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:
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
3 Chemistry of copper
sulphides
4 Mechanisms for
general corrosion
5 Corrosion due to
complex formation
6 Theory for pitting
corrosion
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;
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 |
a = 3.89 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:
|
|
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.
|
|
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: 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:
since the flux is used for forming the sulphide.
This equation can be integrated to:
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:
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.
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