Nanocalorimetric sensor schematic, not to scale. (a) Top view, showing the metal heater layer, the supporting frame, and the ultrathin membrane. (b) Cross-section view. The sample (not shown) is usually deposited on the face of the membrane and directly opposite the metal heater.
Bright-field TEM micrographs for Bi and In films of two different thicknesses, showing the effect of heating. (a) Unheated Bi film, 5 nm thick, made up of unconnected, polygonal particles. (b) Another 5–nm Bi film, after being heated above . (c) Unheated 10–nm Bi film. Here, the film has formed an interconnected network. (d) Heated 10–nm Bi film. The particle size has increased dramatically over the heated 5–nm film, and the particles are also larger than in the heated In film of the same nominal thickness. (e) Unheated 5–nm In film. (f) Heated 5–nm In film. (g) Unheated 10–nm In film. (h) Heated 10–nm In film.
Mean particle radius vs average film thickness for Bi, In, and Sn. Data for Sn films above were not available. Note that, at , the Bi islands are larger than the In islands, even though the same amount of material was deposited. We speculate that this occurs because unheated Bi films are an interconnected network at film thickness, while In films are still composed of individual particles, as can be seen in Fig. 2.
Results from a two-step deposition, which created a bimodal particle size distribution. A Bi deposition was made in order to form large particles, then an additional deposited to form small ones. (a) A TEM micrograph showing a few very large particles combined with many smaller ones. (b) Heat-capacity data from the 10- and the films. The smaller particles have a lower , which can be seen in the small melting peak at . (c) Size distribution histogram for a deposition. (d) The low-radius section of a size distribution histogram for a film.
TEM micrographs and curves for three different Bi films. Top to bottom, the micrographs are of heated Bi films with nominal thicknesses of 0.3, 0.6, and thick. Particles get larger as the total deposition increases, and the melting temperature increases with the increasing size. Base line also increases, as the total deposited mass increases with thickness. In other words, .
Heat capacity as a function of thickness measured by the QCM. The dashed line represents the expected value calculated using bulk values for , , and the area of the deposited film. There is a decrease in , showing the difference in sticking between the initial surface of the calorimeter and the Bi-coated QCM.
Real-time calorimetry taken simultaneously with deposition. A constant, slow evaporation rate was established, and calorimetric scans taken at intervals. The shutter was opened, and (per the QCM) was deposited onto the sensor, simultaneous with the calorimetric scans. This figure shows the heat capacity as the evaporation proceeded.
Heat of fusion and melting temperature for a series of Bi films. (a) Heat of fusion as a function of film thickness for 23 different samples. Film thickness was calculated from the measured , bulk , and the area of the film. The bulk heat of fusion is shown by the dashed line. (b) Melting temperature for some of the thinner films, showing a decrease for thin films with small particles.
Melting temperatures as functions of particle sizes, using eight films with nominal thicknesses between 0.3 and . The dotted line is for Bi, . The dashed line shows the expected behavior calculated from the values using the HMM model and surface energies according to G. Allen et al. (Ref. 6). The dash-dot line is a linear fit to the squares. The experimental values for are obtained using the mapping procedure described in Ref. 10.
Comparison of our work with that from two other researchers. The dotted line is for Bi, . The dashed and dash-dot lines are the same as in Fig. 9. For clarity, only one point (the media) is shown for each of the eight films from this work.
Amount of superheating found by different researchers for Bi. At low rates, only a few degrees of superheating have been previously observed. At very high rates, the amount of superheating approaches . Note that the superheating for G. Allen et al., Peppiatt, and Murphy et al. is above , while for this work it is above the calculated from Eq. (1). The work of Murphy et al. was on a bulk, (0001)-oriented, Bi single crystal; all other work was on Bi nanoparticles.
Some material properties of Bi (see Ref. 6).
Experimentally observed superheating of various elements, both embedded in a matrix and freestanding.
Calculated Hamaker constants for several materials (see Ref. 37). The calculation was performed using frequency-dependent, complex dielectric functions.
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