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Correlation between the hydrogen chemical potential and pop-in load during in situ electrochemical nanoindentation
Scripta Materialia xxx (2015) xxx–xxx
Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Correlation between the hydrogen chemical potential and pop-in load during in situ electrochemical nanoindentation Afrooz Barnoush ⇑, Nousha Kheradmand, Tarlan Hajilou Department of Engineering Design and Materials, Richard Birkelands vei 2b, 7491 Trondheim, Norway
a r t i c l e
i n f o
Article history: Received 4 June 2015 Accepted 14 June 2015 Available online xxxx Keywords: Hydrogen embrittlement Nanoindentation Electrochemical Dislocation nucleation Steel
a b s t r a c t The variation in the pop-in load during electrochemical nanoindentation of Fe 3 wt.% Si alloy at different cathodic polarizations was measured. It is clearly shown that a higher hydrogen chemical potential results in a lower pop-in load, which is an indication of easier dislocation nucleation below the tip. Classic dislocation theory and defactant model are used to analyze the data and calculate the excess hydrogen on the dislocation line at different electrochemical potentials. Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
It is now well established that the hydrogen interaction with dislocations plays a crucial role during hydrogen embrittlement, through both experimental observation [1–10] and theoretical computation [11–17]. Apart from transmission electron microscopy, one of the most successful recent methods delivering direct evidence for dislocation activity in the metals is nanoindentation [18–27]. During the nanoindentation of perfectly prepared samples with a very low dislocation density, it is possible to observe a homogeneous dislocation nucleation (HDN) below the surface in the volume. The small size of the indenter used during the nanoindentation confines the sheared volume below the surface to a region smaller than the mean dislocation spacing, i.e., 1 lm for a sample with a dislocation density of 1012m2. Then plasticity starts under this condition by HDN within this small sheared volume beneath the tip, and manifests itself in the form of a sudden jump in load–displacement curves, which is usually called pop-in or the yield point phenomenon [28–31]. There have been attempts to study the effect of hydrogen on dislocation nucleation by means of nanoindentation [32–34]. However, in all these attempts, the samples are charged ex situ and then tested with nanoindentation. This limits the testing to metals and alloys which have a very high solubility for hydrogen, like austenitic stainless steels [33], or for which the hydrogen desorption is inhibited by an oxide layer as in vanadium [34]. For most other alloys and metals, it is not possible to study the hydrogen effect on dislocation ⇑ Corresponding author. E-mail addresses: [email protected] (A. Barnoush), nousha. [email protected] (N. Kheradmand), [email protected] (T. Hajilou).
nucleation after ex situ hydrogen charging. The main reason is the depletion of the hydrogen or the formation of a hydrogen concentration gradient close to the surface of the sample as a result of hydrogen outgassing and desorption from the surface within a short time after the ex situ hydrogen charging. Hence, within the HDN site, which is a few tens of nanometers below the surface, the hydrogen is already depleted or reduced to a very low concentration and no effect will be registered with the nanoindenter. Therefore, we have developed the so-called in situ electrochemical nanoindentation (ECNI) setup by integrating a three electrode miniaturized electrochemical cell into a nanoindentation instrument so the samples can be electrochemically charged in situ with hydrogen [35,36]. The ECNI has been intensively used for studying the hydrogen effect on HDN in different alloys and metals charged in situ with hydrogen evolved from aqueous electrolytes [37–40]. It should be noted that one big shortcoming of aqueous solutions is their high solubility for oxygen. Due to the limited volume of our cell, it is not possible to remove the oxygen by bubbling with inert gas. This dissolved oxygen can interact with the surface and as a result, corrosion and out-of-control reactions can take place locally on the sample surface, which in turn contaminate the electrolyte and roughen the surface through localized corrosion. Therefore, a typical ECNI test in aqueous solution is limited to a few hours of testing, which in turn limits the number of different conditions (cathodic and anodic) that can be tested. In this paper, we report the very first attempts to perform ECNI inside a glycerol based electrolyte. The advantage of this electrolyte is its extremely low solubility and diffusivity for oxygen [41,42]. This makes it possible to perform ECNI over a very long time without any alteration
http://dx.doi.org/10.1016/j.scriptamat.2015.06.021 1359-6462/Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: A. Barnoush et al., Scripta Mater. (2015), http://dx.doi.org/10.1016/j.scriptamat.2015.06.021
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A. Barnoush et al. / Scripta Materialia xxx (2015) xxx–xxx
of the sample surface and its impact on the nanoindentation measurements. The sample we used was a commercial Fe-3 wt.% Si alloy received in coil form with 1 mm thickness. The composition of the alloy is given in Table 1, as provided by the producer. A circular Fe-3 wt.% Si sample was cut from the coil by spark erosion and heat treated at 1200 °C for one week in order to achieve big grains in the range of a few millimeters. Nanoindentation tests at all cathodic and anodic conditions were confined to a single grain to exclude any orientation effects. The specimen was mechanically and electrochemically polished according to the procedure given in [43]. The details of the experimental setup are given elsewhere [44]. The experiments were performed with a Hysitron Tribo-IndenterÒ. The indenter tip, designed specially for testing in liquid, was a Berkovich diamond tip. The load function used for the indentation consisted of a loading segment with a 12.5 mN/s loading rate and a 0.5 s holding time at the peak value of 2500 lN, with an additional 0.25 s holding time at 10% of the peak value during unloading for drift correction [39]. In order to avoid any Cl ion contamination of the electrolyte, a double junction Hg/HgSO4 reference electrode was used and all potentials are reported versus this electrode. The resulting representative load–displacement (L–D) curves at different potentials are shown in Fig. 1. The topography of the sample surface during the course of the test was continuously inspected by means of imaging the sample surface using the same tip as for nanoindentation. The topography images from the sample surface at three different conditions are also shown in Fig. 1, where the alteration in the surface RMS roughness was less than 1 nm over 1 lm2. This ensures that the observed changes in the pop-in load are not due to the change of the surface, but the dissolution of hydrogen in the metal at cathodic polarizations. The variation of the mean pop-in load at different potentials together with its standard deviation are given in Fig. 2. During nanoindentation, the shear stress resulting in HDN can be assumed to be the maximum shear stress beneath the indenter at the onset of a pop-in. According to continuum mechanics, the position and value of the maximum shear stress, zðsmax Þ and smax , are given by [39].
1 3PR 3 zðsmax Þ ¼ 0:48 4Er
smax ¼ 0:31
6E2r 3 2
pR
Fig. 1. Representative load–displacement curves in air (Black), at 1000 mV cathodic potential (Red), at 1300 mV cathodic potential (Magenta), and at 1000 mV anodic potential (Green). Insets show the topography of the surface at the respective conditions. All topography images have the same height color scale and are directly comparable with each other. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
ð1Þ Fig. 2. Variation of the mean pop-in load by potential for Fe-3 wt.% Si alloy
!13 P
ð2Þ circular dislocation loop with radius r under the action of a uniform shear stress s is given by the following [46]:
where P is the applied load, R is the radius of the tip curvature, and Er is the reduced modulus [39]. A more realistic analysis of the shear stress and its position below the surface can be done by considering the grain orientation, the anisotropic elastic properties of the materials, and resolving the shear stress on probable slip systems below the tip [2]. Here, for the sake of simplicity, we only consider the simple isotropic continuum approach. For Fe-3 wt.% Si and a diamond tip, Er is equal to 201 GPa [45]. The tip radius was found to be 1750 nm by fitting a Hertzian model to the elastic loading part of the L–D curves. If we insert this tip radius into Eq. (2), we obtain a maximum shear stress for each pop-in load. This maximum shear stress is responsible for the HDN at zðsmax Þ below the tip. Classic dislocation theory predicts that the free energy required for HDN of a
DG ¼ 2pr cdis pr 2 bs
ð3Þ
The elastic self-energy, cdis , of a full circular dislocation loop in an infinite isotropic elastic solid is given by
cdis ¼
2 2 m Gb r 4r ln 2 1m 4 qcore
ð4Þ
where b is the Burgers vector (0.25 nm), G is the shear modulus (85 GPa), m is Poisson’s ratio (0.3), and qcore is the dislocation core radius. We can assume that the maximum shear stress in Eq. (2) acts uniformly on a small volume in the range of several Burgers vectors. The isotropic continuum mechanics calculation shows that
Table 1 Composition of Fe-3 wt.% Si alloy used in this study. Element
C
Si
Mn
P
S
Cr
Ni
Mo
Cu
Al
Ti
Nb
V
B
Zr
Ce
Weight%
0.003
2.383
0.202
0.013
0.012
0.033
0.048
0.015
0.020
0.365
0.005
0.020
0.002
0.0008
0.005
0.009
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A. Barnoush et al. / Scripta Materialia xxx (2015) xxx–xxx
3
this assumption is reasonable [36]. The maximum of the free energy for the formation of a dislocation loop given by Eq. (3) at any given applied shear stress s which is exchangeable with the indentation load P according to Eq. (2), defines the activation energy for HDN [35]. The size of the dislocation loop which maximizes the free energy is the critical dislocation loop radius r c for the given shear stress s and is the smallest loop radius which can grow further at the given shear stress level without increasing the total energy of the system. The maximum of DG can be calculated by setting @ DG=@r equal to zero. Since the thermal energy contribution to the HDN at room temperature is negligible, in order to observe HDN at room temperature the shear stress should be high enough so that the activation energy approaches zero. This results in a critical loop radius equal to [36]:
rc ¼
1 3 e qcore : 4
ð5Þ
By setting e = 2.72 and qcore ¼ 0:18 nm, we get r c ¼ 0:9 nm. The shear stress required for HDN of a loop equal to rc ¼ 0:9 nm in l Fe-3 wt.% Si is equal to 4.6 GPa. This is approximately equal to 18 and is in good agreement with the Frenkel model predication for HDN [36]. The indentation load required to produce this shear stress with the indenter tip we used in our tests (R ¼ 1750 nm) is 1275 lN, which is in good agreement with the experimentally observed pop-in loads in air and also under anodic polarization (see Fig. 2). While the pop-in loads in both air and under anodic polarization are within the range predicted by our model, the pop-in load under cathodic polarization, i.e., while the sample is charged with hydrogen, is not. According to the Defactant model [47], hydrogen can be assumed to be a defactant and reduces the formation energy of defects. In the case of dislocations as linear defects, the hydrogen segregation on the dislocation line reduces the line energy of the dislocation and results in an easier formation of the dislocation loop during the nanoindentation, which in turn manifests itself in the L–D curves as a pop-in at lower loads. Interestingly, the pop-in load scales itself also with the amount of the applied cathodic polarization, as shown in Fig. 2. This strongly supports the Defactant theory and a reduction in the line energy of the dislocations in the presence of hydrogen, as according to this theory the reduction in the dislocation line energy depends on the hydrogen chemical potential. Kirchheim proposed the following relation for the hydrogen excess on the dislocation dis H
line C at constant temperature (T), volume (V), dislocation length (ldis ), and number of hydrogen atoms (nH ) [48].
Cdis H ¼
@ cdis @ lH V;T;ldis ;nH
Fig. 3. Variation of the dislocation line energy at different potentials
where F is the Faraday constant and z ¼ 1 is the stoichiometric number of electrons consumed in the electrode reaction. The open circuit potential (OCP) of the Fe-3 wt.% Si sample in electrolyte used in this work was 700 mV. Assuming a total value of the IR drop (/IR ) and a polarization (/Pol ) equal to 250 mV, we can simply convert the applied potentials to chemical potentials of the hydrogen on the surface. After a certain amount of polarization due to the evolution of the hydrogen gas on the sample surface, Eq. (7) can no longer be applied. This is the case at 1300 mV and hence we simply noted that the lH at this potential will be slightly higher than the lH at 1200 mV. The slight change in the pop-in load after polarization to 1300 mV confirms this assumption. The black curve in Fig. 4 shows the variation of the dislocation line energy cdis with the chemical potential of the hydrogen. The calculated dis Cdis H for Fe-3 wt.% Si using Eq. (6) and the variation of CH with
the hydrogen chemical potential is shown in Fig. 4 as the red colored curve (in the on-line version). The calculated Cdis H is on the same order of magnitude as the existing measurements of the excess hydrogen in Vanadium [34] and in Palladium [49], and as far as we know, is the only existing experimental measurement of Cdis H in an iron base alloy. In summary, nanoindentation tests were performed on in situ electrochemically hydrogen-charged Fe-3 wt.% Si alloy, at different potentials. While hydrogen charging clearly reduced the pop-in
ð6Þ
In order to calculate Cdis H , we need to calculate dislocation line energy cdis and hydrogen chemical potential lH . Now, cdis can be estimated from the pop-in load data at different cathodic polarizations. For each measured pop-in load under cathodic polarization, we use the difference between the line energy calculated from the pop-in data and the line energy of the critical loop rc expected to nucleate with zero activation energy at a load of 1275 lN. The resulting curve of changes in the dislocation line energy at different cathodic polarizations is shown in Fig. 3. For the next step, we need to convert the electrochemical potentials in Fig. 3 to chemical potentials so we can use Eq. (6) to calculate Cdis H . This can be done using the Nernst equation relating the applied potential / to the chemical potential of the species taking part in a given electrochemical reaction. In our system we have only one electrochemically active species, i.e., hydrogen, therefore we can write the Nernst equation as
lH ¼ zFð/ /OCP /IR /Pol Þ
ð7Þ
Fig. 4. The variation of the dislocation line energy and hydrogen excess on the dislocation line as a function of hydrogen chemical potential.
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A. Barnoush et al. / Scripta Materialia xxx (2015) xxx–xxx
load, this reduction in the pop-in load scaled up with the amount of the cathodic polarization, providing clear evidence that the HDN is enhanced in the presence of hydrogen. The obtained experimental data were analyzed based on the ‘‘defactant’’ concept, i.e., a reduction of the defect formation energy in the presence of hydrogen as a defactant solute. The experimentally measured pop-in loads were used to calculate the dislocation line energy. Then, the reduction in the dislocation line energy with the increase of hydrogen concentration was calculated. Finally, the hydrogen excess at the dislocation core was also calculated. As a result, the experimental evidence provided by the ECNI demonstrates the usefulness of this experimental technique combined with the novel thermodynamic ‘‘defactant’’ concept as an alternative way of describing solute–defect interaction in general, and hydrogen embrittlement or hydrogen/deformation interaction in particular. The Research Council of Norway is acknowledged for support to the Norwegian Micro- and Nano-Fabrication Facility, NorFab (197411/V30) and funding through the Petromaks Programme, Contract No. 234130/E30. This work was partly supported by EU 7th framework program through the project MultiHy (Multiscale Modelling of Hydrogen Embrittlement) under project No. 263335.
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Please cite this article in press as: A. Barnoush et al., Scripta Mater. (2015), http://dx.doi.org/10.1016/j.scriptamat.2015.06.021
Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Correlation between the hydrogen chemical potential and pop-in load during in situ electrochemical nanoindentation Afrooz Barnoush ⇑, Nousha Kheradmand, Tarlan Hajilou Department of Engineering Design and Materials, Richard Birkelands vei 2b, 7491 Trondheim, Norway
a r t i c l e
i n f o
Article history: Received 4 June 2015 Accepted 14 June 2015 Available online xxxx Keywords: Hydrogen embrittlement Nanoindentation Electrochemical Dislocation nucleation Steel
a b s t r a c t The variation in the pop-in load during electrochemical nanoindentation of Fe 3 wt.% Si alloy at different cathodic polarizations was measured. It is clearly shown that a higher hydrogen chemical potential results in a lower pop-in load, which is an indication of easier dislocation nucleation below the tip. Classic dislocation theory and defactant model are used to analyze the data and calculate the excess hydrogen on the dislocation line at different electrochemical potentials. Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
It is now well established that the hydrogen interaction with dislocations plays a crucial role during hydrogen embrittlement, through both experimental observation [1–10] and theoretical computation [11–17]. Apart from transmission electron microscopy, one of the most successful recent methods delivering direct evidence for dislocation activity in the metals is nanoindentation [18–27]. During the nanoindentation of perfectly prepared samples with a very low dislocation density, it is possible to observe a homogeneous dislocation nucleation (HDN) below the surface in the volume. The small size of the indenter used during the nanoindentation confines the sheared volume below the surface to a region smaller than the mean dislocation spacing, i.e., 1 lm for a sample with a dislocation density of 1012m2. Then plasticity starts under this condition by HDN within this small sheared volume beneath the tip, and manifests itself in the form of a sudden jump in load–displacement curves, which is usually called pop-in or the yield point phenomenon [28–31]. There have been attempts to study the effect of hydrogen on dislocation nucleation by means of nanoindentation [32–34]. However, in all these attempts, the samples are charged ex situ and then tested with nanoindentation. This limits the testing to metals and alloys which have a very high solubility for hydrogen, like austenitic stainless steels [33], or for which the hydrogen desorption is inhibited by an oxide layer as in vanadium [34]. For most other alloys and metals, it is not possible to study the hydrogen effect on dislocation ⇑ Corresponding author. E-mail addresses: [email protected] (A. Barnoush), nousha. [email protected] (N. Kheradmand), [email protected] (T. Hajilou).
nucleation after ex situ hydrogen charging. The main reason is the depletion of the hydrogen or the formation of a hydrogen concentration gradient close to the surface of the sample as a result of hydrogen outgassing and desorption from the surface within a short time after the ex situ hydrogen charging. Hence, within the HDN site, which is a few tens of nanometers below the surface, the hydrogen is already depleted or reduced to a very low concentration and no effect will be registered with the nanoindenter. Therefore, we have developed the so-called in situ electrochemical nanoindentation (ECNI) setup by integrating a three electrode miniaturized electrochemical cell into a nanoindentation instrument so the samples can be electrochemically charged in situ with hydrogen [35,36]. The ECNI has been intensively used for studying the hydrogen effect on HDN in different alloys and metals charged in situ with hydrogen evolved from aqueous electrolytes [37–40]. It should be noted that one big shortcoming of aqueous solutions is their high solubility for oxygen. Due to the limited volume of our cell, it is not possible to remove the oxygen by bubbling with inert gas. This dissolved oxygen can interact with the surface and as a result, corrosion and out-of-control reactions can take place locally on the sample surface, which in turn contaminate the electrolyte and roughen the surface through localized corrosion. Therefore, a typical ECNI test in aqueous solution is limited to a few hours of testing, which in turn limits the number of different conditions (cathodic and anodic) that can be tested. In this paper, we report the very first attempts to perform ECNI inside a glycerol based electrolyte. The advantage of this electrolyte is its extremely low solubility and diffusivity for oxygen [41,42]. This makes it possible to perform ECNI over a very long time without any alteration
http://dx.doi.org/10.1016/j.scriptamat.2015.06.021 1359-6462/Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: A. Barnoush et al., Scripta Mater. (2015), http://dx.doi.org/10.1016/j.scriptamat.2015.06.021
2
A. Barnoush et al. / Scripta Materialia xxx (2015) xxx–xxx
of the sample surface and its impact on the nanoindentation measurements. The sample we used was a commercial Fe-3 wt.% Si alloy received in coil form with 1 mm thickness. The composition of the alloy is given in Table 1, as provided by the producer. A circular Fe-3 wt.% Si sample was cut from the coil by spark erosion and heat treated at 1200 °C for one week in order to achieve big grains in the range of a few millimeters. Nanoindentation tests at all cathodic and anodic conditions were confined to a single grain to exclude any orientation effects. The specimen was mechanically and electrochemically polished according to the procedure given in [43]. The details of the experimental setup are given elsewhere [44]. The experiments were performed with a Hysitron Tribo-IndenterÒ. The indenter tip, designed specially for testing in liquid, was a Berkovich diamond tip. The load function used for the indentation consisted of a loading segment with a 12.5 mN/s loading rate and a 0.5 s holding time at the peak value of 2500 lN, with an additional 0.25 s holding time at 10% of the peak value during unloading for drift correction [39]. In order to avoid any Cl ion contamination of the electrolyte, a double junction Hg/HgSO4 reference electrode was used and all potentials are reported versus this electrode. The resulting representative load–displacement (L–D) curves at different potentials are shown in Fig. 1. The topography of the sample surface during the course of the test was continuously inspected by means of imaging the sample surface using the same tip as for nanoindentation. The topography images from the sample surface at three different conditions are also shown in Fig. 1, where the alteration in the surface RMS roughness was less than 1 nm over 1 lm2. This ensures that the observed changes in the pop-in load are not due to the change of the surface, but the dissolution of hydrogen in the metal at cathodic polarizations. The variation of the mean pop-in load at different potentials together with its standard deviation are given in Fig. 2. During nanoindentation, the shear stress resulting in HDN can be assumed to be the maximum shear stress beneath the indenter at the onset of a pop-in. According to continuum mechanics, the position and value of the maximum shear stress, zðsmax Þ and smax , are given by [39].
1 3PR 3 zðsmax Þ ¼ 0:48 4Er
smax ¼ 0:31
6E2r 3 2
pR
Fig. 1. Representative load–displacement curves in air (Black), at 1000 mV cathodic potential (Red), at 1300 mV cathodic potential (Magenta), and at 1000 mV anodic potential (Green). Insets show the topography of the surface at the respective conditions. All topography images have the same height color scale and are directly comparable with each other. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
ð1Þ Fig. 2. Variation of the mean pop-in load by potential for Fe-3 wt.% Si alloy
!13 P
ð2Þ circular dislocation loop with radius r under the action of a uniform shear stress s is given by the following [46]:
where P is the applied load, R is the radius of the tip curvature, and Er is the reduced modulus [39]. A more realistic analysis of the shear stress and its position below the surface can be done by considering the grain orientation, the anisotropic elastic properties of the materials, and resolving the shear stress on probable slip systems below the tip [2]. Here, for the sake of simplicity, we only consider the simple isotropic continuum approach. For Fe-3 wt.% Si and a diamond tip, Er is equal to 201 GPa [45]. The tip radius was found to be 1750 nm by fitting a Hertzian model to the elastic loading part of the L–D curves. If we insert this tip radius into Eq. (2), we obtain a maximum shear stress for each pop-in load. This maximum shear stress is responsible for the HDN at zðsmax Þ below the tip. Classic dislocation theory predicts that the free energy required for HDN of a
DG ¼ 2pr cdis pr 2 bs
ð3Þ
The elastic self-energy, cdis , of a full circular dislocation loop in an infinite isotropic elastic solid is given by
cdis ¼
2 2 m Gb r 4r ln 2 1m 4 qcore
ð4Þ
where b is the Burgers vector (0.25 nm), G is the shear modulus (85 GPa), m is Poisson’s ratio (0.3), and qcore is the dislocation core radius. We can assume that the maximum shear stress in Eq. (2) acts uniformly on a small volume in the range of several Burgers vectors. The isotropic continuum mechanics calculation shows that
Table 1 Composition of Fe-3 wt.% Si alloy used in this study. Element
C
Si
Mn
P
S
Cr
Ni
Mo
Cu
Al
Ti
Nb
V
B
Zr
Ce
Weight%
0.003
2.383
0.202
0.013
0.012
0.033
0.048
0.015
0.020
0.365
0.005
0.020
0.002
0.0008
0.005
0.009
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A. Barnoush et al. / Scripta Materialia xxx (2015) xxx–xxx
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this assumption is reasonable [36]. The maximum of the free energy for the formation of a dislocation loop given by Eq. (3) at any given applied shear stress s which is exchangeable with the indentation load P according to Eq. (2), defines the activation energy for HDN [35]. The size of the dislocation loop which maximizes the free energy is the critical dislocation loop radius r c for the given shear stress s and is the smallest loop radius which can grow further at the given shear stress level without increasing the total energy of the system. The maximum of DG can be calculated by setting @ DG=@r equal to zero. Since the thermal energy contribution to the HDN at room temperature is negligible, in order to observe HDN at room temperature the shear stress should be high enough so that the activation energy approaches zero. This results in a critical loop radius equal to [36]:
rc ¼
1 3 e qcore : 4
ð5Þ
By setting e = 2.72 and qcore ¼ 0:18 nm, we get r c ¼ 0:9 nm. The shear stress required for HDN of a loop equal to rc ¼ 0:9 nm in l Fe-3 wt.% Si is equal to 4.6 GPa. This is approximately equal to 18 and is in good agreement with the Frenkel model predication for HDN [36]. The indentation load required to produce this shear stress with the indenter tip we used in our tests (R ¼ 1750 nm) is 1275 lN, which is in good agreement with the experimentally observed pop-in loads in air and also under anodic polarization (see Fig. 2). While the pop-in loads in both air and under anodic polarization are within the range predicted by our model, the pop-in load under cathodic polarization, i.e., while the sample is charged with hydrogen, is not. According to the Defactant model [47], hydrogen can be assumed to be a defactant and reduces the formation energy of defects. In the case of dislocations as linear defects, the hydrogen segregation on the dislocation line reduces the line energy of the dislocation and results in an easier formation of the dislocation loop during the nanoindentation, which in turn manifests itself in the L–D curves as a pop-in at lower loads. Interestingly, the pop-in load scales itself also with the amount of the applied cathodic polarization, as shown in Fig. 2. This strongly supports the Defactant theory and a reduction in the line energy of the dislocations in the presence of hydrogen, as according to this theory the reduction in the dislocation line energy depends on the hydrogen chemical potential. Kirchheim proposed the following relation for the hydrogen excess on the dislocation dis H
line C at constant temperature (T), volume (V), dislocation length (ldis ), and number of hydrogen atoms (nH ) [48].
Cdis H ¼
@ cdis @ lH V;T;ldis ;nH
Fig. 3. Variation of the dislocation line energy at different potentials
where F is the Faraday constant and z ¼ 1 is the stoichiometric number of electrons consumed in the electrode reaction. The open circuit potential (OCP) of the Fe-3 wt.% Si sample in electrolyte used in this work was 700 mV. Assuming a total value of the IR drop (/IR ) and a polarization (/Pol ) equal to 250 mV, we can simply convert the applied potentials to chemical potentials of the hydrogen on the surface. After a certain amount of polarization due to the evolution of the hydrogen gas on the sample surface, Eq. (7) can no longer be applied. This is the case at 1300 mV and hence we simply noted that the lH at this potential will be slightly higher than the lH at 1200 mV. The slight change in the pop-in load after polarization to 1300 mV confirms this assumption. The black curve in Fig. 4 shows the variation of the dislocation line energy cdis with the chemical potential of the hydrogen. The calculated dis Cdis H for Fe-3 wt.% Si using Eq. (6) and the variation of CH with
the hydrogen chemical potential is shown in Fig. 4 as the red colored curve (in the on-line version). The calculated Cdis H is on the same order of magnitude as the existing measurements of the excess hydrogen in Vanadium [34] and in Palladium [49], and as far as we know, is the only existing experimental measurement of Cdis H in an iron base alloy. In summary, nanoindentation tests were performed on in situ electrochemically hydrogen-charged Fe-3 wt.% Si alloy, at different potentials. While hydrogen charging clearly reduced the pop-in
ð6Þ
In order to calculate Cdis H , we need to calculate dislocation line energy cdis and hydrogen chemical potential lH . Now, cdis can be estimated from the pop-in load data at different cathodic polarizations. For each measured pop-in load under cathodic polarization, we use the difference between the line energy calculated from the pop-in data and the line energy of the critical loop rc expected to nucleate with zero activation energy at a load of 1275 lN. The resulting curve of changes in the dislocation line energy at different cathodic polarizations is shown in Fig. 3. For the next step, we need to convert the electrochemical potentials in Fig. 3 to chemical potentials so we can use Eq. (6) to calculate Cdis H . This can be done using the Nernst equation relating the applied potential / to the chemical potential of the species taking part in a given electrochemical reaction. In our system we have only one electrochemically active species, i.e., hydrogen, therefore we can write the Nernst equation as
lH ¼ zFð/ /OCP /IR /Pol Þ
ð7Þ
Fig. 4. The variation of the dislocation line energy and hydrogen excess on the dislocation line as a function of hydrogen chemical potential.
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A. Barnoush et al. / Scripta Materialia xxx (2015) xxx–xxx
load, this reduction in the pop-in load scaled up with the amount of the cathodic polarization, providing clear evidence that the HDN is enhanced in the presence of hydrogen. The obtained experimental data were analyzed based on the ‘‘defactant’’ concept, i.e., a reduction of the defect formation energy in the presence of hydrogen as a defactant solute. The experimentally measured pop-in loads were used to calculate the dislocation line energy. Then, the reduction in the dislocation line energy with the increase of hydrogen concentration was calculated. Finally, the hydrogen excess at the dislocation core was also calculated. As a result, the experimental evidence provided by the ECNI demonstrates the usefulness of this experimental technique combined with the novel thermodynamic ‘‘defactant’’ concept as an alternative way of describing solute–defect interaction in general, and hydrogen embrittlement or hydrogen/deformation interaction in particular. The Research Council of Norway is acknowledged for support to the Norwegian Micro- and Nano-Fabrication Facility, NorFab (197411/V30) and funding through the Petromaks Programme, Contract No. 234130/E30. This work was partly supported by EU 7th framework program through the project MultiHy (Multiscale Modelling of Hydrogen Embrittlement) under project No. 263335.
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