The osmotic pressure of Hes-He4 mixtures has been measured at temperatures 0.027-0. 65 K, for concentrations up to 10-mole % He, and for hydrostatic pressures of 0.26, 10, and 20 atm.The osmotic pressure was measured directly with a sensitive specially designed diaphragm pressure gauge. The temperatureand concentrationdependenceof the osmotic pressure is in fair agreement with the effective, interactiontheoryproposed by Bardeen, Baym, and Pines (BBP).It also agrees with a simple empirical model whichavoids the complicated calculations involved in obtaining the thermodynamic properties at finite tempexatures from the BBP theory. The model fits the temperature dependence of other thermodynamic properties of solutions. The osmotic pressure at absolute zero at 10 and 20 atm is used to determine the Hes effective mass and somewhat speculative values of the BBP quasiparticle interaction V(k) underpressure. The interaction under pressure is found to have a minimum at a nonzero value of k, and it may give rise to a "supermobile" transition at comparatively high temperatures.

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From measurements of the velocity of second sound and the osmotic pressure the inertia! mass of 3 He in superfluid 4 He has been obtained as a function of temperature and concentration. The results indicate that (i) the 3 He quasiparticle spectrum is not quite parabolic and (ii) part of the quasiparticle effective interaction is velocity dependent or "nonlocal" and resembles the interaction of spheres moving through a nonviscous classical fluid.As usually interpreted, the Landau and Pomeranchuk 1 (LP) and Bardeen, Baym, and Pines 2 (BBP) theories of liquid 3 He-4 He mixtures predict that at low temperatures, where the phonon and roton densities are negligible, the normalfluid density p" should be given bywhere n 3 is the 3 He number density and the mass m should be independent of temperature and 3 He concentration. This result depends on two assumptions: (i) The quasiparticle energy e, which is the energy change on adding one 3 He of momentum p to a very weak solution of 3 He in 4 He, is given byand terms in higher powers of p 2 may be neglected. (ii) In the BBP theory, which takes into account an effective interaction between 3 He quasiparticles, the interaction v(r) is assumed to i to depend only on the interparticle distance r and not on the particle velocities with respect to the superfluid. The interaction energy is thus unchanged when the quasiparticles are accelerated with respect to the superfluid, and therefore v(r) (or its Fourier transform V k ) does not contribute to the normal-fluid inertial mass.If we define an empirical inertial mass m^Pn/ns,determination of the temperature and concentration dependence of m i allows one to test assumptions (i) and (ii). In this Letter we obtain p" and m { from measurements of the velocity of second sound. An equation for the velocity of second sound in the low-frequency, hydrodynamic limit has been derived by Khalatnikov. 3 This rather complicated equation, which depends only on thermodynamic and Galilean-in variance arguments, can be written as (l^){~(^4/91n^) r ,p + (^T/C)(aS/ain|) r ,p 2 } Pn/Ps+P? where Z=n 3 /n 40 =X/(l + aX), /= 1 +a-m 3 /m 4 = 0.53. (4) (5) (This result assumes that n 3 =n 40 X/(l + aX) and it therefore neglects, among other things, thermal expansion. The approximations involved have been investigated and can be justified.) In Eqs. (3)-(5), X is the atomic concentration of 3 He, n 40 is the number density of pure 4 He, a is the BBP parameter 0.284 (see, for instance, Edwards, Ifft, and Sarwinski 4 ), M 4 is the 4 He chemical potential, and S and C are the entropy and specific heat per atom of 3 He. [Using £ «1 and V 4 (T,X) = M 4 (?\ 0)-7r/w 4O , where ir is the osmotic pressure of the solution, Eq. (3) can be trans-formed to p n u 2 2 -(87r/ain£) s , P .The analogy between second sound in the mixture and ordinary sound in the quasiparticle gas is quite clear. 5 The derivative 37r/8ln| can be regarded as the "osmotic bulk modulus" of the mixture.] To determine p" from the second-sound velocities we used Eq. (3) with 3pt 4 /31n4 and 9S/ 31ni...

IntroductionCarbon fibers are produced commercially from rayon, phenolics, polyacrylonitrile (PAN), or pitch. The last are further divided into fibers produced from isotropic pitch precursors, and those derived from pitch that has been pretreated to introduce a high concentration of carbonaceous mesophase. Over the past few decades, interest in research and manufacturing carbon fibers has overwhelmingly centered on producing fibers with high tensile strength and high modulus for lightweight, high performance composites, where polymers, metals, and carbon can form the continuous matrix. The fibers most commonly used in advanced materials are produced from PAN or mesophase pitch. Graphitized mesophase pitch fibers tend to have higher modulus and lower tensile strength than the PAN-based equivalents. They have advantages in applications requiring high stiffness, high electrical and thermal conductivity, low thermal expansion, and high temperature oxidation resistance, while PAN fibers are employed where high strength is required.

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