(a) Quartz crystal axes and AT-cut crystal. (b) Frequency shift over QCM resonant frequency, df/f, as a function of temperature for three different cut angles. (Related Article(s): Reprinted with permission from http://large.stanford.edu/courses/2007/ph210/hellstrom2/. Original source: J. Janata, Principles of Chemical Sensors (Plenum, Year: 1989)
and Related Article(s): G. Sauerbrey, Z. Phys.155, 206 (Year: 1959)10.1007/BF01337937
. Copyright 1989, Springer.) 27
Frequency shift versus temperature for the AT crystals employed here, cut at 35 ° 13′ ± 1′. Image supplied by the Colorado Crystal Corporation. The upper left inset is a typical frequency response to an ambient temperature step function. (Reprinted with permission from Related Article(s): A. W. Warner “Micro weighing with the quartz crystal oscillator–theory and design,” in Ultra Micro Weight Determination in Controlled Environments, edited by S. P. Wolsky and E. J. Zdanuk (Interscience, New York, Year: 1969)
, Fig. 5.2. Copyright 1969, Interscience.) Abrupt decreases in the temperature surrounding the QCM result in transient and positive frequency jumps while abrupt increases in temperature result in transient drops in frequency.
Experimental apparatus. (a) Customized RHK STM sample holder. The upper right inset is a blank crystal (left) and a sample with electrodes on both sides (right). (b) Schematic of thermocouple connection between RHK STM sample holder and sample stage (courtesy of A. Kollin). (c) Image of RHK UHV300 STM sample stage (courtesy of S. Palmer).
Frequency shift versus time at room temperature on a gold electrode, where the tip and sample temperatures are equal. The frequency increases when the tip is in contact with sample surface by ∼+30 Hz during indentation and all shifts are abrupt.
Frequency shift vs. time for a sample that is warmer than the tip. The sample is a 14% Au-Ni alloy at 62 ± 0.5 °C and the tip is close to room temperature. The tip depth is 3.0 nm and the oscillation velocity amplitude is 111.5 cm/s.
Frequency shift versus time for a sample that is cooler than the tip. The sample is a 14% Au-Ni alloy at 68.5 ± 2 °C and the tip is close in temperature to the chamber wall held at 101 ± 0.5 °C. The tip depth is 2.0 nm and the oscillation velocity amplitude is 143.5 cm/s. The shaded region corresponds to times when the tip is in contact with the sample surface. The frequency shift is ∼+70 Hz during tip indentation.
Frequency shift versus time with chamber walls at elevated temperature as the sample temperature is increased. The chamber wall temperature was kept at 145.5 ± 0.5 °C. The tip depth is 3.0 nm and oscillation velocity is 143.5 cm/s. Sample temperatures from clockwise are (a) at 96 ± 0.5 °C, (b) at 105 ± 0.5 °C, (c) at 118.5 ± 0.5 °C, and (d) at 128.5 ± 0.5 °C. The shade parts represent the process that the tip is in contact with sample surface. The data presented in (c) correspond to the tip and sample contact at the same temperature.
Initial frequency jump Δf initial jump versus temperature between the tip and sample surface. Tip indentations were repeated at different positions with depth ∼2 nm and oscillation driving voltage ∼3.0 V. Frequency shifts were averaged values for different measurements. The data are well described by Δf initial jump = A + B(ΔT) with A = 2.45 ± 0.81 and B = −0.79 ± 0.05
Schematic diagram of a STM tip with contact radius R in contact with a sample surface below it. The tip is comprised of two parts. The upper part, the tip body, is a cylinder, and the lower part is a truncated cone with half angle α.
Temperatures distribution on a sample surface under a thermal current over 0 < r < R. The y value is proportion to the maximum temperature at the center.
Temperature changes of different part of the system due to various temperature differences between the tip and sample surface. These results are obtained from Eqs. (8) and (9) with the parameters described in text. The temperature is in °C.
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