On the relative efficacy of electropermeation and isothermal desorption approaches for measuring hydrogen diffusivity

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On the relative eﬃcacy of electropermeation and isothermal desorption

approaches for measuring hydrogen diﬀusivity

Alfredo Zafraa, Zachary Harrisb, Evzen Koreca, Emilio Mart´ınez-Pa˜nedaa,∗

aDepartment of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK

bDepartment of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15261,

USA

Abstract

The relative eﬃcacy of electrochemical permeation (EP) and isothermal desorption spectroscopy

(ITDS) methods for determining the hydrogen diﬀusivity is investigated using cold-rolled pure

iron. The diﬀusivities determined from 13 ﬁrst transient and 8 second transient EP experiments,

evaluated using the conventional lag and breakthrough time methods, are compared to the results

of 10 ITDS experiments. Results demonstrate that the average diﬀusivity is similar between the

second EP transient and ITDS, which are distinctly increased relative to the ﬁrst EP transient.

However, the coeﬃcient of variation for the ITDS experiments is reduced by 2 and 3-fold relative

to the ﬁrst and second EP transients, conﬁrming the improved repeatability of ITDS diﬀusivity

measurements. The source of the increased error in EP measurements is systematically evaluated,

revealing an important inﬂuence of assumed electrochemical boundary conditions on the analysis

and interpretation of EP experiments.

Keywords:

Hydrogen diﬀusion, Electro-permeation, TDS, Isothermal desorption, repeatability

1. Introduction

The deployment and safe operation of hydrogen transport and storage infrastructure is being

threatened by the degradation of metals when exposed to hydrogen [1–3]. However, despite over

a century of study [4–7], hydrogen-assisted cracking (HAC) remains a relevant failure mode for

metallic structural components exposed to hydrogen-producing/containing environments across a

number of industrial sectors [8]. Current best practices for designing against and prognosis of HAC

involve the use of linear elastic fracture mechanics (LEFM)-based damage tolerant design [9–11].

∗Corresponding author.

Email address: e.martinez-paneda@imperial.ac.uk (Emilio Mart´ınez-Pa˜neda)

Preprint submitted to International Journal of Hydrogen Energy October 5, 2022

arXiv:2210.01462v1 [physics.chem-ph] 4 Oct 2022

While fundamentally robust, the implementation of LEFM-based approaches can be complicated

by the sensitivity of HAC behavior to changes in microstructural [12–15], mechanical [16–18], and

environmental [19–21] parameters. As such, it is critical that the inﬂuence of these factors be well

understood when evaluating new alloy systems for use in hydrogen-rich environments.

From an environmental perspective, the parameters most pertinent to HAC are the diﬀusible

hydrogen concentration (CH,Dif f ) and the hydrogen diﬀusivity (D) in the material of interest [22–

25]. Regarding the former, CH,Dif f represents the hydrogen content available to participate in

the hydrogen-assisted fracture process and is strongly dependent on the operative environment

conditions (i.e., solution composition/pH, electrochemical potential, hydrogen pressure/fugacity,

etc. [5, 19, 26–30]). It is well-established that susceptibility to HAC is dependent on CH,Dif f .

For example, the threshold stress intensity associated with the onset of hydrogen-assisted cracking

(KT H ) has been observed to decrease as CH,Diff increases [31–34]; this dependence is explicitly

incorporated into proposed models for KT H [35–37]. Similarly, the Stage II hydrogen-assisted crack

growth rate has been correlated with hydrogen diﬀusivity across a range of relevant alloy systems

[38–40], particularly under severe hydogen-producing conditions [18]. As with KT H , the hydrogen

diﬀusivity is a critical parameter in existing models for the Stage II crack growth rate [21, 36].

These direct linkages between hydrogen-metal interaction parameters and HAC metrics under-

scores the importance of characterizing these factors when assessing the compatibility of a new

alloy for use in aggressive environments [41, 42]. While all hydrogen-metal interactions are critical

to understand and contribute to HAC susceptibility, the hydrogen diﬀusivity is of particular impor-

tance given that it (1) aﬀects the rate at which a given concentration is obtained in the material,

and (2) is explicitly required for the interpretation of some hydrogen-metal interaction experiments

(e.g., barnacle cell electrode [43]). There are two primary experimental methods for determining

the hydrogen diﬀusivity [42]: permeation and thermal desorption. Permeation experiments are

performed using a thin membrane of the material of interest that separates two environments.

Hydrogen is generated on one side of the membrane, diﬀuses through the material, and exits the

membrane at the other side, where the rate of hydrogen egress is measured [42]. For electrochem-

ical permeation (EP) experiments, hydrogen uptake is driven by cathodically polarizing one side

of the membrane and then measuring the current induced by hydrogen oxidation on the egress

side [44]. Standard analysis methods are then used to determine the hydrogen diﬀusivity from the

permeation data [45]. While permeation generally involves starting with nominally hydrogen-free

specimens, diﬀusivity measurements using thermal desorption methods utilize samples that have

ideally been hydrogen pre-charged with a spatially uniform hydrogen concentration. Samples are

then placed into an ultra-high vacuum system, which is heated to a speciﬁc temperature (i.e.,

isothermal conditions) and the rate of hydrogen egress is monitored with a mass spectrometer

[46, 47]. The diﬀusivity is then determined through ﬁtting the hydrogen egress rate versus time

proﬁle using either numerical [48] or analytical methods [47].

While both approaches have been widely utilized in the open literature, each approach has

been historically leveraged for a speciﬁc subset of conditions. Isothermal desorption spectroscopy

(ITDS) is commonly employed for slow-diﬀusing materials and often involves large specimens to

minimize the eﬀects of hydrogen egress while the sample analysis chamber is brought to ultra-

high vacuum and the selected isothermal condition is reached [46, 47, 49–51]. Conversely, EP is

generally employed on thin (<1 mm thick) membranes of fast-diﬀusing material [44, 52]. While

data obtained from each method are often compared via literature sources, direct assessments of

the relative eﬃcacy of the two techniques are minimal given their use under distinct conditions.

However, recent advances in thermal desorption systems, such as the introduction of conduction-

based heating and improved vacuum system design for more rapid sample introduction, now enable

the use of ITDS for material/sample combinations that were previously considered incompatible

with this technique. For example, Zafra et al. [53] recently demonstrated that ITDS and EP

methods yielded similar average diﬀusivities for thin (<1 mm thick) sheet specimens of cold-rolled

pure Fe. Critically, this direct comparison revealed that the error in replicate ITDS measurements

was noticeably reduced relative to the replicate EP experiments [53]. It is well-known that EP

experiments are prone to signiﬁcant scatter, which has been historically attributed to numerous

factors: the need for sample conditioning prior to starting the permeation experiment [28, 54–

58], surface eﬀects [59, 60], trapping eﬀects [61–63], concentration-dependent diﬀusion [64, 65],

analysis method assumptions [52, 66–68], failure to reach true steady-state conditions [69], and

test-to-test variations in specimen thickness, environmental parameters, among other [70, 71]. The

work of Zafra et al. [53] suggests that this longstanding issue of error in EP experiments may be

circumvented via the more widespread adoption of ITDS, but this prior study only performed

two experiments per technique. As such, additional experiments are needed to more rigorously

compare the ITDS and EP methods for measuring hydrogen diﬀusivity.

The objective of this study is to provide the ﬁrst statistically signiﬁcant comparison of EP

and ITDS approaches for measuring hydrogen diﬀusivity. A total of 21 permeation experiments

are performed on cold-worked pure iron and then analyzed using the standard breakthrough and

lag time methods [45]. The EP experiments are then compared to the results of ten ambient

temperature ITDS experiments. These large datasets are subsequently leveraged to comment

on the relative accuracy of each technique, the importance of assumed boundary conditions when

analyzing EP data, and the broader implications of these ﬁndings for the hydrogen community. The

results obtained reveal a higher sensitivity of ITDS measurements and demonstrate its applicability

to fast diﬀusion materials.

2. Experimental Methods

2.1. Material

This study was conducted using cold-rolled pure iron procured in the as-rolled condition from

Goodfellow Ltd. as a 1-mm thick sheet. The supplier reported a purity of >99.5 wt. %Fe and

a 50% reduction as the average degree of cold work. Permeation and TDS experiments were

performed on plate specimens with nominal dimensions of 250 mm x 250 mm x 1 mm and 10 mm

x 10 mm x 1 mm, respectively. The specimens were excised from the sheet using an abrasive saw.

In order to ensure consistent surface conditions between experiments, both faces of every sample

were mechanically ground using SiC papers, ﬁnishing with 1200 grit.

2.2. Hydrogen permeation tests

Thirteen EP experiments were performed at room temperature (22±1◦C) using a modiﬁed

Devanathan-Stachurski double-cell. The specimen thickness, L, was 0.92±0.02 mm and a circular

area of 2 cm2(16-mm diameter) was exposed to both sides of the double-cell.

The hydrogen reduction cell was ﬁlled with 3 wt. % NaCl solution and contained a typical

three-cell electrode system, with a Pt counter electrode, silver/silver chloride (Ag/AgCl) reference

electrode, and the sample as the working electrode. Hydrogen production was achieved by applying

a cathodic current density, Jc, of 5 mA/cm2to the cold-rolled Fe membrane using a Gamry

1010B potentiostat operated in galvanostatic mode. The corresponding cathodic potential (vs.

Ag/AgCl) was measured at the beginning of the test to ensure consistent charging conditions

between specimens. The hydrogen oxidation cell was ﬁlled with 0.1 M NaOH solution and also

contained a Pt counter electrode and Ag/AgCl reference electrode, with a second Gamry 1010B

potentiostat operated in chronoamperometry mode to record the permeation current density, Jp,

as a function of time. Both solutions were actively deaerated via bubbling with pure nitrogen,

which was initiated 1 hour before the beginning of the permeation test and continued through the

end of the experiment. For each experiment, a thin Pd layer was electroplated onto the specimen

surface facing the oxidation side of the double-cell to enhance the hydrogen oxidation reaction

kinetics and avoid disturbances in the permeation signal from iron oxidation [72–74].

To ensure the eﬃcient oxidation of hydrogen atoms reaching the anodic side of the specimen,

the anodic surface was polarized at -25±11 mVAg/AgCl, which corresponds to the nominal open-

circuit potential (OCP) for this environment. The permeation current density was then allowed

to stabilize until reaching a baseline below 0.1-0.2 µA/cm2, after which the galvanostatic cathodic

charging was started on the reduction side of the double-cell. A hydrogen concentration gradient is

thus generated in the specimen, with hydrogen atoms permeating through the iron membrane from

the cathodic to the anodic side. During the test, Jpdescribes an exponential rising transient until

reaching a maximum permeation current density, which is commonly known as the steady-state

permeation current, Jss. Further details regarding the EP procedure as well as a schematic repre-

sentation of the experimental setup (including the reduction and oxidation reactions) are provided

elsewhere [53]. After completing the ﬁrst permeation transient (Jc=5 mA/cm2), a second transient

was performed on eight of the samples by increasing Jcto 10 mA/cm2. These experiments were

performed to assess whether the variability in diﬀusion coeﬃcient would improve under conditions

where surface and trapping eﬀects on permeation are reduced [75].

Consistent with precedent literature [26, 52, 75–82] and current permeation testing standards

[45, 83], the hydrogen diﬀusion coeﬃcient, D, of both permeation transients was determined using

the breakthrough time and lag time methods, which are based on the following relationship:

D=L2

Mt (1)

where tand M are determined by which method is being employed. For the breakthrough method,

M has a value of 6 and tis deﬁned as the breakthrough time, tbt, which corresponds to the time

where Jp/Jss=0.1. Conversely, for the lag time method, M is equal to 15.3 and tis deﬁned as

the lag time, tlag, which is determined by the time when Jp/Jss=0.63. Both approaches represent

closed-form solutions of Fick’s second law under the assumption that that the hydrogen subsurface

concentration is a constant, ﬁnite value at the entry side and zero at the exit side of the membrane.

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OntherelativeecacyofelectropermeationandisothermaldesorptionapproachesformeasuringhydrogendiusivityAlfredoZafraa,ZacharyHarrisb,EvzenKoreca,EmilioMartnez-Pa~nedaa,aDepartmentofCivilandEnvironmentalEngineering,ImperialCollegeLondon,LondonSW72AZ,UKbDepartmentofMechanicalEngineeringandMaterialsSci...

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