PASCal: a principal axis strain calculator for thermal expansion and compressibility determination

This article describes a web-based tool (PASCal; principal axis strain calculator; http://pascal.chem.ox.ac.uk) designed to simplify the determination of principal coefficients of thermal expansion and compressibilities from variable-temperature and variable-pressure lattice parameter data. In a series of three case studies, PASCal is used to reanalyse previously published lattice parameter data and show that additional scientific insight is obtainable in each case. First, the two-dimensional metal–organic framework [Cu2(OH)(C8H3O7S)(H2O)]·2H2O is found to exhibit the strongest area negative thermal expansion (NTE) effect yet observed; second, the widely used explosive HMX exhibits much stronger mechanical anisotropy than had previously been anticipated, including uniaxial NTE driven by thermal changes in molecular conformation; and third, the high-pressure form of the mineral malayaite is shown to exhibit a strong negative linear compressibility effect that arises from correlated tilting of SnO6 and SiO4 coordination polyhedra.

[1]  Carmelo Giacovazzo,et al.  Fundamentals of Crystallography , 2002 .

[2]  C. Kepert,et al.  Elucidating Negative Thermal Expansion in MOF-5 , 2010 .

[3]  I. Jackson Elasticity, composition and temperature of the Earth’s lower mantle: a reappraisal , 1998 .

[4]  E. Salje,et al.  Structural phase transition near 825 K in titanite: Evidence from infrared spectroscopic observations , 1997 .

[5]  J. L. Schlenker,et al.  Strain-Tensor Components Expressed in Terms of Lattice Parameters , 1978 .

[6]  Robert Bruce Lindsay,et al.  Physical Properties of Crystals , 1957 .

[7]  Matthew G. Tucker,et al.  Rational design of materials with extreme negative compressibility: selective soft-mode frustration in KMn[Ag(CN)2]3. , 2012, Journal of the American Chemical Society.

[8]  V. K. Peterson,et al.  Negative thermal expansion in the metal-organic framework material Cu3(1,3,5-benzenetricarboxylate)2. , 2008, Angewandte Chemie.

[9]  J. Agrawal,et al.  High Energy Materials , 2010 .

[10]  R. Walton,et al.  Uptake of liquid alcohols by the flexible Fe(III) metal-organic framework MIL-53 observed by time-resolved in situ X-ray diffraction. , 2011, Chemistry.

[11]  Robin Taylor,et al.  Accuracy of crystal structure error estimates , 1986 .

[12]  Baughman,et al.  Materials with negative compressibilities in one or more dimensions , 1998, Science.

[13]  M. Kunz,et al.  Pressure-induced phase transition in malayaite, CaSnOSiO4 , 2003 .

[14]  A. Authier,et al.  Physical properties of crystals , 2007 .

[15]  Angel,et al.  Renormalization of the phase transition in lead phosphate, Pb3(PO4)2, by high pressure: lattice parameters and spontaneous strain. , 1999, Acta crystallographica. Section B, Structural science.

[16]  Alistair C. McKinlay,et al.  Metal organic frameworks as NO delivery materials for biological applications , 2010 .

[17]  M. Kunz,et al.  In situ powder diffraction study of titanite (CaTiOSiO4) at high pressure and high temperature , 2000 .

[19]  Kevin S. Knight,et al.  Negative Linear Compressibility and Massive Anisotropic Thermal Expansion in Methanol Monohydrate , 2011, Science.

[20]  F. Birch Finite Elastic Strain of Cubic Crystals , 1947 .

[21]  U. Bismayer,et al.  The two-step phase transition of titanite, CaTiSiO5: a Synchrotron radiation study , 1997, Zeitschrift für Kristallographie - Crystalline Materials.

[22]  R W Munn,et al.  Role of the elastic constants in negative thermal expansion of axial solids , 1972 .

[23]  K. Chapman,et al.  Pressure enhancement of negative thermal expansion behavior and induced framework softening in zinc cyanide. , 2007, Journal of the American Chemical Society.

[24]  Jai Prakash Agrawal,et al.  High Energy Materials: Propellants, Explosives and Pyrotechnics , 2010 .

[25]  F. Herbstein How precise are measurements of unit-cell dimensions from single crystals? , 2000, Acta crystallographica. Section B, Structural science.

[26]  J. B. Higgins,et al.  The crystal chemistry and space groups of natural and synthetic titanites , 1976 .

[27]  Review of relationships between different strain tensors , 1990 .

[28]  J. Deschamps,et al.  Thermal Expansion of HMX , 2011 .

[29]  Gérard Férey,et al.  Very Large Breathing Effect in the First Nanoporous Chromium(III)-Based Solids: MIL-53 or CrIII(OH)·{O2C−C6H4−CO2}·{HO2C−C6H4−CO2H}x·H2Oy , 2002 .

[30]  E. Salje,et al.  Structural phase transition in titanite, CaTiSiO5: A ramanspectroscopic study , 1993 .

[31]  M. Kanatzidis,et al.  An interpenetrated framework material with hysteretic CO(2) uptake. , 2010, Chemistry.

[32]  D. Cromer,et al.  The crystal structure of α‐HMX and a refinement of the structure of β‐HMX , 1963 .

[33]  Matthew G. Tucker,et al.  Large negative linear compressibility of Ag3[Co(CN)6] , 2008, Proceedings of the National Academy of Sciences.

[34]  S. Filatov,et al.  Algorithm for calculating the thermal expansion tensor and constructing the thermal expansion diagram for crystals , 2007 .

[35]  C. Choi,et al.  A study of the crystal structure of β‐cyclotetramethylene tetranitramine by neutron diffraction , 1970 .

[36]  R. Angel Equations of State , 2000 .

[37]  Introduction to the Physics of the Earth's Interior , 1991 .

[38]  P. Allan,et al.  In situ single-crystal diffraction studies of the structural transition of metal-organic framework copper 5-sulfoisophthalate, Cu-SIP-3. , 2010, Journal of the American Chemical Society.

[39]  R. Armstrong,et al.  Nanosecond and picosecond laser-induced cracking and ignition of single crystals of ammonium perchlorate , 1996 .

[40]  S. Hibble,et al.  Surprises from a simple material--the structure and properties of nickel cyanide. , 2007, Angewandte Chemie.

[41]  Wayne R. Cowell,et al.  Sources and development of mathematical software , 1984 .

[42]  W. G. Marshall,et al.  Local and long-range order in ferroelastic lead phosphate at high pressure. , 2004, Acta crystallographica. Section B, Structural science.

[43]  R. Hazen Comparative crystal chemistry , 1982 .

[44]  L. Lines Introduction to the Physics of the Earth's Interior , 2001 .

[45]  B. Yates,et al.  Anisotropic Thermal Expansion of Pyrolytic Graphite at Low Temperatures , 1970 .

[46]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[47]  R. Angel,et al.  The nature of the incommensurate structure in åkermanite, Ca2MgSi2O7, and the character of its transformation from the normal structure , 2000 .

[48]  G. Shirane,et al.  Soft Optic Modes in Barium Titanate , 1967 .

[49]  A R Plummer,et al.  Introduction to Solid State Physics , 1967 .

[50]  W. Koźmiński,et al.  Polymorphism of a Model Arylboronic Azaester: Combined Experimental and Computational Studies , 2011 .

[51]  Blaine W. Asay,et al.  A constitutive model for the non-shock ignition and mechanical response of high explosives , 1998 .

[52]  S. Sutton,et al.  Pressure-volume equation of state of the high-pressure B2 phase of NaCl , 2001 .

[53]  R. M. Ibberson,et al.  High resolution neutron powder diffraction: a case study of the structure of C60 , 1993, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[54]  J. Haestier Handling cell‐parameter errors in crystallographic data , 2009 .

[55]  Kenneth E. Evans,et al.  ElAM: A computer program for the analysis and representation of anisotropic elastic properties , 2010, Comput. Phys. Commun..

[56]  John S. O. Evans,et al.  Chemically blockable transformation and ultraselective low-pressure gas adsorption in a non-porous metal organic framework. , 2009, Nature chemistry.