Filament Temperatures from Geometry-Independent Electron Emission Functions

Abstract

By expressing the surface area of an electricalIy heated body in terms of its current-voltage characteristics and substituting in the Richardson equation, electron emission functions ](i) having the linear form log f(i) ----~--~/T are derived which fix the temperature of the body independent of its crosssectional area or dimensions. The functions f(i) can be directly determined experimentally; a and ~ are logarithmic functions of resistivity, emissivity, and the electron emission constants. In the simplest case a simultaneous measurement of electron emission and heating current is sufficient to fix the temperature. The method has particular application to vapor deposited filaments, and experimental determination of the emission functions has been made for "asdeposited" zirconium and thorium. For the former a spread in temperature prediction at 1600~ of +--5 ~ was obtained from filaments 2-18 cm in length and 0.03-0.17 cm in diameter; for similar thorium filaments the spread was ___30 ~ Resistivities, emissivities, and electron emission constants were measured for both metals from 1300 ~ to 1800~ and found to be consistent with literature data and the derived functions.The temperatures of unviewable filaments of known geometry have been estimated variously (1) by measurement of heating current I, resistance R, voltage drop E or heat dissipation W, making use of either an initial calibration or of known values of resistivity or emissivity. In cases where a filament of length L is of unknown diameter, it is in principle possible to regard the function EP/3/L as being constant at a fixed temperature (1-3) for a cylindrical filament; the function can be determined experimentally for filaments of irregular surface (2). Although this function can be used to regulate the growth temperature in a vapor deposition process (2, 4) it is found to give variable temperature definition (5, 6) and to be impurity sensitive (5). In the converse case of filament vaporization (3) the function was found to decrease in value as vaporization proceeded.In the present work four electron emission functions are derived which enable the temperature of an unseen filament of unknown diameter or dimensions to be determined from the measurement of its electron emission and, variously, heating current, voltage drop, or both. It is shown experimentally that the functions derived can be applied to "iodide" zirconium and thorium filaments, giving somewhat better temperature estimation for filaments of comparable purity than the EI1/3/L function, and considerably less temperature spread for filaments of differing purity. Physical and emission data determined for "as-deposited" filaments of both metals are presented, together with the experimentally determined values of the emission functions for each.Application of the method and the choice of emission function are discussed. Derivation of FunctionsThree diameter independent functions are derived, two of these requiring only one variable, besides electron emission, to be measured. A fourth, geometry i...