Quantitative Phase Analysis

The method developed and implemented by us for determining the quantitative content of phases in a mixture (up to six phase components) is based on a mathematical algorithm for its  refinement simultaneous with the refinement of the parameters of the crystal structure (atomic coordinates, atomic filling coefficients of the corresponding positions, temperature factors, texture) of each phase.

The reflection intensity of each single phase in a mixture can be represented as:

,

where for each phase: I(hkl)^I is the reflection intensity from hkl plane ; c_i is the volume concentration; Q_i is the scattering ability per unit volume ; m_i is the linear absorption coefficient; d_i is the average particle size of the i-phase component ; is the average linear absorption coefficient of the mixture; I₀ is the intensity of the incident beam.

The scattering ability of the i-th phase of the mixture, in turn, is calculated as:

Q_i =

where I(hkl)ⁱ⁰   is the scattering intensity; V_i is the volume of the unit cell of the i-phase component . 

The set of programs for quantitative phase analysis developed has been tested on many standard mixtures (samples with known quantitative phase composition). If the texture in the sample is insignificant, the average particle size is small (up to 1 mm), or the values ​​of linear coefficients are close (), the uncertainty in determining the quantitative content of phase components does not exceed 2%. If at least one of the specified conditions is violated, the correct determination of grain sizes in phase components (by optical or electron microscopy methods, etc.) becomes very important. Some problems are also associated with the correct consideration of texture, which can lead to an increase in the error in determining the quantitative content of phases (up to 6%).

Fig. 1 illustrates the result of determining the quantitative ratio of sulfofluoride phases in the synthesis product of dysprosium sulfofluoride: Dy₃S₂F₄ (Yb₃S₂F₄ -type structure, calculated content of 56 wt. %) and DySF (PbFCl-type structure, calculated content of 44 wt. %), R_I = 0.074.

 

 

Fig.1 Graphical result of quantitative phase analysis  (circles – experimental values ​​of intensities, solid black and red lines – processed)

 

Return

 Return