Fig. 2: Repeated heating and cooling scans for a series of DWNTs.

Arrows show the direction of temperature change during the scan. a CNT G is a (29,1)@(35,6) DWNT as identified by TEM and ED (left half: measured ED pattern, right half: simulated ED pattern using code DIFFRACT) (i). The initial heating at \(1.2\times {10}^{-6}\) bar (ii) from room temperature (\({T}_{{{{{{\rm{o}}}}}}}\)) produces a large \({T}_{\max }\) = 701.1 K but subsequent cooling (iii), heating (iv), cooling then heating (v), and final cooling (vi) shows no other hysteresis. \({T}_{\max }\) values from (ii) to (vi) are 423.1, 423.3, 405.0, and 400.0 K, respectively. b CNT X is a (28,5)@(28,11) DWNT by ED (i) and when the initial scan at \(1.9\times {10}^{-8}\) bar starts at 445.7 K towards 643.8 K with subsequent cooling to \({T}_{{{{{{\rm{o}}}}}}}\), the large \({T}_{\max }\) is not observed, but rather 350.6 K for (ii), upon reheating (iii) yielding 356.5 K, cooling (iv) 354.4 K, heating (v) 368.7 K and final cooling (vi) 354.3 K. c CNT F is a (19,3)@(22,11) DWNT from ED (i) and heating from RT at \(1.2\times {10}^{-6}\) bar (ii) shows the high \({T}_{\max }\) at 565.4 K initially, but the value falls to a consistent 350 K upon heating again from \({T}_{{{{{{\rm{o}}}}}}}\) (iii), tracing the same trajectory on repeating (iv) with \({T}_{\max }\) = 352.3 K and again (v) at 355.0 K. For all 93 scans analyzed in this work, the features of these trajectories are consistently observed. The red trace line in the plot is an analytical fit using Eq. (6), and the fitting parameters are provided in Supplementary Table 12. The scale bar in ED is 2 nm⁻¹. Source data are provided as a Source Data File.