X-Ray Diffraction (XRD) Testing Data Analysis

MSE Supplies offers XRD data analysis services to support your XRD testing needs. We currently provide four types of analysis: phase identification, quantitative analysis (including K-value method and Rietveld refinement), crystallinity analysis, and grain size analysis. 

Phase Identification

Phase identification confirms the crystalline phases (composition) in a sample, defined as compounds with fixed structures formed by various elements (including elemental substances and solid solutions). It provides information on phase composition and structure, such as identifying quartz (SiO₂) polymorphs like α-quartz and β-quartz under different conditions.

Commonly used software includes JADE and HighScore, while frequently used databases are:

• PDF4+/PDF5 (ICDD)
• ICSD (Inorganic Crystal Structure Database)
• CSD (Cambridge Structural Database)
• COD (Crystallography Open Database)

K-value method

The K-value is the ratio of diffraction intensity between a pure substance and an internal standard. By adding a known weight of the standard to a sample and calculating the intensity ratio of the target phase to the standard, the target phase content can be determined.

This method is suitable for samples without amorphous phases. The sample is prepared on an X-ray diffractometer, and its diffraction pattern is measured. The integral intensities of selected peaks are used to calculate the mineral content.

Rietveld Refinement

The Rietveld method determines structural and peak shape parameters by iteratively fitting an assumed crystal structure model to measured polycrystalline diffraction patterns using full-pattern fitting and non-linear least squares. It calculates crystalline phase content from parameters like scaling factors.

By leveraging full-pattern data, the method addresses issues such as peak overlap, preferred orientation, and zero-point shifts with high accuracy. It is ideal for quantitative analysis of polycrystalline samples without amorphous phases, provided structural models are available.

Crystallinity Analysis

For samples with amorphous phases, XRD patterns consist of crystalline diffraction peaks and amorphous diffuse peaks. Crystallinity is the proportion of crystalline material in the sample, calculated as the ratio of the crystalline peak area (Ic​) to the total area of crystalline (Ic​) and amorphous peaks (Ia​):

Crystallinity=Ic​/(Ic + Ia)​​

Crystalline and amorphous peaks are distinguished by their FWHM (Full Width at Half Maximum), where peaks with FWHM > 3° are typically amorphous. For poorly crystallized samples, care is needed to distinguish peak types, often requiring references.

The calculation process involves importing data into software and performing full-pattern fitting using the pseudo-Voigt function. PDF cards are used for phase fitting when available; otherwise, a linear baseline is applied for peak identification and fitting. The integral areas of crystalline and amorphous peaks are then calculated to determine the relative crystallinity of the sample.

Grain Size Analysis

Grain size is calculated using the Scherrer equation:

D=Kλ/Bcosθ

where D is the grain size (nm), K is the Scherrer constant (typically 0.89), B is the integral FWHM, θ is the diffraction angle, and λ is the X-ray wavelength (0.154056 nm). Each diffraction peak yields a grain size, and the average D-value of all peaks for a given phase is typically used as the grain size. In specific cases, such as determining grain size in a particular direction, the FWHM of the corresponding diffraction peak is used. This method applies to grain sizes ≤100 nm.

The listed price is for reference only. Please request a quote for the actual cost.

Analytical Service Minimum order requirement: $250 per order. A $200 handling fee will be applied if order is below $250.

Please contact sales@msesupplies.com for additional information and instructions on our Analytical Services program. Confirmation of the sample(s) requirements, SDS sheets and additional information is needed prior to processing the Analytical Service order. 

***Please do not ship any samples without authorization from MSE Supplies***