Copyright ©JCPDS - International Centre for Diffraction Data 2005, Advances in X-ray Analysis, Volume 48.
RIETVELD PROCESSING OF PHASES IN HIGHLY
TEXTURED REFRACTORY STEELS
Jorge L. Garin and Rodolfo L. Mannheim
Universidad de Santiago de Chile
Department of Metallurgical Engineering
Casilla 10233, Santiago, Chile
ABSTRACT
Quantitative phase analysis by means of X-ray diffraction Rietveld refinement was performed on
cast heat-resistant steels of the HC (25Cr-3Ni) and HD (30Cr-6Ni) type. These kinds of alloys
usually contain strong preferred orientations due to dendritic solidification of the austenitic and
ferritic solid solution phases, which must be taken into account whether accurate processing of
powder diffraction data is required. The X-ray powder diffraction data analysis was performed in
such a way that the strong orientation effects caused by the solid solution components austenite
and ferrite were adequately corrected by using the March-Dollase model. The results obtained
indicate that among all the other compounds, a proper correction of the texture effects of the
solid solution phases is mandatory to yield a successful matching of the calculated X-ray
diffraction profile with the experimental data.
INTRODUCTION
A number of cast high-alloy stainless steels have been developed for a variety of service
requirements among many industrial applications. These materials, currently known as heatresistant steels or simply refractory steels, compose a unique family of Fe-Cr-Ni alloys having
excellent mechanical properties such as toughness, strength, and corrosion resistance for service
at elevated temperatures, normally above 873 K [1-3]. Depending upon the chromium and nickel
content, the microstructure of the casting can result in a fully austenitic (γ), ferritic (α), or
duplex-phase distribution, together with a fine dispersion of carbides or intermetallic compounds
in the matrix [4], which increases high-temperature strength considerably. Alloys with carbon
contents greater than 0.20 wt % show chromium carbides in the microstructure, regardless of
solution treatment. In ferritic or partly ferritic steels the ferrite pools undergo a transformation to
the intermediate phase σ and, to a lesser extent, to phase χ when the alloy is heated above 813 K.
Particularly the formation of sigma-phase can be very detrimental in many applications because
of its influence on the mechanical properties of the material; in fact, embrittlement and corrosion
penetration may result. Sigma-phase usually precipitates when the alloy is subjected to lengthy
heating in the range from 813 K to 1173 K [5-7]. This phase is a complex intermetallic
compound of Fe and Cr, which considerably affects the toughness and creep properties. The
structure type of the compound is based upon an ideal stoichiometric composition AX2,
Pearson’s code tP30, and space group P42/mnm [8,9]. Since the chemical composition in the FeCr system is approximately Cr6Fe7, the Fe and Cr atoms are disorderly located with fractional
site occupation factors among the suitable equivalent positions in the space group, disclosing a
polyhedral array of the Frank-Kasper type. Sigma preferably nucleates along grain boundaries of
δ-ferrite-austenite, α-ferrite-austenite, or δ-ferrite-δ-ferrite. Figure 1 shows a phase diagram of
82
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Copyright ©JCPDS - International Centre for Diffraction Data 2005, Advances in X-ray Analysis, Volume 48.
the Cr-Fe-Ni system [10], where the phase boundaries can be clearly visualized. Compounds
with nearly equi-atomic composition in Fe and Cr are formed by an order-disorder
transformation of the alpha-phase, while those with smaller contents of Cr precipitate through a
eutectoid transformation of the kind α = γ + σ [11]. Other important precipitates in the ferriticaustenitic matrix of these alloys are carbides of the type M7C3 and M23C6 [12], where the
equivalent site positions of the M-metal are randomly occupied by Fe and Cr atoms. Owing to
their strong effect on the mechanical properties of the alloys, the determination of relative
amounts of all phases in the microstructure demand a rather precise processing of the
experimental data. Taking into account the usually complex diffraction patterns, which disclose
many overlapping reflections, and the strong preferred orientations of the matrix phases caused
by solidification dendrites formed in thin casting sections, the present investigation attempts to
validate the use of the Rietveld method to resolve the referred difficulties in two representative
alloys, such as HC-type (mainly ferritic microstructure) and HD (ferritic-austenitic
microstructure).
Figure 1. Cr-Fe-Ni phase diagram: isothermal section at 300 K.
EXPERIMENTAL
The preparation of the alloys analyzed in this study was carried out in an induction furnace
(INDUCTOTHERM) of 30 kg capacity equipped with a high-alumina crucible. Cr and Ni
contents were adjusted to yield the standard composition of the HC- and HD-type refractory
steels. All casts were poured in Y-shape molds, manufactured with self-hardening phenolic resin,
according to the A395 ASTM standard, to give samples of 13 mm and 50 mm thickness. Hence
the average chemical composition of the resulting Y-shape ingots, determined by means of
emission spectroscopy (SPECTROLAB), is detailed in Table 1. The contents of the main
elements match the standard composition ranges defined for these steels (ASTM A297, 608).
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Copyright ©JCPDS - International Centre for Diffraction Data 2005, Advances in X-ray Analysis, Volume 48.
Table 1. Chemical composition of the samples (wt. %).
Sample
C
0,53
0,36
HC
HD
Cr
25,02
31,23
Ni
4,26
6,08
Si
0,66
0,43
Mn
0,43
0,38
P
0,05
0,04
S
0,04
0,05
Mo
0,10
0,14
Specimens suitable for heat treatment, light microscopy, and X-ray diffraction experiments, of
dimensions 45 × 25 × 5 mm3, were machined from the test section of the Y-blocks; the
observation surfaces were prepared by typical metallographic techniques, up to wet polishing
with alumina of 0.05 µm particle size. The heat treatment processes carried out to induce sigmaphase precipitation consisted of heating the samples at 1053 K for various periods of time, in the
range from 1 to 104 hours; for the sake of the present work, two representative samples have
been considered, i.e. 24 hour treatment for the HC-steel and 80 hours for the HD-steel. The
metallography carried out on the heat-treated specimens revealed the microstructures shown in
Figures 2(a) and 2(b); the matrix is composed of ferrite (gray background), containing a
distribution of big austenite isles (white zones). The precipitation of sigma-phase can be
visualized along the ferrite-austenite grain boundaries in Figure 2(a) and Figure 2(b), while some
precipitation has also occurred inside the grains as shown only in Figure 2(a). The darkest small
areas in the pictures correspond to metal carbides which form eutectic mixtures in Figure 2(a)
and isolated carbides in Figure 2(b). On the other side, the orientation effects of the austenite
grains are clearly illustrated in Figure 2(b).
(a)
(b)
Figure 2. Microstructure of the samples: (a) HC-steel, (b) HD-steel.
The X-ray powder diffraction data were collected on a SIEMENS D5000 diffractometer
equipped with a diffracted-beam graphite-monochromator, CuKα radiation (λ=0.15406 nm, 40
kV, 30 mA), Bragg-Brentano geometry, θ-θ scan, sample spinning, divergence slit of 1 mm,
antiscatter slit of 1 mm, and receiving slit of 0.1 mm.
RESULTS
The Rietveld refinements were performed based upon typical measurement and global
parameters, using the distribution package for DBWS-9807a system of programs [13,14]. The
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Copyright ©JCPDS - International Centre for Diffraction Data 2005, Advances in X-ray Analysis, Volume 48.
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powder diffraction patterns of both specimens resulted in strong preferred orientation effects of
the austenite and ferrite solid solution phases along [123] and [111] directions respectively. It is
well known that body-centered and face-centered cubic metals usually have their columnar
grains with [100] normal to the mold wall and parallel to the direction of the heat flow. However,
there are exceptions; when the ideal direction of the heat flow deviates from being normal to the
wall, the resulting orientations are not typical. In the present work this phenomenon was caused
by the insertion of chilling copper plates in the bottom of the mold, giving rise to preferred
orientations of the type [123] and [111]. Hence the correction term in the Rietveld refinement
utilized the March-Dollase function [15], calculated as:
PK = (G21 cos2 α + (1/G1) sin2 α)-3/2
(1)
where α is the angle between the normal to the diffracting plane and the presumed cylindricalsymmetry axis of the texture, and G1 is a numerical refinable parameter. This model was
privileged over the Rietveld-Toraya model, where the G1 adjustable parameter tends to be highly
correlated with the scale parameter if preferred orientations are strong. Due to the somewhat
simpler formation of dendrites in the castings, the uniaxial March-Dollase model is applicable to
cast steels, and so has been extensively used by the authors within this scope. Conversely,
preferred orientations resulting from cold work will demand a more-complex texture model
where the orientation distribution function must be taken into account.
The pseudo-Voigt function was used for the simulation of the peak shapes [16]. Finally, the
background was modeled by a 3rd order polynomial in 2θ with refinable coefficients. A total of
five phases were considered in the refinement process, namely Fe(Cr,Ni) ferrite, Fe(Cr,Ni)
austenite, sigma phase, Cr23C6, and Cr7C3. The crystal data utilized in the calculation were those
reported from single-crystal analysis of sigma-phase [17,18], Cr23C6 [19], and Cr7C3 [20]. At the
first step, scaling factors, overall temperature factors, background, lattice constants and profile
parameters were fitted, then preferred orientations parameters were taken into account due to
marked texture effects of the ferritic and austenitic phases. Figure 3 illustrates the final Rietveld
plot of the HC sample. Although not shown here, similar results were obtained from the HD
steel. Afterward, the content of the component phases of the microstructure, as calculated
through the expression [21]:
Wp =
S p ( ZMV ) p
(2)
N
∑ S (ZMV )
i =1
i
i
is detailed in Table 2, together with the resulting numerical criteria of fit, Rp and Rwp [22].
Table 2. Content of phases in the microstructure (mass %).
Sample
α
γ
σ
Cr23C6
Cr7C3
Rp
Rwp
HC
75.41
13.40
9.81
0.11
1.27
0.09
0.13
HD
50.10
13.2
38.2
0.12
1.13
0.08
0.12
Copyright ©JCPDS - International Centre for Diffraction Data 2005, Advances in X-ray Analysis, Volume 48.
Figure 3. Final Rietveld plot of the HC sample.
CONCLUDING REMARKS
Two samples of different heat-resistant steels with severe preferred orientations of the solid
solution component phases were quantitatively analyzed by means of Rietveld refinement. The
main advantage of this processing was the use of the March-Dollase model for correction of the
strong texture effects on the diffraction pattern, which yielded the lower R-values and much
better represented the relative amounts of phases in the samples. This statement is based upon
comparison to poor-quality data obtained by means of computer-aided microscopy, where image
analysis depends greatly upon the ability of the optical system to resolve the subject in question.
In this study, the presence of more than three phases made it very hard to obtain accurate results.
ACKNOWLEDGEMENTS
Support for this work was provided by Universidad de Santiago de Chile and FONDECYT
Project N° 1020058. The authors greatly appreciate this assistance.
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