展开更多
The effect of (Pt-loaded)TiO2 crystallite diameter (i.e. Scherrer size) on the photocatalytic water splitting rate was investigated. (Pt-loaded)TiO2 powders with a wide range of crystallite diameters from about 16 to ...The effect of (Pt-loaded)TiO2 crystallite diameter (i.e. Scherrer size) on the photocatalytic water splitting rate was investigated. (Pt-loaded)TiO2 powders with a wide range of crystallite diameters from about 16 to 45 nm with a blank region between about 23 and 41 nm were prepared by various annealing processes from an identical TiO2 powder. Water splitting experiments with these powders were carried out with methanol as an oxidizing sacrificial agent. It was found that the photocatalytic water splitting rate was sensitively affected by the crystallite diameter of the (Pt-loaded)TiO2 powder. More concretely, similar steep improvements of photocatalytic water splitting rates from around 15 and a little over 2 to about 30 μmol·m-2hr-1?were obtained in the two (Pt-loaded)TiO2 crystallite diameters ranging from 16 to 23 and from 41 to 45 nm, respectively.展开更多
X-ray crystallography is concerned with discovering and describing the crystal structure. High-temperature superconductivity in ceramic oxides is a new technology in which advances are occurring at a rapid pace. Here,...X-ray crystallography is concerned with discovering and describing the crystal structure. High-temperature superconductivity in ceramic oxides is a new technology in which advances are occurring at a rapid pace. Here, the author describes some properties of a new nano crystalline ceramic type II superconductor, PbBaTiO. Type II superconductors are usually made of metal alloys or complex oxide ceramics. The PBT perovskite phase structure was prepared by the conventional solid state reaction technique. The sample was analyzed by X-ray Diffraction (XRD), Particle size determination, SEM and EDX. The comparison of XRD results with JCPDS files confirmed the tetragonal structure of the sample with a = b ≠ c and α = β = γ = 90°. Scanning electron microscopy (SEM) studies revealed that its particle size was in the nanometer range. It also confirmed the calculated value of particle size from Debye Scherrer’s formula. EDX spectrum shows the elements of the sample. X-ray instrumental peak broadening analysis was used to evaluate the size and lattice strain by the Williamson-Hall Plot method.展开更多
With the discovery of high-TC superconducting materials like Yttrium Barium Cupric Oxide, Bismuth Strontium Calcium Copper Oxide and Thallium Calcium Barium Copper Oxide, tremendous interest has developed over the pas...With the discovery of high-TC superconducting materials like Yttrium Barium Cupric Oxide, Bismuth Strontium Calcium Copper Oxide and Thallium Calcium Barium Copper Oxide, tremendous interest has developed over the past two years in understanding these materials as well as utilizing them in a variety of applications. The thin films of these materials are expected to play an important role in the area of microelectronics, especially for interconnects in integrated circuits, Josephson junctions, magnetic field sensors and optical detectors. Here, the authors designed a new nanocrystalline ceramic type II high-TC superconductor, Gadolinium Barium Copper Oxide (GdBaCuO/GBCO). The GBCO perovskite phase structure was prepared by the conventional solid state thermochemical reaction technique involving mixing, milling, calcination and sintering. In GBCO system, the method for controlling microstructure and superconducting state is related to oxygen content consideration because small changes in oxygen concentration can often?lead to huge change in Tc. In order to show the viability of the proposed method, super-conducting powder was prepared in special furnace. The sample was analyzed by X-Ray Diffraction (XRD), an indispensible non-destructive tool for structural materials characterization and quality control which makes use of the Debye-Scherrer method. The comparison of XRD results with JCPDS files confirmed the orthorhombic structure of the sample. Micro-structural features are studied using Scanning Electron Microscopy (SEM) which revealed that its particle size is in the nanometer range. It also confirmed the calculated value of particle size from Debye Scherrer’s formula. EDX plot shows the presence of all the constituents. X-ray instrumental peak broadening analysis was used to evaluate the size and lattice strain by the Williamson-Hall Plot method.展开更多
In this study, the radio-frequency (RF) sputtering of cerium oxide was explored to determine the effect of the operating conditions on the film growth of cerium oxide on glass, and silicon substrates. The process vari...In this study, the radio-frequency (RF) sputtering of cerium oxide was explored to determine the effect of the operating conditions on the film growth of cerium oxide on glass, and silicon substrates. The process variables were sputtering time, input power and R (Ar/O2) ratio. In order to better understand the influence of process variables on the growth mechanism, the grain size and film thickness of cerium oxides were explored by using SEM, XRD, and α-step processes. From the results of SEM photographs, the grains of cerium oxides could be evaluated by using an imaging analysis technique. On the other hand, from the XRD data, with the aid of Scherrer’s equation, the crystalline sizes of cerium oxide crystals could be determined. The grain size was higher than the primary size, indicating the agglomeration of cerium oxide crystals. In addition, the effects of parameters on crystal size and film thickness are discussed herein following regression.展开更多
The high temperature superconductors are ceramic materials with layers of Copper-oxide spaced by layers containing Barium and other atoms. The Yttrium compound is somewhat unique in that it has a regular crystal struc...The high temperature superconductors are ceramic materials with layers of Copper-oxide spaced by layers containing Barium and other atoms. The Yttrium compound is somewhat unique in that it has a regular crystal structure while the Lanthanum version is classified as a solid solution. The Yttrium compound is often called the 1-2-3 superconductor because of the ratios of its constituents. Lanthanum Zirconium Yttrium Barium Calcium Copper Oxide (LaZrYBaCaCuO) was prepared by the usual solid state reaction method. In order to show the viability of the proposed method, super-conducting powder was prepared in special furnace. The sample was analyzed by X-ray Diffraction (XRD), Particle size determination, SEM and EDX. The comparison of XRD results with JCPDS files confirmed the orthorhombic structure of the sample with a ≠ b ≠ c and α = β = γ = 90°. Scanning Electron Microscopy (SEM) studies revealed that its particle size is in the nanometer range. It also confirmed the calculated value of particle size from Debye Scherrer’s formula. EDX spectrum shows the elements of the sample. X-ray instrumental peak broadening analysis was used to evaluate the size and lattice strain by the Williamson-Hall Plot method.展开更多
文摘Scherrer Equation, L=Kλ/β.cosθ, was developed in 1918, to calculate the nano crystallite size (L) by XRD radiation of wavelength λ (nm) from measuring full width at half maximum of peaks (β) in radian located at any 2θ in the pattern. Shape factor of K can be 0.62 - 2.08 and is usually taken as about 0.89. But, if all of the peaks of a pattern are going to give a similar value of L, then β.cosθ must be identical. This means that for a typical 5nm crystallite size and λ Cukα1 = 0.15405 nm the peak at 2θ = 170° must be more than ten times wide with respect to the peak at 2θ = 10°, which is never observed. The purpose of modified Scherrer equation given in this paper is to provide a new approach to the kind of using Scherrer equation, so that a least squares technique can be applied to minimize the sources of errors. Modified Scherrer equation plots lnβ against ln(1/cosθ) and obtains the intercept of a least squares line regression, ln=Kλ/L, from which a single value of L is obtained through all of the available peaks. This novel technique is used for a natural Hydroxyapatite (HA) of bovine bone fired at 600°C, 700°C, 900°C and 1100°C from which nano crystallite sizes of 22.8, 35.5, 37.3 and 38.1 nm were respectively obtained and 900°C was selected for biomaterials purposes. These results show that modified Scherrer equation method is promising in nano materials applications and can distinguish between 37.3 and 38.1 nm by using the data from all of the available peaks.
基金Sponsored by Key Projects in National Science and Technology Pillar Program of China(2011BAE13B03)Fundamental Research Funds for Central Universities of China(N110502001)
文摘High-energy synchrotron diffraction offers great potential for experimental study of recrystallization kinetics. An experimental design to study the recrystallization mechanism of interstitial-free （IF） steel was implemented. The whole annealing process of cold-rolled IF steel with 80% reduction was observed in situ using high-energy X-ray diffraction （HEXRD）. The results show how the main texture component of IF steel change, i.e. the α [∥rolling direction （RD）] fiber texture decreases and the γ [∥normal direction （ND）] fiber texture increases. The important part of the α fiber texture is that both the {100} and {112} texture decrease at the beginning of recrystallization. The γ fiber texture increases at the early stage of recrystallization which stems from the increase of {111}. Nevertheless, the {111} does not change after recrystallization. The dynamic evolution of the main texture components {100}, {112}, {111} and {111} is given by in-situ HEXRD.
文摘Surface modification of γ-Fe2O3 nanoparticles synthesized by a chemically induced transition has been attempted by adding ZnCl2 during synthesis. The structure of the modified particles was studied using X-ray diffraction (XRD) and transmission electron microscopy (TEM). The experimental results showed that ZnFe2O4 grew epitaxially on the γ- Fe2O3 crystallites to form composite nanoparticles with the spinel structure, on which FeCl3 might be adsorbed. The apparent grain size dc estimated by XRD using the Scherrer equation was larger rather than smaller than the average particle size measured by TEM. This paradox can be explained by the effect of absorption in the coating heterolayer.
文摘High-temperature superconductivity in ceramic oxides is a new technology in which advances are occurring at a rapid pace. Here, the author describes some properties of a new nano crystalline ceramic Type II superconductor, PbSrCaCuO. Type II superconductors are usually made of metal alloys or complex oxide ceramics. The PSCCO perovskite phase structure was prepared by the conventional solid state reaction technique. In order to show the viability of the proposed method, super-conducting powder was prepared in special furnace. The sample was analyzed by X-ray Diffraction (XRD), Particle size determination, SEM and EDX. The comparison of XRD results with JCPDS files confirmed the orthorhombic structure of the sample with a ≠ b ≠ c and α = β = γ = 90°. Scanning electron microscopy (SEM) studies revealed that its particle size is in the nanometer range. It also confirmed the calculated value of particle size from Debye Scherrer’s formula. EDX spectrum shows the elements of the sample. X-ray instrumental peak broadening analysis was used to evaluate the size and lattice strain by the Williamson-Hall Plot method.
文摘Fabrication of PVDF films has been making using Hot Roll Press. Preparation of samples carried out for nine different temperatures. This condition is carried out to see the effect of temperature fabrication on electrical properties and crystallite size of PVDF films. The electrical properties like as surface resistivity are discussion focus in this paper. Surface resistivity properties of PVDF can be improved by mechanical treatment on the varying film thickness and the temperature. To obtain the diffraction pattern of sample characterization is performed using X-Ray Diffraction. Crystallite size of PVDF films calculate from broadening pattern of X-Ray Diffraction. Furthermore, from the diffraction pattern calculated β fraction and crystallite size, for calculation to determine the crystallite size of the sample by using the Scherrer equation. Has been obtained an increase piezoelectric properties of PVDF films that characterized by increasing β fraction. Have been obtained β fraction increased from 25.4% up to 44% for temperatures of 130°C up to 170°C, respectively. Resistivity value has been obtained at temperature 130°C up to 170°C, decreased from 1.23 × 104 Wm up to 0.21 × 104 Wm respectively. From the experimental results and the calculation of crystallite sizes obtained for the samples with temperature 130°C up to 170°C respectively are increased from 7.2 nm up to 20.54 nm. These results indicate that mechanical treatment caused increase β fraction and decrease surface resistivity. Increasing temperatures will also increase the size of the crystallite of the sample. This happens because with the increasing temperature causes the higher the degree of crystallization of PVDF film sample is formed, so that the crystallite size also increases.
文摘Samples of chromium doped ZnO were synthesized using co-precipitation technique at room temperature. Structural and optical properties of Cr doped ZnO samples were investigated by X-ray diffraction technique (XRD and UV-Visible spectroscopy (UV-Vis) respectively. X-ray diffraction (XRD) patterns confirm that the samples have hexagonal (wurtzite) structure with no additional peak which suggests that Cr ions go to the regular Zn sites in the ZnO crystal structure. The lattice constants were calculated using X-ray diffraction data and it is found that lattice parameters decrease with increasing Cr content. The average grain size was calculated using Scherrer’s formula for pure and Cr doped ZnO samples and it is observed that grain size is in the range 11 to17 nm. Band gap of Zn1–xCrxO samples has been evaluated using UV-Vis spectrometer. It is found that the band gap decreases as Cr increases;it is attributed to the s-d and p interactions and the smaller average grain size. It indicates that incorporation of Cr ions into the ZnO matrix. The chemical species of the grown crystals were identified by Fourier transform infrared spectroscopy (FTIR). From FTIR spectra it is observed that IR peaks corresponding to the Zn-O bands. Such results are presented in this paper quantitatively and qualitatively.
文摘The effect of (Pt-loaded)TiO2 crystallite diameter (i.e. Scherrer size) on the photocatalytic water splitting rate was investigated. (Pt-loaded)TiO2 powders with a wide range of crystallite diameters from about 16 to 45 nm with a blank region between about 23 and 41 nm were prepared by various annealing processes from an identical TiO2 powder. Water splitting experiments with these powders were carried out with methanol as an oxidizing sacrificial agent. It was found that the photocatalytic water splitting rate was sensitively affected by the crystallite diameter of the (Pt-loaded)TiO2 powder. More concretely, similar steep improvements of photocatalytic water splitting rates from around 15 and a little over 2 to about 30 μmol·m-2hr-1?were obtained in the two (Pt-loaded)TiO2 crystallite diameters ranging from 16 to 23 and from 41 to 45 nm, respectively.
文摘X-ray crystallography is concerned with discovering and describing the crystal structure. High-temperature superconductivity in ceramic oxides is a new technology in which advances are occurring at a rapid pace. Here, the author describes some properties of a new nano crystalline ceramic type II superconductor, PbBaTiO. Type II superconductors are usually made of metal alloys or complex oxide ceramics. The PBT perovskite phase structure was prepared by the conventional solid state reaction technique. The sample was analyzed by X-ray Diffraction (XRD), Particle size determination, SEM and EDX. The comparison of XRD results with JCPDS files confirmed the tetragonal structure of the sample with a = b ≠ c and α = β = γ = 90°. Scanning electron microscopy (SEM) studies revealed that its particle size was in the nanometer range. It also confirmed the calculated value of particle size from Debye Scherrer’s formula. EDX spectrum shows the elements of the sample. X-ray instrumental peak broadening analysis was used to evaluate the size and lattice strain by the Williamson-Hall Plot method.
文摘With the discovery of high-TC superconducting materials like Yttrium Barium Cupric Oxide, Bismuth Strontium Calcium Copper Oxide and Thallium Calcium Barium Copper Oxide, tremendous interest has developed over the past two years in understanding these materials as well as utilizing them in a variety of applications. The thin films of these materials are expected to play an important role in the area of microelectronics, especially for interconnects in integrated circuits, Josephson junctions, magnetic field sensors and optical detectors. Here, the authors designed a new nanocrystalline ceramic type II high-TC superconductor, Gadolinium Barium Copper Oxide (GdBaCuO/GBCO). The GBCO perovskite phase structure was prepared by the conventional solid state thermochemical reaction technique involving mixing, milling, calcination and sintering. In GBCO system, the method for controlling microstructure and superconducting state is related to oxygen content consideration because small changes in oxygen concentration can often?lead to huge change in Tc. In order to show the viability of the proposed method, super-conducting powder was prepared in special furnace. The sample was analyzed by X-Ray Diffraction (XRD), an indispensible non-destructive tool for structural materials characterization and quality control which makes use of the Debye-Scherrer method. The comparison of XRD results with JCPDS files confirmed the orthorhombic structure of the sample. Micro-structural features are studied using Scanning Electron Microscopy (SEM) which revealed that its particle size is in the nanometer range. It also confirmed the calculated value of particle size from Debye Scherrer’s formula. EDX plot shows the presence of all the constituents. X-ray instrumental peak broadening analysis was used to evaluate the size and lattice strain by the Williamson-Hall Plot method.
文摘In this study, the radio-frequency (RF) sputtering of cerium oxide was explored to determine the effect of the operating conditions on the film growth of cerium oxide on glass, and silicon substrates. The process variables were sputtering time, input power and R (Ar/O2) ratio. In order to better understand the influence of process variables on the growth mechanism, the grain size and film thickness of cerium oxides were explored by using SEM, XRD, and α-step processes. From the results of SEM photographs, the grains of cerium oxides could be evaluated by using an imaging analysis technique. On the other hand, from the XRD data, with the aid of Scherrer’s equation, the crystalline sizes of cerium oxide crystals could be determined. The grain size was higher than the primary size, indicating the agglomeration of cerium oxide crystals. In addition, the effects of parameters on crystal size and film thickness are discussed herein following regression.
文摘The high temperature superconductors are ceramic materials with layers of Copper-oxide spaced by layers containing Barium and other atoms. The Yttrium compound is somewhat unique in that it has a regular crystal structure while the Lanthanum version is classified as a solid solution. The Yttrium compound is often called the 1-2-3 superconductor because of the ratios of its constituents. Lanthanum Zirconium Yttrium Barium Calcium Copper Oxide (LaZrYBaCaCuO) was prepared by the usual solid state reaction method. In order to show the viability of the proposed method, super-conducting powder was prepared in special furnace. The sample was analyzed by X-ray Diffraction (XRD), Particle size determination, SEM and EDX. The comparison of XRD results with JCPDS files confirmed the orthorhombic structure of the sample with a ≠ b ≠ c and α = β = γ = 90°. Scanning Electron Microscopy (SEM) studies revealed that its particle size is in the nanometer range. It also confirmed the calculated value of particle size from Debye Scherrer’s formula. EDX spectrum shows the elements of the sample. X-ray instrumental peak broadening analysis was used to evaluate the size and lattice strain by the Williamson-Hall Plot method.
