Effect of Lattice Strain on Measured Thermal Properties of Fe Nanoparticles - An X-ray Diffraction Study

Endla Purushotham

doi:doi:10.11648/j.ijfmts.20190503.11

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Effect of Lattice Strain on Measured Thermal Properties of Fe Nanoparticles - An X-ray Diffraction Study

Endla Purushotham

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 5, Issue 3)

Received: 7 April 2019 Accepted: 19 July 2019 Published: 6 August 2019

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Abstract

In this paper, nano Fe particles have been produced by ball milling process. Fe powder was ball milled in an argon inert atmosphere Ball milling was carried out for the total duration of 20 hours. The sample was taken out after every 4 hours of milling and it was characterized for its particle size, lattice strain, and Debye-Waller factor, root mean square amplitudes of vibration by X-ray powder diffraction. The high-energy ball milling of Fe after 20 hours resulted in particle size of 39.44 nm and lattice stain 0.68 Lattice strains in Fe powder produced by milling have been analyzed by X-ray powder diffraction. The lattice strain (e) and Debye-Waller factor (B) are determined from the half-widths and integrated intensities of the Bragg reflections. Debye-Waller factor is found to increase with the lattice strain. From the correlation between the strain and effective Debye-Waller factors have been estimated for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied. The lattice strain (e) and Debye-Waller factor (B) are determined from the half-widths and integrated intensities of the Bragg reflections. In Fe, the Debye-Waller factor is found to increase with the lattice strain. From the correlation between the strain and effective Debye-Waller factor, the Debye-Waller factors for zero strain have been estimated for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied. As grinding time increases energy of vacancy formation decreases. However, the milling produces lattice strain and also enhances the effective Debye-Waller factor. By an extrapolation of the plot between the Debye-Waller factor and the lattice strain, the zero strain Debye-Waller factors are obtained for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied.

Published in	International Journal of Fluid Mechanics & Thermal Sciences (Volume 5, Issue 3)
DOI	10.11648/j.ijfmts.20190503.11
Page(s)	63-66
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Ball Milling, X-ray Diffraction, Particle Size, Lattice Strain, Debye-Waller Factor, Vacancy Formation Energy

References

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[2]	Paakkari, T. (1974). Acta Cryst. A30, 83.
[3]	Radchenko, M. E. and Tsvetkov, V. P. (1965). Ukr. fiz. Zh. 10, 99.
[4]	Mohanlal, S. K. (1979). J. Phys. C. 12, 2651.
[5]	Inagaki, M. Furuhashi, H., T Ozeki et al., J Mater Sci. 6, (1971) 1520.
[6]	M Inagaki, H Furuhashi, T Ozeki and S Naka J. Mater. Sci. 8, (1973) 312.
[7]	Sirdeshmukh, D. B., Subhadra, K. G., Hussain, K. A., Gopi Krishna, N., and Rag-havendra Rao. B., Cryst. Res. Technol 28, (1993) 15.
[8]	Gopi Krishna, N., and Sirdeshmukh., D. B., Indian J Pure & Appl Phys. 31, (1993) 198.
[9]	Chipman, D. R., and Paskin, A., J. Appl. Phys. 30, (1959) 1938.
[10]	Gopi Krishna, N and Sirdeshmukh, D. B. Indian J Pure & Appl Phys. 31, 198 (1993).
[11]	Gopi Krishna, N et al, Indian J Phys. 84 (7), 887 (2010).
[12]	Klug, H. P and Alexande L E, X-ray Diffraction Procedures (John Wiley and Sons, U.S.A.) (1974).
[13]	Cromer D T and Waber J T, Acta Cryst. 18 104 (1965).
[14]	International Tables for X-ray Crystallography Vol. III (Kynoch Press, Birmingham) (1968).
[15]	Cromer D T and Liberman D, J. Chem. Phys. 53 1891 (1970).
[16]	Benson G. C, and Gill E. K, Table of Integral Functions Related to Debye-Waller factor, National Research Council of Canada, Ottawa. (1966).
[17]	Vetelino, J. F., Gaur, S. P., Mitra, S. S., Phys. Rev. B5, (1972) 2360.

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Endla Purushotham. (2019). Effect of Lattice Strain on Measured Thermal Properties of Fe Nanoparticles - An X-ray Diffraction Study. International Journal of Fluid Mechanics & Thermal Sciences, 5(3), 63-66. https://doi.org/10.11648/j.ijfmts.20190503.11

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ACS Style

Endla Purushotham. Effect of Lattice Strain on Measured Thermal Properties of Fe Nanoparticles - An X-ray Diffraction Study. Int. J. Fluid Mech. Therm. Sci. 2019, 5(3), 63-66. doi: 10.11648/j.ijfmts.20190503.11

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AMA Style

Endla Purushotham. Effect of Lattice Strain on Measured Thermal Properties of Fe Nanoparticles - An X-ray Diffraction Study. Int J Fluid Mech Therm Sci. 2019;5(3):63-66. doi: 10.11648/j.ijfmts.20190503.11

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@article{10.11648/j.ijfmts.20190503.11,
  author = {Endla Purushotham},
  title = {Effect of Lattice Strain on Measured Thermal Properties of Fe Nanoparticles - An X-ray Diffraction Study},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {5},
  number = {3},
  pages = {63-66},
  doi = {10.11648/j.ijfmts.20190503.11},
  url = {https://doi.org/10.11648/j.ijfmts.20190503.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20190503.11},
  abstract = {In this paper, nano Fe particles have been produced by ball milling process. Fe powder was ball milled in an argon inert atmosphere Ball milling was carried out for the total duration of 20 hours. The sample was taken out after every 4 hours of milling and it was characterized for its particle size, lattice strain, and Debye-Waller factor, root mean square amplitudes of vibration by X-ray powder diffraction. The high-energy ball milling of Fe after 20 hours resulted in particle size of 39.44 nm and lattice stain 0.68 Lattice strains in Fe powder produced by milling have been analyzed by X-ray powder diffraction. The lattice strain (e) and Debye-Waller factor (B) are determined from the half-widths and integrated intensities of the Bragg reflections. Debye-Waller factor is found to increase with the lattice strain. From the correlation between the strain and effective Debye-Waller factors have been estimated for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied. The lattice strain (e) and Debye-Waller factor (B) are determined from the half-widths and integrated intensities of the Bragg reflections. In Fe, the Debye-Waller factor is found to increase with the lattice strain. From the correlation between the strain and effective Debye-Waller factor, the Debye-Waller factors for zero strain have been estimated for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied. As grinding time increases energy of vacancy formation decreases. However, the milling produces lattice strain and also enhances the effective Debye-Waller factor. By an extrapolation of the plot between the Debye-Waller factor and the lattice strain, the zero strain Debye-Waller factors are obtained for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied.},
 year = {2019}
}

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TY  - JOUR
T1  - Effect of Lattice Strain on Measured Thermal Properties of Fe Nanoparticles - An X-ray Diffraction Study
AU  - Endla Purushotham
Y1  - 2019/08/06
PY  - 2019
N1  - https://doi.org/10.11648/j.ijfmts.20190503.11
DO  - 10.11648/j.ijfmts.20190503.11
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 63
EP  - 66
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20190503.11
AB  - In this paper, nano Fe particles have been produced by ball milling process. Fe powder was ball milled in an argon inert atmosphere Ball milling was carried out for the total duration of 20 hours. The sample was taken out after every 4 hours of milling and it was characterized for its particle size, lattice strain, and Debye-Waller factor, root mean square amplitudes of vibration by X-ray powder diffraction. The high-energy ball milling of Fe after 20 hours resulted in particle size of 39.44 nm and lattice stain 0.68 Lattice strains in Fe powder produced by milling have been analyzed by X-ray powder diffraction. The lattice strain (e) and Debye-Waller factor (B) are determined from the half-widths and integrated intensities of the Bragg reflections. Debye-Waller factor is found to increase with the lattice strain. From the correlation between the strain and effective Debye-Waller factors have been estimated for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied. The lattice strain (e) and Debye-Waller factor (B) are determined from the half-widths and integrated intensities of the Bragg reflections. In Fe, the Debye-Waller factor is found to increase with the lattice strain. From the correlation between the strain and effective Debye-Waller factor, the Debye-Waller factors for zero strain have been estimated for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied. As grinding time increases energy of vacancy formation decreases. However, the milling produces lattice strain and also enhances the effective Debye-Waller factor. By an extrapolation of the plot between the Debye-Waller factor and the lattice strain, the zero strain Debye-Waller factors are obtained for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied.
VL  - 5
IS  - 3
ER  -

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Endla Purushotham

Department of Physics, S R Engineering College (Autonomous), Warangal, India

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Endla Purushotham. (2019). Effect of Lattice Strain on Measured Thermal Properties of Fe Nanoparticles - An X-ray Diffraction Study. International Journal of Fluid Mechanics & Thermal Sciences, 5(3), 63-66. https://doi.org/10.11648/j.ijfmts.20190503.11

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ACS Style

Endla Purushotham. Effect of Lattice Strain on Measured Thermal Properties of Fe Nanoparticles - An X-ray Diffraction Study. Int. J. Fluid Mech. Therm. Sci. 2019, 5(3), 63-66. doi: 10.11648/j.ijfmts.20190503.11

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AMA Style

Endla Purushotham. Effect of Lattice Strain on Measured Thermal Properties of Fe Nanoparticles - An X-ray Diffraction Study. Int J Fluid Mech Therm Sci. 2019;5(3):63-66. doi: 10.11648/j.ijfmts.20190503.11

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@article{10.11648/j.ijfmts.20190503.11,
  author = {Endla Purushotham},
  title = {Effect of Lattice Strain on Measured Thermal Properties of Fe Nanoparticles - An X-ray Diffraction Study},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {5},
  number = {3},
  pages = {63-66},
  doi = {10.11648/j.ijfmts.20190503.11},
  url = {https://doi.org/10.11648/j.ijfmts.20190503.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20190503.11},
  abstract = {In this paper, nano Fe particles have been produced by ball milling process. Fe powder was ball milled in an argon inert atmosphere Ball milling was carried out for the total duration of 20 hours. The sample was taken out after every 4 hours of milling and it was characterized for its particle size, lattice strain, and Debye-Waller factor, root mean square amplitudes of vibration by X-ray powder diffraction. The high-energy ball milling of Fe after 20 hours resulted in particle size of 39.44 nm and lattice stain 0.68 Lattice strains in Fe powder produced by milling have been analyzed by X-ray powder diffraction. The lattice strain (e) and Debye-Waller factor (B) are determined from the half-widths and integrated intensities of the Bragg reflections. Debye-Waller factor is found to increase with the lattice strain. From the correlation between the strain and effective Debye-Waller factors have been estimated for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied. The lattice strain (e) and Debye-Waller factor (B) are determined from the half-widths and integrated intensities of the Bragg reflections. In Fe, the Debye-Waller factor is found to increase with the lattice strain. From the correlation between the strain and effective Debye-Waller factor, the Debye-Waller factors for zero strain have been estimated for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied. As grinding time increases energy of vacancy formation decreases. However, the milling produces lattice strain and also enhances the effective Debye-Waller factor. By an extrapolation of the plot between the Debye-Waller factor and the lattice strain, the zero strain Debye-Waller factors are obtained for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied.},
 year = {2019}
}

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TY  - JOUR
T1  - Effect of Lattice Strain on Measured Thermal Properties of Fe Nanoparticles - An X-ray Diffraction Study
AU  - Endla Purushotham
Y1  - 2019/08/06
PY  - 2019
N1  - https://doi.org/10.11648/j.ijfmts.20190503.11
DO  - 10.11648/j.ijfmts.20190503.11
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 63
EP  - 66
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20190503.11
AB  - In this paper, nano Fe particles have been produced by ball milling process. Fe powder was ball milled in an argon inert atmosphere Ball milling was carried out for the total duration of 20 hours. The sample was taken out after every 4 hours of milling and it was characterized for its particle size, lattice strain, and Debye-Waller factor, root mean square amplitudes of vibration by X-ray powder diffraction. The high-energy ball milling of Fe after 20 hours resulted in particle size of 39.44 nm and lattice stain 0.68 Lattice strains in Fe powder produced by milling have been analyzed by X-ray powder diffraction. The lattice strain (e) and Debye-Waller factor (B) are determined from the half-widths and integrated intensities of the Bragg reflections. Debye-Waller factor is found to increase with the lattice strain. From the correlation between the strain and effective Debye-Waller factors have been estimated for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied. The lattice strain (e) and Debye-Waller factor (B) are determined from the half-widths and integrated intensities of the Bragg reflections. In Fe, the Debye-Waller factor is found to increase with the lattice strain. From the correlation between the strain and effective Debye-Waller factor, the Debye-Waller factors for zero strain have been estimated for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied. As grinding time increases energy of vacancy formation decreases. However, the milling produces lattice strain and also enhances the effective Debye-Waller factor. By an extrapolation of the plot between the Debye-Waller factor and the lattice strain, the zero strain Debye-Waller factors are obtained for Fe. The variation of energy of vacancy formation as a function of lattice strain has been studied.
VL  - 5
IS  - 3
ER  -

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