THERMODYNAMIC MODEL FOR SOLID IRON IN AlFeCu ...

L. Nascimento et al. Thermodynamic model for solid iron in AlFeCu
THERMODYNAMIC MODEL FOR SOLID IRON IN AlFeCu
QUASICRYSTALLINE ALLOYS
MODELO TERMODINÂMICO DO FERRO EM LIGAS
QUASICRISTALINAS DE AlFeCu
L. NascimeNto 1* ; L.c.L. agostiNho 2 ; B.F. cavaLcaNti. 3
1 Departamentode Física – DF/cceN-UFPB, cidade Universitária - caixa Postal: 5008-ceP: 58059-900, João
Pessoa-PB,
1* luciano.fisicaufpb@gmail.com
2 Departamento de Química- DQ/CCT-UEPB, Rua Juvêncio Arruda,s/n-Bodocongó – CEP: 58109-790,Campina
grande-PB,
2 cristina.uepb@gmail.com
3 Departamento de Hidráulica e Engenharia Civil, DHEC/CCT-UFCG, Av. Aprígio Veloso,882-Bloco CM-
1°Andar - CEP:58.109-970-Campina Grande-PB,
3 bernardete.ufcg@gmail.com
ABSTRACT: In the preparation of quasicrystalline alloys such as AlFeCu it is generally utilized iron in solid state. Iron as a
constituent of quasicrystals contributes to the activity to reform methanol vapor. Before its acid/base treatment iron does not
complex with copper; i.e., does not produce compounds and does not mutually dissolve in solid state. In order to understand
the behavior of iron “per se” in aqueous solution it was applied a thermodynamic model in which is used the free Gibbs
energy to obtain pH and pε parameters which are related to iron redox reactions. The standard free energy of formation ΔG°f
of a substance is dependent upon its chemical bonds and is related with the equilibrium constant of the involved reactions.
The model here introduced is applied to the system of solid iron such as Fe(s): Fe 2+ - Fe 3+ - Fe 2 o 3 (hematite) – Fe 3 o 4 (magnetite)
and the water system at a low molar concentration and at ambient temperature. From the dissociation equations of
the systems under investigation it was determined values of the dissociation constant for unity activity. The next step was
to determine for each species of the systems investigated the Gibbs standard free energy in order to obtain pε value. Buffer
capacity was also analyzed for each system and it were determined the respective slopes. In both systems Fe(s): Fe 2+ and
Fe(s): Fe 3+ the slope of the straight line defined as dpε/ dpH are equal to zero. The same happens in the analysis of Fe 2+ : Fe 3+ .
Others slopes obtained are all negative. Considering that the temperature adopted was 25°C, the results are valid only for
this temperature.
Keywords: Iron Thermodynamic Model; Standard Free Energy; Quasicrystals.
RESUMO: No preparo de ligas quasicristalinas do tipo AlFeCu é geralmente usado o ferro em estado sólido. O ferro como
constituinte de quasicristais contribui à atividade para a reforma de vapor de metanol. Antes da lixiviação, o ferro não se
mistura com o cobre; ou seja, não formam compostos e nem se dissolvem mutuamente no estado sólido. Com vistas ao entendimento
do comportamento do ferro “per se” em solução aquosa foi aplicado um modelo termodinâmico no qual se usa
a energia livre de Gibbs para a obtenção dos parâmetros pH e pε que estão relacionados às reações redox do ferro. A energia
livre padrão de formação de substâncias ΔG°f depende de suas ligações químicas e se relaciona às constantes de equilíbrio
das reações envolvidas. O modelo apresentado considera o sistema de ferro sólido tal que Fe(s): Fe 2+ - Fe 3+ - Fe 2 o 3 (hematita)
– Fe 3 o 4 (magnetita) e o sistema água a uma concentração molar baixa e à temperatura ambiente. A partir das equações
de dissociação9 dos sistemas analisados foram obtidas as constantes de dissociação para atividade unitária. A seguir, foi
determinada, para cada espécie dos sistemas analisados, a energia livre padrão de Gibbs, obtendo – se o valor de pε. A capacidade
de tamponação foi analisada para cada sistema e foram obtidas as respectivas declividades. Em ambos os sistemas
Fe(s): Fe 2+ e Fe(s): Fe 3+ a declividade da reta dada por dpε/dpH é igual a zero. O mesmo acontece na análise de Fe2 + : Fe 3+ .
As demais declividades obtidas foram negativas. Considerando que a temperatura adotada foi de 25°C, os resultados são
válidos apenas para esta temperatura.
Palavras-chaves: Modelo Termodinâmico do Ferro; Energia Livre Padrão; Quasicristais.
68 Ciência & Tecnologia dos Materiais, Vol. 24, n.º 1/2, 2012

Thermodynamic model for solid iron in AlFeCu L. Nascimento et al.
1. INTRODUCTION
Quasicrystals are atomic ordered structures that exhibit
quasiperiodic translational order of long range. These structures
show forbidden crystallographic symmetries and are
prepared by fast cooling techniques. With respect to the
synthesis of metastables and stables quasicrystals via reaction
of solid state it is used grinding at high energy. After this
process, chemical treatments are applied during some hours
at temperature above 300°C in environment or in other medium.
Samples are then characterized by using X – ray photoelectron
spectroscopy (XPS) and X – ray stimulated Auger
electron spectroscopy (XAES). Figure 1 shows a quasicrystal
formed by using AlCuFe metallic alloy.
Fig. 1. AlCuFe quasicristalline alloy [4].
Pure metals that are used to form quasicrystalline alloys suffer
oxidation under several conditions; i. e., in vacuum, in
normal air and after liquid immersion.
Several studies were performed in order to determine the oxidation
chemistry of pure metals that form metallic alloys. To
attain such objective, data of XPS and XAES spectra obtained
in fixed angle were analyzed for each element of the metallic
alloy. For AlCuFe alloys the studies showed that the 2ρ XPS
line falls at 707 eV in pure metal indicating the presence of
hematite Fe 2 o 3 which is illustrated in Figure 2.
Fig. 2. X – ray photoelectron spectroscopy (XPS) of AlCuFe alloy after several
treatments according to PINHEIRO, P. J. et alii., 1999 [5].
Literature also shows that a variety of iron oxides is formed.
Great part of these oxides can be distinguished in XPS by
binding energy shifts in the range of 1, 2 to 5, 1 eV [1]. Oxidation
is signaled by characteristic growth at 710 eV indicating
the presence of Fe 2 o 3 (hematite). At high temperature the
oxidation becomes more aggressive. With respect to AlCuFe
alloys aluminum oxides under all conditions of alloys preparation.
Copper is protected from oxidation as well as iron
except when the alloy is immersed in water. This protection
is due to the formation of a passivating layer of Al. Vacuum
oxidation is relatively mild, air oxidation is severe and oxidation
from liquid immersion is the most severe.
Solubility of iron under different conditions at equilibrium
can be conveniently calculated with stability diagrams such
as Eh – pH diagram. These diagrams utilize Nernst equations
besides chemical and thermodynamic relationships and
standard free energies values from literature. Another way
to analyze the interrelationship between chemical and thermodynamic
processes is the equations related to pε and pH
parameters.
In the same way that an acid is able to donate a proton and a
base to accept a proton there are substances which have the
capacity to donate electrons (reductors) and others to accept
electrons (oxidants).
For iron in the ferrous state occurs an oxidation reaction and
there is formation of ferric iron species. Similarly, ferric iron
as oxidant suffers a reduction reaction and there is formation
of ferrous iron species. Solid iron Fe(s) used to prepare
metallic alloys for the formation of quasicrystals is the most
reduced state while ferric ionic species is the most oxidized.
This paper shows the development of a thermodynamic model
for solid iron system which encompasses the formation of
oxidant and reduced iron species besides the formation of
hematite and magnetite. The objective is to show the thermochemical
behavior of iron that is used in metallic alloys
preparation for the formation of quasicrystals after immersion
in water.
2. Theoretical Considerations
pH is defined as the availability of hydrogen ions in solution. In
practice, pH is defined according to the following equation:
pH = - log (H + ) = - log fH + [H + ] = - log [H + ] (1)
The above expression is valid for unity activity coefficient of
hydrogen ion.
The standard free energy for the formation of 1 mol of substance
from pure elements is defined as the standard free energy
of formulation. Its equation for a particular reaction is
given by [2]:
ΔG°r = ∑ ΔG°f (products) - ∑ ΔG°f (reactants) (2)
ΔG°f values for almost all chemical substances of interest
are well defined in literature at 25°C temperature. This is the
temperature used in the model development.
Ciência & Tecnologia dos Materiais, Vol. 24, n.º 1/2, 2012 69

L. Nascimento et al. Thermodynamic model for solid iron in AlFeCu
In turn, the relationship between the equilibrium constant k’
of, for instance, a monoprotic weak acid/base and the standard
free energy change of reaction is given by:
ΔG°r = - RT lnk’a = -2, 303 RT log k’a (3)
For the values of R (gas constant) and absolute temperature
at 25°C (T = 298,13K) :
pk’a = - log k’a = ΔG°r / 1, 364 (4)
pε is related to the standard free energy by the equation:
pε = ΔG°r/n 2, 303 RT (5)
In all thermochemical studies the standard free energy of formation
of hydrogen ion from 1/2H 2 O is G°f of hydrogen elements
equal to zero.
3. THESI MODEL DEVELOPMENT
3.1. Initial Considerations
Thesi Model (Thermodynamic on Solid Iron) is based on
equations of k’, ΔG°r , pH and pε as given above. The model
is applied to solid iron which forms the system Fe(s) = Fe 3+
- Fe 2+ - Fe 2 o 3 – Fe 3 o 4 ; i.e., iron in ferric and ferrous state as
well as hematite and magnetite. In the present study it was
considered for total solid iron a molar concentration of 10 -6
mol/L which means a solution with 0, 06 mg/L of iron.
The main dissociation reactions of the system are as follows:
Fe(s) ↔ Fe 2+ + 2e - (oxidation) (6)
Fe(s) ↔ Fe 3+ + 3e - (reduction) (7)
2Fe(s) + 3H 2 o ↔ Fe 2 o 3 + 6H + +6e - (8)
3Fe(s) + 4H 2 o ↔ Fe 3 o 4 + 8h + + 8e - (9)
3.2. Analysis of the Iron Redox Systems
Each equation of the solid iron system is analyzed “per se” in
order to determine values for the chemical equilibrium constant
k’, pε, pH and Gibbs standard free energy [3].
Table 1 shows the selected values of Gibbs standard free energy
of formation for iron species at 25°C and one atmosphere
of pressure. Briefly, the main analysis of the iron system is:
Table 1. Values of Gibbs standard free energy of formation
for iron species at 25°C and one atmosphere of pressure 3 .
Chemical species
Standard free energy of formation
in kg cal/mol
h o 2 - 56,69
Feo - 59,38
Fe o 2 3
- 179,10
Fe o 3 4
- 242,30
Fe2+ - 20,30
Fe3+ -2,52
Fe(s): Ferrous Iron System.
Equilibrium Constant for unity activity and pε value given
by:
k’ = (Fe2+ ) (e- ) 2 ; pε = -1/2 log k´+ 1/2 log (Fe2+ )
Gibbs free energy for reaction of equation (6):
ΔG°r = ΔG°f (Fe2+ ) = - 20,3 kg cal mol-1 .
hence:
log k´= -14,98 e pε = -10, 45.
The slope of the straight line for constructing a stability diagram
is obtained from:
dpε/dpH = 0.
(1) Fe(s): Ferric Iron System.
Equilibrium Constant for unity activity and pε value
given by:
k’ = (Fe3+ ) (e- ) 3 ; pε = - 2, 62
Gibbs free energy for reaction of equation (7):
ΔG°r = ΔG°f (Fe3+ ) = - 2,52 kg cal mol-1 .
Hence, the equilibrium constant k’ is given by:
log k´= 1, 85
Slope given by: dpε/dpH = 0.
(2) Fe(s): Fe 2 o 3 System.
Equilibrium Constant for unity activity and pε value
given by:
k’ = 1/(H + ) 6 ( e- ) 6 ; pε = 1/6 log k´- pH
Gibbs free energy for reaction of equation (8):
ΔG°r = 3 ΔG°f (H O) - ΔG°f (Fe o ) = 9,03 kg cal mol 2 2 3 -1 .
log k´= - 6,62 e pε = - pH – 1,1.
Slope given by: dpε/dpH = -1. For pH = 0, then pε = -1,1.
(3) Fe(s): Fe 3 o 4 System.
Equilibrium Constant for unity activity and pε value
given by:
k’ = 1/ (H + ) 8 (e- ) 8 ; pε = - pH – 1, 43
Gibbs free energy for reaction of equation (9):
ΔG°r = 4 ΔG°f (H O) - ΔG°f (Fe o ) = - 15,54 kg cal
2 3 4
mol-1 .
Results obtained are given by:
log k´= - 11,4; Slope is given by: dpε/dpH = -1. For pH
= 0 then pε = -1,43.
(4) Fe 3+ : Fe 2+ System.
Initial equation for the system is given by:
Fe 2+ ↔ Fe3+ + 1e- (10)
70 Ciência & Tecnologia dos Materiais, Vol. 24, n.º 1/2, 2012

Thermodynamic model for solid iron in AlFeCu L. Nascimento et al.
Equilibrium Constant in terms of activity:
k’ = (Fe3+ ) (e- ) /(Fe2+ )
Gibbs free energy for reaction of equation (10):
ΔG°r = ΔG°f (Fe3+ ) - ΔG°f (Fe2+ ) = 17,78 kg cal mol-1 .
Results for pε and slope of the straight line:
pε = - log k’ = 13,04 and slope : dpε/dpH = 0.
(5) Fe o : Fe o System
2 3 3 4
Equilibrium reaction of the system is given by:
3 Fe o + 2h 2 3 + + 2e- ↔ 2 Fe o + h O (11)
3 4 2
Equilibrium Constant for unity activity and pε value
given by:
k’ = 1/ (H + ) 2 (e- ) 2; pε = 1/2log k´- pH
Gibbs free energy for reaction of equation (11):
ΔG°r = 2 ΔG°f (Fe o ) + ΔG°f (H O) – 3 ΔG°f (Fe o )
3 4 2 2 3
= -4,0 kg cal mol-1 .
Results given by:
pε = 1, 45 – pH; slope : dpε/dpH = -1. For pH = 0, then
pε = 1,45.
(6) Fe 2+ : Fe 2 o 3 System.
Equilibrium reaction of the system is defined as follows:
2Fe2+ + 3h o ↔Fe o + 6H 2 2 3 + + 2e (12)
k’ = 1/ (H + ) 6( e- ) 2
Gibbs free energy for reaction of equation (12):
ΔG°r = ΔG°f (Fe o ) – 2 ΔG°f (Fe 2 3 2+ ) - 3 ΔG°f (H O) = 2
32 kg cal mol-1 .
The results are given by:
log k´= - 23, 46 e pε = - 3pH + 17,6 and slope : dpε/dpH
= -3. For pH = 0 then pε = 18.
Fe 2+ : Fe 3 o 4 System.
Equilibrium reaction given by:
3Fe2+ + 4h o ↔Fe o + 8h 2 3 4 + + 2e (13)
k’ = 1/(H + ) 8( e - ) 2 /(Fe 2+ ) 3
Gibbs free energy for reaction of equation (13):
ΔG°r = ΔG°f (Fe o ) – 3 ΔG°f (Fe 3 4 2+ ) - 4 ΔG°f (H O) = 2
45,4 kg cal mol-1 .
Results for k’ and pε :
log k’ = - 33,25 ; pε = - 4pH + 25,6.
Slope is given by: dpε/dpH = -4. For pH = 0 then pε =
25,6
(7) Fe 3+ : Fe 2 o 3 System:
Equilibrium reaction defined as follows:
2Fe 3+ + 3 h 2 o ↔ Fe 2 o 3 + 6H + (14)
Equilibrium Constant for unity activity given by:
k’ = (H + ) 6 /(Fe3+ ) 2
Gibbs free energy for reaction of equation (14):
ΔG°r = ΔG°f (Fe o ) - 2 ΔG°f (Fe3+) - 3 ΔG°f (H O) =
2 3 2
4 kg cal mol-1 .
Results for k’ and pH:
log k´= 2,93; pH = 1,5.
In stage (5) of the model it was necessary to verify if Fe(s)
is limited by ferrous species or by ferric species and also by
Fe 2 o 3 and Fe 3 o 4 . Table 2 shows all data determined for pk’,
pε, pH and slope for all the stages of the model here developed.
Table 2. Results obtained from the study on the Fe(s) = Fe 2+
- Fe 3+ - Fe 2 o 3 – Fe 3 o 4 system with data of Gibbs free energy
from literature at temperature of 25°C.
System conditions pk’ pε ph slope
Fe(s): Fe 2+
Fe(s): Fe 3+
Fe(s): Fe 2 o 3
Fe(s): Fe 3 o 4
Fe3+: Fe 2+
Fe 2 o 3 : Fe 3 o 4
Fe 2+ : Fe 2 o 3
Fe 2+ : Fe 3 o 4
Fe 3+ : Fe 2 o 3
[Fe 2+ ] = 10 -6 mol. L -1
[Fe 3+ ] = 10 -6 mol. L -1
[Fe 2 o 3 ] = 10 -6 mol. L -1
[Fe 3 o 4 ] = 10 -6 mol. L -1
[Fe 3+ ] = [Fe 2+ ]
4. CONCLUSIONS
[Fe 2 o 3 ] = [Fe 3 o 4 ] = 1
[Fe 2+ ] = [Fe 2 o 3 ] = 1
[Fe 2+ ] = [Fe 3 o 4 ] = 1
[Fe 3+ ] = 10 -6 mol. L -1
Ciência & Tecnologia dos Materiais, Vol. 24, n.º 1/2, 2012 71
14,98
- 1,86
6,62
11,4
13,04
-2,93
23,15
33,25
-2,93
-10,45
-2,62
-1,1
-1,43
13,04
1,47
17,6
25,63
Based on the data and reactions involved in the development
of the Thesi Model, the following conclusions can be made:
• The interrelationship between chemical and redox equations
represented by pk’, pH and pε reflect the net effect
of chemical and thermodynamic processes in oxidation
analysis of solid iron.
• It was observed a strong pH influence in all equations developed
in the study especially in the oxi – reduction equation
of solid iron Fe(s) and ferrous ion, Fe 2+ . In the system
defined by ferrous iron and hematite, pH appears to be on
the acid side.
• The influence of temperature was not analyzed. However
it is very important for all stages of the model. Some researches
has showed that during formation of AlCuFe metallic
alloys at high temperatures and further immersion
in water only iron is oxidized. The cooling process and
-*
-
-
0
0
-
0
0
0
1,5
0
0
-1
-1
0
-1
-3
-4
-

L. Nascimento et al. Thermodynamic model for solid iron in AlFeCu
leaching into acid solutions can create a severe oxidation
state.
• It is necessary to measure pH and temperature increase
and verify iron species formation after liquid immersion
in order to determine iron oxidation during the process for
preparation of quasicrystals.
ACKNOWLEDGEMENTS
The National Council of Scientific and Technological
Development-CNPq is acknowledged for financially supporting
this research.
REFERENCES
[1] MOULDER, J.F. et al., Handbook of X – ray
Photoelectron Spectroscopy. eden Prairie, minnesota:
Perkin – elmer corporation, 1992.
[2] ROBIE, R.A.; WALDBAUM, P.R. “Thermodynamic
properties of minerals and related substances at 25°C
and one atmosphere pressure and at higher temperatures”.
Geological Survey Bulletin, 1968.
[3] STUMM, W.; MORGAN, J. “Aquatic Chemistry”.
1990.
[4] CHEUNG,Y.L.,CHAN,C.K., ZHU,H.Y. (2001),
Characterization of Icosahedral phase in as-cast quasicristalline
Al 65 Cu 20 Fe 15 alloys,Materials Characterization
47, p. 299-305.
[5] PINHEIRO, P. J. et alii. Surface oxidation of AlCuFe
alloys: a comparison of quasicrystalline and crystalline
phases. Philosophical Magazine B, 1999; 79 (1);
91-110.
72 Ciência & Tecnologia dos Materiais, Vol. 24, n.º 1/2, 2012