We have studied the motion of the wire in solid 4He over a wide range of temperatures and driving forces. We have studied several different solid samples. We grow the samples by varying the pressure at an approximately constant temperature. For the measurements presented below, the samples were grown at low temperatures, below 10 mK. Different samples show qualitatively similar behavior. At low driving forces (low stress), we observe slow motion of the wire in both the hcp and bcc phases above 1 K. This type of motion was studied previously in the vicinity of the bcc-hcp phase transition [11, 12] and is thought to be due to the diffusion of vacancies around the wire via quantum tunneling [13]. The first attempt at measuring the motion of an object through solid helium was made by Andreev et al. [14] in 1969. Later measurements were performed on dragging rods and spheres through the solid [15] and also on the plastic deformation of single crystals [16].
Below we present some preliminary measurements on the behaviour of the wire at high driving forces (high stress). All the measurements were taken at temperatures above 1 K and at pressures close to the melting curve. At lower temperatures we see no significant motion of the wire down to temperatures below 10 mK. Measurements made with lower driving forces will be discussed elsewhere.
Measurements in the hcp Phase
Figure 3 shows measurements for large driving forces in the hcp phase at a temperature of T=1.15 K and a magnetic field of B=1.99 T. At a time t=927 s the driving force is ramped linearly from F=−9.3 mN to F=+9.3 mN over a period of 105 s. At first, the wire remains stationary at a position x=0.08 mm. At t=1343 s, the wire suddenly moves to x=0.9 mm and then abruptly stops. It remains here until t=1921 s when the wire suddenly moves to x≈1.0 mm. After this there are a further five steps and the wire finally reaches x≈1.5 mm at t=6627 s, more than an hour after the force was changed. Then, at t=7033 s force is ramped back to F=−9.3 mN over a period of 105 s. Just before the end of the ramp, the wire suddenly moves to x=0.07 mm for a short period and then moves to x=−0.8 mm.
The behaviour is highly stochastic, the step distance and the time at which a step occurs vary randomly over a wide range. If the driving force is kept at a constant value, then the wire will continue to step in the direction of the force until it reaches the wall of the cell. (When it touches the wall it often becomes partially stuck and larger forces are needed to detach it.) During a step, the wire velocity is very large. For the data shown in Fig. 3, the time between the measurement points is approximately 60 ms. The larger steps are seen to occur over a time period of Δt≈300 ms and the velocity of the crossbar during the step often exceeds 1 mms−1. Such velocities are enormous compared to typical velocities, v≈1 nms−1, observed at low driving forces [11].
We further note that the steps are only observed in the hcp phase at temperatures above ∼1.1 K and we do not observe any changes in pressure during the steps.
Measurements in the bcc Phase
Figure 4 shows measurements in the bcc phase. We plot the position of the wire crossbar versus time, note that the time axis now spans more than 4×105 s≈5 days. The driving force starts at a large positive value, F=3.1 mN. At time t=1602 s the force is ramped linearly to a large negative value F=−3.1 mN over a time period of 80 s. The wire responds immediately, moving in the direction of the force. The initial wire velocity, v∼−1 μms−1, is much slower than that observed during the step-like motion in the hcp phase discussed above. However the wire velocity falls rapidly at first, reaching a near constant value of v∼−7 nms−1 after ∼5000 s. The motion then remains quite uniform until the driving force is quickly ramped to zero at t=80937 s.
Remarkably the wire is not stationary in the absence of an applied force. Instead, it relaxes very slowly towards some new position. The initial velocity after removing the driving force is comparable to the velocity before removing the force, but is in the opposite direction. The velocity then slows over the next couple of days, reaching a near constant value of v≈0.4 nms−1, indicated by the dashed line in the Fig. 4. By comparing with our measurements at low driving forces, we conclude that the bare restoring force of the wire, which can be found from the data in Fig. 2, is roughly ten times too small to account for the late time behaviour. Presumably after waiting for a sufficient time, the wire will stop at some final resting place which will depend on its history. However, the time scales are very long, even after several days the wire shows no sign of slowing further.