II. Determination of Thermodynamic Data 3. Experimental ...

Thermodynamics and Kinetics of Solids 21________________________________________________________________________________________________________________________

15.10.01

II. Determination of Thermodynamic Data

3. Experimental Methods

3.1. Calorimetric Methods

Determination of the enthalpy of formation or reaction byapplying an apparatus with known heat capacity(calorimeter). Measurements of the temperature change.The heat capacity of the calorimeter is given by the waterequivalent:

q T = WDT (3.1)

Classification of calorimeters:i) Isothermal Calorimeter

Calorimeter temperature Tc = surrounding temperatureTs = const. Best known example: Ice calorimeter

ii) Adiabatic CalorimeterTc = Ts ≠ const.Applicable for comparatively slow reactions (e.g. thesolution of metals in acids)

iii) Heat Flux CalorimeterTs - Tc = const.Simpler construction than the adiabatic calorimeter.Suitable for determining transition enthalpies but notreaction enthalpies (since the temperature may becommonly not kept constant).

iv) Isoperibolic CalorimeterTs = const. Tc is measured during and after thereaction. Most commonly applied calorimeter.

Important: Exact knowledge of the reaction products isnecessary. No parasitic reactions should occur.

Temperature Measurementi) Mercury-in-Glass Thermometer

Precision: up to ± 0.0005 °C. Calibration above 6 °Cwith an overlap in the range from 9-33 °C.

ii) Platinum Resistance ThermometerApplication of Pt wire coils. Because of preciseelectrical measurement 8 x higher resolution.Wheatstone’s bridge.

iii) ThermocouplesSensitivity of a single thermocouple is too low;accordingly series application of thermocouples (up to1000 elements; 10-7 °C temperature difference ismeasurable). In the case of 10 copper-constantancouples 1mV corresponds to 2.34 °C temperaturedifference.

iv) Thermistors

Resistance element is a semi-conductor, e.g. SiC. The(negative) temperature coefficient is much larger thanin the case of metals. ª 10-6 °C temperature differenceis measurable. Difficulty: Reproducibility

v) Optical Pyrometers

Determination of the Water EquivalentEndothermic reactions: Application of a metal (e.g. Cu,Ag or Hg in glass) with known heat capacity atapproximately the same temperature as in the case of thelater measurement. Al2O3 may be used at hightemperatures.Exothermic reactions: Electrical heating

q = RI2 t J (3.2)

Determination of Heat Capacities in a DroppingCalorimeter

Determination of the heat equivalent between roomtemperature and various higher temperatures. Applicationof isoperibolic or isothermal calorimeters.The substance is being heated to the desired temperatureand dropped into the calorimeter. The hot sample is eitherdirectly dropped into the liquid within the calorimeter(water, paraffin,...) or into a beaker that is surrounded bywater.In the case of phase changes, undefined final states mayoccur because of the fast cooling.

Levitation-CalorimetryPt-resistance furnaces: T < 1800 K. For highertemperatures electromagnetic levitation.

Adiabatic CalorimeterDetermination of the generated heat from electrical data.

Determination of Melting and Transformation EnthalpiesDTA: Sample and a reference body are nearly identicallytreated thermally. The temperature difference betweenboth is measured.

DSC: The necessary energy for heating the sample iscompared to a reference sample (within the sametemperature interval). Instead of thermometricmeasurement (as in the case of DTA), the electricalenergy is measured differentially. Precision ª ± 0.2%.Determination of Enthalpies of Reaction and Formation,

Reaction Bomb Calorimetry

22 Thermodynamics and Kinetics of Solids________________________________________________________________________________________________________________________

15.10.01

In the calorimeter a combustion with a gas (up to 25 atm)

as one of the reactants is performed. The bomb has to be

closed gas tight during the reaction which may be

explosion-like. The reaction is initiated by an electrical

current. As gases are mostly used: O2, F2, Cl2, N2.

Impurities such as C, H or N may contribute largely to

the enthalpy of combustion.

3.2. Equilibria with a Gas Phase.

Determination of the change in Gibbs energy from the

equilibrium constants:

A + B = C + D

K =acaDaAaB

= exp -DG0

kTÊ

Ë Á

ˆ

¯ ˜ (3.3)

e.g.,

As = Ag K = pA

As + Bg = Abs K =1pB

As = Adessolved

In the case that the gas phase is a complex mixture ofspecies (for example, MoO3(s) Æ Mo3O9(g), Mo4O12(g),

Mo5O15(g)) it is necessary to measure the individual

gaseous components, which is commonly very difficult.

Static Methods for the Determination of Vapor Pressures

i) Application of manometers, e.g. a quartz spiral-

manometer with a mirror or membrane-zero-

manometer.

Determination of the vapor concentration by optical

absorption or emission (T up to 1000 °C)

ii) Gas-Condensed Phase Equilibria in Closed Systems.

Dewpoint method:

Electrically heated furnace with two independently

heated regions. Temperature increase of the entire

furnace, afterwards cooling of the part of the furnacewithout sample until dew occurs. Precision ± 1 °C.

Example: sample = brass; condensation of zinc.

The vapor pressure of zinc at the temperature of the

formation of dew corresponds to the zinc pressure of

brass at the temperature of the sample.

Isopiestic Method:

Formation of an equilibrium vapor pressure over an

alloy at high temperature and the pure volatile

component at lower temperature. The temperatures at

the hot and cold end are fixed. The equilibrium

composition of the alloy is being determined.

Sievert’s Method:

Determination of the solubility of gases in metals.

Heating of the metal in a closed cylinder combined

with a burette which is connected via a three-way-

valve with a pump and a gas supply. A known gas

volume is given and the decrease in volume is

observed.

Dynamic Vapor Pressure Methods

Boiling Point Method:

Determination of the boiling point (vapor pressure =

atmospheric pressure) from the discontinuity of the

weight-temperature curve or the pressure change at

constant temperature.

Transport Method:

For the determination of the vapor pressure of a metal or

the volatile component of an alloy, a constant flux of

inert gas is passed over the sample. The gas takes up the

vapor at a rate which depends on the relative pressure and

flow rate. The vapor is condensed at a lower temperature

and the mass is determined.

Other Heterogeneous Equilibria

Systems which contain more than 1 gas. Consideration of

reactions between one gas and one condensed phase with

the formation of at least one volatile product.

H2 - CH4 - equilibria: H2, metal, its carbides and methane.

H2 - NH3 - equilibria: Nitridation of iron

2 Fe4 N + 3 H 2 g( ) = 2 NH3( ) g + 8 Fe

H2 - H2O – equilibria: Reduction of metal oxide (e.g.

'FeO' + H2 = Fe+ H2O)

H2 - H2S - equilibria: e.g. Ag2S + H2 (g) = 2 Ag + H2S (g)

at 600 - 1280 °C.

Other equilibria: CO, CO2, SO2 - O2 - SO3.

Methods on the Basis of Evaporation Rates

Determination of the vapor pressure of a substance from

the evaporation rate into a vacuum:

i) Knudsen

ii) Langmuir

Knudsen: Effusion


15.10.01

The pressure is given by

p =mtA

2p RTM

= 0, 02256mtA

TM

atm (3.4)

m: Mass of the vapor with the molecular weight M,

which evaporates from an area A during the period of

time t.

Langmuir: Sample is exposed to vacuum (no equilibrium

as in the case of the Knudsen method)

The mass is mostly much lower.

Mass loss mL = 44 t A a pKMT

a: Evaporation coefficient (0< a £ 1). pK: Vapor pressure

as determined by the Knudsen method.

The Knudsen cell is often used in combination with a

mass spectrometer (Identification of the gaseous species).

Knudsen-Effusion: Determination of the mass at room

temperature before and after the experiment or incombination with a vacuum microbalance (25 g, 1 mg

resolution) with continuous monitoring of the mass

(example: Determination of the activity of Si in transition

metal-silicides; by mixing with SiO2, SiO vapor instead

of Si vapor is generated and the measuring temperature is

reduced from > 2000 K to 700 K).

For highest resolution: Condensation of a known fraction

of a gas with a radioactive isotope onto a target and

radiochemcial analysis. Example (Fig. 3.1.):

Determination of the chromium activity in chromium

alloys (1400 °C) with condensation of chromium onto

molybdenum as target disc; dissolution of Cr in acid and

determination of the radioactivity. Alternatively, MoO3

was formed by oxidation, which could be pressed into

pellets.

Problems may be the interaction with the sample holder

and temperature gradients. Therefore, resistance furnaces

are being used.

Complex gas phases: Application of a mass spectrometer.

Ionization of the effusion molecular beam bybombardment with monoenergetic electrons. The

Fig. 3.2. Combination of a Knudsen cell with a massspectrometer

Fig. 3.1. Effusion cell for the determination of the vapor

pressures of metalls (1200 - 1400 ° C)

gis

Fig. 3.3. Ion current vs. electron energy for monoatomic species

(a) and molecular species (b)


15.10.01

ionization source is as close to the Knudsen cell aspossible (Fig. 3.2.).

2 methods for the separation of the ions:i) Continuous extraction by fixed acceleration

potentials,ii) Pulsed acceleration potentials with separation into

groups with constant time of flight (TOF).(advantage of i: high resolution, ii) nearly simultaneousdetection)

Fig. 3.3. shows a typical ionization efficiency curve for asimple monoatomic gas and the fragmentation ofcomplex molecules (e.g., M2 + e- Æ M+ + M + 2e-).

The ionic current is commonly measured by aphotomultiplier. Relationship between the peak intensityof the species in the mass spectrometer and the pressure:

p =KI+ T

s D D E (3.5)

(K: Geometric constant, I+: Measured ion current, T:Absolute temperature., s : Detector efficiency, DE :Electron beam energy).

From

Mg + Ng Æ Mng

results for the vapor pressures from the ionic currents

∂

∂ 1T( )

logIMN

+ TI

M + IN +

= -DHo

R(3.6)

In case that dimeric species M2 or N2 are being observed,the constants of the reactions.

M2 + N Æ MN + Mand

N2 + M Æ MN + N

may be described in a good approach by the relativeamounts of the ionic currents:

Ka =IMN

+ IM+

IM 2

+ IN+ ; Kb =

IMN+ IN

+

IN 2

+ IM+ (3.7)

Instrumental and geometrical factors are eliminated inthis case. Practical difficulties often: Pressure of thedimer M2

+ is commonly one order of magnitude lowerthan that of the monomer.

While the lower vapor pressure limit is ª 10- 4 mm Hg inthe case of the Knudsen method, measurements accordingto the Langmuir method may be performed atconsiderably lower pressures. The Langmuir Method isoften applied in order to increase the rate of the weightloss (especially suitable for substances with highsublimation energies).

Examples:Fig. 3.5.: shows the resulting activities of Cu - Ge alloys.

Fig. 3.4. shows the ratio of the ion currents of copper andgemenium in the case of liquid Cu – Ge alloys

Fig. 3.4. : Cu - Ge (l) : Ion current ratios at 1400 °C


15.10.01

Fig. 3.6. shows induction heated metals cooling of the

surface (e.g. Cu) in a molydeum brat. Oxides dissociate

in the case of evaporation; the large evaporation

enthalpies results in a is observed because of.

EMF-Measurements

The energy of the chemical reaction generates an EMF.

Problems: Suitable electrolytes, reversible electrode

processes, electronic conduction of the electrodes.

Determination of the dissociation pressure of an M/MO

System:

Pt , M, MO Electrolyte (O- -) O2 (1 atm), Pt

M + O- - Æ MO + 2e- 12 O2 + 2e- Æ O- -

Total cell reaction 12 O2 + M Æ MO

Dissociation pressure of Ag / Ag Br:

Ag Ag Br Br2 , C

Ag Æ Ag+ + e- 12 Br2 + e- Æ Ag+ Æ Ag Br

Total reaction:

Ag + 12 Br2 Æ Ag Br

D G = - n F E

Compared to the application of solid electrolytes, molten

salts have the general disadvantage that several ions are

commonly mobile.

Moltoen salts: Often alcali chlorides with dissolved salt

Fig. 3.5. Activities in the system Cu - Ge (l)

Fig. 3.6. Langmuir apparatus for the determination of reaction

pressures

Fig. 3.7. Galvanic cell for EMF measurements using moltenchlorides


15.10.01

of the transfered metal. (Eutectic mixtures of LiCl und

KCl: m. p. 359 °C).

C , M M Cl2 Cl2,g,C

Problems: Hydrolysis of the molten salts by atmospheric

moisture. Dispersion of the molten metal in the

electrolyte.

Determination of the EMF by extrapolation of the

current-voltage curve to I = 0:

Ag Ag Cl M Pb Cl2 Pb

Glass electrolytes: Determination of the Na – activity in

molten Na - Hg- and Na - Cd - systems (300 - 400 °C), or

the Ag-activity in Ag-Au.

Ceramic solid electrolytes

Kiukkola + Wagner (1957):

Pt , Ni , NiO ZrO2 Fe , FeO , Pt

Cell reaction: NiO + Fe = FeO + NiElectronic Conductivity of the electrolyte dependent on

P O 2. Application of ZrO2 and ThO2 in series.

Reference electrode. Inert Gas / Vacuum.

Gas electrode: H2 - H2O , CO - CO2 , ...

Secondary equilibria:

Pt, MnO, MnS (SO2 = 1 atm) ZrO2 O2 , Pt

Left hand electrode reaction:

MnS + 30-- Æ SO2 + MnO + 6e-

Electrolyte with dispersed second phase, e.g.

Ni Ni F2 Sr F2 Sr F2 - La F3 Co , Co F2

Electrolyte with gas sensitive electrode:

P H 2 Na2S Na - b - Al2O3 Na2S , PH2 S PH 2

orPSO 2

, Ps2 ZrO2 PO 2

orCu , Cu2S CaS CaF2 CaS Fe, FeS

3.3. Estimation of Thermodynamic Data

Because of the lack of available thermodynamic data it is

Abb. 3.8. EMF-measurement using a glass electrolyte

Fig. 3.10.: Coulometric titration of Cu, Cu2O ThO2-Y2O3

(O) Pb (l)

Fig. 3.9. Sample holder for EMF measurements using solid

electrolytes.

Experimentalarrangement


15.10.01

of large interest to estimate data with sufficient precision.

Heat Capacities.

Dulong-Petit’s law: atomic heat of the elementsª 6.2 cal / K at room temperature. Since the atoms of

solids are fixed in the lattice there are no degrees of

freedom by rotation or translation. However, there exist

3 degrees of freedom of vibration (which have to be

counted twice). Accordingly, we have above Debye’s

temperature

Cv =6

2R= 25.1 J/K ⋅ mol (3.8)

Cp - Cv ª 0.84…2.09 J / K · mol at room temperature.

Accordingly

Cp ª 25.9…31.5 J / K · mol (3.9)

Kellogg (1967): Estimation of heat capacities of

predominant ionic compounds at 298 K by adding thecontributions of a cationic and anionic groups (q (cat) , q

(an)). Average values were determined from these

experimental data (Tables 3.1. and 3.2.)

C p 298 K( ) = qÂ (3.10)

For Al2 (SO4)3 holds

Cp (298 K) = 2q (Al+++) + 3q (SO4--) = 269.03 J / K · mol

(measured value: 259.41 J / K · mol)

The heat capacities increase with temperature and are

approximately the same for all compounds per ion oratom at the melting point. Ünal (1977): 30.3 ± 2.1 J / K ·

mol.

Empirically observed temperature dependence:

Cp = a + b x 10-3 T + c x 105 T-2 (3.11)

(The T-2 term reflects the bending at lower temperatures

above 298 K and at the Debye temperature). The result of

analyzing 200 inorganic compunds is

a =Tm 10-3 q + 1.125 nÂ( ) - 0.298 n 105 Tm

-2 - 2.16 n

Tm 10-3 - 0.298(3.12)

b =6.125 n + 105 n Tm

-2 - qÂTm 10-3 - 0.298

(3.13)

c = -4.12 n (3.14)

(n: number of atoms of the molecule, Tm: melting point in

K)

If no more precise data are known

about the heat capacity of a

compound, one may assume

D Cp ª 0 (3.15)

for reactions in the condensed state

(postulate of the additivity of the heat

capacities of the elements or reactants

= Neumann-Kopp’s Rule). This holdswell for alloys but also in a firstapproach for compounds with

Tab. 3.2. Anionic contributions to the heat capacity at

298 K

Tab. 3.1. Cationic contributions to the heat capacity at 298 K


15.10.01

coordination lattices. In other words, it is

DG (T) = DH (298 K) - TDS (298 K) (3.16)

The enthalpies of transitions,melting and evaporation have to betaken into consideration, however.Estimated average values for changesof the heat capacity for differentreactions with gases:

Cp [J / K · mol]A(s) = A(g) -7.5A(l) = A(g) -9.6AxBy(s) = AxBy(g) -9.6 (x+y)AxBy(l) = AxBy(g) -11.3 (x+y)A(g) + x B2(g) = AB2x(s) +12.5xA(s) + B2(g) = AB2x(l) +14.2xA(s) + B2(g) = AB2(g) -9.2

Enthalpies and entropies oftransitions, melting and evaporationMethods for the estimation of thesedata are rather reliable if the molecularstructure of the substance is known.

Evaporation: Pictet (1876), Trouton(1884): The entropy of evaporation(i.e. enthalpy / absolute temperature ofthe evaporation is approximately thesame for all compounds

DSe =LeTe

ª 92,1 J / K ⋅ mol (3.17)

Fig.. 4.11. shows that the Trauton constant increaseshowever with the boiling point:

LeTe

= 0, 01037 Te + 75, 96 kJ / K ⋅ mol (3.18)

Melting. The melting entropy is not a constant as in thecase of evaporation). The change of the ordering bymelting is smaller than by evaporation. The variation ofthe ordering of a solid material by the various chemicalbinding forces results in a proportionally large effect onthe melting entropy.

Crompton (1895), Richards (1897), Tammann (1913):Pure metals:

DSm ª 9,2 J / K = const. (3.19)

More precise investigations have shown, however, thatthe melting entropy increases slightly with thetemperature. For fcc-metals it is:

DSm = 7,41 + 1,55 x 10-3 Tm J / K · mol (3.20)

Fig. 3.11. Le / Te vs Te for pure elements and inorganiccompounds

Tab. 3.3. Melting entropies for inorganic compounds


15.10.01

For bcc-metals holds:

DSm = 6,78 + 0,71 x 10-3 Tm J / K · mol (3.21)

For covalent metals, DSm is substantially higher than 9.2J / K.

Compounds: Predictions are difficult since the meltingentropy depends on the nature of the atomic ordering andthe type of chemical bond. To a certain degree, thecrystalline structure provides an indication of the type ofbinding; however, AgCl and NaCl oder CaCl2 and MgF2

have the same structure but different melting entropies

(Table 3.3.).

Entropies and Entropy Changes.Standard entropies: Nearly all elements have beenmeasured.For inorganic compounds, Latimer (1951) found that thestandard entropies may be added up from empiricallyobserved values for the anionic and cationic constituents(308 mainly ionic compounds). (Tables 3.4., 3.5.)

In order to obtain the standard entropy of a solidcompound, the value for the cation has to be multipliedby the number of cations in the molecule and added to thevalue obtained for the anion.

Example: S (Al2(SO4)3 , 298 K) = (2 x23.4) + (3 x 64.2) = 239.4 J / K · mol.

Entropies of Mixing (Non-metallicSolutions):Example: Mixing of cations in doubleoxides (spinels, MX2O4, with 1/3 ofthe cations on tetrahedral sites and 2/3on octahedral sites; no mixing effectat “correct” occupation of sites; if,however, X occupies partiallytetrahedral sites and M partiallyoccupies octahedral sites,

(Mx X1-x) [M1-x X1+x] O4

an effect of mixing occurs:

x = 0: normal spinel; x = 1: inversespinel.

The value x may be determined fromthe equilibrium constant of the

exchange reaction

(M) + [X] = [M] + (X).

The result is:

DH (exchange) = - RT ln 1- x( )2

x 1+ x( )(3.22)

and in the following contribution of thecation mixture is observed:

Tab. 3.4. "Latimer" Entropiebeiträge {M}

Tab. 3.5. "Latimer" Entropiebeiträge n{X} als Funktion der Ladungszahl n derKationen


15.10.01

S = -R [x lnx + (1 - x) ln (1 - x) + (1 - x) ln 1 - x

2+ (1 + x) ln

1 + x2

] (3.23)

Temkin’s-Rule for the calculation of the activities inmixtures of non-metallic compounds (which provides arelationship between the activities and numbers of atomsin each molecular species). For mixtures of A2Y - B2Y-holds:

aA 2 Y = NA 2Y2 , a B 2 Y = NB 2 Y

2 (3.24)

For ideal random mixtures RT ln aA 2Y = -T D sA 2Y( ) the

result is

D sA2 Y = -2R ln NA 2Y = -R ln NA 2 Y2 (3.25)

Analogously holds for the reduction of Cr2O3 by Al:

2 Al + Cr2O3 Æ 2 Cr + Al2O3

K =aCr

aAl

Ê

Ë Á

ˆ

¯ ˜

2 a Al 2O 3

aCr 2O3

Ê

Ë Á Á

ˆ

¯ ˜ ˜ @

aCr

a Al

Ê

Ë Á

ˆ

¯ ˜

2 NAl 2O3

NCr 2O 3

Ê

Ë Á Á

ˆ

¯ ˜ ˜

2

(3.26)

(Fe, Mn)3 C : a Fe 3C = NFe 3C3

Another contribution to the entropy besides theconfiguration entropy is the thermal entropy (by thechange of the vibration of the cations and theirsurrounding oxygen ions when mixed oxides are formed).For spinels such as Fe3O4, FeAl2O4, FeV2O4 und FeCr2O4

holds DS = -7.32 + DSm J / K · mol.

Formation EnthalpiesThe determination of the Gibbs energy requiresinformation about the formation enthalpies. The methods

are often not very precise and are restricted to a relativelysmall number of compounds.

The enthalpies of the elements in their standard stateat 298.15 K are set to 0. The temperature dependence ofthe formation enthalpies is generally small.

In order to obtain a consistent basis for comparison,the formation of 1 mol AxBy with x + y = 1 is beingconsidered.

It is expected that the compound with the highestmelting point has the highest formation enthalpy. If the

melting points of the other compounds (of the samesystem) are considerably smaller, straight lines to the

pure elements may be drawn in the DH - x – presentationin a first approach.

Abb. 3.12. Lithium-tin phase diagram

Abb. 3.13. Formation enthalpies in the lithium-tin system

Tab. 3.6. Thermodynamics and cation distribution in spinels


15.10.01

Homologeous SeriesThere is a certain relationship betweenthe formation enthalpies of metalcompounds and the order number ofthe metal in the periodic system in thecase of the same stoichiometry andsame radical.

Pettifor (1986): Reorganisation ofthe periodic table according to"Mendeleev-numbers” (Figs. 3.14,3.15)

Volume Change and FormationEnthalpyOriginally it has been assumeds p e c i f i c a l l y f o r intermetalliccompounds that the deformation orpolarization of the atoms of both metal atoms by theformation of the alloy depends on the affinity. Therelationship holds, however, also for simple inorganicsaltlike compounds, though the change intensity is mainlycaused by the formation of ions. Percentage of volumechange:

DV =100 eMV - AVÂ( )

AVÂ

MV: Molecular volume of the compound, AVÂ : Sum

of the atomic volumina of both components, e = 0.95(CsCl-structure), 0.825 (NaCl-structure) (Fig.. 3.16).

The deviation from the curve is £ 25 kJ/g-atom.

4. Examples of Thermochemical Treatment of MaterialsProblems

4.1. Iron and Steel Production

Fig. 3.15. The line shows the sequence of the elements through the modified periodicsystem according to “Mendeleev’s number”.

Fig. 3.14. Formation enthalpies of carbides and nitrides with acubic NaCl-structure. The plot is made in the Pettifor’sarrangement of the periodic system

Fig. 3.16. Heat generation and degrees in volume at theformation of compounds with simple structures


15.10.01

Removal of dissolved oxygen in molten steel by theaddition of an element which may form an oxide ofhigher stability than that of iron.

i) Si:SiO2 (s) =Si (l) + O2 (g)DG0 = 952697 - 203.8 T J

O2 (g) = 2 Odissolved, Fe

DG = -233676 + 50.84 T + 38.28 T log N0 J

Si (l) = Sidissolved, Fe

DG = -131378 + 15.02 T + 19.14 T log NSi J

For the reaction

SiO2 (s) = Sidissolved, Fe + 2 Odissolved, Fe (4.1)

this results in the following Gibbs reaction energy

DG = 587643 - 137.94 T + 38.28 T log N0 + 19.14 Tlog NSi (4.2)

In equilibrium we have with DG = 0

2 log N0 + log Nsi = - 30700 T-1 + 7.20 (4.3)

At 1600 °C holds

2 log N0 + log NSi = -9.19 (4.4)

On the basis of equilibrium process (CI, CSi) follows

CO2 CSi = 2.7 · 10- 5 (4.5)

The concentrations are rather small and a small amountof Si has to be added.

ii) AlAnalogously holds for

Al2O3 (s) = 2 Aldissolved, Fe + 3 Odissolved, Fe (4.6)

CO3 CAl

2 = 10-13

This value does not correspond, however, to theexperimental result. Possible reasons: Reaction of Al isfaster than the dissolution of Al in the melt; formation ofthe spinels FeAl2O4 from FeO and Al2O3.

Removal of carbon from Fe-Cr-C- and Fe-Si-C-alloys (l):Liquid Fe-Cr-alloys are being formed by the reduction ofoxides in spark-arc furnaces at T ª 1700 °C.

Reduction of the C-content to ª 0.01 weight-%.Reaction:

23 Cr + CO (g) Æ 1

3 Cr2O3 + C (4.7)

K = aCr2 O3

13

aCr23 PCO

(4.8)

This allows to calculate Pco for the equilibrium of an Fe-Cr-C-alloy with pure Cr2O3.Equilibrium constant:

log K = 12580 T- 1 - 9.10 (4.9)

aCr = 0.1 fi aC = 3 x 10-4 (for pure Cr2O3 and pCO = 1 atmat 2000 K).

II. Determination of Thermodynamic Data 3. Experimental ...

Documents

Transcript of II. Determination of Thermodynamic Data 3. Experimental ...