Rik's Python script for InSb Pressure Gauge

This page is an attempt to sum up the stuff I've picked up about HTML forms from magazines, reference manuals, other www pages etc.
Mostly I've been using the page as a test bench, and then kept the results for future reference.
And if anyone else can benefit from it, then that's good.

Of course, there must be a lot missing. And there may even be some things that are completely wrong. And since I don't have neither the time nor the will to test all different browsers, your results may differ from what I write. Initially, I mostly used Netscape 2.0. For the latest update I ran through the examples again, this time with Mozilla 1.5. However, most of the stuff described here is old news and should by now be usable in any environment.

The use of pressure cells in solid state physics is becoming more and more important due to the enormous possibility given by the effect of a gradual increase of pressure in on solids. The crystal structure can be heavily modified and consequently also the electronic structure may change dramatically driving the system through important and unexplored phase transition.

The knowledge of pressure is of course fundamental: it is often important to study a system at the edge of a phase transition where the physical properties of the matter drastically change. In order to do this a precise measurement of the pressure is required.

Many experimental groups are equipped with different kinds of pressure cells made of ultra-resistent materials and very often designed for very special purposes always related to the experimental techniques that will be used. Even though there are common problems that arise when such pressure cells are exposed to extreme conditions such as cryogenic temperatures and/or pressure: for example, every pressure cell is loaded with a pressure-transmitting medium which should guarantee hydrostatic pressure conditions during the experiment. This medium (liquid He, daphne oil, kerosene, etc.) can itself undergo phase transitions which could give volume change, change in viscosity etc. and finally alter the pressure inside the pressure cell. For this reason it is important to have the possibility to monitor "real-time" the situation in our experiemntal system and in particular in a pressure cell.

A material that is suitable for pressure measurement is the heavily n-doped InSb.

The resistance of this material is strongly temperature and pressure dependent. The calibration procedure consists in measuring the temperature dependence of the resistance R(P=0,T) (for example using a 4-points measuremnt) and than normalizing it by the resistance at liquid nitrogen R(P=0,77 K) In this way it is possible to define

r(T) = R(P=0,T)/R(P=0,77 K)

This normalized curve can be fitted using a simple polynomial function of the following form

r(T) = A0 + A1T + A2T2 + A3T3 + A4T4

The parameters A_i are sample-dependent except in the case where two samples are cut out from the same wafer. In the table below those value are already provided but in general they should be changed accordingly to your gauge characteristic temperature dependence.

Once known the r(T) function three is another parameter required in order to extract the pressure: the resistance of the gauge at ambient temperature (294 K) which serves together with r(T) as a calibration point (in the case of gauges coming from the same batch r(T) won't change but the resistance itself will depend by the geometry of the sample and of the contacts).

At this point the gauge is ready to be inserted in the pressure equipment. During the cryogenic measurement it is fundamental to record the temperature T and the corresponding resistance R(P=???,T). With these two informations it is possible to extract the pressure at each temperature point just by properly filling the missing parameters in the table below.

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