System two-component

The three two-component systems Al203-Si02, Mg0-Si02 and Ca0-Si02 described in this section are of importance for several high-refractory and cement mineral compositions with high-temperature stability. 

Phase Diagram Despite the wide occurrence of mullite in refractories and fine ceramics such as porcelain, and copious research having been carried out in this system, there remains considerable debate regarding the nature of the binary 

Mg3[Si4 (0H)2 Oio] 3 MgSiOj -t SiOj -I- HjO, thus avoiding the transformation of protoenstatite to clinoenstatite. 

Two compment systems. Let us now consider systems of two component substances which can react with one another. The reaction may consist of the formation of solutions, or of one or more chemical compounds. By solutions we mean phases which contain both components, and which remain homogeneous when their percentage composition is varied continuously within certain limits. As each component of the system and each compound of the components can exist in at least three modifications, it would at first sight appear possible for a great number of such phases to exist in equilibrium with one another. We shall see, however, that the number of phases which can exist in contact with one another is limited in various ways. 

In certain cases different solids form homogeneous phases with one another, so-called sohd solutions. This also has the effect of reducing the number of phases which can exist in equihbrium with one another. 

Apart from these considerations, the number of phases is limited in a quantitative manner by thermodynamics. If we assume, in the first instance, that the two component substances form only two phases with one another, we have for these two phases two equations of condition of the form 

The six variables p, T, c, Ca, c, Cg, are therefore connected by four equations, so that only two of them can be chosen at will. The system has therefore two degrees of freedom. 

We arrive at the same conclusion if we assume that one of the two components is present in one phase only, as is often the case in practice, for example in the equilibrium, salt solution — water vapour. Here the concentration of the salt in the gaseous phase is practically zero. Thus the variable Cg disappears, but so also does equation (4), as the only process consistent with the nature of the system is the transfer of one component (water) from the one phase to the other. Here again there are 5 — 3 = 2 degrees of freedom. 

From Equation (13.9), it follows that the number of degrees of freedom for a two-component system 

In a reduced-phase diagram for a two-component system, T = 2 for a single phase and an area is the appropriate representation. F = 1 for two phases in equilibrium, and a curve that relates the two variables is the appropriate representation. As the composition of the two phases generally is different, two conjugate curves are required. 

Although the phase mle is concerned with the number of relationships among system variables that are represented by the equilibrium curves, it provides no information about the nature of those relationships. We will consider the dependence of the chemical potential on the system variables for various systems in later chapters. 

The KB theory, as well as its inversion, has been used mainly for two-component systems. The KB results for a two-component system may be obtained from the 

With this notation we can express all the thermodynamic quantities paj , Va, and Kt in terms of the Kirkwood-Buff integrals, Gap  

In equations (4.48)-(4.51), we have completed the process of expressing the thermodynamic quantities in terms of the molecular quantities. We now examine a few limiting cases. In the limit pB — 0, we have 

This is just the compressibility equation for a one-component system ((AiA and pA are the limiting values of Gaa and pA as pB — 0, respectively). Similarly, from (4.49) and (4.50) we obtain, in this limit, 

for the component A, we simply get the molar (or molecular) volume of pure A, whereas for component B, we get the partial molar volume at infinite dilution. 

For a binary A-B alloy, another independent parameter, Xb (or = 1 — Xg) must be added to the fixed-stoichiometry order parameters in the preceding section. The phenomenological form of the Landau expansion, Eq. 17.2, can be extended to include Xb and has been used to catalog the conditions for many transitions in two-component systems [3]. 

Decomposition and Order-Disorder Transformations on a B.C.C. Lattice.1 Suppose that two species, A and B, occupy a b.c.c. lattice. If unlike bonds have lower molar enthalpies than like bonds [i.e., Bab Haa + Bbb)], then at low temperatures, ordered structures result in which the nearest-neighbors of A atoms are 

Considering Fig. 17.4, the development of the B2 structure creates two sublattices from the original A2 structure. One of the B2 sublattices consists of the b.c.c. unit-cell centers (indicated by /3 in Fig. 17.4) are displaced from the b.c.c. corners (a in Fig. 17.4) by a/2(lll). An ordering transformation produces sublattices, a and /3, with differing site fractions, xB and Xg. Their difference becomes a structural order parameter  

77 evolves from zero toward equilibrium finite values 7eq. Symmetric stable values exist because the b.c.c. corner sites are equivalent to the b.c.c. center sites—any result must be invariant to exchange of a with /3 sublattices. Compositions on the two sublattices must be coupled to the local average composition, 

2The molar enthalpy and the molar internal energy of bonding, Hab and Uab, are related to the bond energies Eab at constant pressure and at constant volume, respectively. 

The three variables that can affect the phase equilibria of a binary system are temperature, pressure and concentration. The behaviour of such a system should, therefore, be represented by a space model with three mutually perpendicular axes of pressure, temperature and concentration. Alternatively, three diagrams with pressure-temperature, pressure-concentration and temperature-concentration axes, respectively, can be employed. However, in most crystallization processes the main interest lies in the liquid and solid phases of a system a knowledge of the behaviour of the vapour phase is only required 

Four different types of two-component system will now be considered. Detailed attention is paid to the first type solely to illustrate the information that can be deduced from a phase diagram. It will be noted that the concentration of a solution on a phase diagram is normally given as a mass fraction or mass percentage and not as mass of solute per unit mass of solvent , as recommended for the solubility diagram (section 3.3). Mole fractions and mole percentages are also suitable concentration units for use in phase diagrams. 

If a solution represented by point x is cooled, pure solid benzene is deposited when the temperature of the solution reaches point X on curve AB. As solid benzene separates out, the solution becomes more concentrated in naphthalene and the equilibrium temperature of the system falls, following curve AB. If a solution represented by point y is cooled, pure solid naphthalene is deposited when the temperature reaches point Y on the solubility curve the solution becomes more concentrated in benzene and the equilibrium temperature follows curve CB. Point B, common to both curves, is the eutectic point (—3.5°C and 0.189 mass fraction of naphthalene), and this is the lowest freezing point in the whole system. At this point a completely solidified mixture of benzene and naphthalene of fixed composition is formed it is important to note that the eutectic is a physical mixture, not a chemical compound. Below the eutectic temperature all mixtures are solid. 

If the solution y is cooled below the temperature represented by point Y on curve BC to some temperature represented by point z, the composition of the system as a whole remains unchanged. The physical state of the system has been altered, however it now consists of a solution of benzene and naphthalene containing solid naphthalene. The composition of the solution, or mother liquor, is given by point z on the solubility curve, and the proportions of solid naphthalene and solution are given, by the so-called mixture rule , by the ratio of the lengths zZ and zZ, i.e. 

A process involving both cooling and evaporation can be analysed in two steps. The first is as described above, i.e. the location of points z, Z and Z this represents the cooling operation. If benzene is evaporated from the system, z no longer represents the composition thus the new composition point z (not shown in the diagram) is located along line ZZ between points z and Z. Then the ratio z Z/z Z gives the proportions of solid and solution. 

If the behavior of the solution is not ideal, we have the Ught-scattering equation in the following forms  

Let us collect all the relations for this special case. From (6.7.28) and (6.7.24), 

Relations (6.7.30)-(6.7.33) comprise seven equations (the first comprises four equations), from which we can solve for the seven thermodynamic quantities (a = A, B, p = A, B), Va (a = A, B), and Kt- 

Before solving these equations, we write the explicit form of the determinant 

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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. 

The adsorption of detergent-type molecules on fabrics and at the solid-solution interface in general shows a complexity that might be mentioned briefly. Some fairly characteristic data are shown in Fig. XlIl-15 [242]. There is a break at point A, marking a sudden increase in slope, followed by a maximum in the amount adsorbed. The problem is that if such data represent true equilibrium in a two-component system, it is possible to argue a second law violation (note Problem Xni-14) (although see Ref. 243). 

Figure A2.5.3. Typical liquid-gas phase diagram (temperature T versus mole fraction v at constant pressure) for a two-component system in which both the liquid and the gas are ideal mixtures. Note the extent of the two-phase liquid-gas region. The dashed vertical line is the direction x = 1/2) along which the fiinctions in figure A2.5.5 are detemiined.

Figure A2.5.4 shows for this two-component system the same thennodynamic fimctions as in figure A2.5.2, the molar Gibbs free energy (i= + V2P2> the molar enthalpy wand the molar heat capacity C. , again all at...

Although the previous paragraphs hint at the serious failure of the van der Waals equation to fit the shape of the coexistence curve or the heat capacity, failures to be discussed explicitly in later sections, it is important to recognize that many of tlie other predictions of analytic theories are reasonably accurate. For example, analytic equations of state, even ones as approximate as that of van der Waals, yield reasonable values (or at least ball park estmiates ) of the critical constants p, T, and V. Moreover, in two-component systems... 

Flalf a century later Van Konynenburg and Scott (1970, 1980) [3] used the van der Waals equation to derive detailed phase diagrams for two-component systems with various parameters. Unlike van Laar they did not restrict their treatment to the geometric mean for a g, and for the special case of b = hgg = h g (equalsized molecules), they defined two reduced variables. 

If the two constituting molecular volumes are identical in a two component system, we can obtain [37, 38]... 

To describe the state of a two-component system at equilibrium, we must specify the number of moles nj and na of each component, as well as—ordinarily- the pressure p and the absolute temperature T. It is the Gibbs free energy that provides the most familiar access to a discussion of equilibrium. The increment in G associated with increments in the independent variables mentioned above is given by the equation... 

Osmotic pressure is one of four closely related properties of solutions that are collectively known as colligative properties. In all four, a difference in the behavior of the solution and the pure solvent is related to the thermodynamic activity of the solvent in the solution. In ideal solutions the activity equals the mole fraction, and the mole fractions of the solvent (subscript 1) and the solute (subscript 2) add up to unity in two-component systems. Therefore the colligative properties can easily be related to the mole fraction of the solute in an ideal solution. The following review of the other three colligative properties indicates the similarity which underlies the analysis of all the colligative properties ... 

Reinforcing Resins. Reinforcement and stiffness of a compound can also be achieved with the use of reactive resins. Resins consisting of two-component systems of resorcinol or resorcinol condensation products and a methylene donor such as hexamethoxymethylmel amine (HMMM) or hexamethyltetramine (HMT) are the most popular in tires. These materials can be prereacted and added to the formula, or for more effective results they can react in situ ie, they can be added separately into the formula and react when the tire is vulcanized. 

For a two-component system in which one component exists only in the vapor phase, equation 20 is reduced to the following ... 

M. Broul, J. Navlt, and O. Souhnel, Solubility in Inorganic Two-Component Systems Elsevier, Amsterdam, the Netherlands, 1981, pp. 412—413. 

Sulfur as an Additive for Asphalt. Sulfur-extended asphalt (SEA) binders are formulated by replacing some of the asphalt cement (AC) in conventional binders with sulfur. Binders that have sulfur asphalt weight ratios as high as 50 50 have been used, but most binders contain about 30 wt % sulfur. Greater latitude in design is possible for SEA paving materials, which are three-component systems, whereas conventional asphalt paving materials are two-component systems. Introduction of sulfur can provide some substantial benefits. At temperatures above 130°C, SEA binders have lower viscosities than conventional asphalt. The lower viscosity enables the plant to produce and compact the mix at lower temperatures than with conventional... 

Sanitary ware, including tubs, showers, combined units, basins, and toilet tank, may be made of thermoformed ABS or acryHc sheet, molded glass-fiber-reinforced polyester, or cast acryHc resins. The glass-polyester type dominates the tub/shower market. It is possible to install the units as a two-component system, assembled in place. Gel coats may be of thermoformed decorative acryHc skins. To reduce the smoke generated by fire, methyl... 

A method of resolution that makes a very few a priori assumptions is based on principal components analysis. The various forms of this approach are based on the self-modeling curve resolution developed in 1971 (55). The method requites a data matrix comprised of spectroscopic scans obtained from a two-component system in which the concentrations of the components are varying over the sample set. Such a data matrix could be obtained, for example, from a chromatographic analysis where spectroscopic scans are obtained at several points in time as an overlapped peak elutes from the column. 

Silicone reliners are supplied as either a one-component system that cures in the presence of moisture or heat, or a two-component system containing base and catalyst. Both types adhere poody to denture base and carmot be polished satisfactorily. Some silicones support propagation of bacteria such as Candida albicans. Acrylic-based sifloxane monomers and resins have been proposed for overcoming these deficiencies (211). 

Fig. 3. Binary activity coefficients for two component systems having (a) positive and (b) negative deviations from Raoult s law. Conditions are either...

The second type is a stable dispersion, or foam. Separation can be extremely difficult in some cases. A pure two-component system of gas and liquid cannot produce dispersions of the second type. Stable foams can oe produced only when an additional substance is adsorbed at the liquid-surface interface. The substance adsorbed may be in true solution but with a chemical tendency to concentrate in the interface such as that of a surface-active agent, or it may be a finely divided sohd which concentrates in the interface because it is only poorly wetted by the liquid. Surfactants and proteins are examples of soluble materials, while dust particles and extraneous dirt including traces of nonmisci-ble liquids can be examples of poorly wetted materials. 

For simplicity, consider a two component system. The volume frac tion of a component is... 

Teaching yourself phase diagrams part 2 one and two component systems... 

The conventional polyisocyanurate may be prepared with a two-component system using standard polyurethane foaming equipment. It is usual to blend isocyanate and fluorocarbon to form one component whilst the activator or activator mixture form the second component. 

In 1975 Wacker-Chemie introduced silicones under the name of m-polymers. These are also room temperature curing liquid polymers which give rubbery materials on cross-linking and are available both as one- and two-component systems. Their particular feature is that they contain dispersions of copolymers such as those of styrene and n-butyl acrylate in the shape of rods or rice grains in the fluid silicone polymer. A small amount of the organic copolymer is also grafted onto the silicone backbone. 

Variety of form. Rubber base adhesives can be supplied for assembly operations as solvent or water-borne dispersions, hot melts, precast films, extruded tapes or reinforced films. In addition solvent and water-borne dispersions can be supplied as single or two-components systems. 

The term modified two-component urethanes refers to systems in which one or more of the reactants in a two-component system are temporarily blocked to prevent reaction. The modified two-component system does not have the long shelf life of a standard one-component blocked system. 

Two-component systems consist of (1) polyol or polyamine, and (2) isocyanate. The hardening starts with the mixing of the two components. Due to the low viscosities of the two components, they can be used without addition of solvents. The mass ratio between the two components determines the properties of the bond line. Linear polyols and a lower surplus of isocyanates give flexible bond lines, whereas branched polyols and higher amounts of isocyanates lead to hard and brittle bond lines. The pot life of the two-component systems is determined by the reactivity of the two components, the temperature and the addition of catalysts. The pot life can vary between 0.5 and 24 h. The cure at room temperature is completed within 3 to 20 h. 

Broul, M., Nyvlt, J. and Soliiiel, O., 1981. Solubility in inorganic two-component systems. Prague Academia. 

Eutectic growth is a special mode of solidification for a two-component system. Operating near a specific point in the phase diagram, it shows some unique features [121,137]. 

Basically there are two types of systems ideal and nonideal. These terms apply to the simpler binary or two component systems as well as to the often more complex multicomponent systems. 

Moisture-curable urethane systems (one-pack) can be considered as two-component systems which use atmospheric moisture as the second component. One-pack urethane coatings can be produced that are similar in physical properties to the two-pack systems for almost all applications. These highly complex systems can have a great deal of flexibility. Claimed advantages are a one-pack system, rapid cure, even at low temperatures, excellent chemical and abrasion resistance and good flexibility. Although these systems have been available for some time in other countries of Europe, they are only recently beginning to be of interest in the UK. 

The fundamental difference between pure metals and impure metals and alloys arises from the fact that there is only one atomic species present in the former, while there are two or more present in the latter thus a pure metal is a single-component system, a pure binary alloy is a two-component system, while impure metals and alloys, strictly speaking, are multi-component... 

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