Abstract
Negative thermal expansion (NTE) materials and structures exhibit the anomalous property of shrinking rather than expanding when heated. This work examines the potential of multi-material planar re-entrant and non-re-entrant honeycombs to exhibit anomalous thermal expansion properties. Expressions for the coefficient of thermal expansion as a function of the geometric parameters and intrinsic thermal expansion properties were derived for any in-plane direction. It was shown that re-entrant honeycombs, a metamaterial which is well known for its auxetic characteristics, can be made to exhibit NTE in specific directions when constructed from conventional positive thermal expansion (PTE) materials, provided that the slanting ligaments expand more than the vertical ligaments when heated and that the geometry is amenable. Conversely, it was shown that the construction of such honeycombs from NTE components will not necessarily result in a system which exhibits NTE in all directions. Furthermore, conditions which result in honeycombs demonstrating zero thermal expansion (ZTE) coefficients in specific directions were also explored.
Highlights
One of the “anomalous phenomena” which has been given considerable attention in the past decades is that of “negative thermal expansion” (NTE), i.e., shrinkage, rather than expansion, of a sample when this is subjected to an increase in temperature (Takenaka, 2018; Chen et al, 2015; Evans et al, 1997)
Common mechanisms operating at the nanoscale include ones which manifest a “rotating squares” profile in one of their planes where Negative thermal expansion (NTE) is manifested due to increased vibrational motion leading to closure of the motif with an increase in Negative Thermal Expansion Honeycombs temperature (Pryde et al, 1997; Bieniok and Hammonds, 1998; Heine et al, 1999; Dove et al, 2000; Tao and Sleight, 2003; Dove, 2019) and the “winerack” mechanism where NTE results from a scissors-like deformation (Goodwin et al, 2008)
2) For re-entrant honeycombs, intrinsic NTE properties of the ligaments do not guarantee an overall negative thermal expansion of the macrostructure since excessive shrinkage of the slanting ligaments when heating could lead to annihilation of the NTE effects and produce conventional macroscopic positive thermal expansion properties
Summary
One of the “anomalous phenomena” which has been given considerable attention in the past decades is that of “negative thermal expansion” (NTE), i.e., shrinkage, rather than expansion, of a sample when this is subjected to an increase in temperature (Takenaka, 2018; Chen et al, 2015; Evans et al, 1997). The angles between the ligaments remaining constant, as clearly illustrated, which shows a system at an elevated temperature T To + ΔT where h 7.5 (25% increase from 6), l 4 (100% increase from 2) and θ remains at 30°, the system shrinks in the vertical Ox2 direction from X2 8.54 to X2 8.07 (5.44% shrinkage) but exhibits conventional thermal expansion in the horizontal Ox1 direction (see Table 1 for measurements) This confirms that, through their design, the re-entrant honeycombs have the capability to exhibit linear negative thermal expansion when constructed out of conventional positive thermal expansion (PTE) materials. Maximum/minimum thermal expansion, including maximum NTE when present, occur at ζ 90+ (Ox2 axis) where the thermal expansion coefficient is given by Eq 12 and at ζ 0+, which corresponds to the Ox1 axis where the thermal expansion coefficient is always equal to αl since: dα (ζ ) dζ
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