Phase diagram helium

The mysteries of the helium phase diagram further deepen at the strange A-line that divides the two liquid phases. In certain respects, this coexistence curve (dashed line) exhibits characteristics of a line of critical points, with divergences of heat capacity and other properties that are normally associated with critical-point limits (so-called second-order transitions, in Ehrenfest s classification). Sidebar 7.5 explains some aspects of the Ehrenfest classification of phase transitions and the distinctive features of A-transitions (such as the characteristic lambda-shaped heat-capacity curve that gives the transition its name) that defy classification as either first-order or second-order. Such anomalies suggest that microscopic understanding of phase behavior remains woefully incomplete, even for the simplest imaginable atomic components. 

Fig. 17-1. Helium phase diagram near absolute zero.

Fig. 6.6. Isotherms in the (p—X2) plane of the mercury-helium phases diagram at 1490 C and 1518 C. Dot-dash curve is the critical line connecting critical points open circles), heavy solid lines represent solubility curves and are extrapolated (dashed curves) to p = 11 g cm". Coordinates of selected tie lines light solid lines) are given in Table 6.1.

Fig. 6.6 Isotherms in the (p — X2) plane of the mercury-helium phases diagram at 1490°C and 1518°C. 206...

Even at the lowest temperatures, a substantial pressure is required to soHdify helium, and then the soHd formed is one of the softest, most compressible known. The fluid—soHd phase diagrams for both helium-3 and helium-4 are shown in Eigure 1 (53). Both isotopes have three allotropic soHd forms an fee stmeture at high pressures, an hep stmeture at medium and low pressures, and a bcc stmeture over a narrow, low pressure range for helium-4 and over a somewhat larger range for helium-3. The melting pressure of helium-4 has been measured up to 24°C, where it is 11.5 GPa (115 kbar) (54). 

Fig. 2. Phase diagram for helium-4 where CP is the critical poiat. To convert MPa to psi, multiply by 145.

Fig. 3. Phase diagram for helium-3 where A, B, and A1 represent the three superfluid phases and PCP is the polycritical poiat. The dashed lines iadicate the...

The phase diagram for helium is shown here, (a) What is the maximum temperature at which superfluid helium-II can exist (b) What is the minimum pressure at which solid helium can exist (c) What is the normal boiling point of helium-I ... 

Use the phase diagram for helium in Exercise 8.13 (a) to describe the phases in equilibrium at each of helium s two triple points (b) to decide which liquid phase is more dense, helium-1 or helium-II. 

An exceptional case of a very different type is provided by helium [15], for which the third law is valid despite the fact that He remains a liquid at 0 K. A phase diagram for helium is shown in Figure 11.5. In this case, in contrast to other substances, the solid-liquid equilibrium line at high pressures does not continue downward at low pressures until it meets the hquid-vapor pressure curve to intersect at a triple point. Rather, the sohd-hquid equilibrium line takes an unusual turn toward the horizontal as the temperature drops to near 2 K. This change is caused by a surprising... 

The densities of liquid and solid helium are different thus, AVm of Equation (8.9) is not zero. Yet the horizontal slope of the melting line of the phase diagram shows that dP/dT is zero near 0 K. Hence, it is clear that A5m of Equation (8.9) must be zero at 0 K, that is, that 5m,ok is zero for liquid He as well as for solid He. 

Stability Limit 1, With the exception of helium and certain apparent exceptions discussed below. Fig. I gives a universal phase diagram liir all pure compounds The triple point of one P and one T is the single point at which all three phases, crystal, liquid, and gas. are in equilibrium. The triple point pressure is normally below atmospheric. Those substances, c.g.. CO . / - 3H85 mm. 7, = -5ft.fi C. for which it lies above, sublime without melting ai atmospheric pressure. 

Helium-4 Normal-Superfluid Transition Liquid helium has some unique and interesting properties, including a transition into a phase described as a superfluid. Unlike most materials where the isotopic nature of the atoms has little influence on the phase behavior, 4He and 3He have a very different phase behavior at low temperatures, and so we will consider them separately Figure 13.11 shows the phase diagram for 4He at low temperatures. The normal liquid phase of 4He is called liquid I. Line ab is the vapor pressure line along which (gas + liquid I) equilibrium is maintained, and the (liquid + gas) phase transition is first order. Point a is the critical point of 4He at T= 5.20 K and p — 0.229 MPa. At this point, the (liquid + gas) transition has become continuous. Line be represents the transition between normal liquid (liquid I) and a superfluid phase referred to as liquid II. Along this line the transition... 

First of all, the term supercritical fluid does not refer to superfluid helium, a state of matter for He and " He near absolute zero.ril As shown in the phase diagram in Ch. 1, a supercritical fluid refers to the state of matter above its critical point. The critical point is a temperature and pressure, Tg and Pc, at which two phases of a substance in equilibrium with each other become identical, forming one phase. Above the critical temperature, Tc, a substance can not... 

These unusual pseudobinary phase diagrams were derived initially by Meijering (1950) from a simple mixture model for ternary mixtures. Much later, Blume, Emery and Griffiths (1971) deduced the same diagrams from a three-spin model of helium mixtures. The third diagram on the right of figure A2.5.30 is essentially that found experimentally for the fluid mixture He+ He the dashed line (second-order transition) is that of the A,-transition. 

A phase diagram is a map that indicates the areas of stability of the various phases as a function of external conditions (temperature and pressure). Pure materials, such as mercury, helium, water, and methyl alcohol are considered one-component systems and they have unary phase diagrams. The equilibrium phases in two-component systems are presented in binary phase diagrams. Because many important materials consist of three, four, and more components, many attempts have been made to deduce their multicomponent phase diagrams. However, the vast majority of systems with three or more components are very complex, and no overall maps of the phase relationships have been worked out. 

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