Contains reports on one research project.Joint Services Electronics Program (Contract DAAB07-74-C-0630

Strandberg, Malcom W. P.

Contains research objectives and summary of research.Joint Services Electronics Program (Contract DAAB07-71-C-0300

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X. TRANSPORT PHENOMENA IN SOLIDSAcademic and Research StaffProf. M. W. P. StrandbergProf. R. L. KyhlJ. D. KiersteadGraduate StudentsJ. U. Free, Jr.A. TachagumpuchRESEARCH OBJECTIVES AND SUMMARY OF RESEARCHJoint Services Electronics Program (Contract DAAB07-71-C-0300)M. W. P. StrandbergWe are studying thermal transport in germanium single crystals. Both bulk trans-port phenomena and surface boundary layer thermal conductance effects are beingexplored experimentally and theoretically. In the experiments'we use ballistic heatpulses with superconducting bolometer detectors, or the electrical impedance of thin-film bolometers, which may be interpreted to yield a value for the boundary layer ther-mal conductance. In particular, we are studying the effect of impurities on the bulkphonon transport properties and the effect of surface preparation on the thermal boundarylayer conductance. Heat pulse techniques also appear to be particularly useful instudying the effect of minibands, produced by superlattices in single crystals, on trans-port properties of the crystal. We are trying to obtain a suitable crystal with superlat-tice structure and to design appropriate experiments to study the effects.QPR No. 112

Transport Phenomena in Solids

Contains research objectives and summary of research.Joint Services Electronics Program (Contract DAAB07-74-C-0630

X. TRANSPORT PHENOMENA IN SOLIDSAcademic and Research StaffProf. Malcom W. P. StrandbergProf. Robert L. KyhlJohn D. KiersteadRESEARCH OBJECTIVES AND SUMMARY OF RESEARCH JSEPJoint Services Electronics Program (Contract DAAB07-74-C-0630)Malcom W. P. StrandbergOur experimental work has centered on the study of surface thermal resistance, orKapitza resistance, at liquid helium temperatures. We have been studying the timebehavior of the temperature of a block of insulating crystal which is disturbed, by a heatpulse, from equilibrium with a thermal reservoir. The time decay of the temperature ofthe block to equilibrium can be interpreted to yield a value for the surface thermal con-ductance. The transient temperature of the block can be measured, even in the presenceof slow drifts in the temperature of the reservoir. To check these data we also measurethe influence of the thermal impedance of the block on the electrical impedance of a tinybolometer that has been evaporated on the block to monitor the temperature of the block.The frequency dependence of the electrical impedance of the bolometer varies becauseof the frequency dependence of the thermal impedance of the block, which in turn dependson the boundary thermal conductance of the block.Once a thorough understanding of the thermal properties of the block has been estab-lished, other materials (metals, for example) can be studied by evaporating a film onthe block, or otherwise establishing thermal contact between the metal and the block.The perturbation of the thermal properties of the block produced by the foreign materialthen gives information about the thermal properties of the foreign material.We have finished preliminary measurements on quartz, sapphire, and germanium.On all of these materials the thermal impulse response of the block temperature deter-mined with a superconducting bolometer has been measured and partially analyzed.Impedance studies have been completed for sapphire and quartz. These data precipitateda large theoretical effort to develop a new model for the boundary thermal conductance.This was necessary, since the decay of temperature of the blocks proved not to be asingle exponential. Correspondingly, the thermal impedance varied over a decade ratherthan over an octave as would be expected for a simple exponential decay. We have hadsome initial success in explaining these results by using a two-thermal-reservoir modelfor the crystal; that is, a model in which two nearly uncoupled degrees of freedom carrythe thermal energy. For example, these could be the longitudinal and transverse latticemode branches. The thermal resistance at the boundary which we determine from thismodel is in agreement with the value determined by other methods. JSEPPR No. 115 103

IX. TRANSPORT PHENOMENA IN SOLIDSAcademic and Research StaffProf. Malcom W. P. StrandbergJohn D. KiersteadA. SURFACE THERMAL ENERGY TRANSPORT JSEPJoint Services Electronics Program (Contract DAAB07-74-C-0630)Malcom W. P. Strandberg1. ApproachTechnical heat transport parameters are usually determined from thermometry ona system with a known thermal flux. Elements of virtuosity are required to make thesemeasurements useful, since the temperature drops at the surfaces are very small. Thefluxes at low temperatures must be milliwatts or less so as not to overload the refrig-eration system. The thermal conductance is of the order of 0. 1 W/°K-cm 2 . Hence wemust measure tens of microdegrees.We have been studying the time behavior of the temperature of a block of insulatingcrystal when it is disturbed from equilibrium with a thermal reservoir by a heat pulse.The time decay of the temperature of the block to equilibrium can be interpreted to yielda value for the surface thermal conductance. The transient temperature of the block canbe measured easily even in the presence of slow drifts in the temperature of the reser-voir. To check these data, we also measure the influence of the thermal impedance ofthe block on the electrical impedance of a tiny bolometer which has been evaporated onthe block to monitor the temperature of the block. The frequency dependence of the elec-trical impedance of the bolometer then varies because of the frequency dependence ofthe thermal impedance of the block. This in turn depends on the boundary thermal con-ductance of the block.Once a thorough understanding of the thermal properties of the block has been estab-lished, other materials, metals, for example, can be studied by evaporating a film onthe block, or otherwise establishing thermal contact between the metal and the block.The perturbation of the thermal properties of the block produced by the foreign materialthen gives information about the thermal properties of the foreign material.2. ProgressWe have finished preliminary measurements on quartz, sapphire, and NaCl from1-3. 6*K. The thermal impulse response of the block temperature as determined witha superconducting bolometer has been measured and partially analyzed. Impedancestudies have also been started.We are now searching for the most efficient method for reducing these data. Above JSEPPR No. 116(IX. TRANSPORT PHENOMENA IN SOLIDS)JSEP the lambda point, 2. 17* K, the relatively small thermal diffusivity of helium I adds acharacteristic feature to the temperature decay signal, a long time-constant tail. Havingavailable the different time behavior of the various components of the temperature tran-sient signal in the long time interval that we record, we are able to separate the variouscomponents readily. By going below the lambda point in bath temperature, we are ableto increase the helium diffusivity by a factor of more than 6 orders of magnitude, so thatthe component arising from the helium I diffusivity vanishes dramatically. Our methodthus allows us to gather data above the lambda point. This temperature region must beavoided in the alternative stationary-flux method because of the small diffusivity ofhelium I.In order to confirm our present understanding of the observed phenomena, we haverecently made a series of measurements of the Kapitza resistance, that is, the boundarythermal conductance between a solid surface and liquid or vapor helium. These mea-surements were made with a set of NaC1 blocks of different volume-to-surface ratios.Since the decay time of the block temperature that indicates the thermal energy in thevolume of the block depends on the surface area, the observed decay of the temperatureof the block will have one time constant that depends on the volume-to-surface ratio;hence, it is geometry-dependent.The situation that we have studied is analogous to the situation that occurs when mea-suring the surface impedance of a microwave cavity resonator by recording the timedecay of the electromagnetic energy in the cavity after an impulse excitation of the cav-ity. The energy stored in the volume of the cavity is lost through the walls in an amountgiven by the integral over the cavity surface of the electromagnetic Poynting's vector.Changing the geometry of the cavity while holding the resonance frequency constant thenleads to a system in which the decay times are geometry-dependent.In the case of the transport of thermal energy, the block is resonant at innumerableacoustic frequencies, so it is really an untuned resonator. The crystal can be mademore or less pure so that volume scattering can be varied at will. For a pure crystal,the mixing of modes will only occur at the surface. The three acoustic branches canthus be thought of as three nearly independent acoustic energy reservoirs. The decayof the block temperature, as monitored by a tiny thin-film bolometer evaporated on theblock could therefore indicate several rates of decay of the thermal energy of the block,if the phonon transmission coefficient depended on frequency.The data indicate that we can determine the Kapitza resistance from the time-domaintransient and that the Kapitza transient decay time constant scales properly with theJSEP sample volume -to- surface ratio.PR No. 116

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Transport Phenomena in Solids

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