Phase diagram of helium

The phase diagram of helium is shown here. Helium is the only known substance that has two different liquid phases called helium-I and helium-II. (a) What is the maximum temperature at which 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 (d) Can solid helium sublime (e) How many triple points are there ... 

Now we demonstrate that the phase diagram of helium is a typical diagram of substance with a bulk second liquid. 

The phase diagram of helium is shown. Helium is the only... 

Liquid helium has many unique properties. One of the first properties to attract attention was the absence of a solid-liquid-vapor triple point. The phase diagram of helium-4 differs in form from that of any other known sub-... 

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... 

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... 

FIGURE 6.17 Phase diagram of He. Source Adapted from W. E. Keller, Hdium-3 and Helium-4, Plenum Press, New York, 1969. 

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. 

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). 

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. 

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... 

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