## Comparing XRD Geometries and a Case Study in using the Seeman-Bohlin Geometry in a portable diffractometer.

**X-ray diffraction **

**What is X-ray diffraction?**

X-ray Diffraction (XRD) is a non-destructive technique that provides detailed information about the crystallographic structure, chemical composition, and physical properties of materials. A common analytical technique for the comprehensive examination of the structure of crystalline materials; in other words, scanning a material’s fingerprint. Often used for identifying and quantifying material phases and investigating crystallinity of materials

From EAG SMART Chart –

**What are the applications of portable XRD?**

- Firstly, Identification/quantification of crystalline phase
- Measurement of average crystallite size, strain, or micro-strain effects in bulk materials and thin film
- Determination of the ratio of crystalline to amorphous material in bulk materials and thin films
- Phase identification for a large variety of bulk and thin-film samples
- Detecting minor crystalline phases (at concentrations greater than ~1%)
- Determining crystallite size for polycrystalline films and materials
- Determining percentage of material in crystalline form versus amorphous
- Measuring sub-milligram loose powder or dried solution samples for phase identification

**Different approaches to XRD Analysis**

**Bragg-Brentano geometry **

** **

The Bragg-Brentano geometry is the most used among diffractometers. In the diffractometer the relationship between θ (the angle between the direction of the incident beam and the specimen surface) and 2θ (the angle between the directions of incident beam and the diffracted beam) is maintained throughout the analysis.

rs and rd are fixed and equal and define the diffractometer- or measuring circle in which the specimen is always at the center.

The geometry is called θ − 2θ geometry if the tube is fixed and the rotation of the specimen and receiving slit are coupled in a ratio θ : 2θ.

It is called θ − θ geometry if the specimen is fixed and both the tube and receiving slit rotate at an equal angle θ.

During rotation of the components the radius of the focusing circle changes.

**Seeman-Bohlin geometry **

The Seeman-Bohlin diffractometer can have a fixed tube and specimen. The radius, rd varies with 2θ to maintain the focusing geometry.

Alternatively, the source and receiving slit rotate at an equal angle θ and both rs and rd vary to remain on the focusing circle. During rotation of the components the radius of the focusing circle remains the same.

For accurate measurement, the diffractometer components have to be aligned in such a fashion that the following conditions are satisfied:

- line source, specimen surface, and receiving slit are all parallel,
- the specimen surface coincides with the diffractometer axis for the Bragg-Brentano geometry or with the diffractometer circle for the Seeman-Bohlin geometry,
- the line source and receiving slit lie on the diffractometer circle

**Seeman-Bohlin Geometry versus Bragg-Brentano Geometry**

Though the Bragg-Brentano geometry is most used in diffractometers, the Seeman-Bohlin can be a serious alternative.

When it comes to capturing the diffraction pattern, the latter has some advantages.

With equal radius, the Seeman-Bohlin geometry provides double the resolving power of the Bragg-Brentano geometry.

The resolving power is defined as d/ ∆d and is obtained by differentiating Bragg’s law for n=1:

λ = 2d sin θ .

d θ /dd = 1/d tan θ (1)

thus d /∆d = −1 /∆θ tan θ (2)

The variation in angle with respect to the specimen, ∆θ, in relation to the displacement along the circumference of diffractometer circle, ∆S, differs for both geometries:

∆θ = ∆S/ 2R for the Seeman-Bohlin (a) and

∆θ = ∆S/ R for the Bragg-Brentano geometry (b).

This is displayed in figure below. For the Seeman-Bohlin geometry the resolving power is:

d /∆d = −2R ∆S tan θ (3)

whereas for the Bragg-Brentano geometry:

d /∆d = −R ∆S tan θ (4)

where R is the radius of the diffractometer circle.

When a square box will be taken as outline of the occupied space the volume differs for both geometries.

For equal occupied space the radius of the Seeman-Bohlin geometry would be 1 /2 √ 2 times the radius of the Bragg-Brentano geometry In this case the difference in resolving power would be about 40%.

## CASE STUDY OF RESOLUTION OF THE PLANET PORTABLE XRD

appnote3-Resolution_of_the_planet

Download our App Note on the Resolution of the Planet Portable XRD when compared to standard laboratory systems

# Conclusion

The attainable resolution of the planet compares well to the attainable resolution of a standard laboratory-based instrument. The attainable resolution of the planet is best in class among currently available portable X-ray diffractometers.

**References**

- Design of an X-ray diffractometer (XRD) for a Mars-rover, Master’s thesis R.W.J. Melenhorst DCT 2006.14
- Report on Resolution of the Planet – XploreX EU
- EAG Smart Chart