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(1) h = L 4 / A − 2 (2) S = 4. ρ L + 2 h An indication of the average crystal lengths within the fibrils was obtained by measurement of the integral breadth of the 002 and 004 reflection of cellulose-I, at 17.2° and 34.9° 2θ respectively.
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The sharper 002 and 004 meridional peaks were corrected for the effect of instrumental broadening, according to equation (6), where the integral breath IB = peak height/peak area, and IBexp and IBstd respectively are the integral breadths of the fitted peak and the diffraction standard.
The integral breadth of a polycrystalline silicon standard was taken as 0.148°.
Crystallite size of α-MoO3 amounted to ~ 60 nm as calculated from the integral breadths of XRD peaks using the Scherrer equation [15].
Above 700 K the integral breadths of thermally treated Mo(O,N 3 became similar to those of α-MoO3.
Williamson–Hall (WH) plot is the plot of the integral breadth in the reciprocal space (ΔK = βcosθ/λ, β-FWHM of XRD line) with respect to reciprocal lattice space (K = 2sinθ/λ).
The relationship of the internal strain ϵ and the integral breadth β value of each (00L) peak of the GdBCO film is as the expression: 16 ϵ 2 = β 2 cos 2 θ sin 2 θ, (1).
The size of the crystal grain was obtained from the peak width of X-ray diffraction using the two major models known and employed in bulk materials: the integral breadth and the Warren Averbach methods.
Because of the characteristic evolution of integral breadth with temperature as depicted in Figure 3 the changes observed were interpreted in terms of varying disorder in the crystallites of Mo(O,N 3.
However, the value of integral breadth as used for dimensional calculations is not dependent on the mathematical peak form.
Conversely, above ~623 K the integral breadth determined for Mo(O,N 3 changed dramatically while the effect decreased going from 020 to 110 and 101.
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