Journal of Low Temperature Physics, Vol. 124, Nos. 34, 2001
Giant Heat Release and Time-Dependent Thermal Expansion of Nb-Ti-D C. Kockert, S. Abens, U. Escher, B. Kluge, A. Gladun,* S. Sahling, and M. Schneider Institut fur Tieftemperaturphysik, Technische Universitat Dresden, 01062 Dresden, Germany *E-mail: gladunphysik.tu-dresden.de (Received January 15, 2001; revised March 20, 2001)
Glasslike anomalies of low-temperature thermal properties were observed for the polycrystalline Nb 37 Ti 63 alloy and Nb 37 Ti 63 doped with deuterium. A giant heat release effect was found in (Nb-Ti) 92 D 8 corresponding to a spectral density of two level systems of 7.8 } 10 45 J &1 m &3. After rapid cooling of the sample a length relaxation with a quadratic dependence on the starting temperature was detected obeying a logarithmic time dependence. The results fit to the standard tunneling model assuming a temperature and time independent Gruneisen parameter. A constant Gruneisen parameter is compatible with a constant deformation potential # but requires * V to depend on 22 0 . For both systems the thermal expansion coefficient exhibits a linear temperature term in the superconducting state dominating below 1 K. 1. INTRODUCTION Different systems of disordered crystals with glasslike low temperature elastic and thermal properties can be understood in terms of a broad distribution of two-level systems (TLS) as proposed by the standard tunneling model (STM) for amorphous systems. 1, 2 Due to this broad distribution a long-time heat release after rapid cooling was found for different amorphous and glasslike crystalline materials. 35 Together with the heat release, a time dependent change of the sample length is possible according to the STM and the soft potential model. 6 However, the resolution of the present dilatometers is not high enough to observe this effect on typical amorphous solids like vitreous silica. In order to find glasses with a larger effect, we investigated the heat release of different glasslike crystalline materials and found a giant heat release in (Nb-Ti)D with high Ti and D concentrations. This encouraged us to measure the thermal relaxation of 477 0022-2291010800-0477819.500 2001 Plenum Publishing Corporation
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the sample length, after rapid cooling from higher temperatures, for this system. Glasslike excitation spectrums have been reported in Nb-Zr 7 and Nb8 Ti alloys for certain ranges of composition. In these |-; alloys the bodycentered cubic ; phase can coexist with precipitates of a metastable hexagonal | phase. The transformation between these structures is diffusionless and is assumed to give rise to the low energy glasslike TLS. 7 Glasslike acoustic properties were observed in Nb-Ti for Ti concentrations between 40 and 80 at 0. 9 The ; phase structure can be stabilized by charging NbTi with hydrogen or deuterium. 10, 11 At the same time, a new class of TLS is produced by H (D) with a high density of states of TLS, depending on the Ti and H (D) concentration.4, 12 The solubility of H (D) increases with Ti concentration. Neutron scattering experiments have shown that the H (D) is trapped near the Ti atoms. 13 Heat release experiments with concentrations of up to 20 at0 Ti and up to 4 at 0 D showed that the heat release is more strongly dependent on the Ti concentration than on the D concentration. 4 In addition, larger values of the heat release were observed for D in comparison with H at the same concentration, 4 in contrast to heat capacity measurements, where no significant isotope effect was found. 12 In this paper we present the results of heat release and time dependent thermal expansion measurements on a Nb 37 Ti 63 alloy with and without 10 at0 D. The investigations are complemented by measurements of the thermal expansion coefficient. A few of our results on Nb-Ti-D have been reported previously. 14
2. EXPERIMENTAL 2.1. Measurement of Heat Release In the long-time heat release measurement the sample is suspended by thin threads in the sample chamber of a calorimeter and rapidly cooled down from the starting temperature T 1 to a (phonon) temperature T 0 by a mechanical heat switch. Then the sample is thermally isolated by opening this switch. Since tunneling systems with relaxation time { longer than the cool down time remain in a nonequilibrium state, their following relaxation leads to an energy transfer Q4 from the tunneling systems to the phonons which can be detected by measuring the temperature rise of the sample: Q4 (T 1 , T 0 , t)+Q4 A +Q4 B =C(T 0 )(dTdt),
(1)
Giant Heat Release and Time-Dependent Thermal Expansion of Nb-Ti-D
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where C is the heat capacity of the sample, including the heater, the thermometer and the copper wire of the heat switch. It was measured in a separate run. dTdt is the temperature drift measured near T 0 , Q4 A the heat flow due to the electrical wires and sample support and Q4 B the parasitic heat flow caused mainly by electromagnetic noises and the measuring power of the thermometer. Q4 B was measured for low starting temperature T 1 and for a long time, when the heat release of tunneling systems is negligible. For example, Q4 B =1.7 nW was obtained in the experiment with (Nb-Ti) 92 D 8 . The heat link Q4 A is given by Q4 A =(T 0 &T (t))R A , where T (t) is the measured temperature of the sample. The experimentally determined heat resistance R A equals 10 7 KW at T 0 =1.3 K. The temperature of the sample chamber, measured by a calibrated Ge-thermometer, is held constant at T 0 by a temperature controller. If the sample temperature gets too high, the sample is cooled down again to T 0 by closing the heat switch for a short time. To be sure of starting from thermal equilibrium, the sample was kept at the starting temperature for at least twice the maximum measuring time before cooling. The maximum measuring time is limited by the fluctuation of the parasitic heat flow of 50 pW.
2.2. The Dilatometer Measurements of thermal expansion were performed using a low temperature capacitance dilatometer based on the apparatus of Pott and Schefzyk. 15 The measuring cell is shown schematically in Fig. 1. The sample of 10 mm length and about 6 mm thickness is clamped between the fixed and the movable parts of the cell, which are fixed together by two spring washers. The cell is anchored to a copper block held at the desired temperature. At T>2 K the thermal contact is enhanced by helium exchange gas. Length changes of the sample result in a change of the gap of a plate capacitor. The temperature T is recorded by a Cernox resistor and can be stabilized by a temperature controller. The cell is manufactured from high purity copper and is calibrated by measuring a copper sample whose expansion values are taken from Kroger and Swenson. 16 By additional measurements performed on high purity aluminum, 16 deviations from the ideal capacitor behavior due to tilted, non-flat plates and field inhomogeneities at their edges are included in the cell calibration. The resolution is 1 } 10 &2 A1 . Experiments above 2 K are performed in a 4He cryostat. For 0.3 K
