Measuring the Crystallite Size of Graphite in Calcined Petroleum Coke

Calcined Petroleum Coke (CPC) is a graphite-based material commonly used in metallurgy, fuel production, and aluminum production. As a derivative of raw petroleum coke, it occurs through a high-temperature process. 

CPC has excellent electrical conductivity and contains high amounts of carbon. The CPC’s potential quality as an electrode is dependent on the crystallite size (CS, L_c).  Because of this, it is critical to evaluate the CPC crystallite size. X-Ray diffraction (XRD) is an excellent method for CS determination that is in accordance with the ASTM D5187 standard.

L_c is calculated using the formula:

 Δpo = 2(sinθ₂  – sinθ₁)/λ

This formula comes from the fundamental relationship between the size and the peak width of scattering domains. This was established in the Scherrer equation.¹

where: θ₁ = lower angle at half peak intensity width

θ₂ = higher angle at half peak intensity width

λ = incident wavelength

L_c = (Kλ)/((β_obs – β_inst)cosθ)

K = arbitrary constant 0.89–1.39

λ. = incident wavelength

β_obs = measured peak line breadth

β_inst = instrument peak line breadth contribution

θ = angular location of the diffraction peak in degrees 

Later formulas can derive an expression for L_c that is accurate for calcined petroleum coke. 

L_c = 0.89/Δpo

The Williamson-Hall plot starts from the deconvoluting contributions of strain and size on the peak widening, resulting in more precise L_c values. ²

ε_str = strain component 

Instrument and Software

Figure 1 shows the Thermo Scientific™ ARL™ X’TRA Companion X-Ray Diffractometer. It is a simple, user-friendly benchtop XRD system for process control and more advanced applications.

The ARL X’TRA Companion uses a 160 mm radius θ/θ goniometer in Bragg-Brentano geometry paired with a 600 W X-Ray source (Cu or Co).

Soller slits and divergence manage the axial and radial adjustment of the beam, while a variable beam knife reduces air scattering. 

Additional options include an integrated water chiller. With a state-of-the-art solid-state pixel detector (55 x 55 μm pitch), the ARL X’TRA Companion offers exceptionally speedy data collection and arrives with one-click Rietveld quantification capabilities and automated result transmission to a Laboratory Information Management System (LIMS).

Figure 1. ARL X’TRA Companion diffraction system. Image Credit: Thermo Fisher Scientific – Production Process & Analytics

Experimental 

Using Cu Kα (1.541874 Å) radiation, graphite certified reference material RDC-1104 from R&D carbon was measured in reflection for two minutes. To minimize penetration depth error, the sample was prepared in a zero-background sample holder, and sample spinning was used during acquisition.

Figure 2. Measurement of RDC-1104 Graphite sample. Data were obtained at room temperature. Image Credit: Thermo Fisher Scientific – Production Process & Analytics

Results

Making use of the Scherrer formula with the FWHM of the [002] reflection of graphite leads to a L_c of 28.0 Å (see Figure 2). This is in ideal comparison to the certified value of 28.5(15) Å.

The FWHM was ascertained through profile fitting the graphite [002] reflection with a Pseudo-Voigt function. This method is compliant with ASTM D5187 because it is a computational approach to determine L_c. The Williamson-Hall method did not influence the analysis results as this graphite sample exhibits no strain.

Conclusion

The ARL X’TRA Companion is well suited to ascertain the crystallite size in CPC samples according to ASTM D5187.

References and Further Reading

1. P. Scherrer, Göttinger Nachrichten Gesell. 1918 2, 98-100.
2. G. K. Williamson, W. H. Hall, Acta Metall. 1953, 1, 22-31.

This information has been sourced, reviewed and adapted from materials provided by Thermo Fisher Scientific – Solutions for Industrial and Safety Applications.

For more information on this source, please visit Thermo Fisher Scientific – Production Process & Analytics.