X-ray diffraction peak width as hardness indicator

In X-ray diffraction (XRD) the diffracted peak position shift as a function of an incident X-ray beam angle correlates to the residual stress of the sample. The width of the diffracted peak also holds information about the microstructure of the material. In this article the correlation between the peak width and hardness of the material is demonstrated.

What is hardness?

Hardness is often used in everyday language. In materials science, hardness is a measure of the resistance to localized plastic deformation, which can be measured in a quantitative way. There are multiple standardized indentation hardness scales, for example Rockwell, Vickers and Brinell.
When a component is manufactured a certain level of hardness is desired to maximize the wear resistance and lifetime. In some cases, the level of hardness may not be what was desired due to some manufacturing process step or material property, hence the hardness needs to be verified as a quality control measure.

Micrograph of a weld seam cutout with Vickers (HV1) mapping
Figure 1: Micrograph of a weld seam cutout with Vickers (HV1) mapping. Courtesy of LUT.

What is peak width?

In XRD residual stress measurements the peak position of diffracted photons as a function of the incident beam angle is recorded. Strain in the sample material lattice causes these peaks to shift during tilting, from which the residual stress state can be analyzed. In Fig. 2 the XRD diffraction data with multiple X-ray beam incident angles are shown, where the peak shift can be seen due to residual stress in the material.

Figure 2: XRD diffraction data with multiple tilt angles showing peak shift due to residual stress.

The width of the diffraction peak is typically represented by the full width at half maximum (FWHM) value. The value is self-explanatory: How wide is the peak at the half of the maximum height (Fig. 3). When the microstructure of a material changes i.e. there are additional interstitial elements in the lattice, the peak width increases. This typically also means that the material gets harder. The peak width is also affected for example by the instrument itself, the grain size of the material and certain residual stress types.

Full width at half maximum of a diffraction peak from XRD measurement
Figure 3: Full width at half maximum of a diffraction peak from XRD measurement.

In Fig. 4 diffraction peaks from locations with varying level of hardness is shown.

Figure 4: a FWHM mapping measurement with XRD. Different peaks are from different locations from the sample where the hardness has also changed.
Figure 4: Peak width variation from a FWHM mapping measurement with XRD. Different peaks are from different locations from the sample where the hardness has also changed.

FWHM measurement method

Typically in residual stress measurements the FWHM is a by-product of the actual measurement data. But when one is only interested in the peak width the measurement routine can be vastly simplified. It’s not necessary to measure from multiple tilting angles, meaning that the diffractometer does not need to be tilted during a single measurement.
With the advancements in X-ray detection, a single exposure can be done in less than a second. This opens doors for continuous movement measurement of the peak-width. Sample can be moved continuously under the diffractometer (or vice versa) and continuous data can be collected instead of stop-and-go measurements.

Samples

Jominy bar sample was manufactured and the hardness (Rockwell C HRC) profile measured at the Tampere University. Jominy bar end-quench test is a procedure used for measuring steel hardenability. By end-quenching a varying hardness is achieved along the sample. Linear FWHM mapping was measured with Xstress DR45 and Xstress XY (Fig. 5).

Jominy bar sample and the measurement setup. Red arrow shows the mapping direction.
Figure 5: Jominy bar sample and the measurement setup. Red arrow shows the mapping direction.

A welding cut-out sample was provided by Lappeenranta-Lahti University of Technology (LUT). Hardness mapping measurements (Vickers 1kg (HV1)) were carried out also at LUT. The FWHM mapping was carried out with Xstress DR45 and Xstress XY (Fig. 6). A total of about 800 measurement points were collected and the mapping lasted for 8 minutes.

Welding cut-out sample FWHM mapping
Figure 6: Welding cut-out sample FWHM mapping with Xstress DR45.

Results and discussion

Jominy bar results

From Fig. 7 it can be seen that both FWHM and the HRC values descend when going further away from the quench end, as can be expected. Unfortunately no measured HRC valued had been measured between 30 – 50 HRC as that range is very narrow and mechanically difficult to measure.
In Fig. 8 the HRC values are plotted as a function of FWHM values. It can be seen that between 30 HRC – 60 HRC the FWHM correlate quite linearly to each other with a good sensitivity, whereas in the softer region (15 HRC – 30 HRC) the FHWM values start to lose sensitivity to the hardness. Nevertheless, for a given sample material the harder the material the wider the diffraction peak is.

FWHM and HRC values as a function of location on the Jominy bar
Figure 7: FWHM and HRC values as a function of location on the Jominy bar.
HRC values as a function of FWHM values
Figure 8: HRC values as a function of FWHM values.

Weld cut-out sample results

In Fig. 9 the XRD FHWM data from the weld cut-out sample is shown.

FWHM data from the weld cutout
Figure 9: FWHM data from the weld cutout.

In Fig. 10 the Vickers hardness mapping is shown. Notice that the hardness mapping area was much smaller than the XRD mapping area. Due to this reason the FWHM data was interpolated for same coordinate values, after which each FWHM value was correlated to the corresponding hardness value. The correlation graph is in Fig. 11.

Vickers hardness data
Figure 10: Vickers hardness data.
Vickers hardness and FWHM correlation
Figure 11: Vickers hardness and FWHM correlation.

Conclusions

In this study the possibilities of peak position as a hardness indicator was demonstrated. With the state of the art XRD equipment a hardness mapping of large areas can be analyzed in minutes in a completely non-destructive way.

Instruments used for this application

Xstress

Xstress DR45

Newest generation of X-ray diffractometers delivering high quality data faster than ever before.

Xstress_DR45_XY_closeup

Xstress XY

Xstress XY table with optimized footprint can be attached to the Xstress Cabinet. Travel is 200 mm in the X and Y directions with accuracy of ±0.015 mm. X-Y movements are operated in Xstress Studio software. Xstress Studio provides also visualization for the movements.

Article Type: Application note
Technology: X-ray diffraction
application: Heat treatmenthardness