Thermodynamic Measurements of Alloys and Compounds by Double Knudsen Cell Mass Spectrometry and Their Application to Materials Processing

Abstract

For the development and optimization of materials processing a collection of thermodynamic information concerning substances that participate in the reactions is important. One fundamental way to obtain such information is to measure the vapor pressure of gas species under conditions where they are in equilibrium with the condensed phases. Over the past 60 years Knudsen cell mass spectrometry has been used to identify and quantitatively determine gas species at high temperatures. This article describes thermodynamic foundation and examples of measurements in order to demonstrate the use of mass spectrometry focusing on the field of process metallurgy and recycling processes.

INTRODUCTION

A Knudsen effusion cell and a mass spectrometer have been used to measure vapor pressure, which plays an important role in evaluating the stability of a substance and discussing the mechanism of reactions. In contrast to preceding articles, where mass spectrometric measurements made at high temperatures are reviewed,^1–3) this paper focuses on their relationship to materials processing. Two examples of processes, steel production and non-ferrous metallurgy, are first discussed, and a thermodynamic interpretation of the reactions is then linked with mass spectrometry in order to review its applications in the area of process development. Successive research by the authors’ group is introduced, with practical examples of such measurements.

EXAMPLES OF MATERIAL PROCESSING

Most of the metal elements found in nature are a mixture of compounds, such as oxides, sulfides and chlorides. Among the variety of processes for production of metals⁴⁾ the following represents a typical case. Ore is processed to concentrate the target compounds, which are then smelted to obtain crude metals. Impurities in the metals are then removed in refining processes, resulting in the production of pure metals.

In one example, iron ore (Hematite: Fe₂O₃) is reduced with coke in a blast furnace. The carbon monoxide formed from coke reacts with Fe₂O₃, which is temporarily converted to magnetite (Fe₃O₄).⁵⁾   

(1)

The magnetite is then reduced at higher temperature in the furnace and converted into wüstite (Fe_1−xO) and eventually iron (Fe). The product is “pig iron,” which contains numerous impurities, including carbon (about 4%), sulfur (0.02%) and phosphorus (0.1%).⁶⁾ Sulfur and a part of the phosphorus are removed from pig iron by a “hot metal pretreatment,” after which the carbon and phosphorus content is lowered by blowing oxygen through the molten pig iron in a converter (i.e., a basic oxygen furnace, BOF). Carbon contents as low as 0.03% and as high as 1% are made in a BOF.⁶⁾ The obtained steel might be further processed (e.g., via the Ruhrstahl Heraeus (RH) degassing process) before casting.

In another example, copper is obtained from its ore (Chalcopyrite; CuFeS₂) by the following technique. The copper concentrate (mainly CuFeS₂) is partially oxidized in a flash smelter, where the iron forms slag with added SiO₂.   

(2)

The sulfide produced by the smelting process is called “matte.” It is treated in the molten state by blowing with oxygen-rich air, and converted into copper (98–99%).   

(3)

Impurities in the crude copper are removed by electrolysis, where copper and less noble impurities dissolve at the anode while pure copper (99.99%) becomes plated on the cathode.

SEPARATION AND REFINEMENT TECHNIQUES CONSIDERED FROM THE VIEWPOINT OF THERMODYNAMICS

The standard Gibbs free energy of formation

Carbon and phosphorus are removed in the BOF converter. Figure 1 shows a schematic illustration of dephosphorization by blowing O₂ through molten pig iron into which lime (CaO), iron oxide (FeO), etc. have been injected. Phosphorus in the iron is oxidized and forms CaO–P₂O₅ slag. To estimate the phosphorus content realized by the reaction and determine suitable processing conditions, thermodynamic information regarding the system (i.e., an equilibrium state which might eventually be achieved) is needed. As the phase diagram in Fig. 2 shows, CaO is converted into (CaO)₄P₂O₅ via reaction with oxidized phosphorus.⁷⁾ Therefore the chemical equilibrium between CaO and (CaO)₄P₂O₅, which is expressed by Eq. (4) needs to be considered.   

(4)

Fig. 1. Schematic illustration of dephosphorization.

Fig. 2. CaO–P₂O₅ Pseudo-binary phase diagram.⁷⁾

In an equilibrium state, the change in Gibbs energy (∆G) is 0 (i.e., the Gibbs energy of formation (∆G_f) of a species on the left side equals that of the right side in Eq. (4)). The standard Gibbs energy of formation, ΔG°_f, is defined as the change in Gibbs energy that accompanies the formation of 1 mol of the substance from its constituent elements in their standard states (the most stable state at standard pressure, conventionally 1 atm or 1 bar). For example, the ΔG°_f of CaO is defined as the change in Gibbs energy in Reaction (5).   

(5)

The standard Gibbs energy of formation has been reported for a number of substances.^8,9)

In contrast to solid and liquid phases, the Gibbs energy of gaseous species is strongly dependent on partial pressure. The Gibbs energy of a perfect gas of 1 molar at pressure p is related to its standard value G° by   

(6)

Here, R and T are the gas constant and temperature, respectively. A standard state of gaseous species is often defined as p°=1 atm or 1 bar, as in Eq. (5).

This means that the ∆G_f for P₂ and O₂, is determined by RT ln p/p° because ΔG°_f is 0 for pure and stable gases at standard pressure. On the other hand, if CaO and (CaO)₄P₂O₅ are assumed to be stoichiometric, ∆G_f equals ΔG°_f. According to the above definition, the ∆G for Reaction (4) is expressed as follows.   

(7)

In the equilibrium state (ΔG=0), ΔG°_f of (CaO)₄P₂O₅ is expressed by the vapor pressures of P₂ and O₂ as follows.   

(8)

If (CaO)₄P₂O₅ is highly stable (i.e., the ΔG°_f,(CaO)4P2O5 is highly negative), the equilibrium vapor pressure of P₂ is low, and thus P in a hot metal can be removed to a low level by CaO. Equation (8) also indicates that a higher oxygen pressure results in a lower P level when (CaO)₄P₂O₅ and CaO are in equilibrium.

Vapor pressure measurements of P₂ and O₂ above a mixture of (CaO)₄P₂O₅ and CaO give the value of ΔG°_f of (CaO)₄P₂O₅, provided that ΔG°_f of CaO is known. The measurements will be shown below as an experimental example.

Activities of elements in a solution

To discuss the dephosphorization that occurs as the result of a hot metal pretreatment (Fig. 1), not only information about Reaction (4) but the equilibrium between P₂ and molten iron also needs to be considered.   

(9)

Contrary to a stoichiometric compound (CaO)₄P₂O₅, the P content in the molten iron varies depending on the P₂ vapor pressure. Therefore, the activity of the solute, a, needs to be taken into account for the consideration of its partial molar Gibbs energy (i.e., chemical potential, μ). Similar to a species in the vapor state, the activity of the dissolved element is defined by a ratio of its partial pressure relative to that of the standard state.   

(10)

The chemical potential of i is expressed by Eq. (11) using its value for the standard state, μ°.   

(11)

The standard state of a dissolved element is often defined as 1 wt%, and relationships between the solute concentration and its vapor pressure have been examined. The dissolution of P in Fe has been studied by various methods including vapor pressure measurements.^10–13)

In contrast to the above instance of dilute solutions, when reactions between condensed phases are considered (e.g., alloy formation or the phase separation of multiple metals), information regarding the entire composition of the system is needed. As an example, a schematic phase diagram for an A–B eutectic system is given in Fig. 3, showing an A-based region (α), a B-based region (β) and a liquid phase depending on temperature and composition. Figure 3(b) schematically illustrates the activities of A and B at T₁, which are defined by Eq. (10) with a reference state defined as pure A and B, respectively. The α (x_B=x₁) and β (x_B=x₂) phases coexist because the chemical potentials of the constituent elements must be equal between the phases at equilibria.

Fig. 3. Schematic illustrations of (a) A–B binary phase diagram and (b) activity curves.

APPLICATIONS OF KNUDSEN CELL MASS SPECTROMETRY TO THERMODYNAMIC MEASUREMENTS

A Knudsen cell is a container with an effusion hole (orifice), and is employed in measurements of the equilibrium vapor pressures of substances^14,15) (Fig. 4(a)). The substance to be measured is contained in the cell and placed in a vacuum as illustrated in Fig. 4(b). When the mean free path of the vapor species is more than 10 fold that of the orifice, the rate of effusion from the orifice into the vacuum equals the rate at which the molecules strike an isometric wall. Therefore, if an evaporating species is known, the weight change of the cell, including the sample, or the deposition of the evaporated species collected on an outer target indicates the value of p. The relationship between the vapor pressure (p) and weight change (∆m) due to effusion over a certain time (∆t) is expressed by Eq. (12), where A is the area of the orifice and M is the molecular weight of the species.   

(12)

If the evaporating species is unidentified, Eq. (12) cannot be used to obtain the vapor pressure. Knudsen cell mass spectrometry was therefore developed to identify such vapor species.¹⁶⁾ Effusions of a vapor species from a Knudsen cell are detected by a mass spectrometer in the form of a separate ion current according to its mass-to-charge ratio. The vapor pressure of species i, p_i, is expressed by Eq. (13), where I_i is the ion current resulting from the detection of i.   

(13)

Here S_i is a coefficient which depends on the ionization cross section, the sensitivity of the detector, and so on. Because S_i is not typically a constant, it is generally difficult to determine the vapor pressure from the observed current. Belton and Fruehan^17–21) and other groups^22–28) used the Knudsen cell mass spectrometer to conduct activity measurements on binary alloy systems, by applying the Gibbs–Duhem equation (Eq. (14)).   

(14)

where x_A and x_B are the mole fractions of the two constituent metals of the binary alloy and their activities are a_A and a_B, respectively. Equation (15), which is derived from Eq. (14), means that the ratio of two ion currents provides information on activity by disposing of the influence from the uncertainty of S_i.   

(15)

In an attempt to obtain easier measurements, a double Knudsen cell mass spectrometer was developed^29–31) (Fig. 5). As explained below in detail, more than one cell is used in this technique and vapors from the cell are detected under identical conditions. Because S_i and T for the cells are the same, the vapor pressure of a sample can be calculated from that of a reference substance (p_i,Ref) and the ratio of ion currents (Eq. (16)). The direct comparison of ion currents is advantageous in terms of activity measurements, which is defined as a ratio of vapor pressures (Eq. (10)).   

(16)

Fig. 4. Outline of a Knudsen cell.

Fig. 5. Double Knudsen cell mass spectrometer used in this study.

PRACTICAL EXAMPLES

Apparatus

The double Knudsen cell mass spectrometer used by the authors’ group is shown^32–45) in Fig. 5. It accommodates four cells in the chamber, and each sample can be measured in turn by rotating the cell holder. The dimensions of each cell were 10 mm o.d., 8 mm i.d., and a height of 20 mm, and the lid contains an orifice with a diameter of 0.4–1 mm. After the cells are placed in the chamber, it is evacuated by a rotary pump and turbo molecular pump to a pressure of 10⁻³ Pa. The cells are heated by means of a tantalum electric resistance heating element, and the temperatures are monitored by three thermocouples (Pt/13%Rh–Pt) placed in holes drilled at the bottom of the cell holder. Species that are evaporating from the cells are monitored as separate ion currents according to their mass-to-charge ratio (m/z) by a quadrupole mass spectrometer (QMS, Inficon, Transpector TH200), which was located on the top of the chamber. The emission current of the filament and ionization potential of the QMS were 2000 μA and 1.634×10⁻¹⁷ J (102 eV), respectively.

Experimental examples are shown below.

Thermodynamic measurement of calcium phosphates

This section describes an earlier study on the equilibrium of Eq. (4) by our group.³⁹⁾ Figure 6(a) shows the configuration of the cells. The molybdenum Knudsen cells had an orifice with a diameter of 0.4 mm. As shown in Eq. (8), a vapor pressure measurement on a mixture of CaO and (CaO)₄P₂O₅ gives the standard Gibbs energy (∆G°) for Reaction (4). It should be noted that the vapor pressure of O₂ from the mixture can change depending on that of P₂. In this study, the vapor pressure of P₂ was fixed by adding a Cu–P alloy with a known composition.

Fig. 6. (a) Configuration of cells for measurements of a mixture of CaO and (CaO)₄P₂O₅. (b) Ion currents observed from the cells at 1623 K. Results at other temperatures are shown elsewhere.³⁹⁾

The reference substance was Cr–Cr₃P–Cr₂O₃ placed in an Al₂O₃ crucible. Vapor pressures of gaseous species can be calculated from thermodynamic data for Cr₂O₃ and Cr₃P, of which thermodynamic property was preliminarily examined.³⁶⁾

The observed ion currents at 1623 K are shown in Fig. 6(b). Ion currents with m/z=47 and 62 (I₄₇ and I₆₂) were from the samples, indicating the presence of PO(g) and P₂(g). The evaporation of Cr and Cu was also observed as reported. Other gas species (O₂ and PO₂(g)) were difficult to detect, due to their low vapor pressures, and thus, the ∆G° for Reaction (4) was calculated using I₄₇, I₆₂ and thermodynamic data for the following reaction.   

(17)

The standard Gibbs energy of Reaction (4) was calculated to be   

(18)

The result was in good agreement with previous studies using chemical equilibration techniques,^46,47) confirming the utility of the double Knudsen cell mass spectrometry for use in conjunction with oxide systems.

Non-ferrous alloy: Cu–Ni solid solution

As indicated by Eq. (15), when vapors of two components are detectable as ion currents, the activities in a binary alloy system can be determined by applying the Gibbs–Duhem equation without using a value of S_i. Alternatively, the double Knudsen cell mass spectrometer allows the determination of activity by comparing its ion current between the alloy and a reference substance. We have, in past studies, applied the technique to various systems, including iron–zinc³³⁾ and rare earth alloys.^{37,40,42,44,45)}

For example, activity measurements on copper–nickel (Cu–Ni) alloys are demonstrated here. Cu and Ni show a complete solid solubility at high temperatures as shown by the phase diagram⁴⁸⁾ in Fig. 7(a). Cu–Ni samples with molar fractions of Cu, x_Cu, ranging from 0.1 to 0.9 at intervals of 0.1 were prepared. 0.2 g of the alloy sample and pure Cu were placed in Al₂O₃ inner crucibles, which were contained in Mo Knudsen cells having an orifice with a diameter of 1 mm (Fig. 7(b)). Because the evaporation of Ni from the samples was not clearly observable due to its low vapor pressure, only Cu was monitored by measuring ion currents of each sample for a period of 10 min in the range of m/z from 63 to 65 between 5 min background measurements.

Fig. 7. (a) Cu–Ni binary phase diagram. (b) Configuration of cells. (c) Ion currents observed on samples at 1373 K. (d) Obtained Cu activity compared with another study.⁴⁹⁾

The ion currents from the Cu–Ni samples (x_Cu=0.7 and 0.9) and pure Cu at 1373 K are shown in Fig. 7(c). Currents with m/z=63 and 65 were clearly observed, indicating the presence of both ⁶³Cu and ⁶⁵Cu. The activity of Cu in the alloys was calculated using Eqs. (10) and (16), where the averaged ion currents (I₆₃ and I₆₅) were used after subtracting the background currents. The results are shown in Fig. 7(d), where the reference state of a_Cu is pure, solid Cu. Compared to activities determined by other techniques such as electromotive force measurements,⁴⁹⁾ the results obtained in this study were in good agreement especially at high x_Cu.

As described above, Cu is produced from ore through smelting and successive electrorefining. In the recycling of metals from waste materials such as electronic scrap, however, the conventional processes cannot be directly applied because of the various elements that are present, unlike ore. Therefore, to consider effective treatments for their separation, it is important to have information regarding the behaviors of the impurities in each refining process (e.g. microstructure formation during solidification after smelting and elemental distribution).

Thermodynamic investigations on well-known binary alloys such as Cu–Ni have been performed by many researchers. More complex compounds also have been studied if they are practically important. The data are organized and software has been developed to permit easier equilibrium computation. However, for the development of a recycling process for recovering valuable metals from waste materials, a wider variety of alloys should be studied in the future. Knudsen cell mass spectrometry, which enables the direct detection of vaporized species, is applicable for vapor pressure measurements of multi-component systems.

CONCLUSION

Making effective use of metals and energy resources is becoming increasingly important, while, concurrently, a reduction in environmental load and cost is essential in the development of materials processing. A wide variety of elements are involved in recycling processes, which demand that multi-component systems be given careful consideration. Because thermodynamic information helps us to develop and optimize processes, activity measurements with a mass spectrometer promise to play an even important role in the future.

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