Corrosion of copper in anaerobic clay

 

Prerequisites for pitting and

 

whiskers formation

 

Erik Levlin

Water Resources Engineering

Royal Institute of Technology

 

 

April 1995

 

This is a modified version of:

 SVENSK KÄRNBRÄNSLEHANTERING

SKB Inkapsling, Projekt PM Dok. Nr.95-3420-09, Reg. Nr. 3411-1141, 1995.

 

A follow upp report from april 1996

 

Korrosion av koppar i anaerob lera

Förutsättningar för gropfrätning och whiskersbildning

Högaktivt kärnavfall planeras att slutförvaras i kopparbehållare inbäddade i bentonitlera i berggrunden på ett djup av 500 m. Potentiella risker för säkerheten är förekomsten av hål i behållarna uppkomna genom gropfrätning eller av whiskers som växer in kopparn. Baserat på observationer i litteraturen, tillsammans med teoretiska diskussioner av mekanismerna för gropfrätning och whiskersbildning bedöms att risken för uppkomst av hål i behållarna är liten. En fastsittande och skyddande film av kopparsulfid har observerats på kopparföremål nerbäddade i anaeroba marina sediment. Korrosionspotentialen (413 mV) är mycket lägre än skyddspotentialen (+350 mV), nedanför vilken gropfrätning ej förekommer.

 

Whiskersbildning förutsätter att kopparjonerna är fritt rörliga i kopparsulfiden och den högjonkonduktiva kopparsulfidenfasen β-fas chalcocite (2 Cu/S) med en konduktivitet mellan 0.18 och 0.55 S/cm är stabil vid temperaturer över 100ºC. Förutom chalcocite finns det tre andra stökiometriska föreningar av kopparsulfid; digenite (1,8 Cu/S) djurleite (1,96 Cu/S) och anilite (1,75 Cu/S). Jonledningsförmågan är hos dessa föreningar låg liksom hos andra faser av chalcocite än β-fas. I ett tidigt skede av utfällningen kommer kopparsulfiden troligast att fällas ut som ett skikt på kopparytan varvid whiskersbildning motverkas. Emellertid bör förutsätt-ningarna för tillväxt av kopparsulfidkärnor på kopparytan, som beror på ytenergierna studeras för att avfärda möjligheten av whiskersbildning.

 

 

Content

 

Summary. 2

1            Background. 3

2            Observed corrosion products. 4

3            Chemistry of copper sulphides. 5

4            Mechanisms for general corrosion. 7

5            Corrosion due to complex formation. 7

6            Theory for pitting corrosion. 9

7            Pitting corrosion of copper. 12

8            Formation of whiskers. 13

9            Conclusions. 17

10          References. 18

 

Summary

 

High level nuclear waste is planned to be restored in copper canisters embedded in bentonite clay in the bed rock at a depth of 500 m. Potential risks for the safety of such waste deposit is occurrence of holes in the canisters caused by pitting corrosion or by whiskers growing into the copper. The growth rate of the such whiskers can be calculated to 2*106 cm/s. Since it is important that there is neither pitting corrosion or whiskers formation, this report deals with the prerequisites for pitting and formation of whiskers on copper in anaerobic clay.

 

Based upon observations of corrosion in the litterature together with theoretical discussion about the mechanisms for pitting corrosion and formation of whiskers the risk of getting holes in the canisters is estimated to be small. The very low solubility of copper sulphide, reduces the electrode potential for copper dissolution, and makes corrosion due to hydrogen evolution possible. In absence of oxygen the copper surface is covered by a layer of copper sulphide. An adherent protective copper sulphide coating has been observed on copper artefacts embedded in anaerobic marine sediments.

 

Since the corrosion potential (413 mV) is much lower than the protection potential (+350 mV), pitting corrosion will not occur. The protection potential is the potential below which no initiation of corrosion pits occur and propagating pits initiated at higher potentials are repassivated when the potential is decreased below the protection potential.

 

Since formation of whiskers require that the copper ions are freely mobile in the copper sulphide precipitation of copper sulphide whiskers is not likely to occur. The high ion conducting copper sulphide, the β-phase chalcocite (Cu2S) is stable above 100ºC and the copper ion conductivity is between 0.18 and 0.55 S/cm. Besides chalcocite there are three other stociometric compounds of copper sulphides; digenite (Cu1.8S) djurleite (Cu1.96S) and anilite (Cu1.75S). The ionic conductivity in these compounds and other phases of chalcocite is very low.

 

Formation of a layer in an early stage of precipitation the chalcocite, will decrease the sulphide concentration close to the canister and thereby counteract formation of whiskers. The whiskers growth model require existance of whiskers with a minimal lentgh which increases with decreasing sulphide concentration. However, the conditions for growth of chalcocite nucleus on the copper surface, which depends on the surface energies, should be investigated in order to cancel the possibility of whiskers formation.

 

1          Background

 

High level nuclear waste is planned to be restored in copper canisters in the bed rock at a deep of 500 m. The canisters is embedded in bentonite clay. Corrosion of the copper canisters has been investigated by the Swedish corrosion institute and its reference group /1/ and by Werme et al /2/. Figure 1 shows a potential-pH diagram for the system Cu-S-C-H2O. The line for the hydrogen electrode lies within the stability domain of copper(I) sulphide Cu2S. In anaerobic environment corrosion due to hydrogen evolution is made possible by the low solubility of copper sulphide. Corrosion will occur as uniform corrosion building up a layer of copper sulphide on the copper surface.

 

     2Cu(s) + H2S Cu2S(s) + H2(g)                                                 (1)

 

The rate of corrosion will be controlled by diffusion of sulphide to the copper surface. Since the corrosion is uniform, the amount of sulphide in the clay is to low to give perforation of the canister. A complete depletion of sulphides in the surrounding bentonite will create 1 mm thick layer of copper sulphide. However, an uneven distribution of the anodic reaction on the copper surface may lead to pitting corrosion and perforation of the canister. Hermansson et al /3/ has proposed another risk scenario there sulphide whiskers grows from the copper surface into the bentonite and at the other end grows into the copper creating pin holes in the canister. Since it is important that there is neither pitting or whiskers formation leading to holes in the canister, this report deals with the prerequisites for pitting corrosion and formation of whiskers on copper in anaerobic clay.

 

 

 

Figure 1. Potential-pH diagram for the system Cu-S-C-H2O /2/.

2          Observed corrosion products

 

Corrosion products on copper exposed to water with varying oxygen and sulphide content has been examined by McNeil et al /4/. Adherent, homogeneous films were formed in deaerated solutions (0.02 to 0.1 mg O2 /L) with high concentration of dissolved sulphides (10-2.0 to 10-2.3 M). At the highest initial sulphide concentration adherent films also were formed in partially deareated solutions. Aerated solutions never produced homogeneous adherent coating. Homogeneous coatings were composed of hexagonal chalcocite, Cu2S, crystals, although some Copper-poor compositions were observed. Solubility of copper sulphide is controlled by formation of complexes between copper and polysulphide ions (S22-, S32-, S42-, etc.), which form readily in high-sulphide/low-oxygen waters. An increase of the total sulphide concentration from 10-6 to 10-2 increases the solubility of cupric ions in the presence of chalcocite from 10-11 to about 10-5 M.

 

A range of copper sulphides from chalcocite to covelite, CuS, has been found on archaeological copper items recovered from ship wreck. An adherent protective sulphide coating can form on copper artefacts embedded in anaerobic marine sediments /5/. If an artefact with a chalcocite coating is subsequently exposed to an oxygenated environment, oxidation of chalcocite to covellite can occur.

 

     Cu2S(s) + S2 2CuS(s) + 2e                                                   (2)

 

Since the covelite is less dense than chalcocite the oxidation process will tend to fill any pores in the film and so minimise ingress of oxygen and other oxidants. The poor mechanical properties of such layers make them non protective /6/ for other purposes. For artefacts embedded in the sediments is mechanical properties of the protective layer of less importance.

 

Hallberg /7/ has studied corrosion products on a bronze cannon partially submerged in clay sediment at the bottom of the Baltic sea. The dominating corrosion product was cuprite, Cu2O, which was deposited over most of the cannon together with malachite, Cu2CO(OH)2, magnetite, Fe3O4, and sphalerite, ZnS. Since the amount of reduced species in the clay close to the cannon was to small to correspond to the corrosion products, the corrosion was explained as a result of reduction of tenorite, CuO, which was found as inclusions in the bronze matrix. An alternative explanation is that the corrosion was caused by reduction of oxygen from the sea water on the part of the cannon that was situated above the clay, thus creating an aeration cell /8/ with the part in clay as anode and the part above the clay as cathode. Due to god conductivity of the clay, the corrosion potential of the part in the clay, was raised by the corrosion current into the cuprite area in figure 1.

 

3          Chemistry of copper sulphides

 

The solubility of copper sulphides is low, which decreases the redox potential of copper in contact with hydrogen sulphide. The solubility constants for covelite, CuS, and chalcocite, Cu2S, are:

 

     CuS(s) + 2H+ Cu2+ + H2S(g)                         log(k)=-14.2       (3)

 

     ½Cu2S(s) + H+ Cu+ + ½H2S(g)                    log(k)=-13.3       (4)

 

Copper(I) sulphide usually exists in the approximate composition Cu2-XS (0<x<0.25). Among these composition, there are three stociometric compounds. Besides chalcocite, Cu2S, there are digenite, Cu1.8S, djurleite, Cu1.96S /9,10,11/ and anilite, Cu1.75S /5/. The electro neutrality demands that some of the sulphide or copper ions in the crystal lattice is oxidised to compensate for the deficiency of copper. The copper(I) sulphide is known to be p-type semiconductor and the electrical conductivity increases with increasing copper deficiency. The difference in electronic conductivity varies from 100 S/cm at x=1.99 to 2700 S/cm at x=1.80.

 

Chalcocite exists in three phases /10,12/. Low chalcocite, γ-phase, is monoclinic and stable below 103oC. The hexagonal β-phase is stable between 103oC and 430oC. Above 430oC chalcocite transforms into a mixture of an face centred cubic α-phase of composition Cu1.999S and copper. Digenite is pseudocubic at room temperature with a phase transition at 80oC to cubic phase and djurleite is orthorhombic with a phase transition to metastable tetragonal phase at 93oC.

 

The conductivity contains a significant electronic component in all phases. The ionic conductivity in both the γ and the α-phase chalcocite is very low due to an ordered arrangement of copper ions. Due to a disordered copper ion arrangement the β-phase chalcocite has a high copper ion conductivity ranging between 0.18 and 0.55 S/cm. It is supposed that the distinction between interstitial ions and lattice ions is lost, and the copper ions appear to have no special position and can move through the whole available space. The ionic conductivity of the β-phase is almost independent of the composition and follows the relation;

 

     σi = σiO exp(-E/kT)                                                                         (5)

 

where σiO = 140 S/cm and E = 0.24 eV.

 

The copper ion conductivity in the sulphide layer deposited on the nuclear waste canisters depends on whether the sulphide is composed of γ-phase or the high ion conducting β-phase. The temperature of the canister will not exceed 70o C /13/, which is below the temperature for transition from γ to β-phase, which is about 100o C. However, the phase transition can be influenced by the substrate on which the copper sulphide is deposited and on the external pressure. When a layer of corrosion products are deposited on a metal surface the crystal lattice of the metal influences the crystal structure of the corrosion products /14/. For instance copper oxides deposited on a copper surface is amorphous and crystallise when the deposited layer is thick enough. Below 100o C chalcocite precipitated on the copper surface may be of β-phase due to influence from the copper metal lattice. The crystal lattice of the copper metal may have an influence of the phase of the chalcocite only if the chalcocite is precipitated as a layer on the copper surface and the chalcocite will transform to γ-phase when it grows out from the surface. According to McNeil et al /4/ copper sulphide films formed on a copper surface at low oxygen concentrations were composed of hexagonal chalcocite crystals, which indicates that the copper metal promotes formation of β-phase.

 

A high external pressure may promote formation of β-phase, which has the highest density. The nuclear waste canisters will be exposed for an external pressure of 16 MPa /13/, which is the sum of the hydrostatic pressure, 6 MPa, and the bentonite swelling pressure, 10 MPa. The volume decrease due to the phase transformation is 1.2%, which can be calculated from the volumes of the crystal unit cells of the two phases, table 2.

 

 

Table 1   Calculation of crystal unit cell volume and density for γ-phase and β-phase chalcocite.

 

 

 

Monoclinic γ-phase /15/

Hexagonal β-phase /16/

 

Unit cell volume

abc sin(β)      = 2191 Å3

a2c sin(60o)       = 90.16 Å3

 

where:

a = 15.246 Å       b = 13.494 Å
c = 13.494 Å       β = 116.35o

a = 3.89 Å
c = 6.88 Å

 

 

48 Cu2S

2 Cu2S

 

Density

45.634 Å3/Cu2S = 5.79 g/cm3

45.08 Å3/Cu2S = 5.86 g/cm3

 

4          Mechanisms for general corrosion

 

The low solubility of copper sulphide, reduces the electrode potential of the copper dissolution, and makes corrosion due to hydrogen evolution possible. The electrode potentials for copper dissolution is:

 

     Cu+ + e Cu(s)                  e = +0.52V + 0.059*log[Cu+]         (6)

 

     Cu2+ + 2e Cu(s)               e = +0.34V + 0.0295*log[Cu2+]      (7)

 

From equation 6 it can be calculated that the concentration of Cu+ must be less than 10-16 M to get the electrode potential for copper dissolution below -413 mV, which is the electrode potential for hydrogen evolution at pH-level 7. This corresponds to a hydrogen sulphide concentration of 10-9 M. The bentonite surrounding the copper canisters have a sulphide content of 0.2 % /2/, which is above 10-9 M. The equation for calculating the corresponding hydrogen sulphide concentration can be made from the chemical formula for dissolution of chalcocite, equation 4.

 

     log[Cu+] + ½log[H2S] + pH = -13.3                                                     (8)

 

However, construction of a Pourbaix diagram assumes that the surface is passivated by formation of a layer of corrosion products, when the solubility of the corrosion products i less than 10-6 M. Then the solubility of the corrosion products is too low there will be no transport from the metal surface and the dissolved metal ions will stay at the surface as corrosion products, which will grow into a protective layer. The minimum hydrogen sulphide concentration for getting less than 10-6 mole Cu/L, is shown by table 2.

 

 

Table 2   The minimum concentration of H2S for getting the solubility of Cu2S and CuS less than 10-6 mole Cu/L, calculated from equation 3 and 14.

 

 

Sulphide corrosion products

log[H2S, M]

 

chalcocite, Cu2S

2(7.3+pH)

 

covelite, CuS

2(4.1+pH)

 

5          Corrosion due to complex formation

 

If hydrogen evolution is possible the copper surface should thereby be protected by a layer of corrosion products. However, if copper complexes is formed the solubility of the corrosion products can be higher than 10-6 M at the same time as the concentration of copper ions in the solution is less than 10-16 M. In that case copper can be transported from the surface as copper complexes, thus preventing formation of a protective layer and corrosion of copper due to hydrogen evolution may be possible.

 

 

Table 3.  Electrode potential for oxidation of sulphide ions to polysulphide /17/.

 

Chemical reaction

Electrode potential

S22 + 2e 2S2

eo = - 0.524 V

2S32 + 2e 3S22

eo = - 0.506 V

3S42 + 2e 4S32

eo = - 0.478 V

4S52 + 2e 5S42

eo = - 0.441 V

 

 

Formation of copper complexes with polysulphide ions (S22-, S32-, S42-, etc.) is reported to cause increased corrosion at a low oxygen content, but not in absence of oxygen /4/. Table 3 shows the electrode potentials for oxidation of sulphide ions to polysulphide ions. The concentration of sulphide ions, that can be oxidised to polysulphides, depends on the concentration of hydrogen sulphide. Sulphide ions is formed from hydrogen sulphide:

 

     H2S HS- + H+                                                 log(k)=-7.1          (9)

 

     HS- S2- + H+                                                   log(k)=-14           (10)

 

These reactions gives the relation between the concentrations:

 

     log[S2-] = log[H2S] + 2pH-21.1                                                      (11)

 

At pH-level 7 is the concentration of S2 107.1 times smaller than the concentration of hydrogen sulphide. The concentration of S22 is at -413 mV 103.8 times larger than the concentration of S2 and 103.3 times smaller than the concentration of hydrogen sulphide. At a low oxygen content the electrode potential can be higher, which increases the concentration of polysulphide ions. In absence of oxygen is the concentration of polysulphide ions to low to give corrosion.

 

 


 


Figure 2. Concentration of solvent species versus electrode potential for a ground water there Cl = 500 mg/L, H2CO3 = 120 mg/L and SO42 = 100 mg/L /1/.

 

 

Copper complexes can also be formed with chloride ions. Figure 2 shows the concentration of complexes versus electrode potential in ground water with a chloride concentration of 500 mg/L or 14.1 mM. The concentration of Cu2Cl42, which is the complex with the highest concentration, is 102.5 times larger than the concentration of cupric ions. A concentration of less than 1013.5 M at electrode potentials for hydrogen evolution, is nevertheless to small to prevent formation of a protective layer on the copper surface.

 

6          Theory for pitting corrosion

 

 

 

Figure 3. Schematic potential pH diagram illustrating criteria for pitting corrosion.

 

 

Though a metal surface is protected by a layer of corrosion products, pitting corrosion may occur at local breakdowns in the protective layer. The criteria for pitting corrosion can be illustrated by a schematical potential-pH diagram shown by figure 3. Increased metal dissolution at the breakdown may give local decrease in pH-level due to hydration of the dissolved metal ions, which may dissolve the protective film resulting into pitting corrosion /18/.

 

For pitting corrosion to occur the corrosion potential must be above the protection potential /19/ in figure 3. The protection potential is the potential below which no initiation of corrosion pits occur and propagating pits initiated at higher potentials are repassivated when the potential is decreased below the protection potential. This implies that the metal have a corrosion potential there a local decrease in pH moves the local conditions into the area of corrosion before the pH reaches the line of minimum pH. The pH-level inside the active pit lies to the left of the border of the corrosion area, since hydration of the dissolved metal ions gradually decreases then the pH moves into the corrosion area. The border determined by the solubility of the metal hydroxide is equal to 10-6 M. Since the corrosion current for the anodic dissolution inside the pit is supplied by the cathodic reaction on the surface area around it, there is a corrosion current going from the surrounding metal surface into the pit. Due to resistance in the solution the ohmic drop causes the potential inside the pit to decrease until it lies at the bottom of the corrosion area. The potential of the surrounding surface must therefore lie above the protection potential, which lies above the potential inside the active pit.

 

The line for minimum pH in figure 3 is the limit for a local pH decrease. Due to variation in anodic dissolution compared to the cathode reaction the pH-level at the metal surface will have variations with the mean value being the same as in the surrounding solution. Hydration of dissolved metal ions at spots with a surplus of metal dissolution will result in a local decrease of the pH-level. This can be illustrated by a formula there the species carrying the corrosion current are marked vertically.

 

(12)

 

The corrosion current is in this case carried by chloride ions, which will result in an enrichment of hydrochloric acid at the anodic areas. Since the anions only are carrying the corrosion current to the anodic areas and not take part in an chemical reaction, the formula is valid for most anions. However, if the corrosion current is carried by hydrogen ions instead of chloride ions the local decrease in pH-level can be counteracted by the hydrogen ions being transported by the corrosion current away from the local acidification, thus preventing further decrease in pH.

 

(13)

 

The line for minimum pH in figure 3 is the pH-level there the decrease in pH due to variations in metal dissolution is counteracted by transport of hydrogen ions by the corrosion current. The pH-level there the hydrogen ions are transported by the corrosion current depends on which other species, such as chloride, that are available for transporting the corrosion current. The ionic mobility is for hydrogen ions 349.6 cm2/mol. and for chloride ions 76.4 cm2/mol /20/. From this it can be calculated that the hydrogen ions will give an equal share to the transport of the corrosion current then the concentration of hydrogen ions is 20% of the concentration of chloride. This corresponds to:

 

(14)

 

At a chloride concentration of 3% the line for minimum pH, there hydrogen ions is be transported away from the local defect, will be around pH-level 1. The local decrease in pH-level can also be counteracted if the corrosion current is carried by anions that consumes the hydrogen ions and thereby prevent pitting. One example is the bicarbonate ion that at pH-levels below 6.4 together with hydrogen ions forms carbon dioxide.

 

(15)

 

7          Pitting corrosion of copper

 

 

 

Figure 4. Potential-pH diagram with pitting and protection of copper /19/.
           
[Cl] = 10-3 M                                             [Cl] = 10-1 M.

 

 

Figure 4 shows two potential-pH diagram for copper in water with chloride concentration 0.001 M and 0.1 M. An increased chloride concentration increases the area of corrosion. The protection potential, marked in the diagrams, is for copper about +350 mV. The diagonal line O is the electrode potential for oxygen reduction and line H is the electrode potential for hydrogen evolution. The black spot in the area for general corrosion, marked with diagonal lines, represents the pH and potential inside a propagating corrosion pit on the same specimen. If the corrosion potential is above the protection potential a local acidification due to hydration of dissolved copper ions makes the pH-level to decrease and move to the left into the area of corrosion, resulting in pitting corrosion.

 

The corrosion potential lies in aerobic conditions between line O and line H. Pitting corrosion of copper pipes with aerated tap water are classified as type I, II and III /21/. Type I occurs if there is a carbon film on the pipe surface formed by cracking of drawing lubricants when the pipes are annealed. The carbon acts as cathode and raises the corrosion potential and thereby promotes pitting. Pitting type II and III occurs if the if there is a high sulphate content and a low bicarbonate content in the water and can be counteracted by raising the bicarbonate content. Pitting is according to equation 15 counteracted by bicarbonate. The recommendation to avoid pitting is that the bicarbonate content should be at least 70 mg/L, preferably 100 mg/L and that the sulphate content shall be as low as possible, or at least lower than the bicarbonate.

 

In the case of anaerobic conditions, is the cathode reaction hydrogen evolution and the corrosion potential lies below line H, which at pH-level 7 is at -413 mV. This potential is much lower than the protection potential and pitting corrosion will therefore not occur. The possibility that only a thin layer of chalcocite may consist of high ion conducting -phase due to influence of the underlying copper, will cause pitting to be counteracted by a transition to -phase, when the chalcocite grows out from the surface. If only a thin layer on the surface has high copper ion conductivity, chalcocite which locally grows out from the surface will thereby grow more slowly than chalcocite formed there the chalcocite layer is thinner. The chalcocite will thereby be precipitated as a thin layer on the surface with no tendency to pitting corrosion.

 

Hypothetically, increased copper dissolution at defects in the chalcocite coating may create a local decrease in pH-level resulting in pitting corrosion. According to equation 4 precipitation of chalcocite from hydrogen sulphide produces hydrogen ions. For getting a layer of chalcocite due to hydrogen evolution the hydrogen sulphide concentration must be above 10-9 M. From table 2 it can be calculated that this gives that the pH-level of the local defect must be below -2.8 to make the solubility of chalcocite less than 10-6 mole Cu/L. The rate of corrosion of the copper canisters is determined by the diffusion of hydrogen sulphide to the copper surface and the copper concentrations are very low, less than 10-16 M. An increased copper concentration, from 10-16 M to for instance 10-10 M, is to small to result in production of more chalcocite and hydrogen ions and thereby a local decrease in pH-level. A local increase in copper concentration will only result in a higher electrode potential for copper dissolution, thus decreasing the copper dissolution. It will not result in an increased transport of copper ions from the surface since the copper ion concentration at the surface must probably be higher than 10-6 M to give a concentration difference high enough for diffusion to occur. A local decrease in pH-level that may result in pitting corrosion will therefore not occur.

 

8          Formation of whiskers

 

Hermansson et al /3/ suggests a mechanism for corrosion there copper sulphide is precipitated as whiskers growing from the copper surface out into the bentonite. The whiskers will at the other end grow into the copper and create pin hole in the copper canister. Whether the copper sulphide will be precipitated as whiskers will depend on if the sulphide can be supplied to the growing copper sulphide without diffusion in the bentonite. The large mobility of copper ions in the sulphide will make it possible for the copper sulphide to "continuously grow as whiskers in the parts with accessible sulphide". The conclusion is that the sulphide don't need to be transported to the copper through water solution based transport and that diffusion of sulphide in the bentonite will not be the rate limiting factor. However, for copper sulphide precipitation diffusion in the bentonite will be necessary. Commercial bentonite have a sulphide content of 0.2 % /2/. The copper sulphide contains about 33% sulphide and 66% copper. To create copper sulphide, sulphide from a 165 times larger volume of bentonite has to be concentrated to the growing copper sulphide. Irrespective the physical shape of the copper sulphide, the concentration of sulphide to the copper sulphide has to be done by diffusion through the bentonite.

 

 

 

Figure 5. Illustration of whiskers growth model proposed by Pettersson /22/.

 

 

Figure 5 shows an illustration of a model for whiskers growth proposed by Pettersson /22/, there the growth rate depends on the diffusion of sulphide in the bentonite and the spacing between the growing whiskers:

 

The basis of the proposal is that the copper ions in the sulphide are freely mobile so that there is no diffusion barrier inside the sulphide which limits the growth rate. The geometry assumed is that the whisker with radius ri growths into the bentonite surrounded by other whiskers so that the whiskers form a lattice with a distance of 2R between neighbouring whiskers. Each whisker is thus surrounded by a cylinder of bentonite which has been depleted of sulphide ions. Sulphide for growth is taken from a hemispherical area with radius R in front of the whisker. In steady state the growth rate of the whisker into the bentonite is v. At the same time the whisker growths into the copper with the rate 2v. If the concentration of sulphide ions in the bentonite is cs, the densities of bentonite and sulphide differ by a factor of 2.5 and Cu2S contains 20 wt% S, there is the following relation between R and ri:

 

       cs*R2 = 3*2.5*0.2*(ri)2                                                            (16)

 

The factor 3 is inserted because when the sulphide grows the distance dx into the bentonite its total growth is 3dx. In the steady state the integrated flux at each radius r must be the same and thus:

 

(17)

 

since the flux is used for forming the sulphide. This equation can be integrated to:

 

(18)

 

where it has been assumed that c=0 at r = ri. Since cs 0.02 % equation 16 shows that R>>ri and the second term can be neglected in equation 18 in calculation of cs, and the growth rate can be calculated:

 

(19)

 

The conclusion is that thin whiskers grow faster than thick whiskers. There is however a lower limit to the size of a whisker. It can not be so thin that the surface energy expended in forming the whisker exceed the free energy gained. Reasonably values of surface energy and free energy gives a minimum ri larger than 106 cm. From a practical value of ri = 104 cm, D = 8*107 cm2/s and cs = 0.02 % the growth rate v can be calculated to  2*106 cm/s.

/22/

 

The basis that the copper ions are freely mobile require that the copper sulphide consist of the high ion conducting b-phase chalcocite, which is stable above 100oC. The copper ion conductivity of the b-phase is, depending on the temperature (equation 5), between 0.18 and 0.55 S/cm /10,12/. This is of course not freely mobile, but if this mobility is high enough not to create diffusion barrier inside the sulphide needs to be examined.

 

Another limitation with the model is that it is valid for steady state growth. Sulphide ions at the hemispherical area in front of the growing whiskers must diffuse to a growing whiskers and not to the copper surface. That means that a sulphide ion at the point A in figure 5 must be closer to the nearest whisker than to the copper surface. The distance from A to the surface must be larger than R, which require existence of whiskers with a minimum length of 3R. Since R depends on cs and ri (equation 16) the minimum length, lmin, will depend on the diameter, d, and cs according to:

 

                                                                               (20)

 

As the sulphide concentration in the bentonite, cs, is 0.02 %, the required lmin is 130 times the whisker diameter. With no whiskers the sulphide ions may diffuse toward the surface and there precipitate as a layer. The sulphide concentration close to the surface will then decrease, resulting in an increased lmin and thus make whisker formation less possible. Precipitation of a layer on the copper surface during early stage of chalcocite precipitation, which is observed on archaeological objects /5/, will prevent formation of whiskers.

 

If there is a high energy barrier in forming chalcocite nucleus on the copper surface, sulphide ions in the bentonite may diffuse to the nearest chalcocite nucleus even if the copper surface lies closer. If these nucleus will grow into a surface film or into whiskers will then depend on the chalcocite-copper surface energy, γc-c, compared to the chalcocite-bentonite surface energy, γc-b, illustrated by figure 6. If γc-c is smaller than γc-b, the growing nucleus will spread out over the copper surface forming a chalcocite layer. Otherwise it can growth out from the surface and form the necessary nucleus for Petterssons model. The surface energies γc-c and γc-b and the conditions for growth of chalcocite nucleus has to be investigated in order to totally cancel the possibility of whiskers formation. Another obstacle for whiskers formation in bentonite clay is that the growing whiskers has to push the clay particles asides to make space for the growing whiskers and chalcocite has poor mechanical strength /6/.

 

 

 

Figure 6. Precipitation of chalcocite depending on the surface energy chalcocite-copper γc-c compared to the surface energy chalcocite-bentonite γc-b.

 

 

 

Figure 7. Illustration of precipitation of copper sulphide as layer and as whiskers.

 

 

Figure 7 illustrates a case there precipitation of copper sulphide as whiskers is more likely, for instance if the corrosive media is a gas containing hydrogen sulphide. Outside the diffusion boundary layer the concentration of sulphide will due to convection in the gas be constant. The sulphide will be transported through the diffusion boundary layer by diffusion. If the copper sulphide is precipitated as whiskers the distance for diffusion of sulphide through the diffusion boundary layer will be smaller than if the copper sulphide is precipitated as a layer on the copper surface. If the transport of copper in the copper sulphide is faster than the diffusion of sulphide through the diffusion boundary layer, transport of sulphide to the copper sulphide will be the limiting factor and the copper sulphide will grow as whiskers there the distance for transport of sulphide is smaller. In this case formation of a copper sulphide layer in an early stage of precipitation will not prevent formation of whiskers since the sulphide concentration outside the diffusion boundary layer will be constant by the convection in the gas. Formation of whiskers will prevent convection close to the copper surface and increase the diffusion boundary layer. In the case of copper in bentonite there will be no diffusion boundary layer since there is no transport by convection in the bentonite.

 

9          Conclusions

 

In the case of anaerobic corrosion of copper, observations of corrosion in the litterature, together with theoretical discussion about the mechanisms for pitting corrosion and formation of whiskers shows that;

     At a low oxygen content copper can form complexes with polysulphide ions, which may cause corrosion.

     In total absence of oxygen the copper surface will be protected by a layer of copper sulphide.

     An adherent protective copper sulphide coating has been observed on copper artefacts embedded in anaerobic marine sediments.

     Since the corrosion potential lies below -413 mV, which is much lower than the protection potential at +350 mV, pitting corrosion will not occur.

     A local decrease in pH-level resulting in pitting corrosion due to dissolution of the copper sulphide layer, will not occur.

     Since the high ion conducting copper sulphide, the β-phase chalcocite, is stable above 100oC, precipitation of copper sulphide whiskers is not likely to occur.

     Without whiskers, with a lentgh of 130 times the diameter, the copper sulphide will most likely precipitate as a layer on the copper surface.

     Formation of a layer of copper sulphide will decrease the sulphide concen­tration close to the canister and thereby prevent formation of whiskers.

     The conditions for growth of chalcocite nucleus on the copper surface and the surface energies has to be investigated in order to cancel the possibility of whiskers formation.

The risk of getting holes in copper canisters for high level nuclear waste embedded in bentonite clay is therefore estimated to be small.

 

10        References

 

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8.    Levlin E
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Distribution of atoms in high chalcocite, Cu
2S,
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18.  Levlin E
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