Liquidus lines

The cloudiness of ordinary ice cubes is caused by thousands of tiny air bubbles. Air dissolves in water, and tap water at 10°C can - and usually does - contain 0.0030 wt% of air. In order to follow what this air does when we make an ice cube, we need to look at the phase diagram for the HjO-air system (Fig. 4.9). As we cool our liquid solution of water -i- air the first change takes place at about -0.002°C when the composition line hits the liquidus line. At this temperature ice crystals will begin to form and, as the temperature is lowered still further, they will grow. By the time we reach the eutectic three-phase horizontal at -0.0024°C we will have 20 wt% ice (called primary ice) in our two-phase mixture, leaving 80 wt% liquid (Fig. 4.9). This liquid will contain the maximum possible amount of dissolved air (0.0038 wt%). As latent heat of freezing is removed at -0.0024°C the three-phase eutectic reaction of... 

DEF. The phase boundary which limits the bottom of the liquid field is called the liquidus line. The other boundary of the two-phase liquid-solid field is called the solidus line. 

The liquidus lines start from the melting points of the pure components. Almost always, alloying lowers the melting point, so the liquidus lines deseend from the melting points of the pure components, forming a shallow V. 

DEF. The bottom point of the V formed by two liquidus lines is the euteetie point. 

Most alloy systems are more complicated than the lead-tin system, and show intermediate phases compounds which form between components, like CuAlj, or AljNi, or FojC. Their melting points are, usually, lowered by alloying also, so that eutectics can form between CuAlj and A1 (for example), or between AljNi and Al. The eutectic point is always the apex of the more or less shallow V formed by the liquidus lines. 

From 245°C to 183°C. The liquidus is reached at 245°C, and solid (a lead-rich solid solution) first appears. The composition of the liquid moves along the liquidus line, that of the solid along the solidus line. This regime ends when the temperature reaches 183°C. Note that the alloy composition in weight % (64) is roughly half way between that of the solid (81 wt%) and liquid (38 wt%) so the alloy is about half liquid, half solid, by weight. 

C. Consider the cooling of an Al-6% Si casting alloy. The liquidus is reached at about 635°C, when solid (Al) starts to separate out (top of Fig. A1.32). As the temperature falls further the liquid composition moves along the liquidus line, and the amount of solid (Al) increases. When the eutectic temperature (577°C) is reached, about half the liquid has solidified (middle of Fig. A1.32). The solid that appears in this way is called primary solid, primary (Al) in this case. 

When a metal is cast, heat is conducted out of it through the walls of the mould. The mould walls are the coldest part of the system, so solidification starts there. In the Al-Si casting alloy, for example, primary (Al) crystals form on the mould wall and grow inwards. Their composition differs from that of the liquid it is purer, and contains less silicon. This means that silicon is rejected at the surface of the growing crystals, and the liquid grows richer in silicon that is why the liquid composition moves along the liquidus line. 

The phase-diagram (temperature vs concentration) for a eutectic two-component alloy shows at low temperatures a central two-phase region and two solid one-phase regions at low and high relative concentrations. At the eutectic temperature the liquid phase at an intermediate concentration can all of a sudden coexist with the two solid phases. Upon further increase of temperature, the liquidus lines open up a V-shaped liquid... 

A hyper-eutectic alloy containing, say, 50% Sb starts to freeze when the temperature reaches the liquidus line (point a in Fig. 20.39). At this temperature pure pro-eutectic Sb nucleates as the temperature continues to fall, more antimony is deposited from the melt, and the composition of the liquid phase moves down the liquidus line to the eutectic point. When this is reached, the remainder of the melt solidifies. The microstructure of alloys of eutectic composition varies somewhat with alloy system, but generally consists of an aggregate of small particles, often platelets, of one of the phases comprising the eutectic in a continuous matrix of the other phase. Finally, the microstructure of the hypereutectic 50% Sb alloy already mentioned... 

A salt hydrate consists of two components, the salt (e.g. CaCL) and water (e.g. 6H2O). The single phase of the salt hydrate is first heated up from point 1 (solid) to point 2. At point 3 the liquidus line is crossed and the material would be completely liquid. Upon heating or cooling, between point 2 and 3,2 phases are formed, the liquid and a small amount of a phase with less water (point 4). If these phases differ in density, this can lead to macroscopic separation of the phases and therefore concentration differences of the chemicals forming the PCM material (points 5 and Figure 104 right). 

Analytical equations for the solidus and liquidus lines can now be obtained from these equations by noting that xAq + x[ q =1 and xA + XgS =1, giving... 

These two simultaneous equations can then be solved numerically to calculate the solidus and liquidus lines. 

For the niobium-copper system different phase diagrams of the simple eutectic type (with the eutectic point very close to Cu) have been proposed, either with an S-shaped near horizontal liquidus line or with a monotectic equilibrium. It was stated that the presence of about 0.3 at.% O can induce the monotectic reaction to occur, whereas if a lesser amount of oxygen is present no immiscibility gap is observed in the liquid. 

The shape, the slope, of the liquidus line (or liquidus surface) is obviously an important point which has to be considered. 

Figure 6.10. A generic binary phase diagram is shown for an A-B system in which two compounds, AB and ABm, are formed. Different parts of the liquidus line are indicated. 1 is the line of primary crystallization of the terminal solid-solution based on the component A (which, on cooling, will be followed by the peritectic formation of AB ) 2 is the line of primary crystallization of the compound AB (to be followed by the eutectic crystallization of AB + ABm) 3 and 4 are lines of primary crystallization of ABm (to be followed, respectively, by the crystallization of the eutectic AB + ABm or of the eutectic AB, + B-based solid solution).

In these phase diagrams, the liquidus line represents the temperature at which one of the components crystallizes, while, below the solidus line, the whole system solidifies. Between the solidus and liquidus lines are the regions where solid and liquid coexist. Since there is no solid phase above the liquidus lines and the liquid is thermodynamically stable. Ding et al. suggested that the liquidus temperatures should be adopted as the lower boundary of the liquid phase, instead of the solidus temperatures. The patterns of these phase diagrams are... 

Typically, the liquidus lines of a binary system curve down and intersect with the solidus line at the eutectic point, where a liquid coexists with the solid phases of both components. In this sense, the mixture of two solvents should have an expanded liquid range with a lower melting temperature than that of either solvent individually. As Figure 4 shows, the most popular solvent combination used for lithium ion technology, LiPFe/EC/DMC, has liquidus lines below the mp of either EC or DMC, and the eutectic point lies at —7.6 °C with molar fractions of - 0.30 EC and "-"0.70 DMC. This composition corresponds to volume fractions of 0.24 EC and 0.76 DMC or weight fractions of 0.28 EC and 0.71 DMC. Due to the high mp of both EC (36 X) and DMC (4.6 X), this low-temperature limit is rather high and needs improvement if applications in cold environments are to be considered. 

Estimations of metastable melting points are invariably problematical. They are inherently semi-quantitative in nature and depend on die extent of the required extrapolation of stable liquidus lines which can be far away from the element for which the extrapolation is being made. 

The other single phase region is the liquid L. In addition to the two phase a+0 region, there are two other two phase regions L + a and L + 0. Just as in the isomorphous diagram the solidus and liquidus lines are connected by tie-lines of constant temperature. In a like manner, the a + 0 region is also considered to possess tie-lines joining the two solid-solution or solvus curves. 

Thermodynamic definitions show that the first term of Eq. (1) is the enthalpy of mixing, AHu, while the second term is the negative of the excess entropy of mixing, ASm, multiplied by T. When all four parameters are zero, the liquid is ideal with a zero enthalpy and excess entropy of mixing. What has been called the quasiregular model, a = b = 0, has been used by Panish and Ilegems (1972) to fit the liquidus lines of a number of III—V binary compounds. The particular extension of this special case of Eq. (1) to a ternary liquid given by... 

In the notation used here, congruently melting, narrow-homogeneity-range compounds form in the A-C and B-C binaries of the A-B-C system. These are, of course, the Ga-Sb and In-Sb binaries for the Ga-In-Sb system and the Hg-Te and Cd-Te binaries for the Hg-Cd-Te system. For these binaries it is desired to apply the auxiliary conditions of Eqs. (16) and (17) as well as fit other experimental data before fitting the liquidus lines and then the ternary data. For this purpose it is necessary to carry the development of the model somewhat further. At the same time some insight into the behavior of the model can be attained. We show this development specifically for the A-C or... 

Inserting Eq. (91) into Eq. (93) for the liquidus line of AC(s) gives the liquidus temperature at x =. The experimental value TAc is treated as special and it is required that the resulting equation be satisfied for T=TAC. The equation then becomes a restriction on the interaction coefficients. We use it to provide a relation between cos and vs in terms of the other coefficients and a new model parameter z, the value of z at x = and T = TAC. The relation is... 

Best-Fit Parameters, Measure of Fit to the Liquidus Line, and Calculated InSb-Sb Eutectic for the In-Sb System ... 

For the liquidus of InSb(s) there are 13 points from thermal analysis, which include a eutectic point at 494 + 0.5°C and xSb = 0.69 (Liu and Peretti, 1952), as well as three points from dissolution experiments by Hall (cited in Shunk, 1969). The best-fit interaction coefficients, the fit to the liquidus line of InSb(s), liquidus points (Liu and Peretti, 1952), av, and the calculated eutectic temperature and composition are given in Table II. It is emphasized that the values of the interaction coefficients are such that Eqs. 

Fig. 1. Calculated liquidus line for In-Sb and experimental points. Squares are from Liu and Peretti (1952), triangles are from Shunk (1969). 

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