Thermodynamic Evaluation of the

Propensity of Niobium to Absorb

Hydrogen During Fabrication of

Superconducting Radio Frequency

Accelerator Cavities

Richard E. Ricker

Prepared for

Dr. Ganapati R. Myneni

U.S. Department of Energy

Thomas Jefferson National Accelerator Facility

Newport News, Virginia 23606

NISTIR 7635
 

NISTIR 7635

Thermodynamic Evaluation of the

Propensity of Niobium to Absorb

Hydrogen During Fabrication of

Superconducting Radio Frequency

Accelerator Cavities

Richard E. Ricker

Materials Performance Group 

Metallurgy Division 

Materials Science and Engineering Laboratory 

October 2, 2009

U.S. Department of Commerce 

Gary Locke, Secretary 

National Institute of Standards and Technology 

Patrick D. Gallagher, Deputy Director 
1 

Thermodynamic Evaluation of the Propensity of Niobium to Absorb Hydrogen 

During Fabrication of Superconducting Radio Frequency Accelerator Cavities 

Richard E. Ricker 

Materials Performance Group 

Metallurgy Division 

Materials Science and Engineering Laboratory 

National Institute of Standards and Technology 

US Department of Commerce 

Gaithersburg, MD 20899-8553 

ABSTRACT

 During the fabrication of niobium superconducting radio frequency (SRF) particle 

accelerator cavities procedures are used that chemically or mechanically remove the passivating 

surface film of niobium pentoxide (Nb2O5). Removal of this film will expose the underlying 

niobium metal and allow it to react with the processing environment. If these reactions produce 

hydrogen at sufficient concentrations and rates, then hydrogen will be absorbed and diffuse into 

the metal. High hydrogen activities could result in supersaturation and the nucleation of hydride 

phases. If the metal repassivates at the conclusion of the processing step and the passive film 

blocks hydrogen egress, then the absorbed hydrogen or hydrides could be retained and alter the 

performance of the metal during subsequent processing steps or in-service. This report examines 

the feasibility of this hypothesis by first identifying the postulated events, conditions, and 

reactions and then determining if each is consistent with accepted scientific principles, literature, 

and data. Established precedent for similar events in other systems was found in the scientific 

literature and thermodynamic analysis found that the postulated reactions were not only 

energetically favorable, but produced large driving forces. The hydrogen activity or fugacity 

required for the reactions to be at equilibrium was determined to indicate the propensity for 

hydrogen evolution, absorption, and hydride nucleation. The influence of processing conditions 

and kinetics on the proximity of hydrogen surface coverage to these theoretical values is 

discussed. This examination found that the hypothesis of hydrogen absorption during SRF 

processing is consistent with published scientific literature and thermodynamic principles. 

 

I. INTRODUCTION

 The propensity of active metals to absorb hydrogen during service in environments 

containing water or water vapor is a well-known and thoroughly studied phenomenon,[3-5] but 

the possibility of similar processes occurring during fabrication is frequently overlooked. During 

the fabrication of niobium (Nb) superconducting radio frequency (SRF) cavities for use in 

particle accelerators, there are a number of processing steps where the passivating film of 

niobium pentoxide (Nb2O5) is removed by chemical or mechanical means. When this occurs, the 

underlying metal is put into direct contact with the processing environment and is free to react 

with this environment. If the subsequent reactions produce hydrogen at sufficient concentrations 
2 

and rates, the metal will absorb hydrogen and the metal could become supersaturated with 

respect to hydride phases. When the passive film reforms at the end of the processing step, this 

film may block the egress of the absorbed hydrogen allowing it to remain in the metal and 

influence performance during subsequent processing steps or when placed in-service. Since this 

hypothesis might explain the differences observed between nominally identical samples of ultra 

high purity Nb SRF cavities and the influence of different annealing treatments and temperatures 

on performance, it is becoming the subject of research at a number of institutions.[6-9] 

However, a clear and concise presentation of this hypothesis that identifies the required steps and 

reactions and proves that these processes are thermodynamically favorable and consistent with 

established scientific fact is required to enable studies and critical evaluation that could lead to 

improvements in SRF cavity performance. The objective of this document is to evaluate the 

feasibility of the hypothesis that hydrogen may be absorbed during processing of Nb and alter 

the performance of this metal during subsequent processing steps (e.g. forming) or in service. 

 

II. BACKGROUND

A. Niobium Metallurgy

 Niobium (Nb) is the 41'st element of the periodic chart and has a relative molecular mass of 

92.906, a specific gravity of 8.4. Niobium is also known as Columbium (Cb) in the older 

literature. Niobium is steel-grey body centered cubic (bcc) metal that has found a number of uses 

in aerospace and medical applications.[10,11] However, the vast majority of Nb reduced from raw 

ores each year is used as an alloying element in steels.[10,12] Niobium has a positive influence on 

the strength and formability of steel alloys and is used as a microalloying element in the ultra 

low carbon steels or interstitial free steels used for forming automotive bodies[13-15] and in the 

high-strength low alloy steels used in shipbuilding[16-18] and the new X-series of alloys used 

for pipeline construction.[19-21] These alloys are noted for their formability, strength, and 

resistance to hydrogen embrittlement though hydrogen embrittlement in these steels has been 

attributed by some authors to the affinity of Nb rich phases for hydrogen.[22] Niobium also finds 

many uses in the form of niobium oxide (Nb2O5) due to the stability, clarity, and index of 

refraction of glasses made with this oxide.[23] One of the properties that Nb is best known for is 

superconductivity.[23] Niobium is a classical (low temperature) superconductor that transitions 

from normal metallic conduction to superconductivity at 9.2 K making it ideally suited for the 

construction of superconducting radio frequency (SRF) cavities for high-energy physics 

experiments where a project may require over 5.0 x105

 kg of ultra high purity metal.[24] 

 Since understanding the forming properties of this element would help us understand 

fundamental issues in forming and the influence of this element on the formability of steels, the 

Metallurgy Division of NIST began working with Department of Energy, Thomas Jefferson 

National Accelerator Facility (JLab). Initially, the NIST Chemical Science and Technology 

Laboratory (CSTL) and the NIST Center for Neutron Research (NCNR) collaborated with JLab 

investigating techniques for analyzing the hydrogen content of processed Nb sheet.[25,26] The 

Metallurgy Division of the Materials Science and Engineering Laboratory (MSEL) became 

involved when issues related to residual stresses in deep drawn cavities and springback became a 

concern.[27] These interactions resulted in cross-fertilization of research ideas including 
3 

experiments on large grained samples,[28] the use of mechanical properties to detect interstitial 

hydrogen,[29] and the hypothesis of hydrogen absorption.[5] 

B. Niobium is an Active Metal that Passivates

 Noble and active are terms commonly used to classify the behavior of metals. In general, the 

term noble is applied to metals that are immune to reaction with their environment and active 

metals spontaneously react with their environment. Clearly, this depends on the environment. 

From an aqueous corrosion standpoint, an active metal is one that will spontaneously react in 

normal aqueous environments under ambient conditions without the application of any external 

force or energy. In scientific terms, an active metal is one where the metallic state is not the 

lowest energy state for the atoms of the element in contact with water molecules. Instead, the 

atoms of an active metal prefer to exist as positively charged ions in either a soluble complex or 

in an oxide, hydroxide, or similar compounds. A metal is said to be noble if the metallic state is 

the lowest energy state in the environment and the metal is immune to reactions unless an 

external force is applied. Ions of noble metals in these environments will spontaneously reduce 

their oxidation states and plate out on surfaces in the metallic state if species that can be oxidized 

are present (displacement plating). 

Figure 1 - Equilibrium potentials for pure metals at pH 7.00 as a function of density.[30] 

 Figure 1 is a plot of the specific gravity (density) of the metallic elements of the periodic 

chart and the Gibbs free energy for the reaction of these elements with water to form an oxide or 

hydroxide in neutral aqueous solutions.[30] There are two dashed lines in this figure that identify 

the potentials where the cathodic reduction reactions 

 

1

2 O2(diss) + H2O(l) + 2e 2OH

(aq) (1) 

and 
4 

 

H2O(l) + e OH

(aq) + 1

2 H2(g) (2) 

are at equilibrium under ambient conditions in neutral pH water (pH  7.0). All of the elements 

with equilibrium potentials below the upper dashed line in this figure produce electrons with 

enough energy when they oxidize to spontaneously reduce any oxygen dissolved in aqueous 

solutions according to the reaction of eq. (1). The second, lower, dashed line is a similar line for 

the cathodic reduction reaction of eq. (2). Metals that have equilibrium potentials below this line 

produce electrons with enough energy when they oxidize to spontaneously reduce the hydrogen 

ions in water. That is, they will drive the reaction of eq. (2) in the forward direction and the rate 

will vary with the excess Gibbs energy or distance below this line. Metals below the lower line 

spontaneously react with any aqueous environment and metals between the two lines react in 

aqueous environments only when O2 is present. Metals above the upper line require more 

aggressive oxidizers to make them react in this environment. 

 The discussion above only examined reactions with neutral pH water. There are a wide 

range of pHs and aeration levels consistent with the term “aqueous environments under ambient 

conditions” and some metals will prefer the metallic state in some conditions and ionic states in 

others. To help understand these cases, Pourbaix and co-workers[31] advocated the use of 

electrochemical equilibrium diagrams (E-pH diagrams). For these diagrams, the solution pH is 

plotted on the horizontal axis with the driving force for electrochemical reactions on the vertical 

scale. At constant pressure, the force driving chemical reactions is normally quantified by the 

thermodynamic quantity Gibbs free energy or Gibbs energy (G). For reactions on the surface 

of an electrode immersed in an electrolyte, the driving force is quantified by the potential 

difference between the electrode and a standard reference reaction with a defined or well-known 

Gibbs free energy and reference potential. The hydrogen evolution reaction at standard state is 

frequently used for this reference potential and potentials measured against this electrode (ESHE) 

are related to Gibbs free energy through the relationship 

 ESHE = G /nF (3) 

where n is the change in the oxidation state, F is Faraday’s constant, and G for the hydrogen 

evolution reaction at standard state is defined as zero by convention of the International Union of 

Pure and Applied Chemists (IUPAC).[32] This is a very important relationship because it relates 

electrochemical measurements of voltage and current directly to chemical thermodynamics and 

kinetics. It also creates a direct link between these quantities and the activity of hydrogen on the 

surface of an electrode. That is, since the chemical reaction occurring in the standard hydrogen 

electrode that is used as the zero point of potential for electrochemical measurements is 

 H+ + e 1

2 H2 (g) (4) 

and hydrogen is a reference phase for thermodynamic tables with G=0 for all reactants in their 

standard states,[32] electrode potentials measured against this scale are directly relatable to 

chemical thermodynamics. Furthermore, since the standard state for this reaction is hydrogen 

ions with an activity of 1.0 (pH=0) on the surface of platinum metal in equilibrium with 

hydrogen gas at a pressure of 105

 Pa (0.987 atm), this relationship also directly relates tabulated 

data on chemical thermodynamics and the Gibbs free energy change for a reaction (G) to a 
5 

potential and the activity of hydrogen molecules on the surface of an electrode where that 

reaction is occurring. That is, potential, Gibbs free energy, and the activity of hydrogen 

molecules on the surface of the electrode (fugacity) are all related through the reaction of eq. (4), 

the relationship of eq. (3), and the standard principles of chemical thermodynamics. 

Figure 2 - Electrochemical equilibrium (E-pH) diagram for Nb in water without consideration of niobium 

hydride phases. 

 Figure 2 is the E-pH diagram for Nb in water determined using the thermodynamic data of 

Wagman[32] and Pourbaix[31,33]. This figure contains two dashed lines labeled “a” and “b” to 

represent the reactions of eqs. (1) and (2) respectively similar to the lines in Fig. 1, but now with 

a slope of -0.059 V/pH since the equilibrium potential for these reactions depends on the pH of 

the solution. By examining this figure, it can be seen that Nb has 4 phase fields (Nb, NbO, 

NbO2, and Nb2O5) and no soluble ions. In the range between the dashed lines where water is 

stable, the lowest energy state for Nb atoms is as ions in the pentoxide. This diagram shows that 

Nb has a very high reactivity with water, but also has high probability that it will react to form a 

passivating surface oxide film that makes it appear inert. The high reactivity is shown by the 

potential difference between the upper edge of the field where metallic Nb is stable and the line 

where the fugacity of hydrogen is 105

 Pa (line “a”). This indicates a large driving force for the 

reduction of hydrogen ions and the lack of any soluble ions, assuming the fluoride ion or other 

ions that form soluble complexes are not present, indicates that mass transport will not be able to 

remove the products of this reaction before the surface becomes covered isolating the underlying 

metal from the environment. In other words, Nb is an active metal that will appear to be noble 

due to the formation of a passivating layer (i.e. a passive metal, or in the older literature, a valve 

metal).[34] In some cases, the underlying metal is so active that the even the application of 

strong cathodic currents cannot reduce the protective oxide film. 

 Figure 2 was calculated considering only Nb metal, ions, and oxide or hydroxide phases. 

This diagram neglects the possibility of the formation of Nb hydrides and "NbH(?)" is included 

in the figure to indicate this fact. The purpose of this figure is to establish the phases that may be 
6 

present on Nb at the start of processing. Then, the reactions between these phases and the 

processing environment will be considered with the reaction products and their activities 

estimated. Once the activities of the reaction products are estimated, then the effects of the 

presence of these products at the expected activities will be considered including the possibility 

of the nucleation of niobium hydride phases. 

C. Passive Metals and Hydrogen Absorption 

 

 The ability of active metals to react with water and absorb hydrogen is a well-known 

phenomenon.[3-5] It is also well known that similar reactions can result in hydrogen uptake 

during chemical processing, finishing, or cleaning of metals.[35] However, it is not uncommon 

for these possibilities to be ignored for a number of reasons including: (i) under appreciation of 

the activity of the metals involved (passivity creates a false impression of nobility), (ii) limited 

exposures times, (iii) ambient or low temperatures, and (iv) the assumption that absorbed 

hydrogen will desorb before it can cause harm. There are standardized tests developed 

specifically for the evaluation the effects of cleaning and processing solutions on hydrogen 

uptake by metals.[36] In the case of passive metals, the passive films can be a very effective 

barrier to hydrogen uptake due to the relatively low solubility and diffusivity of hydrogen in 

these films as well as their effect on reaction kinetics and hydrogen reduction rates. 

Unfortunately, the low solubility and diffusivity of these films can also block hydrogen 

desorption. Frequently, steels are plated with Cu or Cd to prevent hydrogen absorption and it has 

been found that if the samples are not hydrogen free before they are plated then hydrogen 

embrittlement may occur. Plating and passivation have been used to seal hydrogen into samples 

and prevent hydrogen desorption between charging experiments and hydrogen content 

measurements. 

 Charging hydrogen into passive metals to study its effects on properties can be particularly 

difficult for metals that form oxide films that cannot be reduced by strong cathodic currents. 

Typically, four different approaches are used when exposure to hydrogen gas and cathodic 

charging fail to introduce hydrogen into these metals: (1) cathodic charging in aggressive 

solutions containing species that form soluble complexes (e.g. F-), (2) removal of the passive 

film and replacing it with a coating of Pd or Ni,[37] (3) exposure to water vapor at moderately 

elevated temperatures,[38] and (4) mechanical abrasion.[2] All have proven successful for 

different metals and alloys, but we will focus on those relevant to hydrogen uptake during Nb 

processing. Figure 3 shows a schematic for the hydrogen absorption mechanism observed by 

Scamans and Tuck[1] in samples of an Al alloy in a transmission electron microscope when 

water vapor was allowed to leak into the vacuum chamber. The passive film was observed to 

form hydrogen gas blisters that cracked allowing the environment access to the underlying metal. 

Exposure to water vapor saturated air is a common test for Al alloys and similar blisters are 

frequent observed.[39] Slow continuous abrasion has also been used on Al alloys.[2] Figure 4 

plots hydrogen content data as a function of polishing time taken from the work of Ciraldi.[2] 

This figure clearly shows a slowly increasing hydrogen content with time, but one that agrees 

well with the diffusivity data for hydrogen in Al alloys available in the literature.[5] In some 

cases, hydrogen absorption by passive metal is so difficult when the passive film is stable that 

many do not realize that these metals are susceptible to the influence of hydrogen, but unique 
7 

Figure 3 - Schematic of blisters observed 

when an Al alloy was exposed to water 

vapor in an electron microscope. [1] 

processing conditions that are specifically designed to attack or remove the passive film defeats 

this natural protection system enabling hydrogen entry and embrittlement. 

 

 

D. Hydrogen Absorption and Evolution

 Figure 5 is a schematic representation of the steps in hydrogen evolution that accompanies 

anodic dissolution on the bare surface of an active metal in an aqueous solution. This sequence 

begins with the metal in the solution at the potential of zero charge (PZC) in Fig. 5(a). This is a 

theoretical point where the adsorbed polar water molecules are randomly oriented on the surface 

of the electrode. At any other potential, the adsorbed molecules will have a preferred orientation. 

In the case of a negatively charged active metal such as Nb, the water molecules will become 

oriented with the positive hydrogen cations adsorbed down against the surface of the metal as 

shown in Fig. 5(b). If the potential gradient is sufficient, electrons will tunnel through the space 

charge layer reducing the hydrogen cations creating adsorbed H atoms and hydroxyl ions (Fig. 

5(c)). This results in the production of adsorbed hydrogen atoms on the surface the activity of 

which is determined by the potential gradient or the chemical potential. These adsorbed 

hydrogen atoms (H(ads)) will do one of two things: (i) diffuse across the surface until they bump 

into another adsorbed hydrogen atom and recombine to form an adsorbed hydrogen molecule as 

in the reaction 

 

H(ads) + H(ads)  H2(ads) (5) 

or (ii) instead of hopping in the plane of the surface the adsorbed H atoms can jump into the 

surface where they become absorbed H atoms according to the reaction 

Figure 4 - Hydrogen content of an Al alloy measured 

after abrasion for different times in aqueous slurry 

and predicted absorption rates for different hydrogen 

solubility and diffusion coefficients. .[2] 
8 

 

H(ads)  H(abs) (6) 

It is important to recognize that these are not sequential reactions, but are parallel paths that are 

both taken and are both driven by the concentration of the adsorbed hydrogen atoms on the 

surface. At some point, the concentration of the adsorbed H2 molecules on the surface is the 

same as that which would exist for equilibrium with the solution saturated with H2(g) at 1 bar 

pressure (105 Pa). The potential for this equilibrium, Fig. 5(e) is known as the hydrogen 

evolution potential even though hydrogen is not evolved at this potential. If the potential is 

reduced further, the fugacity of the hydrogen molecules on the surface continues to increase until 

there is sufficient driving force to nucleate bubbles of hydrogen gas on the surface as illustrated 

in Fig. 5(f). The pressure of hydrogen required to nucleate these bubbles is much greater than 

atmospheric pressure, so once nucleated, these bubbles rapidly expand until the pressure in them 

approaches atmospheric pressure and the bubbles appear to "pop" on the surface. 

 The purpose of this discussion of the detailed steps in the process of hydrogen evolution and 

absorptions was to make four points: 

1. The activity of the absorbed hydrogen is not limited to the external pressure. - The 

hydrogen is generated as adsorbed atoms on the surface, but this hydrogen cannot 

leave the surface until it recombines with other hydrogen atoms to form molecular 

hydrogen and then enough molecules aggregate to enable heterogeneous nucleation of 

gas bubbles. The fugacity of the adsorbed hydrogen atoms must exceed the external 

pressure to provide enough energy to drive the kinetics of these processes. This 

fugacity can be orders of magnitude greater than the external pressure.[40-42] 

2. Hydrogen can be absorbed when bubbles are not observed. Since a surface 

concentration corresponding to a pressure much greater than ambient pressure is 

required to drive the kinetics hydrogen evolution, hydrogen can be absorbed into 

metals even when hydrogen gas bubbles are not observed. 

3. Promoting hydrogen evolution (bubbling) can reduce absorption. Alterations to the 

alloy or environment that reduce the overpressure required to drive recombination 

and nucleation will accelerate bubbling, but will reduce the hydrogen surface 

concentration driving absorption.[41,43] Conversely, alterations that inhibit the 

processes of hydrogen evolution will tend to increase the fugacity of hydrogen on the 

surface. 

4. Hydrogen reduction comes first. Fig 2 shows that Nb wants to passivate by the 

formation of an oxide when it comes into contact with water, but Fig. 5 shows that the 

polar water molecule will tend to be adsorbed with the hydrogen anion between these 

two reactants. This physical arrangement, and the assumption that electron tunneling 

will be rapid compared to the rearrangement of atoms required for oxide formation 

and growth, implies that the Nb atoms will give their electrons to the hydrogen first 

and then bond with the oxygen. 

A common misconception is that the external air pressure is the maximum surface fugacity of 

hydrogen that can be produced by electrochemical reactions, because it is the pressure in the 

hydrogen bubbles on the surface. A better scenario for understanding this kinetic limit to the 
9 

fugacity of hydrogen on the surface is to think of it as the pressure required to generate the 

observed bubble nucleation rate in a sample that was instantly transferred from a high pressure 

gas chamber to the solution. 

Figure 5 - Schematic illustrating the steps in cathodic reduction and hydrogen evolution on the bare 

surface of a metal. 

III. ANALYSIS OF REACTIONS

 These calculations assume that the passivating film on Nb has been removed by chemical or 

mechanical means and that the underlying metal has been exposed to the unaltered processing 

environment. That is, the calculations will be based on direct reaction between Nb metal and the 

nominal or bulk chemistry of the processing environment. The relative propensity for hydrogen 

absorption will be quantified by the calculation of the activity of hydrogen on the surface 

required for the postulated metal-environment reaction to be in equilibrium. This activity of 

hydrogen will be expressed in terms of the equivalent pressure or fugacity required for 

equilibrium. The standard values used for the calculation of hydrogen fugacity are based on 

measurements of equilibrium for hydrogen at different pressures on platinized Pt, and strictly 

speaking are true only on for this surface, but Valand et al.[44] compared different metals and 

concluded that there was no significant difference between the metals examined (Ni, Fe, Cu, Ag, 

and Au). The sequence of events considered in this report is as follows: 

(1) Nb metal covered with a passivating layer of Nb2O5 as indicated by the region between 

the dashed lines in Fig. 2 is placed in the processing environment. 

(2) Processing commences and passive film breakdown or rupture events occur. These 

events may be due to chemical or mechanical processes, but they probably occur at small, 
10 

occluded, sites distributed over the surface. The actual size, distribution, repassivation 

rate, and frequency of these events will depend on the particular processing conditions. 

(3) Each passive film rupture or breakdown event results in sudden contact between three 

phases: (i) the metal, (ii) remnants of the surface oxide, and (iii) the processing 

environment. At the moment these three phases come into contact, the composition of 

each phase is essentially that of the bulk of the phase. 

(4) Reactions begin immediately and since mass transport is not required initially, reaction 

rates are determined by the driving forces for the initial (bulk) concentrations of the 

reactants and the activation energies for the reactions. 

(5) Reactants are consumed in the occluded region of the passive film breakdown and 

reaction products accumulate. Mass transport is required to replenish reactants and 

remove products and this slows reaction rates and locally alters the chemical environment 

(polarization). The accumulation of reaction products in the occluded region of the 

passive film breakdown promotes the reformation of the passivating film and 

repassivation of the breakdown region probably occurs for Nb in aqueous solutions due 

to the large potential difference ( 0.75 V) between the region where water is stable and 

Nb metal is stable. 

(6) The whole process is repeated such that at steady state passive film rupture and repair 

events are continuously occurring at small, localized, regions distributed over the surface 

of the sample with the rate, size, and distribution of these events determined by the 

chemical and mechanical conditions of the process. In some cases, repassivation may 

occur so quickly that the time bare metal is actually in contact with the solution may be 

less than a millisecond as found for aluminum alloys.[45] 

A. Reactions with Water and Dilute Aqueous Solutions ([H2O]1)

 In water and in many solutions where the activity of water can be assumed to be unity, the 

reactions between Nb and water can be summarized as 

 

xNb(s) + yH2O(l) NbxOy (s) + yH2 (g) (3) 

where x=1 or 2 and y=1, 2, or 5 depending on the stoichiometry of the oxide being formed. 

Keeping in mind the discussion of section II, this reaction is a summary of the starting and 

ending points of the process with Gibbs function (G) for the free energy change in the reaction 

given by the relationship 

 G = G° + RT ln K (4) 

where G° is the free energy change for all reactants in their standard states and K is the reaction 

constant 

 K = [Products]

[Reactants]

 (5) 
11 

where the brackets imply the activity of the species within them. Combining equations (3)-(5) 

and assuming the G=0 at equilibrium gives 

 

 

K = [NbxOy][P(H2 )] y

[Nb]

x

[H2O]

y = exp

G°

RT











 (6) 

Since in this section the activity of water in the solution is assumed to be essentially 1 and the 

activity of pure solid phase is also unity, eq. (6) is simplified further as 

 

 

Peq (H2 )

y = exp

G°

RT











 (7) 

Taking the log (base 10) of this relationship yields 

 

 

 

log Peq (H2 { }) = G°

yRT ln(10) (8) 

Table 1 summarizes the results of the calculations using these equations to determine the 

equilibrium fugacity, Peq (H2 ), for the reaction of Nb with water in dilute aqueous solutions 

where the activity of water can be estimated as unity. 

Table I - Gibbs free energy, equilibrium potential (Eeq), and equilibrium hydrogen fugacity (Peq(H2)) for 

reactions between Nb and water for the thermodynamic data of Wagman et al.[32] 

Product Gf(NbxOy) X Y n G° kJ/mol E(eq) V 

vs. SHE 

log (P(H2)) 

bar 

log (P(H2)) 

Pa 

NbO -378.6 1 1 2 -141.47 -0.733 24.78 29.78 

NbO2 -740.5 1 2 4 -266.24 -0.690 23.32 28.32 

Nb2O5 -1766.0 2 5 10 -580.35 -0.601 20.33 25.33 

 It is interesting to note that since Nb does not form soluble ions in water at any pH between 0 

and 14, that eq. (4) holds for any reaction with an aqueous solution. This means that the fugacity 

of hydrogen for the reaction of eq. (3) holds for all pHs and that the hydrogen fugacity is not a 

function of pH as it is for metals that form soluble ions at low pH values.[33] 

B. Reactions with Water Vapor

 The hydrogen fugacity that can be generated on the surface of bare Nb by reaction with water 

vapor in air, inert gases, or vacuum is the next issue of concern. Since relative humidity (RH) is 

the ratio of the activity of water vapor to that for equilibrium with pure liquid phase water, RH is 

also the activity of water for use in calculation of hydrogen fugacity as in eq. (6). Substituting 

RH for the activity of water in eq. (6) and solving for hydrogen fugacity as in eq. (8) yields 
12 

 

 

log Peq (H2 { }) = G°

yRT ln(10)

+ log(RH ) (9) 

This relationship is very interesting as one can readily see that if one were to conduct an 

experiment in H2(g) at a moderate pressures, the activity of hydrogen in the sample may actually 

be greater than that corresponding to the gas pressure if significant amounts of water vapor are 

present in the gas. For example, CaSO4 desiccant keeps the relative humidity in a desiccator 

below an estimated 0.01% RH. Substituting this value into eq. (9) using Table I indicates that 

the equilibrium fugacity for this environment is still greater than 1021 Pa (1016 bar). Of course, 

mass transport will limit the reaction rate kinetics compared to the kinetics of absorption or 

desorption such that the steady state values will be well below this theoretical limit, but this 

calculation clearly shows that, at least theoretically, exposure to moderate pressures of water 

vapor can result in more hydrogen absorption by Nb than exposure to high pressure hydrogen 

gas. In practice, passivation of the surface limits hydrogen absorption, but significant hydrogen 

absorption can occur in nominally inert environments if water vapor is present and the surface 

cannot passivate. 

C. Solvents and Cutting Fluids

 In the case of organic solvents and cutting fluids, the moisture content of these fluids will 

contribute to hydrogen uptake in the same manner as water vapor impurities in air, inert gases, 

and vacuums. That is, it will occur driven by the fugacity given by eq. (9). Typically, these 

fluids are left open to the air or stored in partially sealed containers and will have sufficient time 

for the activity of the water in these fluids to reach equilibrium with the water vapor in the 

laboratory air. Drying these fluids and keeping them dry may be a means for processing Nb with 

a minimum of hydrogen uptake. A water-free electropolishing solution that uses solvent has 

been reported for Nb.[46] 

D. Concentrated Acid Solutions (BCP)

 The chemical etchant used to polish Nb that is commonly referred to as BCP (for 

buffered chemical polish) is a 1:1:1 or 1:1:2 mixture of HF:HNO3:H3PO4. Assuming that this 

solution is mixed up from standard reagent grade chemicals where the reagent grade acids 

contain significant amounts of water, then the expected composition of the actual solutions is 

given in Table II. 

Table III - Estimated Composition of BCP solutions. 

Acid MW,

g/mol

Reagent

Conc, 

mass %

BCP

1:1:1

mol/L

BCP 

1:1:1,

mass%

BCP

1:1:2

mol/L

BCP 

1:1:2, 

mass%

HF 20.01 49.0 9.63 13.4 7.23 9.6 
13 

HNO3 63.01 70.4 5.30 23.3 3.98 16.7 

H3PO4 98.00 85.5 4.93 33.7 7.40 48.4 

H2O 18.02 100 23.48 29.5 21.02 25.3 

 Concentrated mineral acid mixtures of this type are commonly used for polishing, etching 

and cleaning of metals. In many cases, HCl is used in place of HF and sometimes H2SO4 is used 

in place of H3PO4. The HF acid is used to provide the fluoride ion because this ion tends to form 

soluble complexes with Nb. That is, being more electronegative than oxygen and forming 

soluble species with Nb the fluoride ion tends to react with the oxide on the surface of the Nb to 

form soluble species in reactions of the form. 

 

 

Nb2O5 + ( )z HF 2

x











NbxOyFz

(5x2 y z) + ( ) 5 y H2O + ( ) 2y H +

 (10) 

 

where x, y, and z are variables that depend on the stoichiometry of the soluble ions formed by the 

oxide dissolution reaction. Apparently, the Nb-fluoride ion system is very complex and a book 

was recently published on the fluoride compounds formed with Ta and Nb.[47] 

 Without better information on these reactions, one needs to make some assumption on the 

reactions and activities of reactants and products. Palmieri et al.[46] reported that the reaction 

sequence during BCP is: (i) reaction with HNO3 to form niobium oxide: 

 

6Nb +10HNO3 3Nb2O5 +10NO + 5H2O (11) 

followed by (ii) the dissolution of the oxide by reaction with HF 

 

Nb2O5 +10HF 2NbF5 + 5H2O (12) 

making the total reaction: 

 

3Nb + 5HNO3 +15HF 3NbF5 + 5NO +10H2O (13) 

The literature indicates that the product of this reaction, NbF5, is unstable in the presence of 

water spontaneously decomposing to form HF and Nb oxide.[23] However, the goal of the 

current exercise is to make an estimate of the thermodynamic limit for the fugacity of hydrogen 

that will drive hydrogen absorption in the BCP environment. There are two approaches that can 

be taken for this calculation. First, one can assume a reaction of the form 

 xNb(s) + yHzAc  Nbx Acy(cx) + ( yz)H2 (g) (14) 

dominates the production of hydrogen and then calculate the thermodynamic limit for the 

hydrogen fugacity for this reaction in this environment. For BCP, the literature indicates that HF 

is the acid molecule most likely to react with Nb in this manner and one possibility for 

stoichiometry of this reaction is 
14 

 

2Nb(s) +10HF 2NbF5 + 5H2 (g) (15) 

the change in Gibbs free energy for this reaction with all reactants in their standards states (G°) 

is then 

 

G° = 2* G(NbF5 ) + G(H2 { }) { } 2* G(Nb) +10 * G(HF) (16) 

or 

 

G° = { } 2*(1698.0) + 0 { } 0 +10 * (296.82) = 427.8 kJ / mol (17) 

The constant K for this reaction at equilibrium is 

 

 

Keq = [NbF5]

2

[P(H2 )]5

[Nb]

2

[HF]

10 = exp

G°

RT











 (18) 

Taking the base 10 logs of this relation assuming the activity of the metal is unity yields 

 

 

log[P(H2 )] = G°

5RT ln(10)











 + 2 log[HF] (19) 

Assuming that the concentration of HF in the acid is a good estimate of its activity, then eq. (19) 

becomes 

 

 

log[P(H2 )] =14.99 +1.96 16 (20) 

indicating a hydrogen fugacity of 1016 bar (1021 Pa). This fugacity appears low compared to 

that that can be expected due to the reaction of Nb with the water brought into this solution from 

the reagent grade acids shown in Table II. If one estimated the activity of water in this solution 

by the ratio of the molar concentration of water in this solution to that of pure water, then one 

gets an estimated activity of 0.423 for water in BCP 1:1:1 and 0.378 for water in BCP 1:1:2. 

Substituting these into eq. (9) for the formation of the pentoxide gives 

 

log Peq (H2 { }) = 20.33+ log[ ] H2O 19.9 (21) 

This then indicates that the fugacity driving hydrogen absorption may be as high as 1020 bar 

(1025 Pa). 

E. Electropolishing

 Niobium is frequently electropolished (EP) in a solution of H2SO4 and HF with a 9:1 volume 

ratio at current densities in the range 50-100 mA/cm2. As with the chemical polishing solutions, 
15 

this solution will contain water and Table III contains the information estimated for the actual 

composition of this solution. 

Table IV - Electropolishing (EP) Solution Composition 

Acid MW,

g/mol

Reagent 

Conc, mass

fraction (%)

EP 

9:1 

mol/L

EP 9:1, mass

fraction (%)

HF 20.01 0.490 2.89 0.033 

H2SO4 98.08 0.960 16.20 0.896 

H2O 18.02 1.000 7.02 0.071 

The thermodynamic limit for the hydrogen fugacity in this solution in the absence of any applied 

currents can be estimated in the same fashion as that used for the chemical polishing solutions. 

That is, direct reaction with HF to produce NbF5 according to the reaction of eq. (15) can be 

expected to produce hydrogen fugacities up to 

 

log[P(H2 )] =14.99 + 2 log[HF] 16 (22) 

and the reaction with the water in the solution can be expected to produce hydrogen with 

fugacities up to 

 

log Peq (H2 { }) = 20.33+ log[ ] H2O 19.4 (23) 

Direct chemical reaction in the absence of polarizing current densities will produce hydrogen at 

fugacities up to 1016 bar (1021 Pa) according to eq (22) and 1019.4 bar (1024.4 Pa) according to eq. 

(23). 

 For electropolishing, an auxiliary electrode is added to the solution and a power supply is 

used to apply a current (or potential) to the sample that stimulates the polishing reactions. The 

applied current raises the potential of the sample stimulating anodic dissolution (oxidation) 

reactions and suppressing cathodic (reduction) reactions. Under ideal conditions, only anodic 

reactions occur on the sample (anode) and only reduction reactions occur on the auxiliary 

electrode that is now the cathode. However, in the case of an active metal such as Nb in an 

aqueous electrolyte, the overpotential for the dissolution reactions is so great that it is difficult to 

completely suppress cathodic reactions on the anodic sample. In the case we are examining here, 

the anodic reactions would be either Nb dissolution 

 NbNb+5 + 5e

 (24) 

or repassivation according to a reaction of the form 

 

2Nb + 5H2O  Nb2O5 +10H +

 (25) 
16 

Normally, Nb does not form soluble ions in aqueous solutions, but with the fluoride ion present 

soluble complexes form that reduce the thickness of passivating films accelerating dissolution 

reactons. The cathodic reaction in this solution is then 

 

2H + + 2e H2 (g) (26) 

Since this solution no longer contains the HNO3 molecule, the reduction reaction 

 

3H + + 3e + HNO3 NO + 2H2O (27) 

that is included in eq. (13) cannot occur in this solution. This is why the addition of nitric acid to 

the BCP solution accelerates the polishing reactions. The question to be addressed here is to 

estimate the extent that the applied anodic current suppresses the fugacity of hydrogen on the 

sample surface during electropolishing. If one assumes normal Tafel kinetics for the reaction of 

eq. (26) on the surface of Nb, then the reaction rate measured by the current (ic) is related to the 

overpotential driving the reaction () according to an equation of the form 

 

 

ic = i

0 exp (1)nF

RT











	 (28) 

where n=1, F is Faradays constant,  is the reaction symmetry constant (typically 0.5), and i0 is 

the exchange current density. Rearranging and combining terms eq. (28) becomes 

 

 

=  log ic

i

0





 



 (29) 

where is the Tafel slope. The Tafel slope () and the exchange current density (i0) are 

constants that depend on the material and the solution. Tabulated values for these constants can 

be found in the literature, but data is not available for bare Nb metal in the EP solution. 

However, if one assumes that the values reported for a 1.0 mol/L HCl solution are a good 

estimate for those that will be observed in the EP solution, then one can make estimates of the 

effect of current densities of the magnitude used in electropolishing on the hydrogen fugacity 

driving hydrogen absorption. It is reported that in this environment the values for and i0 are 

0.10 (V) and 1 x10-4 (mA/cm2

) respectively.[4,48] Assuming that the EP current density is 100 

mA/cm2

, then eq. (29) becomes 

 

 

= (0.10) log 100

0.0001





 



  0.6 (30) 

That is, the applied current density corresponds to the application of an overpotential of 

approximately 0.6 V. Since a simple model for the reversible transfer of ions between electrodes 

will show that 

 G = nFE (31) 
17 

This illustrates the fact that one could just as easily done the calculations in this document in 

terms of potentials as well as free energies. Substituting eq. (31) into eq. (8) yields 

 

 

log Peq (H2 { }) = 2FE

RT ln(10) = 

0.0296  20.3 (32) 

That is, it is estimated, assuming that the Tafel slope and exchange current density in the EP 

solution are similar to those for Nb in 1.0 mol/L HCl, that the application of an anodic current of 

100 mA/cm2

 will lower the fugacity driving hydrogen absorption by 20 orders of magnitude. 

Since eq. (23) found that the expected fugacity for unpolarized conditions was less than this 

value (19.4 maximum estimate), this estimate indicates that the hydrogen fugacity for this 

condition is less than 

 

log Peq (H2 { })  1 (33) 

Of course, this estimate contains a large number of rough approximations one of which is the 

assumption that the applied current is evenly distributed so that local cell actions cannot occur in 

occluded regions of the surface, but it is interesting to find that the empirically determined 

polishing conditions that give the best results are almost exactly those that this estimate indicates 

would suppress H2 bubbling from the surface. This could be an indication that suppression of H2

bubbling helps one obtain a better surface finish. 

IV. DISCUSSION

A. Thermodynamic Analysis

 The analysis presented in this document is based entirely on the principles of 

thermodynamics and the assumption of equilibrium. When reactions are occurring and currents 

are flowing, actual conditions will deviate from those of a reversible equilibrium and the 

magnitude of this deviation increases with increasing reaction rate or current density. For this 

analysis, all factors in the system were identified and assumed constant except for the hydrogen 

pressure or fugacity. Then, it was assumed that all of the excess energy driving the reaction 

forward was converted reversibly into hydrogen pressure. The reversible equilibrium fugacity 

calculated in this manner represents the upper limit that the system is attempting to reach for 

these boundary conditions. 

 Since the fugacities determined are based on the assumption of equilibrium, they can only be 

achieved under fully reversible conditions. Irreversible losses will increase with the deviation 

from equilibrium conditions. This creates a discrepancy between the calculated theoretical 

hydrogen fugacity and the actual, steady state, hydrogen fugacity that the metal will experience. 

This discrepancy will increase with the magnitude of the theoretical value. However, if one 

assumes activation controlled kinetics and that the environments do not contain species that 

dramatically alter the kinetics of the relevant processes, then one can expect greater hydrogen 

absorption under conditions with a higher equilibrium hydrogen fugacity. In other words, the 
18 

equilibrium fugacity quantifies the thermodynamic forces behind hydrogen absorption and 

evolution or the natural propensity for these processes on Nb in these environments even if the 

values determine are never actually achieved in practice. 

B. Kinetic Limitations

 Most of the fugacities calculated for the reactions above are absurdly high and kinetics will 

keep these systems from reaching these theoretical values. The kinetic limit to the hydrogen 

fugacity is determined by the sequence of reactions required to remove hydrogen atoms from the 

surface as their concentration increases toward this theoretical value or upper limit. These 

reactions have been studied in detail on a number of different metals and typically the 

recombination reaction, eq. (6), is found to be the rate determining step (in the case of active 

metals such as Nb, the passive film is frequently in place during these measurements making 

them of little value to this discussion).[48] This implies that the fugacity on the surface may be 

orders of magnitude greater than the ambient pressure, but also orders of magnitude below the 

calculated theoretical fugacities. 

 Assuming that mass transport and recombination are much slower than surface adsorption 

and electron tunneling, then the highest hydrogen fugacities are probably reached in first 

milliseconds after bare metal comes into contact with the environment. Assuming that 

repassivation of the surface starts immediately after the initial adsorption and hydrogen reduction 

transient, the reformed passivating film may block hydrogen egress resulting in the hydrogen 

diffusion into the metal (e.g. repassivation of Al alloys starts within the first millisecond of 

exposure).[45] If this is the case, then periodic rupture and repair of the passivating layer in an 

environment containing water could result in significant hydrogen absorption. This analysis 

indicates that it is theoretically possible for abrasion and periodic passive film rupture by 

chemical or mechanical means to introduce more hydrogen into Nb than exposure to high 

pressure hydrogen gas especially if one does not employ measures to remove the passive film 

and stimulate dissociation of the hydrogen gas for the gas phase exposures.[49] In addition, this 

analysis indicates that vacuum annealing to remove hydrogen could actually result in increased 

hydrogen levels if the sample is exposed to water or humid air before the passive film has fully 

reformed and passivated the surface. 

C. Electrochemical Measurements

 A number of investigators have conducted experiments on BCP and EP processes used in the 

fabrication of SRF cavities. Many of these rely on empirical cell voltage measurements. While 

cell voltage is a reliable means for reproducing polishing conditions, it is highly dependent on 

the cell geometry, solution chemistry, and experimental technique. More importantly, it provides 

no useable information on the actual thermodynamic driving forces governing reactions on the 

surface of the sample. One of the most thorough studies was that of Nb in the EP environment of 

Tian et al.[50] These authors used a reference electrode that has a fixed potential with respect to 

the hydrogen electrode that enables them to measure and control the potential difference that 

determines the thermodynamic forces driving the reactions (eq. (3)). These authors found very 
19 

broad current density plateaus in their current-voltage curves. The current density of the plateaus 

was found to depend on the concentration of the species in the environment that reacts with the 

Nb in the passivating oxide to form soluble complexes (the fluoride ion). These results were 

found to be consistent with the duplex salt film model of Landolt and co-workers.[51-55] This 

salt film model is very similar to that proposed in 1953 by Keller et al.[56] to explain the 

structure of the oxide film observed on Al alloys following anodic polarization and exploited by 

Miller et al.[57-61] in the development of a patented process for the fabrication of nanodot or 

quantum dot arrays.[62] Due to the active nature of Nb (Fig. 2), it is highly unlikely that the salt 

film on the surface of this metal during electropolishing is anything other than niobium oxides. 

However, the barrier layer at the bottom of the pores may be the sub-oxides rather than the 

pentoxide which would be the more stable phase in the bulk environment. The formation of 

niobium fluoride complexes would occur at the bottom of these pores and mass transport of the 

negatively charged fluoride ions to the bottom of the pores and/or the transport of the positively 

charged niobium-fluoride complexes out of the pores would be rate limiting (Fig. 6). These ratelimiting processes are responsible for the current density plateaus. That is, increasing the driving 

force has no impact on the observed rate since the boundary conditions determine the rates of 

mass transport are not altered. The current density generated from the area outside the pores can 

be approximated as zero making the total current density a function of the pore geometry and the 

rate of mass transport in the pore by the rate limiting process. 

 

Figure 6 - Schematic of the pore structure found on anodically polarized Al alloys.[57] 

 

 The issue with respect to this report is how does the application of these polarizing potentials 

or currents influence the propensity of Nb to absorb hydrogen from this environment and do the 

measurements of Tian et al.[50] demonstrate that hydrogen will not be absorbed? On a purely 

theoretical basis, this question is answered by the calculations in the electropolishing section 

above and the measurements of Tian et al.[50] support the theoretical result that indicates 

hydrogen absorption by the metal will be suppressed by conditions of this process. However, in 

practice it is difficult to control the distribution of potentials and currents on the surface of a 

sample in an environment where it is this far from equilibrium. In the case of Nb or Al where 

the bare surface current density may be orders of magnitude greater than the externally imposed 

anodic current,[45] the surface will still be covered with oxide even if it is discontinuous and 
20 

inhomogeneous. Electropolishing occurs because a steady state is reached where the oxide is 

removed and replaced either on opposite sides of thin homogeneous oxide film or in a complex 

duplex film and pore structure as shown in Fig. 6. The literature indicates that the latter is 

preferred at the higher current densities that provide reasonable polishing rates. 

 In either case, the chemical potentials of the Nb atoms in the metal are unaltered by the 

application of these polarizing currents and the voltage gradients they produce. The 

thermodynamics of the electrochemical reactions are altered because the ions participating in 

these reactions must move in the voltage gradient and this alters the energy changes the reactions 

produce. If a small region of the surface becomes shielded from the polarizing current and the 

voltage gradient it produces, then the thermodynamic conditions in this occluded region revert to 

those that exist in the absence of the polarizing currents. For example, if the mouth of the pore 

shown in Fig. 6 was suddenly blocked by the precipitation of niobium oxide (by hydrolysis of 

the Nb-F complexes) or a gas bubble, then the voltage gradient would be virtually removed 

allowing direct reaction between the solution at the tip of the pore and the Nb metal. According 

to the calculations above, this should result in the production of hydrogen gas the expansions of 

which would clear the blockage. Investigators have collected the gas observed during anodic 

polarization of metals. For example, Bargeron and Benson[63] analyzed the gas evolved from 

Al during anodic polarization at potentials where thermodynamic consideration would predict 

the gas should be oxygen and they found the gas evolved to be essentially pure hydrogen. 

Similar results have been reported for the gases evolved during anodization of Al alloys.[4] 

D. Niobium Hydrides

 The hydrogen activities calculated in terms of equivalent pressure or fugacity are clearly 

much greater than atmospheric pressure and hydrogen gas bubble nucleation can be expected 

when the surface remains bare for any significant length of time in these environments. 

However, recombination and bubble nucleation can be very slow compared to electron tunneling, 

reduction, and even mass transport. Recombination is typically found to be slower than bulk 

diffusion in hydrogen gas phase desorption experiments on Nb where H2 molecules can desorb 

directly without having to accumulate and nucleate bubbles.[64,65] Therefore, while the actual 

activity of hydrogen on the surface may be considerably less than that estimated by these 

equilibrium calculations, it will be considerably greater than the external pressure and very high 

hydrogen activities may be reached in the first few moments after water contacts bare metal 

because electron tunneling will initially generate adsorbed hydrogen very quickly compared to 

the time required for mass transport or other reactions. The logical conclusion is that while the 

hydrogen activity will not reach the theoretical values, it will be large and this will result in a 

large driving force for hydrogen absorption and reactions with hydrogen including the formation 

of niobium hydrides. 

 Niobium hydrides have been studied extensively and a number of different hydride phases 

have been identified.[66] However, the niobium-hydrogen phase diagram has not been 

completely determined and there are a number of phases that authors have identified by one 

technique or another that have not been confirmed or the phase field clearly identified. 

Manchester and Pitre [66,67] reviewed the literature on niobium-hydrogen phases and compiled the 
21 

data into the assessment of the temperature-composition diagram shown in Fig. 7(a). This 

diagram shows 7 phases: 

1. -Phase: The  phase is essentially the pure Nb body centered cubic (bcc) phase 

interstitially alloyed with H atoms randomly distributed over tetrahedral sites in the 

crystal lattice.[66] 

2. '-Phase: The ' phase is a random interstitial alloy of H in bcc Nb with essentially the 

same crystal structure as the  phase. This designation is used for H concentrations 

above about 24 % mole fraction.[64-66] 

3. -Phase: The phase has a face centered cubic (fcc) orthorhombic structure with H 

atoms occupying four interstitial sites per unit cell in an ordered arrangement with 

essentially the stoichiometry of NbH. This phase forms below 150 °C, but undergoes a 

series of ordering transformations below 30 to 70 °C resulting in the  and  phases. 

4. -Phase: The  phase has the fluorite structure in which the Nb atoms have an fcc 

arrangement with the H atoms occupying tetrahedral sites. The boundaries of this 

phase field are poorly known and dashed lines are used in the diagram of Fig. 7(a) to 

indicate this fact. 

5. -Phase: The phase transforms into the  phase at temperatures below -69 °C. This 

phase has a narrow concentration band around the stoichiometry of Nb4H3 and forms 

out of the phase by long-range ordering the H atoms in the tetrahedral sites while the 

Nb atoms remain unaffected. Apparently, H has significant mobility at these low 

temperatures and Manchester and Pitre[66] report that studies have observed H motion 

at temperatures as low as 0.05 K. 

6,7.  and c Phases: Manchester and Pitre [66] report that at least 5 other phases have been 

reported in the literature, but the experimental evidence is uncertain or unconfirmed. 

These phases are discussed in their paper, but with the exception of the  and c phases, 

these authors elected not to include these phases on the temperature-composition 

diagram. The phase field for these phases is poorly known and dashed lines are used in 

the diagram of Fig. 7(a) to indicate this fact. 

Figure 7 - Niobium-Hydrogen phase diagram reported by Manchester and Pitre[66] (a) and 25 °C 

equilibrium pressure and potential estimates for hydride phases based on the data of Fromm and Jehn 

[68] for the  and +regions and Manchester and Pitre [66] for the + region (b). 
22 

The diagram of Fig 7(b) was determined using the solubility data of Fromm and Jehn[68] for 

the  phase field and +two phase field. The thermodynamic data reported by Manchester and 

Pitre[66] was used to calculate the equilibrium hydrogen pressure over the + two phase region. 

No data was found on the solubility of H in either the phase or the  phase and dashed lines are 

used in this diagram to illustrate this uncertainty. This diagram shows the pressure or fugacity of 

hydrogen that is in equilibrium with the phase of the specified composition at 25 °C. 

Theoretically, a constant H activity should result in the two phase regions where the ratio of the 

phases changes with the overall composition, but not H activity. Added to this diagram to make 

this relevant to the calculations above is a potential scale where the electrode potential on the 

standard hydrogen electrode (SHE) scale for a solution of pH=0 that would generate the same H 

fugacity is calculated. For solutions of other pH, one would subtract 0.0593 V/pH unit from the 

value on this scale keeping in mind that the direction of this scale is inverted to agree with the 

pressure axis. This diagram shows that an H fugacity of slightly less than atmospheric pressure 

(7.0 x104

 Pa) is all that is required to nucleate the most H rich niobium hydride phase. Assuming 

that an H concentration gradient forms with a decreasing concentration from the surface into the 

interior of the metal, then one could expect that all three of the room temperature phases may 

form for this postulated condition (, , and ). If the metal is not treated to remove H or 

dissolve these phases into the bulk, then these phases will be present when the temperature is 

reduced to superconducting temperatures and the ordering reactions will result in the formation 

of the low temperature phases (, , and c). 

 

V. CONCLUSIONS

 The purpose of this report was to evaluate the feasibility of the hypothesis that hydrogen may 

be absorbed during processing of Nb and alter the performance of this metal during subsequent 

processing steps (e.g. forming) or in service. The goal of this evaluation is to enable better 

interpretation of the effects of changes in processing conditions on the performance of 

accelerator cavities or the development of new or modified processes that optimize the 

performance of Nb SRF cavities. This evaluation consisted of (i) identification of the steps, 

conditions, and required reactions, (ii) examination of the scientific literature for established 

precedent in other metals and alloys, (iii) thermodynamic assessment of feasibility of the 

reactions with quantification of the maximum possible hydrogen activity, and (iv) examination 

of the assumptions and limitations of the analysis. This examination found that the hypothesis of 

hydrogen absorption during SRF processing is consistent with published scientific literature and 

thermodynamic principles. 

 This investigation found that not only is hydrogen evolution and absorption feasible when 

water comes into physical contact with bare (unpassivated) Nb metal, but that the driving forces 

for these reaction are quite large. These large driving forces indicate that whenever water comes 

into direct physical contact with bare Nb metal, the reactions will be very rapid until reaction 

products block mass transport and limit the access of the reactants to each other (ie. passivation). 

Since the tunneling of electrons to the adsorbed hydrogen cations of the water molecule will 

precede the reaction between the oxygen and niobium to form the oxide, hydrogen reduction and 

absorption appears to be inevitable under these conditions. The quantity actually absorbed will 
23 

vary with the relative rates and environmental conditions. Also, desorption may occur in some 

cases while in others a more continuous and impervious passivating oxide may block desorption. 

All of the aqueous environments examined have the capability of producing hydrogen when they 

react with bare Nb metal and the thermodynamic calculations indicate that these reactions are 

capable of producing hydrogen on Nb at activities greater than those one can obtain from 

exposing this metal to high-pressure hydrogen gas. Therefore, while reaction kinetics may limit 

the actual quantities generated and absorbed, the possibility of hydrogen absorption should 

always be considered with a process that ruptures the passivating oxide on this metal in the 

presence of water molecules. 

 Theoretically, polarizing currents can be applied to suppress hydrogen evolution. However, 

the distribution of this current over the surface of the sample would be a critical factor in 

determining the success of this approach. Natural perturbations to the current distribution or the 

local shielding of occluded regions from the polarizing current could result in the establishment 

of local electrochemical cells where hydrogen evolution is favorable. This is a significant 

possibility in systems that are far from equilibrium with a large driving force for reaction 

between the metal and the environment. The literature indicates that hydrogen evolution can 

occur on Al alloys even when large anodic currents are applied. Therefore, while theoretically it 

is possible to prevent hydrogen uptake with anodic polarization, in practice it would be 

unreliable particularly for active metals where conditions are far from equilibrium and postprocessing out-gassing treatments and controlled passivation are probably the best approaches 

for the elimination of hydrogen. 
24 

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