ASTM D5187 Standard Test Method for Determination of Crystallite Size (Lc) of Calcined Petroleum Coke by X-Ray Diffraction
10. Procedure
10.1 Prepare and operate the diffractometer in accordance with the manufacturer's instructions. Once established, closely control all instrumental parameters to ensure repeatable analyses.
10.2 Place the packed sample in the instrument's sample holder and energize the X-ray source.
10.3 Obtain a diffraction pattern rate scanned at 1°/min or step scanned at 0.2°/step over the range of 14 to 34° 2Ⓗ. Record the data either on a strip chart recorder scanning at 1°/min or through computer software designed to read and store the angular and intensity measurements.
10.4 For manual interpretation from a strip chart recording, refer to Fig. 1.
10.4.1 Determine the average low and high background (Points A and B, respectively) on the diffraction scan and connect them with a straight line.
10.4.2 Construct Line CD parallel to AB and going through the apex of the peak at point G [(hkl 5 002 at 3.35Å)]. Draw the line such that if the peak is irregular it will pass through the average of the irregularities.
10.4.3 Determine the full width half maximum (FWHM) of the peak by measuring the vertical distance between CD and AB. Construct Line EF such that it intersects the peak at half of its maximum value. The points at which EF intersects the peak are 2Ⓗ1 and 2Ⓗ2, respectively.
10.5 For computer simulation based on the intensities recorded at 0.2° intervals, produce a mathematical representation of the diffraction curve. Determine the baseline, peak, peak height, and half peak height to produce the half peak height angles, 2Ⓗ1 and 2Ⓗ2, as above.
11. Calculation
11.1 Determine the following parameter:
Δpo = 2(sinⒽ2 – sinⒽ1)/λ
where:
λ = the wavelength of the target material of the X-ray tube expressed in angstrom units,
Ⓗ1 = the angle at the half peak intensity (2Ⓗ1/2) width on the low side, and
Ⓗ2 = the angle at the half peak intensity (2Ⓗ2/2) width on the high side.
NOTE 1 - The latter calculations were derived from the Scherrer equation:
Lc = (Kλ)/(β cos Ⓗ)
where:
K = an arbitrary constant that is equivalent to 0.89 for Lc,
λ = wavelength of the source radiation measured in angstroms,
β = line breadth of the pure diffraction peak measured in radians, and
Ⓗ = angular location of the peak maximum (2Ⓗ/2) measured in degrees.
11.2 Determine the mean crystallite height by:
Lc = 0.89/Δpo
NOTE 2 - The above calculation makes the assumption that the true line width is equal to the measured width, the contribution of instrumental line broadening is negligible.
