Measuring seebeck coefficient
A high temperature Seebeck coefficient measurement apparatus and method with various features to minimize typical sources of errors is described. Common sources of temperature and voltage measurement errors which may impact accurate measurement are identified and reduced. Applying the identified principles, a high temperature Seebeck measurement apparatus and method employing a uniaxial, four-point geometry is described to operate from room temperature up to 1300K. These techniques for non-destructive Seebeck coefficient measurements are simple to operate, and are suitable for bulk samples with a broad range of physical types and shapes.
1. An apparatus for measuring a Seebeck coefficient of a sample, comprising:
a first heater assembly having a first bore therethrough exiting at a first substantially perpendicular surface for contacting and producing a first isothermal sample surface;
a first thermocouple having a first axis of a first slender geometry where temperature and voltage are sensed at an end of the first axis, the first thermocouple disposed in the first bore of the first heater assembly to contact the first isothermal sample surface;
a second heater assembly having a second bore therethrough exiting at a second substantially perpendicular surface for contacting and producing a second isothermal sample surface on a sample side opposite the first isothermal sample surface; and
a second thermocouple having a second axis of a second slender geometry where temperature and voltage are sensed at an end of the second axis, the second thermocouple disposed in the second bore of the second heater assembly to contact the second isothermal sample surface.
2. The apparatus of claim 1 , wherein the first bore and the second bore are aligned such that the first axis of the first thermocouple and the second axis of the second thermocouple are substantially collinear.
3. The apparatus of claim 1 , wherein the first thermocouple and the second thermocouple each comprise an electrically insulating cylinder having four bores exiting at an end surface of the cylinder and two thin wires, each wire threaded through two of the four bores and crossing to contact each other at the end surface.
4. The apparatus of claim 3 , wherein the two thin wires comprise material combinations X/Y of niobium/chromel, niobium/tungsten, niobium/tungsten-rhenium, copper/constantan, or gold-iron/chromel, where X is a first wire material disposed on top of a second wire material Y.
5. The apparatus of claim 3 , wherein the electrically insulating cylinder comprises a ceramic.
6. The apparatus of claim 5 , wherein the ceramic comprises mullite.
7. The apparatus of claim 1 , wherein the first heater assembly and the second heater assembly each comprise an insulating ceramic.
8. The apparatus of claim 1 , wherein the first heater assembly and the second heater assembly each comprise a plurality of embedded cartridge heaters.
9. The apparatus of claim 1 , further comprising compressive springs to apply force to the sample between the first heater assembly and the second heater assembly.
10. A method of measuring a Seebeck coefficient of a sample comprising the steps of:
disposing a first heater assembly having a first bore therethrough exiting at a first substantially perpendicular surface to contact the sample and produce a first isothermal sample surface;
disposing a second heater assembly having a second bore therethrough exiting at a second substantially perpendicular surface to contact the sample and produce a second isothermal sample surface on a sample side opposite the first isothermal sample surface;
measuring temperature of the first isothermal sample surface with a first thermocouple having a first axis of a second slender geometry where temperature and voltage are sensed at an end of the first axis, the first thermocouple disposed in the first bore of the first heater assembly to contact the first isothermal sample surface;
measuring voltage of the first isothermal sample surface with the first thermocouple; measuring temperature of the second isothermal sample surface with a second thermocouple having a second axis of a second slender geometry where temperature and voltage are sensed at an end of the second axis, the second thermocouple disposed in the second bore of the second heater assembly to contact the second isothermal sample surface;
measuring voltage of the second isothermal sample surface with the second thermocouple; and calculating the Seebeck coefficient of the sample from the temperatures and voltages of the first isothermal sample surface and second isothermal sample surface.
11. The method of claim 10 , wherein the Seebeck coefficient is calculated from temperature and voltage measurements taken symmetric with time.
12. The method of claim 10 , further comprising aligning the first bore and the second bore such that the first axis of the first thermocouple and the second axis of the second thermocouple are substantially collinear.
13. The method of claim 10 , wherein the first thermocouple and the second thermocouple each comprise an electrically insulating cylinder having four bores exiting at an end surface of the cylinder and two thin wires, each wire threaded through two of the four bores and crossing to contact each other at the end surface.
14. The method of claim 13 , wherein the two thin wires comprise material combinations X/Y of niobium/chromel, niobium/tungsten, niobium/tungsten-rhenium, copper/constantan, or gold-iron/chromel, where X is a first wire material disposed on top of a second wire material Y.
15. The method of claim 13 , wherein the electrically insulating cylinder comprises an insulating ceramic.
16. The method of claim 15 , wherein the ceramic comprises mullite.
17. The method of claim 10 , wherein the first heater assembly and the second heater assembly each comprise boron nitride.
18. The method of claim 10 , wherein the first heater assembly and the second heater assembly each comprise a plurality of embedded cartridge heaters.
19. The method of claim 10 , further comprising compressive springs to apply force to the sample between the first heater assembly and the second heater assembly.
20. An apparatus, comprising:
a first heater assembly means for contacting and producing a first isothermal sample surface, the first heater means having a first bore therethrough exiting at a first substantially perpendicular surface;
a first thermocouple means for measuring temperature and voltage, the first thermocouple means having a first axis of a second slender geometry where temperature and voltage are sensed at an end of the first axis, the first thermocouple means disposed in the first bore of the first heater assembly means to contact the first isothermal sample surface;
a second heater assembly means for contacting and producing a second isothermal sample surface on a sample side opposite the first isothermal sample surface, the second heater assembly means having a second bore therethrough exiting at a second substantially perpendicular surface; and
a second thermocouple means for measuring temperature and voltage, the second thermocouple means having a second axis of a second slender geometry where temperature and voltage are sensed at an end of the second axis and the second thermocouple means disposed in the second bore of the second heater assembly means to contact the second isothermal sample surface.
21. The apparatus of claim 20 , wherein the first thermocouple means and the second thermocouple means each comprise an electrically insulating cylinder having four bores exiting at an end surface of the cylinder and two thin wires, each wire threaded through two of the four bores and crossing to contact each other at the end surface.