Energetics of hydrogen segregation to -Fe grain boundaries for modeling stress corrosion cracking

M. Rajagopalan1, I.Adlakha1, M.A. Tschopp2, and K.N. Solanki1*

1School for Engineering of Matter, Transport, and Energy, Arizona State University

2Dynamic Research Corporation, High Performance Technology Group,

(on site at) U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005

*(480)965-1869; (480)727-9321 (fax), E-mail: , (Corresponding author)

Figure S1 (a) and (b) shows a line plot representation of segregation energy on each atomic plane d/d{hkl} for H-int and 2H-int to α-Fe STGBs. It is evident that there is an energetic preference for H to segregate at the GB region. Also, we can see that the change in segregation energy is not linear with each addition of an impurity atom either for the H-intnor 2H-int. This is because of the limited number of sites available for the second H to be accommodated in the vicinity of the first H atom for it to exhibit a cluster like behavior.

Figure S1. Segregation energy for (a) one-interstitial (H-int) and (b) two-interstitial (2H-int) H atom(s) expressed as a function of normalized interplanar distance, d/d{hkl}, from the GB plane with an increasing Sigma (Σ) value.

The Gaussian distribution parameters, and β were extracted for the whole set of α-Fe STGBs using equation 2. The mean and standard deviations of the distribution parameters for each tilt system and defect configuration are given in Tables S1-S4.

Table S1. The mean and standard deviations of the distribution parameters for segregation behavior of varioushydrogen defect configurations in α-Fe <100> STGBs.

<100> STGBs / H-int / 2H-int
α (eV) / β(Å) / R2 / α (eV) / β(Å) / R2
Mean / -0.62 / 5.01 / 0.92 / -1.96 / 6.21 / 0.89
Standard deviation / 0.27 / 4.73 / 0.10 / 0.27 / 2.98 / 0.098

Table S2. The mean and standard deviations of the distribution parameters for segregation behavior of varioushydrogen defect configurations in α-Fe <110> STGBs.

<110> STGBs / H-int / 2H-int
α (eV) / β(Å) / R2 / α (eV) / β(Å) / R2
Mean / -0.64 / 4.30 / 0.93 / -1.74 / 6.35 / 0.89
Standard deviation / 0.09 / 1.95 / 0.05 / 0.45 / 4.20 / 0.098

Table S3. The mean and standard deviations of the distribution parameters for segregation behavior of varioushydrogen defect configurations in α-Fe <111> STGBs.

<111> STGBs / H-int / 2H-int
α (eV) / β(Å) / R2 / α (eV) / β(Å) / R2
Mean / -0.58 / 6.75 / 0.90 / -1.65 / 5.58 / 0.89
Standard deviation / 0.10 / 0.86 / 0.09 / 0.34 / 2.35 / 0.1

Table S4. The mean and standard deviations of the distribution parameters for segregation behavior of varioushydrogen defect configurations in α-Fe <112> STGBs.

<112> STGBs / H-int / 2H-int
α (eV) / β(Å) / R2 / α (eV) / β(Å) / R2
Mean / -0.64 / 4.23 / 0.96 / -1.76 / 8.44 / 0.76
Standard deviation / 0.05 / 1.36 / 0.03 / 0.37 / 4.27 / 0.22

Furthermore, the statistical model described here was found to accurately predict the segregation behavior Ga atoms across various STGBs in Al [19].

Table S5. The mean and standard deviations of the distribution parameters for Ga segregation behavior in Al <100> STGBs.

<100> STGBs / α (eV) / β(Å) / R2
Mean / -0.28 / 4.12 / 0.88
Standard deviation / 0.04 / 1.28 / 0.09

Table S6. The mean and standard deviations of the distribution parameters for Ga segregation behavior in Al <110> STGBs.

<110> STGBs / α (eV) / β(Å) / R2
Mean / -0.13 / 6.03 / 0.84
Standard deviation / 0.06 / 3.60 / 0.19

Table S7. The mean and standard deviations of the distribution parameters for Ga segregation behavior in Al <111> STGBs.

<111> STGBs / α (eV) / β(Å) / R2
Mean / -0.27 / 6.45 / 0.92
Standard deviation / 0.05 / 3.09 / 0.19

Table S8. Mean statistics for the Gaussian distribution of Ga segregation to Al STGBs. Raw data can be looked up in [1]. Note that in most cases the fitting error, i.e., the R2 coefficient, was greater than 0.84.

GB system / α (eV) / β / R2
<100> / -0.28 / 4.12 / 0.88
<110> / -0.13 / 6.03 / 0.84
<111> / -0.27 / 6.45 / 0.92

Reference

1. M. Rajagopalan, M. A. Bhatia, M. A. Tschopp, D. J. Srolovitz, and K. N. Solanki, Acta Mater. 73, 312 (2014).

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