**3.2 Experimental parameters**

ASTM A516 G60 carbon steel (CS) and UNS 32760 super duplex steel (SDS) samples were used as metallic substrates subjected to the blasting process. The abrasives used encompassed two types of aluminum oxide particulate (sintered bauxite (SB) and demagnetized alumina (DA)). A D8 Discover Bruker AXS was the equipment used for data acquisition. The diffraction parameters are listed as following:


*Identification and Quantification of Phases in Steels by X Ray Diffraction Using Rietveld… DOI: http://dx.doi.org/10.5772/intechopen.91823*

Rietveld analysis was carried out using Diffrac PlusTOPAS (ver 4.2) software [32, 33].

## **3.3 X-ray analysis results**

Diffraction patterns were obtained for both substrate bulks, prior to the blasting process, to work as a reference pattern when measuring the degree of contamination of the samples subsequently analyzed. In the blasted surfaces, α-Fe (ferrite) [34] was observed in CS substrate, while α-Fe and γ-Fe [35] (ferrite and austenite, respectively) were present in the SDS substrate.

The commercial SB abrasive showed a predominance of phase alpha alumina (α-Al2O3) [36] which was verified in the SB abrasive, while the DA abrasive presented a majority of kappa alumina (κ-Al2O3) [37]. **Figure 2** presents the diffraction patterns for the carbon steel substrate before and after abrasive blasting (a) and for the super duplex steel before and after blasting (b), respectively.

**Figure 3** shows the detailed refined scan for the carbon steel substrate blasted with κ-Al2O3 from the DA abrasive and α-Al2O3 originated from the SB abrasive. In the same manner, **Figure 4** presents the result of the refined scan from the SDS substrate blasted with κ-Al2O3 from the DA abrasive and α-Al2O3 originated from the SB abrasive.

#### *3.3.1 Fitting parameters*

techniques. Surface roughness effects can also be considered and compensated by correction functions, which makes the Rietveld method more interesting to this

*(a, b) Abrasive particles hitting a metal substrate surface and (c) abrasive fragments deposited over the surface. (d) A real micrographs of a particulate allocated in the valley created by the particle impact in the surface.*

*Inelastic X-Ray Scattering and X-Ray Powder Diffraction Applications*

In Rietveld analysis of X-ray powder diffraction patterns, the effect of surface roughness (SR) of absorbing polycrystalline samples can be a source of systematic errors [26–30]. The SR effect can reduce the intensity of low-angle reflections and lead to anomalous low values of refined atomic displacement parameters. Depending on the degree of SR, the isotropic atom displacement can lead to negative values, which have no physical meaning. To correct such effects, a SR Suortti Model [31] has

ASTM A516 G60 carbon steel (CS) and UNS 32760 super duplex steel (SDS) samples were used as metallic substrates subjected to the blasting process. The abrasives used encompassed two types of aluminum oxide particulate (sintered bauxite (SB) and demagnetized alumina (DA)). A D8 Discover Bruker AXS was the equipment used for data acquisition. The diffraction parameters are listed as

• Primary optics: Co Göbel Mirror, two slits of 1 mm and 6 mm and a soller slit

• Secondary optics: Kβ filter, 8 mm slit, axial soller slit with divergence of 2.5°.

been used to guarantee a higher flexibility in terms of angular ranges.

type of process.

**Figure 1.**

following:

**3.1 Surface roughness corrections**

**3.2 Experimental parameters**

• Radiation: Co Kα (λ = 1789 Å).

with 2 cm x 1 cm aperture.

• 2θ range = 10° to 110°.

• Scanning velocity was 0.5 s/step.

• Step-size: 0.001°.

**86**

• Current and voltage: 40 mA 35 kV.

• Detector: point scanning detector—PSD type.

The structure refinement functions and parameters are listed as following:


#### **Figure 2.**

*(a) CS substrate after DA and SB blasting and (b) SDS substrate after DA and SB blasting. When blasting is performed with Al2O3 abrasives, one can see contamination by the new peaks introduced to the scans.*

#### **Figure 3.**

*Carbon steel substrate blasted with (a) DA and (b) SB abrasives. Observed data are indicated by thicker lines and calculated data by a solid thinner line. The gray lower curve presents the difference (residue) between the observed and calculated powder diffraction patterns.*

Zero error (2θ) sample displacement, absorption (1/cm), and lattice parameters of the phases were not fixed to provide the best calculated fitting.

#### *3.3.2 Fitting criteria*

Fitting criteria is a way to analyze the accuracy and precision of fitting. Based on the R-weighted pattern (Rwp) and the R-expected pattern (Re), it is possible to calculate the "goodness of fit," or simply *GOF*, to address the calculated values. Eqs. 4 and 5 present the variables used for the calculations for the R-values, which are then used to calculate the GOF [43–45]:

$$\mathbf{R\_{wp}} = \left[ \left( \sum \mathbf{w\_i} (\mathbf{y\_i}(\text{obs}) - \mathbf{y\_i}(\text{calc}))\_2 \right) / \left( \sum \mathbf{w\_i} (\mathbf{y\_i}(\text{obs})\_2) \right) \right] \mathbf{1}/2 \tag{4}$$

$$\mathbf{R\_{exp}} = \left[ (\mathbf{N} - \mathbf{P}) / \left( \sum \mathbf{w\_i} (\mathbf{y\_i} (\mathbf{obs}) \mathbf{2}) \right) \right] \mathbf{1} / 2 \tag{5}$$

$$\mathbf{GOF} = \left[ \left( \mathbf{S}\_{\mathbf{Y}} \right) / \left( \mathbf{N} - \mathbf{P} \right) \right] \mathbf{1} / 2 = \mathbf{R}\_{\mathbf{w}\mathbf{p}} / \mathbf{R}\_{\mathbf{exp}} \tag{6}$$

lower than 1.0 show a model that contain more parameters than can be justified by the quality of the data, as insufficient counting time for processing or high influence

*Quantitative phase calculations results (calculated average and standard deviation for a set of four blasted*

of background, for example.

**Figure 4.**

**Table 1.**

*substrate per abrasive.*

**SB abrasive**

**DA abrasive**

**Table 2.**

*samples).*

**89**

*Super duplex steel substrate blasted with (a) DA and (b) SB abrasives.*

**Abrasive CS substrate SDS substrate** SB 1.14 0.008 1.05 0.007 DA 1.13 0.010 1.07 0.010 MCS 1.09 0.012 1.06 0.010 MSS 1.09 0.011 1.06 0.011

*Identification and Quantification of Phases in Steels by X Ray Diffraction Using Rietveld…*

*DOI: http://dx.doi.org/10.5772/intechopen.91823*

*Fitting criteria for Rietveld calculations: calculated average goodness of fitness for the set of four samples of each*

Super duplex 38.79 1.84 25.01 2.13 36.20 2.92 Carbon steel 79.79 2.37 \* 20.21 2.37

Super duplex 47.31 2.21 36.92 1.16 15.77 2.52 Carbon steel 89.56 0.59 \* 10.45 0.59

**% α-Fe % γ-Fe %Al2O3**

where yi = intensity at the ith step; wi = weighting factor; N = number of observations; P = number of parameters; obs = observed and calc = calculated.

**Table 1** presents the GOF values for each calculation. The calculated values lied between 1 and 1.5, which is an indication of a satisfactory fitting. Numbers greater than 1.5 are usually seen as an inadequate model or false minimum, whereas those

*Identification and Quantification of Phases in Steels by X Ray Diffraction Using Rietveld… DOI: http://dx.doi.org/10.5772/intechopen.91823*

**Figure 4.** *Super duplex steel substrate blasted with (a) DA and (b) SB abrasives.*


#### **Table 1.**

Zero error (2θ) sample displacement, absorption (1/cm), and lattice parameters

*Carbon steel substrate blasted with (a) DA and (b) SB abrasives. Observed data are indicated by thicker lines and calculated data by a solid thinner line. The gray lower curve presents the difference (residue) between the*

Fitting criteria is a way to analyze the accuracy and precision of fitting. Based on

2

� � � � h i

**Table 1** presents the GOF values for each calculation. The calculated values lied between 1 and 1.5, which is an indication of a satisfactory fitting. Numbers greater than 1.5 are usually seen as an inadequate model or false minimum, whereas those

� � h i � �

where yi = intensity at the ith step; wi = weighting factor; N = number of observations; P = number of parameters; obs = observed and calc = calculated.

*<sup>=</sup>* <sup>X</sup>wi yi

ð Þ obs 2

� �*=*ð Þ <sup>N</sup> � <sup>P</sup> � �1*=*<sup>2</sup> <sup>¼</sup> Rwp*=*Rexp (6)

ð Þ obs <sup>2</sup>

1*=*2 (4)

1*=*2 (5)

the R-weighted pattern (Rwp) and the R-expected pattern (Re), it is possible to calculate the "goodness of fit," or simply *GOF*, to address the calculated values. Eqs. 4 and 5 present the variables used for the calculations for the R-values, which

of the phases were not fixed to provide the best calculated fitting.

*Inelastic X-Ray Scattering and X-Ray Powder Diffraction Applications*

ð Þ� obs yi ð Þ calc � �

Rexp <sup>¼</sup> ð Þ <sup>N</sup> � <sup>P</sup> *<sup>=</sup>* <sup>X</sup>wi yi

� �

GOF ¼ Sy

*3.3.2 Fitting criteria*

**Figure 3.**

**88**

are then used to calculate the GOF [43–45]:

*observed and calculated powder diffraction patterns.*

Rwp <sup>¼</sup> <sup>X</sup>wi yi

*Fitting criteria for Rietveld calculations: calculated average goodness of fitness for the set of four samples of each substrate per abrasive.*


#### **Table 2.**

*Quantitative phase calculations results (calculated average and standard deviation for a set of four blasted samples).*

lower than 1.0 show a model that contain more parameters than can be justified by the quality of the data, as insufficient counting time for processing or high influence of background, for example.

#### *Inelastic X-Ray Scattering and X-Ray Powder Diffraction Applications*

**Table 2** presents the quantitative phase analysis results for abrasive contamination in both CS and DSS substrates. 36.20% of the SDS and 20.21% of the carbon steel blasted area were contaminated by SB particles. When analyzing the DA abrasive, 15.77% of the SDS area was contaminated, while 10.45% of the CS substrate depicted particle contamination. The higher percentage of contamination on the SDS substrate can be related with its high values of hardness. The consequences of such higher particle contamination, for the performance of anticorrosive organic coatings, can be found in a subsequent work [46].

3.Three of the solubilized samples did not receive any additional aging heat

*Identification and Quantification of Phases in Steels by X Ray Diffraction Using Rietveld…*

4.Then, a group of 14 samples received an additional aging heat treatment to introduced different fractions of sigma phase. The aging heat treatment was

5.Finally, seven samples were heat treated at 1320 and at 1350°C for different intervals, in order to have high amounts of delta phase but no sigma phase

Phase volumetric fractions were measured in nine different regions of each sample, as depicted in **Figure 6**. Diffraction parameters used were the same

conducted at 1000°C for different time intervals, followed by water

treatment and remained in the solubilized condition.

quenching.

**4.2 X-ray analysis results**

presented in item 3.2 from this chapter.

*DOI: http://dx.doi.org/10.5772/intechopen.91823*

*Schematics of heat treatments performed in the SDSS samples.*

*Schematics of a sample with its nine analyzed points.*

at all.

**Figure 5.**

**Figure 6.**

**91**
