When a heat flux is applied downwards through a sample of ⁴He near the superfluid transition temperature Tλ, the gradient in the temperature self-organizes to the gradient in Tλ caused by gravity. This creates the Self-Organized Critical (SOC) state. Previous experiments have observed the state, measured the self-organization temperature TSOC vs. heat flux, and investigated a remarkable wave that only travels upwards against the flow of the heat flux.
We report the first results of the heat capacity of the SOC state, C∇T, for heat fluxes 60 nW/cm² < Q < 13 uW/cm² and corresponding temperatures 9 nK > TSOC-Tλ > -1.1 uK. We find that C∇T tracks the static (i.e., zero heat flux) unrounded (i.e., in zero gravity) heat capacity C_0 with two exceptions. The first is that within 250 nK of Tλ, C_gradT is depressed relative to C₀ and the maximum in C∇T is shifted to 50 nK below Tλ. The second difference is that at high heat flux, C∇T is again depressed relative to C₀ with the departure starting at about 650 nK below Tλ.
We present the most extensive measurements of the speed and attenuation of the SOC wave to date. We report wave speed measurements taken over our full experimental range 30 nW/cm² < Q < 13 uW/cm² and attenuation results over the limited range that produced enough attenuation to measure. We also report the first accurate calculation of the speed of the SOC wave.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Goodstein, David L.}, } @phdthesis{10.7907/xx11-da13, author = {Mukhopadhyay, Ranjan}, title = {Quantum phase transitions in disordered Bose systems}, school = {California Institute of Technology}, year = {1998}, doi = {10.7907/xx11-da13}, url = {https://resolver.caltech.edu/CaltechETD:etd-02022007-104407}, abstract = {NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document. We study the nature of various quantum phase transitions corresponding to the onset of superfluidity, at zero temperature, of bosons in a quenched medium. Particle-hole symmetry plays an essential role in determining the universality class of the transitions. To obtain a model with an exact particle-hole symmetry it is necessary to use the Josephson junction array Hamiltonian, which may include disorder in the Josephson couplings between phases at different sates. The functional integral formulation of this problem in d spatial dimensions yields a (d + 1)-dimensional classical XY-model with extended disorder, constant along the extra imaginary time dimension – the so-called random rod problem. Particle-hole symmetry may then be broken by adding nonzero chemical potentials or site energies, which may also be site dependent and random. We may then distinguish three cases: (i) exact particle-hole symmetry, in which the site energies all vanish, (ii) statistical particle-hole symmetry in which the site energy distribution is symmetric about zero and hence vanishes on average, and (iii) complete absence of particle-hole symmetry in which the distribution is generic. We explore in each case the nature of the excitations in the nonsuperfluid Pose glass phase. We find, for example, that the compressibility, which has the interpretation of a temporal spin stiffness or superfluid density, is positive in cases (ii) and (iii), but that it vanishes with an essential singularity as full particle-hole symmetry is restored. We then focus on the critical point and discuss the validity of various scaling arguments. In particular, we argue that the dynamical exponent z could be different from d, and the arguments leading to their equality are incorrect. We then discuss the relevance of a type (ii) particle-hole symmetry breaking perturbation to the random rod critical behavior, identifying a nontrivial crossover exponent. This exponent cannot be calculated exactly but is argued to be positive and the symmetry breaking perturbation therefore relevant. We argue next that a perturbation of type (iii) is irrelevant to the resulting type (ii) critical behavior: the statistical symmetry is restored on large scales close to the critical point, and case (ii) therefore describes the dirty boson fixed point. Using various duality transformations we verify all of these ideas in one dimension. To study higher dimensions we attempt, with partial success, to generalize the Dorogovtsev-Cardy-Boyonovsky double epsilon expansion technique to this problem. We find that when the dimension of time […] is sufficiently small the symmetry breaking perturbation of type (ii) is irrelevant, but that for sufficiently large […] this is a relevant perturbation and a new stable commensurate fixed point appears. We speculate that this new fixed point becomes the dirty boson fixed point when […] = 1. We also show that for […], there exists a particle-hole asymmetric fixed point of type (iii), but we provide evidence that it merges with the commensurate fixed point for some finite […]. This tends to confirm symmetry restoration at the physical […] = 1.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Goodstein, David L.}, } @phdthesis{10.7907/1tad-9z23, author = {Lysek, Mark Joseph}, title = {A thermodynamic study of layering and capillary condensation of methane adsorbed on graphite foam}, school = {California Institute of Technology}, year = {1992}, doi = {10.7907/1tad-9z23}, url = {https://resolver.caltech.edu/CaltechETD:etd-08142007-090035}, abstract = {Multilayer films of methane adsorbed on graphite foam have been studied using heat capacity and vapor pressure measurements. An automated, high resolution differential calorimeter was designed and constructed that yielded far better data in much less time. It was found that capillary condensate in the pores of the graphite foam coexists with uniform films as thin as 1.1 layers. Heat capacity features near the triple point previously thought to be the melting of the uniform film are identified as the melting of the capillary condensate. The latent heat of melting of the capillary condensate was measured to be as small as half the bulk value when it was confined inside the smallest pores. The melting temperature of the capillary condensate confirms a simple model for the melting of bulk matter in cylindrical pores. This model explains why the melting temperature is the same for systems with the same chemical potential but on different branches of the hysteresis curve. The model indicates that the capillary condensate may undergo surface melting if the solid does not wet graphite and the condensate undergoes substrate freezing. The phase diagram of the layer closest to the substrate is altered slightly by the finding that this layer melts from the commensurate phase when the uniform film is thicker than 1.1 layers. Heat capacity signals from phase transitions in the uniform films map out complicated phase diagrams in the second, third and fourth layers, including a 2-D triple point and liquid vapor coexistence region for each layer. The layering critical temperatures indicate that the bulk solid-vapor interface may roughen at about 81 K.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Goodstein, David L.}, } @phdthesis{10.7907/w5xh-p756, author = {Maboudian, Roya}, title = {In-Situ Observation of Surface and Near-Surface Modification Using Scattering of Ballistic Phonons}, school = {California Institute of Technology}, year = {1989}, doi = {10.7907/w5xh-p756}, url = {https://resolver.caltech.edu/CaltechETD:etd-02122007-080335}, abstract = {We have investigated the feasibility of phonon-reflection techniques as non-destructive means to probe surface and/or near-surface damage in otherwise highly perfect crystals. A UHV liquid-helium stage, suitable for phonon-reflection measurements, was installed on a beam line of a tandem van de Graaff accelerator which was used to implant MeV ions into the substrate in order to modify the subsurface region in situ. Here, we report our investigation on the effects of 1 MeV Ar⁺ implantation in Al₂O₃ single crystals by monitoring the reflection of terahertz (THz) phonons (50 Å wavelength) from the implanted region. The results are supported by x-ray rocking measurements and Monte Carlo simulations.
Using a 15 kV ion gun on the same beam line we have also bombarded Al₂O₃ crystals coated with thin films of gold. The effects of a 7.5 keV Ar⁺ irradiation on this Au - Al₂O₃ system are also discussed in this thesis.
The relevance of this work is discussed in connection to the observations made by other groups and also to our previous work (reported in Appendix 3) on phonon-induced desorption of He atoms as well as the Kapitza anomaly.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Goodstein, David L.}, } @phdthesis{10.7907/pjk4-9875, author = {Pettersen, Michael Steven}, title = {Melting of Methane Adsorbed on Graphite Studied by Nuclear Magnetic Resonance}, school = {California Institute of Technology}, year = {1988}, doi = {10.7907/pjk4-9875}, url = {https://resolver.caltech.edu/CaltechTHESIS:01222013-152219586}, abstract = {An NMR survey of the system of methane adsorbed on graphite, over a range of 70-105 K in temperature and .87-51 layers in coverage, is presented. The data are analyzed in terms of current models of the phenomena occurring in adsorbed films, such as wetting, roughening, surface melting, and melting.
The interaction between the substrate and adsorbate and its effect on T₁ is quantitatively analyzed in terms of a model of fixed paramagnetic spin centers in the substrate. Since the T₁ effect is very sensitive to the distribution of the adsorbate with respect to the surface, it is shown that it can be used as a powerful diagnostic tool for the study of wetting behavior in thick films where other techniques are insensitive.
While T₂ is also affected by the substrate, we show that it can still be used as a probe of molecular mobility in thin films. Roughening is found to cause an enhancement of mobility in a region of about 4 layers on the surface of the film.
A new, complete thermodynamic model of surface melting, applicable to adsorbed films, is presented, and possible new phase transitions are predicted. The data for methane on graphite are found to be inconsistent with the hypothesis of surface melting.
Finally, the bulk melting transition is traced from thick films all the way down to 1.39 layers. The transition is observed to persist to the thinnest supermonolayer films studied, in a region where previous heat capacity studies have shown the latent heat to vanish.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Goodstein, David L.}, } @phdthesis{10.7907/e8ag-j914, author = {Weimer, Michael Ben}, title = {Thermal Desorption of Helium Films: Theory and Experiment}, school = {California Institute of Technology}, year = {1986}, doi = {10.7907/e8ag-j914}, url = {https://resolver.caltech.edu/CaltechTHESIS:10302019-173639293}, abstract = {
The desorption kinetics of helium films is explored in the context of a phenomenological model wherein the film is assumed to have the thermodynamic properties of bulk liquid and the vapor is described by simple kinetic theory. When supplemented by the condition that desorption proceed at the maximum rate permitted by detailed balance, equations for energy and mass conservation completely determine the dynamics of the system.
The model is applied to the specific problem of characterizing the time response of an adsorbed film when the equilibrium between it and the ambient vapor is perturbed by a sudden change in substrate temperature and the system subsequently evolves toward a new steady state. Analysis reveals that for infinitesimal perturbations from equilibrium the equations of motion are linear and result in exponential solutions for the time dependence of the desorption flux. For finite temperature elevations and realistic adsorption isotherms, however, the equations of motion are highly nonlinear. In either case, isothermal desorption at the temperature of the substrate is shown to be a general feature of the solutions under usual experimental conditions and this considerably simplifies interpretation of the nonlinear problem. Under these circumstances one can identify a continuous succession of coverage-dependent relaxation time scales which are given in terms of instantaneous properties of the adsorption system. These time scales are distinct from, and in general unrelated to, the coverage-dependent mean lifetime of an atom on the surface. To characterize the overall time scale of the nonlinear evolution towards steady state, a global measure is defined in terms of both instantaneous and steady-state properties and used to summarize experimental data.
A direct method for measuring the relaxation time of monolayer helium films flash desorbed from evaporated metal-film substrates is described and used to test the model. The technique is based on a rapid heating scheme made possible by the unique properties of ballistic phonon propagation in single crystals at low temperature. Global time constants extracted from the data in the near-equilibrium regime agree well with the predictions of the model. When these results are combined with earlier data at higher substrate temperatures and different ambient conditions, the picture is consistent with scaling properties implied by the theory. It is shown how the particular dependence on initial conditions of the exponent in a Frenkel-Arrhenius parameterization of the global time constant may be traced to the curvature of the equilibrium adsorption isotherm. This curvature is substantiated by the behavior of the instantaneous relaxation time scales, the time-of-flight spectrum of the desorbing flux, and the kinetics of readsorption.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Goodstein, David L.}, } @phdthesis{10.7907/wf4c-q134, author = {Hamilton, Jeffrey John}, title = {A Thermodynamic Study of Methane Multilayers Adsorbed on Graphite}, school = {California Institute of Technology}, year = {1983}, doi = {10.7907/wf4c-q134}, url = {https://resolver.caltech.edu/CaltechTHESIS:10172019-153324657}, abstract = {Thermodynamic measurements of the properties of methane adsorbed on graphite have been made in the range, roughly, of 1-6 molecular layers and 64-105 K. Interpreting the results in the context of current models, a tentative conclusion that layer by layer critical points occur at approximately constant temperature near 78 K is drawn. A line of melting transitions extending from the bulk triple point, Tt = 90.66 K. into the multilayer region at temperaturesnear 90 K is also observed, and while these transitions do not appear to be first order, there is an associated change in entropy. This change in entropy gradually diminishes, and vanishes entirely at about two layers. It is not clear how this line of transitions ends, but it is thermodynamically forbidden from ending in a critical point. Finally, the Landau potential has been constructed and tabulated as a function of its proper variables, namely temperature and chemical potential. This gives a complete thermodynamic description of the methane film in the range studied.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Goodstein, David L.}, } @phdthesis{10.7907/387M-V435, author = {Moody, Douglas Marion, Jr.}, title = {I. Numerical Solution of the Superfluid Shock Jump Conditions. II. Experimental Investigation of the Liquid Helium II-Vapor Interface}, school = {California Institute of Technology}, year = {1983}, doi = {10.7907/387M-V435}, url = {https://resolver.caltech.edu/CaltechETD:etd-08312006-081008}, abstract = {Numerical Solution of the Superfluid Shock Jump Conditions
The four fundamental conservation equations of superfluid mechanics may be integrated across a one-dimensional discontinuity (shock wave) propagating into undisturbed helium II to yield a set of four algebraic equations (jump conditions) which, when supplemented by thermodynamic state information, establish the equilibrium flow state behind the shock wave for a given wave speed and undisturbed flow state ahead of the shock. These jump conditions have been solved numerically for 19 points on the helium II p-T diagram with upstream Mach number as the independent parameter. Representative results of the calculations are presented for pressure shocks, temperature raising shocks, and temperature lowering shock. The results are compared to previous analytical approximate solutions to test the validity of those approximation. They are also compared to experimental data for shock waves in helium II as a means of testing the correctness of the full, nonlinear two-fluid equations.
Experimental Investigation of the Liquid Helium II-Vapor Interface
An apparatus was designed and constructed to measure the linear reflection and transmission coefficients for weak second sound shocks impinging upon the liquid-vapor interface of helium II. The measured reflection coefficients reproduce the work of previous authors, giving values which are roughly 20% higher than those predicted by thermodynamic equilibrium theory. The transmitted pressure wave speed was measured, and was found to be sonic within the limits of experimental precision. Therefore strength could not be deduced from time of flight measurements. Direct amplitude measurements of this weak wave were prevented by the film which coats the sensors in the vapor. For these reasons, the attempted transmission coefficient measurements were unsuccessful.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Goodstein, David L.}, } @phdthesis{10.7907/7cwm-xp02, author = {Greif, Jeffrey Mark}, title = {Do Helium Monolayer Films Melt by Unbinding of Dislocations?}, school = {California Institute of Technology}, year = {1982}, doi = {10.7907/7cwm-xp02}, url = {https://resolver.caltech.edu/CaltechTHESIS:07122018-101312147}, abstract = {
The Kosterlitz-Thouless-Nelson-Halperin-Young theory of melting in two dimensions by unbinding of thermally excited dislocation pairs is tested against thermodynamic data on monolayer films of 3He and 4He on graphite. It is shown using a new analysis of the theory in the asymptotic region that a definitive test is not possible with these data because the theory is expected to be most accurate in a regime very close to the melting transition which is inaccessible to experiments that are not performed on extremely long time and length scales.
One of the two unknown parameters of the theory, that which measures the resistance to twist of the monolayer with respect to the periodic substrate, is calculated, along with the equilibrium angle, to moderate accuracy using the most recent information about the helium graphite potential from atomic scattering experiments. The other parameter, which characterizes the energy of a dislocation core, is provisionally determined by finding what values make the heat capacity of the film, computed from the theory and elastic data on the film, are consistent with experimental results.
These computations are carried out using the full renormalization group equations, crossing the transition from the solid into into the region where those equations break down, by cutting off the integration at a finite value characteristic of the size of a graphite platelet, which works until the mean distance between free dislocations decreases to approximately the size of the patch. The core parameter falls in a range considerably larger than previously estimated for classical Lennard-Jones solids and other materials. Only at large values can the dislocation heat capacity be suppressed enough not to be inconsistent with experiment.
Non-rigorous interpolation methods were developed to try to include some quantum effects in the heat capacity calculations, but these improved the agreement between the theory and the experiments only slightly.
Also appearing for the first time are extensive tables of the thermodynamic functions of 3He for coverages ranging from .001 to 1 layer and temperatures from 50mK to 10K.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Goodstein, David L.}, } @phdthesis{10.7907/NVXX-BC73, author = {Elgin, Robert Lawrence}, title = {The Thermodynamics of the ⁴HE Submonolayer Film Adsorbed on Grafoil}, school = {California Institute of Technology}, year = {1973}, doi = {10.7907/NVXX-BC73}, url = {https://resolver.caltech.edu/CaltechTHESIS:07022018-115802648}, abstract = {The heat capacity and vapor pressure of thin films of helium adsorbed on graphite have been measured simultaneously. Sufficient data were taken for a complete model~independent thermodynamic analysis from 4.5 K to 15 K and from 0.01 to 1.2 monolayer. Heat capacity down to 1s4 K showed reproducibility with other laboratories.
The data allow definitive tests of many models suggested for these films. Large heat capacity peaks at the melting transition are shown to be the result of interactions with the second layer and the bulk gas phase. Large deviations from ideal gas behavior at low densities are explained quantitatively by interactions with inhomogeneities in the substrate. The data may therefore be corrected to determine experimentally the behavior of strictly two-dimensional helium on a completely homogeneous surfaces.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Goodstein, David L.}, } @phdthesis{10.7907/A99W-KR64, author = {Wallace, John Longstreet}, title = {Equilibrium Properties of Submonolayer He^4 Films}, school = {California Institute of Technology}, year = {1971}, doi = {10.7907/A99W-KR64}, url = {https://resolver.caltech.edu/CaltechTHESIS:06262017-102857880}, abstract = {
Isosteres have been measured for submonolayer films of helium-four adsorbed on a sintered copper sponge precoated with each of the other noble gases, These measurements were carried out at temperatures between 3°K and 4°K, and at coverages between 0.5 and 1.0 monolayer; the pressures encountered were in the range from 10-7 Torr to 10-1 Torr. On the neon-coated substrate, the lower binding energy and higher lateral mobility made it feasible to take useful data at coverages as low as 0.025 monolayer. From the isosteres, information is derived about the partial molar entropy, entropy and heat capacity of the film.
It appears that the submonolayer film is a well-defined entity whose qualitative properties remain unchanged as the substrate precoating is varied, These include a transition into a highly ordered state as the coverage is increased, a total heat capacity which is not monotonic with coverage, and significant lateral mobility. The transition into the ordered state is initiated at higher coverage as the temperature is lowered, and this anomaly is discussed in terms of a model in which two dimensional crystalline patches are broken up by thermal fluctuations.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Goodstein, David L.}, } @phdthesis{10.7907/DQ0R-RX79, author = {Rockwood, Stephen Dell}, title = {Dilution refrigeration and a calorimetric measurement of the quadruple coupling constant in rhenium metal}, school = {California Institute of Technology}, year = {1970}, doi = {10.7907/DQ0R-RX79}, url = {https://resolver.caltech.edu/CaltechTHESIS:08312015-161425022}, abstract = {A dilution refrigerator has been constructed capable of producing steady state temperatures less than .075°K. The first part of this work is concerned with the design and construction of this machine. Enough theory is presented to allow one to understand the operation and critical design factors of a dilution refrigerator. The performance of our refrigerator is compared with the operating characteristics of three other dilution refrigerators appearing in the present literature.
The dilution refrigerator constructed was used to measure the nuclear contribution to the low temperature specific heat of a pure, single-crystalline sample of rhenium metal. Measurements were made in magnetic fields from 0 to 12.5 kOe for the temperature range .13°K - .52°K. The second part of this work discusses the results of these experiments. The expected nuclear contribution is not found when the sample is in the superconducting state. This is believed to be due to the long spin-lattice relaxation times in superconductors. In the normal state, for the temperature range studied, the nuclear contribution is given by A/T2 where A = .061 ± .002 millijoules-K/mole. The value of A is found to increase to A = .077 ± .004 millijoules-K/mole when the sample is located in a magnetic field of 12.5 kOe.
From the measured value of A the splitting of the energy levels of the nuclear spin system due to the interaction of the internal crystalline electric field gradients with the nuclear quadrupole moments is calculated. A comparison is made between the predicted and measured magnetic dependence of the specific heat. Finally, predictions are made of future nuclear magnetic resonance experiments which may be performed to check the results obtained by calorimetery here and further, to investigate existing theories concerning the sources of electric field gradients in metals.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Goodstein, David L.}, }