1 Kinetics of transformation border of metastable miscibility gap in Fe -Cr alloy and limit of Cr solubility in iron at 858 K

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Kinetics of transformation, border of metastable miscibility gap in Fe-Cr

alloy and limit of Cr solubility in iron at 858 K

S. M. Dubiel1,2* and J. Żukrowski2

1AGH University of Science and Technology, Faculty of Physics and Applied

Computer Science, al. A. Mickiewicza 30, 30-059 Kraków, Poland, 2AGH University

of Science and Technology, Academic Center for Materials and Nanotechnology,

al. A. Mickiewicza 30, 30-059 Kraków, Poland

Abstract

The study was aimed at determination of the position of the Fe-rich border of the

metastable miscibility gap (MMG) and of the solubility limit of Cr in iron at 858 K.

Towards this end a Fe73.7Cr26.3 alloy was isothermally annealed at 858 K in vacuum

up to 8144 hours and Mössbauer spectra were recorded at room temperature after

every step of the annealing. Three spectral parameters viz. the average hyperfine

field, <B>, the average isomer shift, <IS>, and the probability of the atomic

configuration with no Cr atoms in the two-shell vicinity of the probe Fe atoms, P(0,0),

gave evidence that the transformation process takes place in two stages. All three

parameters could have been well described in terms of the Johnson-Mehl-Avrami-

Kolmogorov equation, yielding kinetics parameters. The first stage, associated with

the phase decomposition, proceeded much faster than the second stage, associated

with the alpha-to-sigma phase transformation. The most reliable estimation of the

position of the MMG and that of the value of the Cr solubility limit was obtained from

the annealing time dependence of <B>, namely 24.5 at.% Cr for the former and 20.3

at.% Cr for the latter. A comparison of these figures with the recent phase diagrams

pertinent to Fe-Cr system was done.

Key words: Fe-Cr alloys; phase diagram; miscibility gap; solubility limit; Mössbauer

spectroscopy

* Corresponding author: Stanislaw.Dubiel@fis.agh.edu.pl

1. Introduction

Fe-Cr alloys have been likely the most frequently studied binary alloys. The unusual

interest in them follows, on one hand, form their interesting magnetism

(ferromagnetism, antiferromagnetism, spin-glass), and on the other hand from their

technological importance especially in the steel making industry. Regarding the latter

the Fe-Cr alloys make up the major component of stainless steels, among which

ferritic/martensitic (FM) ones have been used as important structural materials in

numerous sectors of industry e. g. power pants (including nuclear ones), chemical

and petrochemical industries. This role of FM steels follows from their excellent

properties and, in particular, high toughness, good resistance to high-temperature

corrosion and low swelling. Accordingly, they have been used in various industrial

branches to produce devices that work at service at elevated temperatures, often in

aggressive environment and under neutron irradiation. Concerning the nuclear power

plants, for example, their life time is limited by a degradation of structural devices like

vessel and primary circuit due to exposure to radiation and high temperature. The

former generates radiation damage and the latter thermal aging. Both result in

degradation of mechanical properties and enhanced corrosion. The main reasons for

the high-temperature degradation are precipitation of: (1) Cr-rich ’ phase and (2) -

phase. Both effects can explained based on the crystallographic phase diagram of

the Fe-Cr system. Following the Fe-Cr phase diagram [1], the maximum temperature

at which precipitation of’ occurs is 900 K. Yet, current in-situ neutron diffraction

studies performed on a quasi equiatomic Fe-Cr alloy found that the top of the

miscibility gap happens rather at 853 K [2]. The’ precipitation causes significant

embrittlement that is known in the literature as “475oC embrittlement” due to the fact

that the highest embrittlement rate is at 475oC. The content of Cr in ’ is greater than

85 at% what makes it so brittle. The -phase, in turn, is prone to precipitate if the

annealing temperature lies between 770 and 1100 K, and the content of Cr is

between 15 and 85 at.%. The ’ precipitates as a consequence of the so-called

phase decomposition that results in formation of Fe-rich () and Cr-rich (’) phases.

An interest in this phenomenon has two aspects. First, one wants to know

mechanism(s) underlying the decomposition process, and, second, borders of the

field in which it occurs (so-called miscibility gap - MG). Two mechanisms have been

suggested based on many studies: (1) nucleation and growth (NG), and (2) spinodal

(SP). The latter is active in the central part of MG, while the former on both “sides” of

the SP field [2]. Thus, the phase fields of NG are close to the Fe-rich and Cr-rich

borders of MG. Fe-rich border of MG is more important from the technological view-

point because it is located close to the Cr concentration at which the Fe-Cr alloy

becomes stainless i.e. 10.5 at%. This Fe-rich border line can be also regarded as

the limit of Cr solubility in iron. Despite numerous studies, both theoretical and

experimental, were dedicated to this matter clear cut picture has not emerged yet.

Theoretical calculations give different predictions, e. g. [1, 3-10], and experimental

data, obtained with different techniques like: transmission electron microscopy,

electron dispersive microscopy, Mössbauer spectroscopy, small angle neutron

scattering, diffuse neutron scattering and resistivity measurements, have a broad

dispersion [6]. The dispersion can be, on one hand, due to diverse sensitivity and

special resolution of various methods applied, and, on the other hand, it can be

caused by different conditions under which samples were investigated (size of

samples, their initial degree of homogeneity and strain as well as the annealing time).

On the contrary, values of the solubility limit determined by means of the Mössbauer

spectroscopy (MS) display systematic trend [11-15]. Thus one can hope that a set of

the Mössbauer data constitutes a good basis for validation of different predictions

pertinent to the matter in question. In this paper it is reported on the data obtained by

studying a Fe73.7Cr26.3 sample isothermally annealed at 858 K for up to 8144 hours.

2. Experimental

Measurements were performed on a 25 m thick foil in form a 20x20 mm rectangle

obtained by rolling down 100 m thick tape of a Fe73.7Cr26.3 alloy. The alloy, in turn,

was prepared by melting in an induction furnace under protective Ar atmosphere

adequate masses of Armco-iron and chromium of 99.9% purity. The obtained ingot

was next rolled down to the thickness of 100 m. Its composition was determined by

a chemical analysis. To stimulate the decomposition/transformation process, the foil

was isothermally annealed under dynamic vacuum (<10-4 Torr) at 858 K for up to

8144 hours. After each annealing step, a 57Fe Mössbauer spectrum was recorded at

room temperature in a transmission mode using a standard spectrometer with a drive

working in a sinusoidal mode. A 57Co/Rh source was used as a supplier of 14.4 keV

gamma rays. Its activity permitted recording a statistically good spectrum in 1024

channels of a multichannel analyzer within a 2 days run.

The spectra were analyzed assuming that an effect of Cr atoms situated in the first-

two neighbor shells around 57Fe probe nuclei, 1NN-2NN, on the hyperfine field, B,

and on the center shift, CS, was additive i.e.

)0,0(),( XnXmXnmX 

, where

X=B or CS,



Xm is a change of X caused by one Cr atom present in 1NN (m=1) or in

2NN (m=2). This procedure has already proved to properly work in the analysis of

Mössbauer spectra registered on various Fe-based binary alloys including Fe-Cr

ones e. g. [11-20]. The total number of possible atomic configurations (m,n) in the

1NN-2NN approximation is equal to 63. However, for x = 26.3 at% most of them have

negligible probabilities hence 17 most probable (according to the binomial

distribution) were taken into account in the fitting procedure (their overall probability

was  0.97). However, their probabilities, P(m,n), were treated in the fitting routine.as

free parameters. As free parameters were also regarded X(0,0), line width (common

to all sextets), G,



B1,



B2, and an angle between the magnetization vector and

normal to the sample’s surface, theta. On the other hand, based on our previous

studies values of CS1 = -0.02 mm/s, and CS1= -0.01 mm/s, were kept constant

[18]. Using this procedure all measured spectra could have been well fitted with the

average values of: B(0,0)=333(2) kGs,



B1=-32.8(5) kGs,



B2=-21.8(3) kGs,

IS(0,0)=-0.103(3) mm/s, G=0.24(1) mm/s.

Examples of the spectra are presented in Fig. 1. The effect of annealing time can be

best seen in the outermost lines. Noteworthy is also low intensity of the second and

fifth lines in the thermally untreated sample. It is due to a texture induced by cold

rolling. Already annealing during 0.25 h has a great effect on the texture. In addition,

the spectra were analyzed using a magnetic hyperfine field distribution method to

independently and visually illustrate the effect of annealing on the hyperfine field.

Selected examples are displayed in Fig. 2.

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1Kineticsoftransformation,borderofmetastablemiscibilitygapinFe-CralloyandlimitofCrsolubilityinironat858KS.M.Dubiel1,2*andJ.Żukrowski21AGHUniversityofScienceandTechnology,FacultyofPhysicsandAppliedComputerScience,al.A.Mickiewicza30,30-059Kraków,Poland,2AGHUniversityofScienceandTechnology,AcademicCent...

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1 Kinetics of transformation border of metastable miscibility gap in Fe -Cr alloy and limit of Cr solubility in iron at 858 K

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