Systems, binary

A binary system consists of two components and is influenced by three variables temperature, pressure, and composition. When two components are mixed together and allowed to equilibrate, three outcomes are possible  

Mutual solubility and solid solution formation over the entire composition range, also known as complete solid solubility. 

Partial solid solubility without the formation of an intermediate phase 

Partial solid solubility with the formation of intermediate phases 

One objective of this section is to qualitatively describe the relationship between these various outcomes and the resulting phase diagrams. First, however, it is important to appreciate what is meant by a solid solution in a ceramic system and the types of solid solutions that occur — a topic that was dealt with indirectly and briefly in Chap. 6. The two main types of solid solutions, described below, are substitutional and interstitial. 

Binary Systems.—Very few of the published data on intermetallic phases are of direct interest to the inorganic chemist those abstracted, however, describe, in general, structural and thermodynamic properties of these systems. In an XPS study, the core levels and valence bands of, inter alia, FeaC and FcaSi and their components have been determined (20—1000 C). Shifts in the Fe (Spa/z), C (Is), and Si (2p) core levels (Table 23) confirm that migration of electrons occurs from Fe to C and from Si to Fe, rendering C negative but Si positive. 

The crystal structures of several binary intermetallics containing Group IV elements have been reported. Independent X-ray studies have shown that the true symmetry of RujOea is not tetragonal but orthorhombic they differ, however, in the assignment of the space group, and the description of the 

Poutcharovsky, K. Yvon, and E. Parthe, J. Less-Common Metals, 1975, 40, 139. 

Unit-cell parameters/A for Li 13814, Li7Sn2, Space and Li5Sn2  

In an analysis of an electron-diffraction study of short-range order in amorphous films of NisGes, the relative arrangement of the atoms in the films has been shown to differ from the co-ordination that is characteristic of the inter-metallic compound. 

A non-ideal binary mixture may exist as a single liquid phase at certain compositions, temperatures, and pressures, or as two liquid phases at other conditions. Also, depending on the conditions, a vapor phase may or may not exist at equilibrium with the liquid. When two immiscible liquid phases coexist at equilibrium, their compositions are different, but the component fugacities are equal in both phases. 

Equilibrium compositions of liquid phases at equilibrium are calculated by equating the component fugacities, similar to vapor-liquid equilibrium calculations, described in more detail in Chapter 2. The activity coefficients may be calculated by equations presented in Section 1.3.3, in particular the UNIQUAC and NRTL equations. The composition dependence of these equations is developed to the point where the same equation with the same constants can predict activity coefficients over wide ranges of composition, thus allowing it to predict two immiscible liquid phases at equilibrium. 

The liquids in the immiscible region boil at a constant temperature of about 

As long as two liquid phases coexist at equilibrium, the boiling point and the 

FIGURE 1.16 Temperature-composition for n-butanol-water (Example 1.12). 

IntegrationofEq. 13.9.1 for a binary system, fromxi = O.Otoxi = 1.0, gives (Prausnitz, 1969)  

Evaluation therefore of the thermodynamic consistency of binary vapor-liquid equilibrium data - at constant temperature (isothermal) or constant pressure (isobaric) conditions - requires knowledge of the values of the corresponding excess property as a function of composition. 

In the typical case such experimental information is not available, and the right-hand side of Eqs 13.9.2 and 13.9.3 is set equal to zero. 

While this is a reasonable assumption for Eq. 13.9.3, it may not always be so for Eq. 13.9.2, especially for very nonideal mixtures. For isobaric data, therefore, the semiempirical test proposed by Herington (1951) 

For isobaric data, the measure of their quality is the quantity CI-J) with J given by  

Compared to unary-phase diagrams, binary ones contain an additional composition variable. Flence, the C increases by 2 in the phase rule. If the system has only one phase, then the degree of freedom becomes 

Point A represents a single-phase region. In this region, both temperature and composition can be varied, and the system still does change its state of equilibrium. 

With two phases present, either temperature or composition needs to be specified to define the system in this area. That means the variance is one. 

Simple binary diagram showing the independence of the system on pressure. 

This value of variance is obtained from Equation 4.6. The maximum number of phases, when F = 0, is obtained from Equation 4.7. 

When we consider the phase relations in systems having two components instead of one, we add one dimension to our diagrams. That is, in unary diagrams all phases have the same composition, and so we don t need an axis showing compositions - we can use both dimensions available on a sheet of paper for physical parameters, and we choose T and P. With two 

An uneducated guess as to the melting temperatures of mixtures of minerals A and B. 

This shows that the maximum number of phases that can coexist at equilibrium in a binary system at an arbitrarily chosen pressure (or temperature) is three (/ = 3 for c = 2, / = 0), which is consistent with our observations. 

This means that to fix all the properties of both kinds of crystals, we need only choose the temperature (pressure being already fixed at 1 bar). However, when the first drop of liquid forms, p = 3 (diopside crystals, anorthite crystals, and liquid), and / = 0. Another word for / = 0 is invariant. When p = 3 on an isobaric plane, we have no choice as to T, P, or the compositions of the phases -they are all fixed. This explains why all mixtures begin to melt at the same temperature, and why the liquid formed is always the same composition no matter what the proportions of the two kinds of crystals. No other arrangement would satisfy the phase rule. 

By imagining tie-lines across the An+L region at successively higher temperatures, we see that the composition of the liquid in equilibrium with anorthite 

Intermetallic Phases.—Binary Systems. Although a vast number of papers describing the results of research into intermetallic phases are published annually, all but a few are of little direct interest to the inorganic chemist. The structural properties of a number of binary intermetallics including a 

Group IV element have been investigated the phases described will 

The crystal structures of PtSi and PtGe have been determined the compounds are isostructural with MnP, space group Pbnm, PtSi having the slightly smaller unit cell (Table 42). The i.r. spectra of the Si and Gef  

A-i) so far known were obtained. The crystal structure of the defect silicide MnSi ( = 0.25—0.30) has been determined and its stoicheiometry defined as Mn2,Si47. New LnSng compounds of face-centred cubic structure (AuCug type) have been prepared for Tb, Dy, Ho, Er, and Y (Table 43) under high pressures (85 kbar) and temperatures (1400 °C) analogous compounds have not been observed in the Lu-Sn and Sc-Sn systems. The magnetic susceptibility and electrical resistivity of the compound EuSng have been determined as a function of temperature (10—300 K). The 

The presence of an ordered structure in the solid solution Fe-18 atom % Ge has been confirmed by electron microdilfraction and Mossbauer spectroscopy. The short-range order in the Ag-Si liquid eutectic alloy has been investigated by -ray diffraction techniques at 840, 850, 870, and 890 The experimental data were found to be consistent with atomic radial-distribution curves calculated on the assumption of a completely random distribution of atoms of different kinds in the liquid. 

2 refers to pressures reaching up to several hundred atmospheres and shows the critical point (C) above which liquid and vapour cannot be distinguished. Finally, fig. 

At very high pressures we see that various polymorphic forms of ice can exist. Any two of these are separated by a line along which they can coexist, while there are 

Phase diagram of water at very high pressures.  

For the moment we shall consider a system of two components A and B which do not form a solid solution. The pressure applied to the system is always assumed to be greater than the vapour pressure of the liquid mixture. The only phases which can be present are therefore the liquid solution A + B, the sofid A and the solid B. We also assume that A and B do not react with one another chemically. 

Consider first the two phase system, solution + solid. Here we have c —2, (f = 2, r =0 so that the phase rule gives w = 2, i.e. the system is divariant. We can therefore fix two of the intensive variables arbitrarily, for example the mole fraction in the solution and the pressure p. The temperature at which equilibrium is established is then a function of these two variables. For many purposes we may consider systems at constant pressure (for example atmospheric pressure). The equilibrium diagram can then be represented in two dimensions as in fig. 13.4 in which CE gives the equilibrium temperature T between solution and solid A as a function of the concentration of the solution Similarly DE corresponds to equilibrium between the solution P. W. Bridgman, J. Chem. Phys., 5, 964 (1937). 

If the critical temperature of the solute is below room temperature, the phase diagram is similar to the one described for the system hydroquinone-argon. No temperature can then be indicated above which hydrates cannot exist. This situation arises for the following solutes argon,48 krypton,48 xenon,48 methane,3 and ethylene.10 

In most cases the critical temperature of the solute is above room temperature. As can be seen in the binary system H2S-H20 drawn in Fig. 6, the three-phase line HL2G is then intersected by the three-phase line HL G. The point of intersection represents the four-phase equilibrium HLXL2G and indicates the temperature 

The composition of the hydrates varies with temperature along the three-phase lines H ice G and HL2G in a way similar to that described for the system hydroquinone-argon. But as already noted in Section II.D this variation is smaller than for the hydroquinone clathrates. Accordingly, a cross section through the P-T-x diagram at constant temperature below 0°C would reveal a two-phase area G+H in which the composition of the latter is less sensitive to pressure than found in the corresponding case for the hydroquinone clathrates (cf. Fig. 4). 

Using this method Miss Mulders19 derived a composition 

02 at temperatures above 700 °C to form y-Ca2Si04, which transforms to a -Ca2Si04 at 1000 °C. With N2, the reaction products again depend on temperature below 900 °C, Ca4SiN4 is obtained by reaction (78), whereas between 900 and 1200 °C pure CaSiN2 is formed [reaction (79)]. 

A new modification of SrSi and the new compound SrGe0 76 have been prepared and their structures determined.765 The two intermetallics are isostructural, crystallizing with orthorhombic symmetry their unit-cell parameters are included in Table 21. A fascinating facet of these structures 

5 positions by four additional Si (or Ge) atoms. In SrGe076, there are defects in the 1, 2, 4, 5 positions, whereas in SrSi no indications of such defects could be found. The geometrical parameters of these units are summarized in the diagrams.765 

The electrical conductivity of single crystals of Mn Shv has been determined parallel to and perpendicular to the c-axis 770 anisotropic behaviour was observed, particularly at low temperatures. Mn27Si47 was found to be a 

An Auger examination of a series of solid and liquid Pb-In solutions has shown that the relative intensity ratio of the Pb and In peaks is a sensitive indicator of changes in surface composition with respect to temperature and bulk composition.772 The surface layers were richer in Pb than the bulk this excess Pb concentration was decreased by the presence of oxygen but increased by carbon. 

Advances in Chemistry American Chemical Society Washington, DC, 1973. 

Some examples of miscibility can be highlighted. For example, thermosetting polymer blends composed of bisphenol A-based benzoxazine (BA-a) and cyanate 

F re 12.S Miscibility of polymer blends by examination of the glass-rubber relaxation temperature. Hollow and full symbols differentiate initial (individual polymers) and final (polymer blend) situations. 

During recent years, polymer blends derived from renewable resources [55] have attracted much scientific, technological and commercial interest, due to the provision of green replacements for the commonly used petroleum-based polymeric materials. In this sense, when the compatibilization of melt-mixed 

The total change in the Gibbs energy resulting from the formation of polymer solutions is, according to (1), subdivided into two parts, the first two terms representing the so-called combinatorial behavior, ascribed to entropy changes  

All particularities of a certain real system (except for the chain length of the polymer) are incorporated into the third term, the residual Gibbs energy of mixing, and were initially considered to be of enthalpic origin. The essential parameter of this part is g, the integral Flory Huggins interaction parameter  

The Flory Huggins interaction parameter constitutes a measure for chemical potential of the solvent, as documented by (6) and (5) it is defined in terms of the deviation from combinatorial behavior as  

For practical purposes, the use of volume fractions (instead of the original segment firactions) as composition variable is not straightforward because of the necessity to know the densities of the components and (in the case of variable temperature) their thermal expansivities. For that reason, (/ is sometimes consistently replaced by the weight fraction w, and N calculated from the molar masses as MpIMi. The X values obtained in this manner according to (8)  

One of the consequences of composition-dependent interaction parameters lies in the necessity to distinguish between different parameters, depending on the particular method by which they are determined. The Flory Huggins interaction parameter % relates to the integral interaction parameter g as  

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Literature references for vapor-liquid equilibria, enthalpies of mixing and volume change for binary systems. 

Timmermans, J. "The Physico-Chemical Constants of Binary Systems in Concentrated Solutions," Vol. 1-4, Interscience, New York, 1959-60. 

Figure 3-2. Second virial coefficients for two binary systems.

Figures 3 and 4 show fugacity coefficients for two binary systems calculated with Equation (10b). Although the pressure is not large, deviations from ideality and from the Lewis rule are not negligible.

Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

Figure 4-4. Representation of vapor-liquid equilibria for a binary system showing moderate positive deviations from Raoult s law.

An adequate prediction of multicomponent vapor-liquid equilibria requires an accurate description of the phase equilibria for the binary systems. We have reduced a large body of binary data including a variety of systems containing, for example, alcohols, ethers, ketones, organic acids, water, and hydrocarbons with the UNIQUAC equation. Experience has shown it to do as well as any of the other common models. V7hen all types of mixtures are considered, including partially miscible systems, the... 

Figure 4-7. Vapor-liquid equilibria and activity coefficients in a binary system showing a weak minimum in the activity coefficient of methanol.

Equations (4) and (5) are not limited to binary systems they are applicable to systems containing any number of components. ... 

Figure 4-8. Vapor-liquid equilibria for a binary system where both components solvate and associate strongly in the vapor phase.

To illustrate calculations for a binary system containing a supercritical, condensable component. Figure 12 shows isobaric equilibria for ethane-n-heptane. Using the virial equation for vapor-phase fugacity coefficients, and the UNIQUAC equation for liquid-phase activity coefficients, calculated results give an excellent representation of the data of Kay (1938). In this case,the total pressure is not large and therefore, the mixture is at all times remote from critical conditions. For this binary system, the particular method of calculation used here would not be successful at appreciably higher pressures. 

The continuous line in Figure 16 shows results from fitting a single tie line in addition to the binary data. Only slight improvement is obtained in prediction of the two-phase region more important, however, prediction of solute distribution is improved. Incorporation of the single ternary tie line into the method of data reduction produces only a small loss of accuracy in the representation of VLE for the two binary systems. 

Using the ternary tie-line data and the binary VLE data for the miscible binary pairs, the optimum binary parameters are obtained for each ternary of the type 1-2-i for i = 3. .. m. This results in multiple sets of the parameters for the 1-2 binary, since this binary occurs in each of the ternaries containing two liquid phases. To determine a single set of parameters to represent the 1-2 binary system, the values obtained from initial data reduction of each of the ternary systems are plotted with their approximate confidence ellipses. We choose a single optimum set from the intersection of the confidence ellipses. Finally, with the parameters for the 1-2 binary set at their optimum value, the parameters are adjusted for the remaining miscible binary in each ternary, i.e. the parameters for the 2-i binary system in each ternary of the type 1-2-i for i = 3. .. m. This adjustment is made, again, using the ternary tie-line data and binary VLE data. 

To illustrate the enthalpy calculations outlined above, Figures 1, 2, and 3 present calculated enthalpies for three binary systems. 

Appendix C-6 gives parameters for all the condensable binary systems we have here investigated literature references are also given for experimental data. Parameters given are for each set of data analyzed they often reflect in temperature (or pressure) range, number of data points, and experimental accuracy. Best calculated results are usually obtained when the parameters are obtained from experimental data at conditions of temperature, pressure, and composition close to those where the calculations are performed. However, sometimes, if the experimental data at these conditions are of low quality, better calculated results may be obtained with parameters obtained from good experimental data measured at other conditions. 

UNIQUAC Parameters for Condensable Binary Systems and Data References... 

Data Sources for Binary Systems with a Condensable Component and a Noncondensable Component... 

IF BINARY SYSTEM CONTAINS NO ORGANIC ACIDS. THE SECOND VIRTAL coefficients ARE USED IN A VOLUME EXPLICIT EQUATION OF STATE TO CALCULATE THE FUGACITY COEFFICIENTS. FOR ORGANIC ACIDS FUGACITY COEFFICIENTS ARE PREDICTED FROM THE CHEMICAL THEORY FOR NQN-IOEALITY WITH EQUILIBRIUM CONSTANTS OBTAINED from METASTABLE. BOUND. ANO CHEMICAL CONTRIBUTIONS TO THE SECOND VIRIAL COEFFICIENTS. 

Usually it is not easy to predict the viscosity of a mixture of viscous components. Certain binary systems, such as methanol and water, have viscosities much greater than either compound. 

The constants k- enable the improved representation of binary equilibria and should be carefully determined starting from experimental results. The API Technical Data Book has published the values of constants k j for a number of binary systems. The use of these binary interaction coefficients is necessary for obtaining accurate calculation results for mixtures containing light components such as ... 

The use of k j is equally necessary for binary systems where the relative volatility is needed with an error of better than 10%. 

In practice, the reference base is usually taken not as a-methylnaphthalene but as heptamethyinonane (HMN), a branched isomer of n-cetane. The HMN has a cetane number of 15. In a binary system containing Y% of n-cetane, the cetane number CN vyOl be, by definition (./ - V ... 

The principal point of interest to be discussed in this section is the manner in which the surface tension of a binary system varies with composition. The effects of other variables such as pressure and temperature are similar to those for pure substances, and the more elaborate treatment for two-component systems is not considered here. Also, the case of immiscible liquids is taken up in Section IV-2. 

Classic nucleation theory must be modified for nucleation near a critical point. Observed supercooling and superheating far exceeds that predicted by conventional theory and McGraw and Reiss [36] pointed out that if a usually neglected excluded volume term is retained the free energy of the critical nucleus increases considerably. As noted by Derjaguin [37], a similar problem occurs in the theory of cavitation. In binary systems the composition of the nuclei will differ from that of the bulk... 

As mentioned in Section IX-2A, binary systems are more complicated since the composition of the nuclei differ from that of the bulk. In the case of sulfuric acid and water vapor mixtures only some 10 ° molecules of sulfuric acid are needed for water oplet nucleation that may occur at less than 100% relative humidity [38]. A rather different effect is that of passivation of water nuclei by long-chain alcohols [66] (which would inhibit condensation note Section IV-6). A recent theoretical treatment by Bar-Ziv and Safran [67] of the effect of surface active monolayers, such as alcohols, on surface nucleation of ice shows the link between the inhibition of subcooling (enhanced nucleation) and the strength of the interaction between the monolayer and water. 

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

Some binary systems show a minimum at a lower eritieal-sohition temperature a few systems show elosed-loop two-phase regions with a maximum and a minimum.) As the temperature is inereased at any eomposition other than the eritieal eomposition v = the eompositions of the two eoexisting phases adjust themselves to keep the total mole fraetion unehanged until the eoexistenee eurve is reaehed, above whieh only one phase... 

Sigaud G, Flardouin F and Aohard M F 1979 A possible polar smeotio A-non-polar smeotio A transition line in a binary system Phys.Lett. A 72 24... 

In general, tests have tended to concentrate attention on the ability of a flux model to interpolate through the intermediate pressure range between Knudsen diffusion control and bulk diffusion control. What is also important, but seldom known at present, is whether a model predicts a composition dependence consistent with experiment for the matrix elements in equation (10.2). In multicomponent mixtures an enormous amount of experimental work would be needed to investigate this thoroughly, but it should be possible to supplement a systematic investigation of a flux model applied to binary systems with some limited experiments on particular multicomponent mixtures, as in the work of Hesse and Koder, and Remick and Geankoplia. Interpretation of such tests would be simplest and most direct if they were to be carried out with only small differences in composition between the two sides of the porous medium. Diffusion would then occur in a system of essentially uniform composition, so that flux measurements would provide values for the matrix elements in (10.2) at well-defined compositions. 

A large number of thermodynamic studies of binary systems were undertaken to find and determine eventual intermolecular associations for thiazole Meyer et al. (303, 304) discovered eutectic mixtures for the following systems -thiazole/cyclohexane at -38.4°C, Wt = 0.815 -thiazole/carbon tetrachloride at -60.8°C, Mt = 0.46 -thiazole/benzene at -48.5°C, nr = 0.70. 

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