Modified Scherrer Equation to Estimate More Accurately Nano-Crystallite Size Using XRD

Affiliation(s)

Department of Materials Engineering, Najafabad branch, Islamic Azad University, Isfahan, Iran.

Department of Materials Engineering, Najafabad branch, Islamic Azad University, Isfahan, Iran.

ABSTRACT

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 Cukα*_{1} = 0.15405 nm the peak at 2*θ* = 170° must be more than ten times wide with respect to the peak at 2*θ* = 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/cos*θ*) 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.

Scherrer Equation,

Cite this paper

A. Monshi, M. Foroughi and M. Monshi, "Modified Scherrer Equation to Estimate More Accurately Nano-Crystallite Size Using XRD,"*World Journal of Nano Science and Engineering*, Vol. 2 No. 3, 2012, pp. 154-160. doi: 10.4236/wjnse.2012.23020.

A. Monshi, M. Foroughi and M. Monshi, "Modified Scherrer Equation to Estimate More Accurately Nano-Crystallite Size Using XRD,"

References

[1] P. Scherrer, “Bestimmung der Gr?sse und der inneren Struktur von Kolloidteilchen mittels R?ntgenstrahlen, Nachrichten von der Gesellschaft der Wissenschaften, G?ttingen”, 1918, pp 98–100.

[2] J. Langford, A. Wilson, “Scherrer after sixty years: A survey and some new results in the determination of crystallite size”, J Applied Crystallography, Vol. 11, 1978, pp. 102–103. doi:10.1107/S0021889878012844

[3] H. Klug, L. Alexander, “X–ray diffraction procedure for polycrystallite and amorphous materials (2th ed.)”, New York: John Wiley and Sons, 1974.

[4] S. Dinilchenko, O. Kukharenko, C. Moseke, I. Protsenko, L. Sukhodub, B. Sulkio–Cleff, “Determination of the bone mineral crystallite size and lattice strain from diffraction line broadening”, Research and Technology Crystal, Vol. 37(11), 2002, 1234–1240.

[5] A. Monshi, S. Soltan Attar, “A New Method to Measure Nano Size Crystals by Scherrer Equation Using XRD”, Majlesi Journal of Materials Engineering, Vol. 2(6), 2009, pp. 9–18 (Persian).

[6] M.R. Foroughi, S. Karbasi, R. Ebrahimi–Kahrizsangi, “Physical and mechanical properties of a poly–3–hydroxylbutyratecoated nanocrystalline hydroxyapatite scaffold for bone tissue engineering”, J. Porous Mater., 2011. doi:10.1007/s10934–011–9518–1.

[7] P. Shipman, G. Foster, M. Schoeninger, “Burnt Bones and Teeth: an Experimental Study of Color, Morphology, Crystal Structure and Shrinkage”, J. Archaeological Sci., Vol. 11, 1984, pp. 307–325. doi:10.1016/0305–4403(84)90013–X

[1] P. Scherrer, “Bestimmung der Gr?sse und der inneren Struktur von Kolloidteilchen mittels R?ntgenstrahlen, Nachrichten von der Gesellschaft der Wissenschaften, G?ttingen”, 1918, pp 98–100.

[2] J. Langford, A. Wilson, “Scherrer after sixty years: A survey and some new results in the determination of crystallite size”, J Applied Crystallography, Vol. 11, 1978, pp. 102–103. doi:10.1107/S0021889878012844

[3] H. Klug, L. Alexander, “X–ray diffraction procedure for polycrystallite and amorphous materials (2th ed.)”, New York: John Wiley and Sons, 1974.

[4] S. Dinilchenko, O. Kukharenko, C. Moseke, I. Protsenko, L. Sukhodub, B. Sulkio–Cleff, “Determination of the bone mineral crystallite size and lattice strain from diffraction line broadening”, Research and Technology Crystal, Vol. 37(11), 2002, 1234–1240.

[5] A. Monshi, S. Soltan Attar, “A New Method to Measure Nano Size Crystals by Scherrer Equation Using XRD”, Majlesi Journal of Materials Engineering, Vol. 2(6), 2009, pp. 9–18 (Persian).

[6] M.R. Foroughi, S. Karbasi, R. Ebrahimi–Kahrizsangi, “Physical and mechanical properties of a poly–3–hydroxylbutyratecoated nanocrystalline hydroxyapatite scaffold for bone tissue engineering”, J. Porous Mater., 2011. doi:10.1007/s10934–011–9518–1.

[7] P. Shipman, G. Foster, M. Schoeninger, “Burnt Bones and Teeth: an Experimental Study of Color, Morphology, Crystal Structure and Shrinkage”, J. Archaeological Sci., Vol. 11, 1984, pp. 307–325. doi:10.1016/0305–4403(84)90013–X