Maximizing negative thermal expansion via rigid unit modes: A geometry-based approach

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 471, Issue 2179, 2015, Pages

  Grima, J N ^a   Bajada, M ^a   Scerri, S ^a   Attard, D ^a   Dudek, K K ^a   Gatt, R ^a  

^a UNIVERSITY OF MALTA   (Malta)

Author keywords

Auxetic; Negative poisson's ratio; Negative thermal expansion; Thermal contraction

Indexed keywords

BUOYANCY; EXPANSION; GEOMETRY; MECHANICAL PROPERTIES; OXIDE SUPERCONDUCTORS; POISSON RATIO; PORE SIZE;

AUXETIC; COEFFICIENTS OF THERMAL EXPANSIONS; INTERNAL ANGLES; NEGATIVE POISSON'S RATIOS; NEGATIVE THERMAL EXPANSION; RIGID UNIT MODES; THERMAL CONTRACTION; THERMO-MECHANICAL CHARACTERISTICS;

THERMAL EXPANSION;

EID: 84937150936     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2015.0188     Document Type: Article

References (73)

1. nd edn. Boca Raton, FL: CRC Press, pp. 167-182.
2. Scheel K. 1907 Ueber die ausdehnung des quartzglases. Verh. Dtsch. Phys. Ges. 9, 3-23.
3. 8. Science 272, 90-92. (doi:10.1126/science.272.5258.90)
4. 8 at high pressure. J. Phys., Condens. Matter 8417, 8417-8428. (doi:10.1088/0953-8984/10/38/004)
5. 3. J. Solid State Chem. 137, 148-160. (doi:10.1006/jssc.1998.7744)
6. Evans JSO. 1999 Negative thermal expansion materials. J. Chem. Soc. 1999, 3317-3326. (doi:10.1039/A904297K)
7. 8 revealed by high pressure inelastic neutron scattering. Phys. Rev. Lett. 86, 4692-4695. (doi:10.1103/PhysRevLett.86.4692)
8. 4. J. Solid State Chem 160, 230-238. (doi:10.1006/jssc.2001.9227)
9. 8. Phys. Rev. B 68, 134101. (doi:10.1103/PhysRevB.68.134101)
10. Tao J, Sleight A. 2003 The role of rigid unit modes in negative thermal expansion. J. Solid State Chem. 173, 442-448. (doi:10.1016/S0022-4596(03)00140-3)
11. Barrera GD, Bruno JAO, Barron THK, Allan NL. 2005 Negative thermal expansion. J. Phys. Condens. Matter 17, R217-R252. (doi:10.1088/0953-8984/17/4/R03)
12. Zhu J, Andres CM, Xu J, Ramamoorthy A, Tsotsis T, Kotov NA. 2012 Pseudonegative thermal expansion and the state of water in graphene oxide layered assemblies. ACS Nano 6, 8357-8365. (doi:10.1021/nn3031244)
13. Chen K, Song S, Xue D. 2013 Vapor-phase crystallization route to oxidized Cu foils in air as anode materials for lithium-ion batteries. Cryst. Eng. Comm. 15, 144-151. (doi:10.1039/C2CE26544C)
14. 12 and their relations to negative thermal expansion. Phys. Rev. B 90, 024305. (doi:10.1103/PhysRevB.90.024305)
15. Bruno J, Allan N, Barron T, Turner A. 1998 Thermal expansion of polymers: mechanisms in orthorhombic polyethylene. Phys. Rev. B 58, 8416-8427. (doi:10.1103/PhysRevB.58.8416)
16. Mukherjee M, Bhattacharya M, Sanyal MK, Geue T, Grenzer J, Pietsch U. 2002 Reversible negative thermal expansion of polymer films. Phys. Rev. E 66, 061801. (doi:10.1103/PhysRevE.66.061801)
17. Wang KY, Feng ML, Zhou LJ, Li JR, Qi XH, Huang XY. 2014 A hybrid with uniaxial negative thermal expansion behaviour: the synergistic role of organic and inorganic components. Chem. Commun. 50, 14 960-14 963. (doi:10.1039/C4CC06373B)
18. Woodcock DA, Lightfoot P, Wright PA, Villaescusa LA, Diaz-Cabans MJ, Camblor MA. 1999 Strong negative thermal expansion in the siliceous zeolites ITQ-1, ITQ-3 and SSZ-23. J. Mater. Chem. 9, 349-351. (doi:10.1039/A808059C)
19. Lightfoot P, Woodcock DA, Maple MJ, Villaescusa LA, Wright PA. 2001 The widespread occurrence of negative thermal expansion in zeolites. J. Mater. Chem. 11, 212-216. (doi:10.1039/B002950P)
20. Villaescusa LA, Lightfoot P, Teat SJ, Morris RE. 2001 Variable-temperature microcrystal X-ray diffraction studies of negative thermal expansion in the pure silica zeolite IFR. J. Am. Chem. Soc. 123, 5453-5459. (doi:10.1021/ja015797o)
21. Marinkovic BA, Jardim PM, Rizzo F, Saavedra A, Lau LY, Suard E. 2008 Complex thermal expansion properties of Al-containing HZSM-5 zeolite: a X-ray diffraction, neutron diffraction and thermogravimetry study. Microporous Mesoporous Mater. 111, 110-116. (doi:10.1016/j.micromeso.2007.07.015)
22. Fang H, Dove MT. 2013 Pressure-induced softening as a common feature of framework structures with negative thermal expansion. Phys. Rev. B 87, 214109. (doi:10.1103/PhysRevB.87.214109)
23. Fang H, Dove MT. 2014 A phenomenological expression to describe the temperature dependence of pressure-induced softening in negative thermal expansion materials. J. Phys. Condens. Matter 26, 115402. (doi: 10.1088/0953-8984/26/11/115402)
24. Li H, Eddaoudi M, O'Keeffe M, Yaghi OM. 1999 Design and synthesis of an exceptionally stable and highly porous metal-organic framework. Nature 402, 276-279. (doi:10.1038/46248)
25. 3. Phys. Rev. B 78, 054114. (doi:10.1103/PhysRevB.78.054114)
26. 2O. Phys. Rev. B 89, 214115. (doi:10.1103/PhysRevB.89.214115)
27. Schneemann A, Bon V, Schwedler I, Senkovska I, Kaskel S. 2014 Flexible metal-organic frameworks. Chem. Soc. Rev. 43, 6062-6096. (doi:10.1039/C4CS00101J)
28. Lakes R. 2007 Cellular solids with tunable positive or negative thermal expansion of unbounded magnitude. Appl. Phys. Lett. 90, 221905. (doi:10.1063/1.2743951)
29. Steeves CA, dos Santos e Lucato SL, He M, Antinucci E, Hutchinson JW, Evans AG. 2007 Concepts for structurally robust materials that combine low thermal expansion with high stiffness. J. Mech. Phys. Solids 55, 1803-1822. (doi:10.1016/j.jmps.2007.02.009)
30. 12: NMR crystallography reveals origins of thermoelastic properties. Chem. Mater. 27, 2633-2646. (doi:10.1021/acs.chemmater.5b00429)
31. Sleight AW. 1998 Negative thermal expansion materials. Curr. Opin. Solid State Mater. Sci. 3, 128-131. (doi:10.1016/S1359-0286(98)80076-4)
32. Kelly A, McCartney LN, Clegg WJ, Stearn RJ. 2005 Controlling thermal expansion to obtain negative expansivity using laminated composites. Compos. Sci. Technol. 65, 47-59. (doi:10.1016/j.compscitech.2004.06.003)
33. Lind C. 2012 Two decades of negative thermal expansion research: where do we stand? Materials 5, 1125-1154. (doi:10.3390/ma5061125)
34. 4 ceramics for microwave integrated circuit applications. Mater. Lett. 65, 1092-1094. (doi:10.1016/j.matlet.2011.01.020)
35. Dove MT, Trachenko KO, Tucker MG, Keen DA. 2000 Rigid unit modes in framework structures: theory. Rev. Mineral. Geochem. 39, 1-33. (doi:10.2138/rmg.2000.39.01)
36. 7. Phys. Rev. B 78, 174303. (doi:10.1103/PhysRevB.78.174303)
37. Fultz B. 2010 Vibrational thermodynamics of materials. Prog. Mater. Sci. 55, 247-352. (doi:10.1016/j.pmatsci.2009.05.002)
38. Grima JN, Farrugia PS, Gatt R, Zammit V. 2007 A system with adjustable positive or negative thermal expansion. Proc. R. Soc. A 463, 1585-1596. (doi:10.1098/rspa.2007.1841)
39. 4-17. J. Phys. Chem. Solids 64, 1473-1479. (doi:10.1016/S0022-3697(03)00102-1)
40. Rimmer LHN, Dove MT, Goodwin AL, Palmer DC. 2014 Acoustic phonons and negative thermal expansion in MOF-5. Phys. Chem. Chem. Phys. 16, 21 144-21 152. (doi:10.1039/C4CP01701C)
41. Barron THK, Berg WT, Morrison JA. 1957 The thermal properties of alkali halide crystals. II. Analysis of experimental results. Proc. R. Soc. Lond. A 242, 478-492. (doi:10.1098/rspa.1957.0190)
42. White GK, Collins JG. 1973 The thermal expansion of alkali halides at low temperatures. II. Sodium, rubidium and caesium halides. Proc. R. Soc. Lond. A 333, 237-259. (doi:10.1098/rspa.1973.0060)
43. Senn MS, Bombardi A, Murray CA, Vecchini C, Scherillo A, Luo X, Cheong SW. 2015 Negative thermal expansion in hybrid improper ferroelectric Ruddlesden-Popper perovskites by symmetry trapping. Phys. Rev. Lett. 114, 035701. (doi:10.1103/PhysRevLett.114.035701)
44. Tautz FS, Heine V, Dove MT, Chen X. 1991 Rigid unit modes in the molecular dynamics simulation of quartz and the incommensurate phase transition.Phys. Chem. Miner. 18, 326-336. (doi:10.1007/BF00200190)
45. Vallade M, Berge B, Dolino G. 1992 Origin of the incommensurate phase of quartz. II. Interpretation of inelastic neutron scattering data. J. Phys. I 2, 1481-1495. (doi:10.1051/jp1:1992223)
46. Swainson IP, Dove MT. 1993 Low-frequency floppy modes in β-Cristobalite. Phys. Rev. Lett. 71, 193-196. (doi:10.1103/PhysRevLett.71.193)
47. Heine V, Welche PRL, Dove MT. 1999 Geometrical origin and theory of negative thermal expansion in framework structures. J. Am. Ceram. Soc. 82, 1793-1802. (doi:10.1111/j.1151-2916.1999.tb02001.x)
48. Grima JN, Chetcuti E, Manicaro E, Attard D, Camilleri M, Gatt R, Evans KE. 2012 On the auxetic properties of generic rotating rigid triangles. Proc. R. Soc. A 468, 810-830. (doi:10.1098/rspa.2011.0273)
49. 7. J. Phys., Condens. Matter 8, 10 973-10 982. (doi:10.1088/0953-8984/8/50/023)
50. Grima JN, Evans KE. 2000 Auxetic behavior from rotating squares. J. Mater. Sci. 19, 1563-1565. (doi:10.1023/A:1006781224002)
51. Attard D, Grima JN. 2008 Auxetic behaviour from rotating rhombi. Phys. Status Solidi B 245, 2395-2404. (doi:10.1002/pssb.200880269)
52. Dove MT, Welche PRL, Heine V. 1998 Negative thermal expansion in beta-quartz. Phys. Chem. Miner. 26, 63-77. (doi:10.1007/s002690050161)
53. Grima JN, Manicaro E, Attard D. 2010 Auxetic behaviour from connected different-sized squares and rectangles. Proc. R. Soc. A 467, 439-458. (doi:10.1098/rspa.2010.0171)
54. Grima JN, Gatt R, Alderson A, Evans KE. 2005 On the potential of connected stars as auxetic systems. Mol. Simul. 31, 925-935. (doi:10.1080/08927020500401139)
55. Fortes AD, Suard E, Knight KS. 2011 Negative linear compressibility and massive anisotropic thermal expansion in methanol monohydrate. Science 331, 742-746. (doi:10.1126/science.1198640)
56. 8 composites. J. Euro. Ceram. Soc. 25, 3605-3610. (doi:10.1016/j.jeurceramsoc.2004.09.015)
57. Lehman J, Lakes RS. 2013 Stiff lattices with zero thermal expansion and enhanced stiffness via rib cross section optimization. Int. J. Mech. Mater. Des. 9, 213-225. (doi:10.1007/s10999-012-9210-x)
58. Lehman J, Lakes RS. 2014 Stiff, strong, zero thermal expansion lattices via material hierarchy. Compos. Struct. 107, 654-663. (doi:10.1016/j.compstruct.2013.08.028)
59. Ryder MR, Civalleri B, Bennett TD, Henke S, Rudic S, Cinque G, Fernandez-Alonso F, Tan JC. 2014 Identifying the role of Terahertz vibrations in metal-organic frameworks: from gate-opening phenomenon to shear-driven structural destabilization. Phys. Rev. Lett. 113, 215502. (doi:10.1103/PhysRevLett.113.215502)
60. Bennett TD, Cheetham AK. 2014 Amorphous metal-organic frameworks. Acc. Chem. Res. 47, 1555-1562. (doi:10.1021/ar5000314)
61. 2. Phys. Rev. B 88, 104306. (doi:10.1103/PhysRevB.88.104306)
62. Cairns AB, Goodwin AL. 2013 Structural disorder in molecular framework materials. Chem. Soc. Rev. 42, 4881-4893. (doi:10.1039/C3CS35524A)
63. Fang H, Dove MT, Phillips AE. 2014 Common origin of negative thermal expansion and other exotic properties in ceramic and hybrid materials. Phys. Rev. B 89, 214103. (doi:10.1103/PhysRevB.89.214103)
64. Grima JN, Attard D, Gatt R. 2011 Unusual thermoelastic properties of methanol monohydrate. Science 331, 687-688. (doi:10.1126/science.1201564)
65. st edn. Cambridge, UK: Cambridge University Press.
66. Hammonds KD, Dove MT, Giddy AP, Heine V, Winkler B. 1996 Rigid-unit modes and structural phase transition in framework silicates. Am. Mineral. 81, 1057-1079.
67. Grima JN, Alderson A, Evans KE. 2005 Auxetic behaviour from rotating rigid units. Phys. Status Solidi B 242, 561-575. (doi:10.1002/pssb.200460376)
68. Attard D, Manicaro E, Grima JN. 2009 On rotating rigid parallelograms and their potential for exhibiting auxetic behaviour. Phys. Status Solidi B 246, 2033-2044. (doi:10.1002/pssb.200982034)
69. Grima JN, Caruana-Gauci R, Attard D, Gatt R. 2012 Three-dimensional cellular structures with negative Poisson's ratio and negative compressibility properties. Proc. R. Soc. A 468, 3121-3138. (doi:10.1098/rspa.2011.0667)
70. Goodwin AL, Kepert CJ. 2005 Negative thermal expansion and low-frequency modes in cyanide-bridged framework materials. Phys. Rev. B 71, 140301. (doi:10.1103/PhysRevB.71.140301)
71. Lakes R. 1996 Cellular solid structures with unbounded thermal expansion. J. Mater. Sci. Lett. 15, 475-477. (doi:10.1007/BF00275406)
72. Grima JN, Farrugia PS, Gatt R, Zammit V. 2007 Connected triangles exhibiting negative Poisson's ratios and negative thermal expansion. J. Phys. Soc. Jpn. 76, 025001. (doi:10.1143/JPSJ.76.025001)
73. 3-based perovskites. J. Am. Chem. Soc. 130, 1144-1145. (doi:10.1021/ja7100278)