**1. Introduction**

Steel is the most common material used on earth. Applications vary from simple cutlery to spacecraft parts and are so vast; one finds even hard to list it all. This is mainly due to the versatility found in this type of iron and carbon alloy, in terms of physical, mechanical, and chemical properties. Also, when compared to other types of materials, steels are economically affordable. Therefore, steel has been studied for many decades and will continue to be so in the forthcoming years. Industrial plants have most of their equipment made of steel. Applications involving the oil and gas industry are very demanding in terms of optimizing the use of these steels for high performance in constant aggressive environments. In this case, the ultimate need is for steels that can resist both heavy loads and aggressive corrosive environments.

Some new classes of steels, such as the duplex steels, are of very much of interest nowadays, because of their good compromise between mechanical resistance and

corrosion protection [1, 2]. As any other metallic material though, they usually need thermal-mechanical processing in order to be adequate to the different uses. Thermal-activated processes may lead to the creation of new phases in the steel—some intentionally promoted, but some not. The knowledge of phase transformations in steels is mandatory to forecast the properties the material will acquire after such transformations [3]. Because steel has a long of range periodic atomic structure, with well-defined crystallographic aspects [4], X-ray diffraction [5] is one of the most important analytical techniques to identify those structures, in order to understand steel properties.

• The preferred orientation function Pk

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

• The background intensity at the i-th step, ybi

X K

yci ¼ s

to thermal treatments performed in specific steels.

**by X-ray diffraction quantitative analysis**

to avoid damages on the performance of the whole system.

can be found in organic coatings [9, 10].

• The structure factor modulus for the kth Bragg reflection |FK|

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

LKjFKj

Wp <sup>¼</sup> sp ZMV � �*<sup>=</sup>*

Quantitative phase analysis using the Rietveld method [8] employs the relative weight fraction W of each phase p in a mixture of n phases calculated according to

> Xn i¼1

where s is the Rietveld scale factor, Z is number of formula units per unit cell, M is the mass of the formula unit (atomic mass unit), and V is the unit cell volume (Å3

The following sections will present two specific cases of the utilization of the Rietveld refinement method with further quantitative phase analysis (QPA). Those practical cases demonstrate how this methodology was applied for the analysis of steel parts, addressing the presence of unwanted phases and phase unbalance due

**3. Case 1: abrasive blasting in steel surfaces—addressing contamination**

Duplex and super duplex steels (DS and SDS, respectively) have been widely used in oil and gas industries because of their advantages over other steel types in terms of mechanical properties and corrosion resistance [1, 2]. The harsh environments where those steels are in service require protection from degradation that

The coating performance is highly dependent on the surface pretreatment and the application procedures [11, 12]. Those must be in accordance with standard documents [13, 14], which include procedures for blast cleaning. Blasting processes though might affect the coating adhesion and corrosion rate, depending on the degree of contamination from the abrasive particulate material used, as those particulates can promote local pH changes and/or galvanic effects [15]. The common abrasives employed for surface treatment of steels are aluminum oxide and martensitic steel abrasives due to their high values of hardness. Pulverization of the grits, however, can lead to undesired particulate depositions over the steel surfaces (**Figure 1**), which induce local alkalization, decreasing the protection. Because of all these factors, substrate contamination needs to be engaged in an efficient fashion,

Determination of the inclusion or second-phase constituent, by metallographic analysis [16], can be used to account for such contamination. However, the technique can be quite time-consuming. Quantitative phase analysis by X-ray diffraction though can be used for such task [17–22]. The Rietveld method can provide very accurate estimative of the relative and/or absolute amount of the component phases [22–25] and has advantages over traditional internal-standard-based

<sup>2</sup> Ø 2ð Þ <sup>Ɵ</sup><sup>i</sup> � <sup>2</sup>Ɵ<sup>k</sup> PKA <sup>þ</sup> ybi (2)

si ð Þ ZMV <sup>i</sup> (3)

).

• The absorption factor A

the equation:

**85**

Lately, the identification and quantification of phases have been upgraded by many methods of peak refinement. These methods provide a good calculation of crystallographic parameters, enabling precise measurements to be performed in different materials. Among those methods, the Rietveld refinement [6] has been gaining space among crystallographers due to its analytical capabilities. A general overview of the Rietveld profile fitting and quantitative phase analysis is provided in the following sections. Then, two specific applications of X-ray diffraction for steel phase analysis are described. The first case refers to the quantification of contaminants on steel substrates after jet impingement, aiming corrosion resistance by organic coatings. The second case is related to the phase transformations occurring in a type of steel used in oil and gas applications, when this material is subjected to high temperatures due to welding procedures or operation in service. In both situations, peak refinement is made, for the calculation of crystallographic parameters and for quantitative phase calculations.

#### **2. Peak refinement and quantitative phase analysis: the Rietveld method**

X-ray profile fitting provides important crystallographic information from the analyzed material. There are several different techniques nowadays, but one of them, known as the Rietveld refinement method, has many advantages over the others. In this method, first presented by Hugo Rietveld to refine nuclear and magnetic structures [6] and lately developed by many scientists [7], least-squares refinements are carried out until the best fit is obtained between the entire observed powder diffraction pattern and the full calculated pattern. The quantity minimized in the least-squares refinement is the residual Sy:

$$\mathbf{S}\_{\mathbf{y}} = \sum\_{\mathbf{i}} \mathbf{w}\_{\mathbf{i}} \left(\mathbf{y}\_{\mathbf{i}} \mathbf{-} \mathbf{y}\_{\mathbf{c}i}\right)^{2} \tag{1}$$

where yi = observed intensity at the i-th step; yci = calculated intensity at the i-th step; wi = 1/yi.

The equation model applied for the method (Eq. 2) considers the following parameters:


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


corrosion protection [1, 2]. As any other metallic material though, they usually need thermal-mechanical processing in order to be adequate to the different uses. Thermal-activated processes may lead to the creation of new phases in the steel—some intentionally promoted, but some not. The knowledge of phase transformations in steels is mandatory to forecast the properties the material will acquire after such transformations [3]. Because steel has a long of range periodic atomic structure, with well-defined crystallographic aspects [4], X-ray diffraction [5] is one of the most important analytical techniques to identify those structures, in

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

Lately, the identification and quantification of phases have been upgraded by many methods of peak refinement. These methods provide a good calculation of crystallographic parameters, enabling precise measurements to be performed in different materials. Among those methods, the Rietveld refinement [6] has been gaining space among crystallographers due to its analytical capabilities. A general overview of the Rietveld profile fitting and quantitative phase analysis is provided in the following sections. Then, two specific applications of X-ray diffraction for steel phase analysis are described. The first case refers to the quantification of contaminants on steel substrates after jet impingement, aiming corrosion resistance by organic coatings. The second case is related to the phase transformations occurring in a type of steel used in oil and gas applications, when this material is subjected to high temperatures due to welding procedures or operation in service. In both situations, peak refinement is made, for the calculation of crystallographic

**2. Peak refinement and quantitative phase analysis: the Rietveld method**

X-ray profile fitting provides important crystallographic information from the analyzed material. There are several different techniques nowadays, but one of them, known as the Rietveld refinement method, has many advantages over the others. In this method, first presented by Hugo Rietveld to refine nuclear and magnetic structures [6] and lately developed by many scientists [7], least-squares refinements are carried out until the best fit is obtained between the entire observed powder diffraction pattern and the full calculated pattern. The quantity minimized

wi yi

where yi = observed intensity at the i-th step; yci = calculated intensity at the i-th

The equation model applied for the method (Eq. 2) considers the following

• The Bragg reflections contributing to a specific intensity yi at every specific i

• The Miller indices, h, k, l, for a Bragg reflection, represented by K

• The Lorentz polarization and multiplication factors LK

–yci

� �**<sup>2</sup>** (1)

Sy <sup>¼</sup> <sup>X</sup> i

order to understand steel properties.

parameters and for quantitative phase calculations.

in the least-squares refinement is the residual Sy:

point in the whole pattern

• The reflection profile function ∅

• A scale factor s

step; wi = 1/yi.

parameters:

**84**


$$\mathbf{y\_{ci}} = \mathbf{s} \sum\_{\mathbf{K}} \mathbf{L}\_{\mathbf{K}} |\mathbf{F\_{K}}|^{2} \oslash \left(2\Theta\_{\mathbf{i}} - 2\Theta\_{\mathbf{k}}\right) \mathbf{P\_{K}} \mathbf{A} + \mathbf{y\_{bi}} \tag{2}$$

Quantitative phase analysis using the Rietveld method [8] employs the relative weight fraction W of each phase p in a mixture of n phases calculated according to the equation:

$$\mathbf{W\_{p}} = \left(\mathbf{s\_{p}} \,\mathbf{ZMV}\right) / \sum\_{i=1}^{n} \mathbf{s\_{i}} \left(\mathbf{ZMV}\right)\_{i} \tag{3}$$

where s is the Rietveld scale factor, Z is number of formula units per unit cell, M is the mass of the formula unit (atomic mass unit), and V is the unit cell volume (Å3 ).

The following sections will present two specific cases of the utilization of the Rietveld refinement method with further quantitative phase analysis (QPA). Those practical cases demonstrate how this methodology was applied for the analysis of steel parts, addressing the presence of unwanted phases and phase unbalance due to thermal treatments performed in specific steels.

## **3. Case 1: abrasive blasting in steel surfaces—addressing contamination by X-ray diffraction quantitative analysis**

Duplex and super duplex steels (DS and SDS, respectively) have been widely used in oil and gas industries because of their advantages over other steel types in terms of mechanical properties and corrosion resistance [1, 2]. The harsh environments where those steels are in service require protection from degradation that can be found in organic coatings [9, 10].

The coating performance is highly dependent on the surface pretreatment and the application procedures [11, 12]. Those must be in accordance with standard documents [13, 14], which include procedures for blast cleaning. Blasting processes though might affect the coating adhesion and corrosion rate, depending on the degree of contamination from the abrasive particulate material used, as those particulates can promote local pH changes and/or galvanic effects [15]. The common abrasives employed for surface treatment of steels are aluminum oxide and martensitic steel abrasives due to their high values of hardness. Pulverization of the grits, however, can lead to undesired particulate depositions over the steel surfaces (**Figure 1**), which induce local alkalization, decreasing the protection. Because of all these factors, substrate contamination needs to be engaged in an efficient fashion, to avoid damages on the performance of the whole system.

Determination of the inclusion or second-phase constituent, by metallographic analysis [16], can be used to account for such contamination. However, the technique can be quite time-consuming. Quantitative phase analysis by X-ray diffraction though can be used for such task [17–22]. The Rietveld method can provide very accurate estimative of the relative and/or absolute amount of the component phases [22–25] and has advantages over traditional internal-standard-based

Rietveld analysis was carried out using Diffrac PlusTOPAS (ver 4.2)

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

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,

The commercial SB abrasive showed a predominance of phase alpha alumina

**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 structure refinement functions and parameters are listed as following:

• Chebyshev polynomial of fourth degree [38] and Topas 1/x background

• PO spherical harmonics [42] model of order 6 for the alumina phase

• Preferred orientation (PO) March-Dollase model [39–41] for calculating the preferred crystal orientations of α-Fe and γ-Fe phases (this is mandatory especially for processed steel products like ingots, sheets, and pipe sections)

*(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.*

function and (background fitting intensities, *yib*)

(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.

software [32, 33].

the SB abrasive.

**Figure 2.**

**87**

*3.3.1 Fitting parameters*

**3.3 X-ray analysis results**

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

respectively) were present in the SDS substrate.

#### **Figure 1.**

*(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.*

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