Thermometer hysteresis

A typical test speed is 32 kph at a load of 55 kg. The surface temperature of the wheel can be measured using an infrared thermometer. Failure will be due to hysteresis work, and the part will decompose from the inside out. 

Another resonant-frequency thermometer is the quartz crystal resonator (Benjaminson and Rowland, 1972), which, if the crystal is properly cut, is quite linear from about 190 to 525 K. Although this thermometer has excellent resolution, it does exhibit hysteresis and drift. The principle of quartz crystal thermometry is based on the temperature dependence of the piezoelectric resonant frequency of a quartz crystal wafer of a given dimension. The angle of cut of the quartz crystal is selected to give as nearly a linear and yet sensitive correspondence between resonant frequency and temperature as possible. This angle of cut is referred to as an LC (linear coefficient) cut. The temperature sensitivity of the quartz crystal thermometer is about 1000 Hz/°C. 

For a quartz thermometer, the resonant frequency of a quartz crystal resonator is strongly related to the temperature variation. With high resolution, the temperature change can be directly determined from the frequency change of a quartz crystal thermometer. A quartz thermometer developed for use between -80 and 250°C [85] has a resolution of 0.1 mK. If used at the same temperature, a comparable precision can be achieved. However, with temperature cycling, hysteresis can reduce its repeatability. An accuracy of 0.05°C can be achieved with calibration. Nevertheless the temperature resolution for the quartz resonator is found to be less accurate at lower temperatures Over the temperature range from 4.2 to 400 K, the temperature resolution with the resonant frequency change for a YS cut quartz crystal thermometer drops from 1 kHz/K at 300 K to 80 Hz/K at 4.2 K [86]. 

Error Analysis and Measurement Assurance. Sources of error in a calibration include (1) difficulty in maintaining the fixed points, (2) accuracy of the standard thermometer, (3) uniformity of the constant temperature medium, (4) accuracy in the signal-reading instrument used, (5) stability of each of the components, (6) hysteresis effects, (7) interpolation uncertainty, and (8) operator error. Techniques for error analysis are described in a number of papers on experimental measurement [104,105]. 

A shorter time effect is the hysteresis of the thermometer. On heating it takes a thermometer bulb several minutes to reach its final volume, but on cooling, it may take many hours. The slow hysteresis effect involves 1-2 scale divisions for every 100 K of temperature change. It is best avoided by using the thermometer only in the heating mode. When cooling is necessary, temperature changes should be kept as small as possible. 

Quartz, since it is a piezoelectric and not a ferroelectric, has no hysteresis loss when it oscillates, thus quartz crystal oscillators are widely used as frequency control devices in radios, computers, and watches. Since the frequency is a function of the mass of the crystal, they can serve as deposition monitors (quartz crystal microbalances) with sensitivities of less than 1 ng. By functionalizing the surface to absorb specific gases, they can also act as chemical sensors. The temperature sensitivity of a quartz crystal oscillator can be minimized by choosing the cut of the crystal relative to the optical axis, which is necessary for its use as a frequency standard. On the other hand, a cut can be chosen to maximize the frequency dependence on temperature and quartz crystal thermometers with millikelvin resolution are available. 

Quartz Thermometers. Development of quartz crystal frequency thermometers continues. These devices use the small but highly reproducible variation of the natural vibration frequency of appropriately cut piezoelectric quartz samples. The sensors are compact and useful over a wide cryogenic range (4-400 K) with an accuracy within a few hundredths of a kelvin. There are, however, some problems with hysteresis and aging. 

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