Atom Graduate Physics Laboratory Handbook: Ferroelectric Crystals
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2.1.7 Ferroelectric Crystals and Critical Phenomena

The transition from a ferroelectric ordered crystal state to a disordered paraelectric state is accompanied by the thermodynamic anomalies of a second order critical point. This is easily seen in measurements of the dielectric constant versus temperature in which the dielectric constant diverges with an exponent at the transition (critical) temperature. The order parameter of the transition, the electric polarization, can also be measured versus temperature to determine the ordering exponent .

The lab has some pieces of the crystal triglycine sulfate (TGS) which can be cleaved to make thin flat samples for capacitance measurements. Our supply of TGS is limited and requires special care to assure its continued usability. Electrodes can be made u sing silver paint or evaporation. The transition is at 49.25°C and can be easily reached in a heated oil bath. The lab has a large dewar, temperature control and a special 0.01°C mercury thermometer for this temperature region. The capacitance can be measured using a capacitance bridge. Since the dielectric constant becomes quite large and temperature depende nt near Tc, achieving good temperature control and sensitive temperature measurements is a major challenge in the measurements.

Extensions of the experiment might include a thermistor bridge for improved temperature resolution, automated recording of 1/ versus T using an X-Y recorder with an AC voltmete r and temperature bridge having recorder outputs. One might also use the X-Y recorder or PC equivalent with an electrometer to measure the field and temperature dependence of spontaneous polarization. The hysteresis loops can be directly recorded on the recorder.

References
  1. F. Jona and G. Shirane, Ferroelectric Crystals, New York: Macmillan (1962), Chaps. I and II. This is a basic reference on the field prior to the ``critical phenomena revolution'' of the 1960's.   QD931.J6.
  2. J. A. Gonzalo, ``Set of Experimental Critical Exponents for Ferroelectric Triglycine Sulfate,'' Phys. Rev. Lett. 21, 749 (1968).
  3. J. A. Gonzalo, ``Critical Behavior of Ferroelectric Triglycine Sulfate,'' Phys. Rev. 144, 662 (1966). Reports measurements of the susceptability exponent, 2#2.
  4. P. P. Craig, ``Critical Phenomena in Ferroelectrics,'' Phys. Lett. 20, 140 (1966). QC1.P656. Reports measurements of the susceptability exponent, 2#2.
  5. K. Ishida, H. Tamada, T. Sekido, Y. Shiosaki and T. Mitsui, ''X-Ray and Dielectric Studies on the Critical Phenomena in Triglycine Sulfate,'' Phys. Lett. 25A, 5 (1967).
  6. T. Sekido and T. Mitsui, ``Dielectric Constant of Triglycine Sulfate at the Curie Point,'' J. Phys. Chem. Solids 28, 967 (1967).
  7. E. Nakamura, T. Nagai, K. Ishida, K. Iroh and T. Mitsui, ''Studies on the Mechanism of the Phase Transition in TGS,'' J. Phys. Soc. Jpn. 28, 271 (1970).
  8. S. Hoshino, T. Mitsui, F. Jona and R. Pepinsky, ``Dielectric and Thermal Study of Tri-Glycine Sulfate and Tri-Glycine Fluoroberyllate,'' Phys. Rev. 107, 1255 (1957). Makes connection between mean field theory and measured quantities.
  9. B. A. Strukov, ``Critical Phenomena in Ferroelectric Crystals and Liquid Crystals'', Izv. Akad. Nauk SSSR, Ser. Fiz. (Bull. Acad. Sci. USSR, Phys. Ser.) 47, 548 (1983).
  10. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena, New York: Oxford University Press (1971). See Chap. 10 on mean field theory.  QD501.S78.
  11. C. B. Sawyer and C. H. Tower, ``Rochelle Salt as a Dielectric,'' Phys. Rev. 35, 269 (1930). Describes a technique for measuring the spontaneous polarization with a scope. This is better done now with a slow sweep and an electrometer to monitor the voltage on the charge-measuring capacitor.
  12. H. Horowitz and W. Hill, The Art of Electronics, (Cambridge University Press, Cambridge, 1989). In  Grad Lab library. Describes a capacitance controlled oscillator circuit which could be used to measure capacitance.
  13. Moore, J. H., Davis, C. C., Coplan, M. A., Building Scientific Apparatus, 2nd Edition, London: Addison Wesley & Co., 1989. In Grad Lab library.  There a useful chapter on temperature measurement and control.
  14. YSI Super-Stable Thermistor descriptions of bridge resistance measurement, temperature probe details, spec sheets for 5K thermistor, least square fitting results for 45 to 55 °C for T(R).
  15. YSI Thermistor Info and Hg thermometer emergent stem corrections.
    16.
  16. Hg Thermometer Stem Corrections.
  17. Properties of Common Liquids.  Useful for calculating heat capacity and time constant of bath.
  18. Dimensions and image of current TGS sample.
    19.
  19. M. E. Fisher, "Renormalization group theory: Its basis and formulation in statistical physics," Reviews of Modern Physics, 70, 653 April (1998)

 

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