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Problem: Montgomery Method

The resistivity of anisotropic samples is studied by using the Montgomery method tex2html_wrap_inline6531 . Assume that a thin, crystalline specimen is cut to square shape, so that the edges coincide with the principal axis of the resistivity tensor tex2html_wrap_inline6533 . There are four contacts at the corners of the sample (Figure 7.1). Dimensions tex2html_wrap_inline6535 , tex2html_wrap_inline6537 , and (perpendicular to the specimen) tex2html_wrap_inline6539 are tex2html_wrap_inline6541 mm and tex2html_wrap_inline6543 mm. In this geometry two elements of the resistivity tensor, tex2html_wrap_inline6545 and tex2html_wrap_inline6547 , can be determined by sending current and measuring voltage between various combinations of the contacts.    

   figure2265
Figure 7.1: Sketch of the geometry used in the Montgomery method of measuring resistivity.

The resistances tex2html_wrap_inline6549 and tex2html_wrap_inline6551 are defined as the ratio of measured voltages and currents in configurations indicated in the figure. tex2html_wrap_inline6553 tex2html_wrap_inline6517 and tex2html_wrap_inline6557 tex2html_wrap_inline6517 are obtained from the data. Use Montgomery's work to determine tex2html_wrap_inline6545 and tex2html_wrap_inline6547 . How would you change the sample geometry if the resistivity anisotropy is expected to be in the range of tex2html_wrap_inline6565 ?  


This document can be accessed on the World Wide Web at "http//:solidstate.physics.sunysb.edu/book/prob/ ".

Laszlo Mihaly
Thu Oct 31 13:23:11 EST 1996


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