Akira Ikushima

Studies on Phase Transitions by AC Calorimetry

As examples of the best use of the so-called AC calorimetry technique, several results are described from various viewpoints. The behavior of heat capacity at ferroelectric, antiferroelectric and structural phase transitions is surveyed from the standpoint of critical behavior, of jump at first order transition, or of a sensitive metod of finding a new phase transition. In two- and three-dimensional antiferromagnets, the critical behavior is discussed with an emphasis on the crossover from the Ising to the Heisenberg system. In the two-dimensional antiferromagnets, the crossover is revealed from the dependence of the critical amplitude on the strength of the Ising-like anisotropy. A hyperscaling relation is proposed at nematic-to-smectic A transition of liquid crystals. Finally, studies of the frequency dependence of heat capacities in the denaturation of proteins and in the order-disorder transition of alloys are reported.

Specific heat of NaNO2 near its transition points

Abstract Using an a.c. technique, the specific heat of NaNO 2 was measured as a function of temperature near its antiferroelectric-to-paraelectric phase transition point ( T N ). The transition was found to be of the second order. The critical exponents are; α = 0·38 for ϵ = 2 × 10 −4 ∼ 1 × 10 −1 , and α′ = 0·18 for ϵ = −2 × 10 −4 ∼ −3 × 10 −3 . The critical exponents deduced from the scaling-law relations are roughly close to the values obtained from a random phase approximation for a system with an isotropic interaction. However, a difference was recognized between the observed exponent for the specific heat and the values theoretically given for T > T N by the random phase approximation for a system with a short-range interaction or for a system with a long-range dipolar interaction. A thermodynamical analysis was made by using the generalized Pippard relation, and the present result was found to be consistent with the pressure dependence of the antiferroelectric transition point.

Surface tension of liquid4He. Surface energy of the Bose-Einstein condensate

The surface tension of liquid4He was measured by means of surface-wave resonance, and the relative variation showed excellent agreement with that previously obtained by a precise capillary-rise method. The absolute value of the surface tension at absolute zero was measured as 354.4±0.5 mdyne/cm, 6% smaller than the previous value. The surface energy associated with the Bose-Einstein condensate wave function was found to dominate the surface tension in the superfluid phase. The condensate fraction other than in the vicinity of the λ point was estimated asn0(0)-n0(T)=A(T/Tλ)α, withn0(0)=0.125±0.025,A=0.177±0.047, and α=5.07±0.17.

Surface tension of liquid3He down to 0.3 K

The surface tension of liquid3He was measured by determining the surface wave velocity in the temperature range from 0.32 to 3.02 K. The decrease of the surface tension from the value at 0 K can be described as 22.3T2 mdyn/cm up to about 0.9 K and is quite different from that of4He. The extrapolated value to 0 K is 155.7±0.5 mdyn/cm. The data below 1.6 K were compared with Saams model, where the surface tension is assumed to be given by the bulk free energy times the surface width and the quasi-two-dimensional free energy. Agreement between the data and the results calculated from the model is much improved if ripplons are taken into account. Data near the gas-liquid critical point, contrary to earlier results, show that the surface tension vanishes with a critical exponent of 1.24±0.05. This is in agreement with Widoms theory.

Ultrasonic Velocities in BaTiO3

The sound velocities in BaTiO 3 has been observed near its paraelectric to ferroelectric phase transition point. The anomalous part of the sound velocity of the longitudinal wave propagating along [100] direction depends on temperature as A [( T - T 0 )/ T 0 ] -ζ with ζ=0.41 and A =1.79×10 4 cm·sec -1 where T 0 is the paraelectric temperature. The critical index ζ is close to the theoretical value of 1/2 as predicted by Dvořak. On the other hand, the velocity of the transverse wave does not show any appreciable critical behavior. The value of A is also compared with the theory given by Dvořak. The observed curve for the longitudinal wave is in good agreement with the theoretical curve, while that for the transverse wave shows a notable discrepancy.

The decay rate of critical fluctuations in3He-4He mixtures near the gas-liquid critical point

We have measured the critical light scattering intensity and the Rayleigh line shape for3He and for3He-4He mixtures with compositionX(3He)=0.95, 0.79, and 0.63 along their respective critical isochores near the plait point. The experimental linewidth of3He is compared with the calculated one from heat conductivity and equation of state measurements, and satisfactory agreement is obtained. For mixtures, gravity effects in our cell of finite height prevent us from reaching the critical point along a path at strictly constant composition and density. HenceTc cannot be determined directly. Using the prediction that the scattered light intensity in the mixtures has the same diverging behavior as for the pure fluid, we determine the reduced temperaturet≡[T − Tc(X)]/Tc from the intensity. The measured Rayleigh line shape can be expressed by a single decay rate Γ as a function oft for a given scattering angle of the light beam. Our experiments show that Γ in the mixtures is only weakly dependent on composition. Our analysis leads to the determination of the mass diffusion coefficientD, which is found to be nearly independent of composition and nearly equal to the thermal diffusivityDT measured for3He. The results are discussed in the light of the predictions from mode coupling theory.

Intensity, correlation, and statistics of Rayleigh-scattered light near the gas-liquid critical point of 3He

The intensity, correlation, and statistics of Rayleigh-scattered light were measured near the gas-liquid critical point of 3He along the coexistence curve and the critical isochore in the temperature region 10−5 < ¦ɛ¦ < 4 × 10−2 (ɛ ≡ ¦T − Tc¦/Tc). From the intensity measurements, the following critical parameters have been obtained: γ = 1.14 ± 0.05, Ν = 0.59 ± 0.04, and ξ0 = 4.8 ± 2Å for T > Tc (along the critical isochore); γ′ = 1.16 ± 0.07, Ν′ = 0.68 ± 0.07, and ξ+ = 4.3 ± 3.2 Å for T < Tc (liquid phase along the coexistence curve); and χ0/χ+ = 3.6 ± 0.4. From the correlation measurements, the total thermal diffusivity along the critical isochore in the hydrodynamic region has been determined to be DT = (1.57 ± 0.10) × 10−4ɛ0.68 ± 0.03 cm2/sec. The temperature and wave-vector dependence of the singular part of the Rayleigh linewidth has been shown to fit Kawasakis modified expression with the parameters ξ0 = 3.3ɛ−0.59 Å and η = 13(1.15 + 3.19 × 10−2 ln ɛ)−1 ΜP. The statistics of the critical fluctuation have been found to be Gaussian.

Rayleigh linewidth in4He near the gas-liquid critical point

Spectra of Rayleigh-scattered light in4He near the gas-liquid critical point have been measured, using a photon correlation method. Fitting the obtained relaxation times to Kawasakis expression with background modification, we have obtained along the critical isochore the correlation length ζ=(3.6±0.78)ε−0.534±0.046 Å and the high-frequency shear viscosity η*=21.5±3.6 µP. η* has been revealed to be in good agreement with the regular part of the viscosity ηr=21±2µP. The singular part of the thermal diffusivity has been determined to beDTs=(4.9±2.7)×10−5ε−0.543±0.046 cm2/sec along the critical isochore.

Surface tension of liquid3He and4He near the liquid-gas critical point

The surface tension of liquid3He and4He was measured near the gas-liquid critical points in the reduced temperature range 3×10−4<t<2×10−1, where t ≡ (Tc−T)/Tc. The critical exponents were found to be μ3=1.289±0.015 for3He and μ4=1.306±0.017 for4He. These values are very close to those for classical liquids, and are consistent with the value of 1.28 predicted by Widom, but are apparently different from the exponents previously obtained for liquid helium isotopes, which are near unity. The critical coefficients show good agreement with the quantum-corrected corresponding states theory for the Lennard-Jones 6–12 potential discussed by Young. The interface thickness is deduced from Widoms theory to bed=d0t−v′ withd30=0.14±0.03nm and v′3=0.57±0.04 for3He, andd40=0.37±0.07 nm and v′4=0.58±0.01 for4He.

Thermal transport phenomena near the lambda line of 3He-4He mixtures

Effective thermal conductivities in the absence of mass diffusion have been measured near the lambda line of 3He-4He mixtures of up to 33% 3He concentration. The thermal conductivity in the normal phase has a rapidly increasing behavior as the temperature approaches the lambda point, but reaches a finite value there. Thermodiffusion ratios have also been measured, and show weak divergences—if any, weaker than logarithmic. Then, by using previous experimental values of the mass diffusivity given by Ahlers and Pobell, the thermal conductivity and the corresponding thermal diffusivity in the absence of the concentration gradient are deduced. The thermal diffusivity diverges with a critical exponent of approximately 1/3 irrespective of 3He concentration. The diffusivities D0 and D2 corresponding respectively to the linewidths of the Rayleigh and the second-sound Brillouin scatterings in the superfluid phase are obtained: D2 diverges with a critical exponent of approximately 1/3 irrespective of 3He concentration, whereas D0 does not diverge at all. As a whole, the mode-coupling theory on the basis of the dynamic scaling hypothesis has been proved to hold in the superfluid transition.