Phase diagram, for helium

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... 

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). 

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... 

The phase diagram for this system, as reported by Naumkin et al. (1970) and Savitskii et al. (1970) is shown in fig. 15. Savitskii et al. did not reveal the purity of their alloying materials but Naumkin et al. reported a 99.7 wt% purity for their lanthanum (impurities, reported in wt%, were 0.04 Ce, 0.07 each Pr and Nd and 0.012 Fe). Their scandium was reported to be 99.7 wt% pure (impurities included 0.11 wt% O). Their alloys were formed by arc-melting the metals under an atmosphere of purified helium. Below the solidus, the body-centered cubic yLa and jSSc form a solid solution. Two eutectoid transformations at about 750°C and 45 at% Sc and 233°C and 14at% Sc result in regions of two-phase immiscibility. 

A phase diagram for the cerium-scandium system has been reported by Naumkin et al. (1964). Distilled scandium of 99.5 (wt )% purity (major impurities 0.2% O, 0.15% Cu, 0.06% Fe, 0.03% N, 0.1% Ti, 0.01% each Al, H, Ca) and 99.5% cerium (major impurities 0.02% each C and Ca and 0.01% each Ta and Fe) were used to prepare the alloys. The alloys were prepared in an arc furnace under helium, remelted three times, then annealed 240hr at 500°C in vacuum. The phase diagram... 

Markova et al. (1967) constructed a phase diagram for the dysprosium-yttrium system utilizing thermal analyses, X-ray diffraction, metallography, hardness and electrical resistance measurements. Their starting materials were distilled yttrium and dysprosium of 99.6 to 99.7(wt )% purity. Both metals contained gaseous impurities as well as the metals Ca, Fe, Cu, Y, Gd, Dy and Ta. Alloys were prepared at approximately 10 at% intervals, arc-melted under purified helium and annealed at 850°C for 70 hr. The structure of all specimens was single phase with the hep lattice. A continuous series of solid solutions between isomorphic modifications was observed. 

Helium has different phase diagrams for the two principal isotopes, and both isotopes exhibit liquid-phase allotropy. Figure 5.4 shows the low-temperature phase diagrams of He and He. The diagram for He (the more abundant isotope) shows two different hquid forms, called helium I and helium II. There are two triple points, one for the two hquid forms and the vapor phase, and one for the two liquid forms and the solid phase. The diagram for He shows three different liquid phases and three triple points. Neither isotope exhibits coexistence between the solid and the vapor, and the sohd phases of both isotopes can exist only at pressures larger than 1 atm. Helium is apparently the only substance that cannot be frozen at 1 atm pressure. 

Stance see Fig. 2.2. The most striking properties, however, are those exhibited by liquid helium at temperatures below 2.17 K. As the liquid is cooled below this temperature, instead of solidifying, it changes to a new liquid phase. The phase diagram of helium thus takes on an additional transition line separating the two phases into liquid He I at temperatures above the line and liquid He II at lower temperatures. The low-temperature liquid phase, called liquid helium II, has properties exhibited by no other liquid. Helium II expands on cooling its conductivity for heat is enormous and neither its heat conduction nor viscosity obeys normal rules (see below). The phase transition between the two liquid phases is identified as the lambda line, and the intersection of the latter with the vapor-pressure curve is known as the lambda point. The transition between the two forms of liquid helium, I and II, is called the X... 

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. 

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. 

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. 

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. 

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