Direct in situ thermometry: Variations in reciprocal-lattice vectors and challenges with the Debye-Waller effect

Conventional in situ transmission electron microscopy (TEM) enables the atomic-scale study of dynamic materials processes on millisecond time scales. Specimen holders capable of being heated to over 1000. °C have provided insight into myriad processes, including nanoscale thermal transport, structural phase transitions, and catalytic reactions. In order for such studies to be accurate and precise, direct determination of the specimen temperature - rather than the heating-element temperature - is critical. Further, such methods should be versatile in that any temperature across a wide range may be measured, irrespective of single-indicator properties specific to the specimen (e.g., first-order phase transition, melting point, etc.). Here, we describe a rigorous approach to direct, in situ thermometry of TEM specimens that exploits lattice thermal expansion and the resultant decrease in diffraction-vector magnitude in reciprocal space. Via sub-pixel measurement of reciprocal-lattice-vector magnitudes, picometer increases in lattice parameters are measured over a continuous temperature range and compared to those expected from the coefficient of thermal expansion. Statistical treatment of several experimental trials conducted on nanostructured aluminum thin films shows excellent agreement with both theory and (indirect) measurement of the in situ heating holder. Additionally, we illustrate how uncontrolled, thermally-induced variation in single-crystal orientation leads to modulation of the excitation error and, therefore, the Bragg-spot intensities resulting in a convolution of heating and tilting effects, thus complicating temperature determination via the Debye-Waller effect.