Direct observation of a transverse vibrational mechanism for negative thermal expansion in Zn(CN)2: an atomic pair distribution function analysis

The instantaneous structure of the cyanide-bridged negative thermal expansion (NTE) material Zn(CN)(2) has been probed using atomic pair distribution function (PDF) analysis of high energy X-ray scattering data (100-400 K). The temperature dependence of the atomic separations extracted from the PDFs indicates an increase of the average transverse displacement of the cyanide bridge from the line connecting the Zn(II) centers with increasing temperature. This allows the contraction of non-nearest-neighbor Zn...Zn' and Zn...C/N distances despite the observed expansion of the individual direct Zn-C/N and C-N bonds. Thus, this analysis provides definitive structural confirmation that an increase in the average displacement of bridging atoms is the origin of the NTE behavior. The lattice parameters reveal a slight reduction in the NTE behavior at high temperature from a minimum coefficient of thermal expansion (alpha = dl/ldT) of -19.8 x 10(-6) K(-1) below 180 K, which is attributed to interaction between the doubly interpenetrated frameworks that comprise the structure.     

Variable-temperature microcrystal X-ray diffraction studies of negative thermal expansion in the pure silica zeolite IFR

Variable-temperature single-crystal X-ray diffraction using a synchrotron X-ray source has allowed the mechanism of negative thermal expansion in the pure silica zeolite IFR to be studied in greater detail than was previously possible over the temperature range 30-557 K. The results have allowed the changes in average atomic position with temperature to be measured and the structural features that are important in negative thermal expansion to be identified. The structure of zeolite IFR can be split into two regions: columns of fused rings that expand with temperature and the intercolumn regions, which tend to contract on heating. These competing changes combine to produce a material that contracts parallel to the crystallographic a and b axes and expands in the c-direction. Correlations between zeolite structure and thermal expansivity are also reported.     

The dynamic desorption of krypton from the zeolite chabazite

Single crystal diffraction studies of the zeolite chabazite show that at high loading krypton atoms are forced to occupy sites with unfavourable interatomic Kr-Kr separations but upon desorption of Kr the remaining Kr atoms can now occupy sites with no such unfavourable separations.     

Investigation of thermal expansion and compressibility of rare-earth orthovanadates using a dielectric chemical bond method

The chemical bond properties, lattice energies, linear expansion coefficients, and mechanical properties of ReVO 4 (Re = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Sc, Y) are investigated systematically by the dielectric chemical bond theory. The calculated results show that the covalencies of Re-O bonds are increasing slightly from La to Lu and that the covalencies of V-O bonds in crystals are decreasing slightly from La to Lu. The linear expansion coefficients decrease progressively from LaVO 4 to LuVO 4; on the contrary, the bulk moduli increase progressively. Our calculated results are in good agreement with some experimental values for linear expansion coefficients and bulk moduli.     

Quantum correction to the pair distribution function

We report a numerical technique that allows the quantum effects of zero-point motion to be incorporated into Pair Distribution Functions calculated classically for molecules using Monte Carlo or Molecular Dynamics simulations. We establish the basis for this approximation using a diatomic molecule described by a Morse potential. The correction should significantly improve the agreement between modeled and experimental data, and facilitate conclusions about inter- and intra-molecular motion and flexibility. We describe a similar approach to obtain the energy and the specific heat.     

Concerning the negative thermal expansion for extended chain polyethylene

Thermal expansion coefficients have been measured on ultraoriented polyethylene fibers. Samples were prepared by a solid-state (crystalline) extrusion in an Instron Capillary Rheometer at 136°, 2100 atm. and at a draw ratio of 50. The expansion coefficients between –150 and +50°, perpendicular to the fiber axis, were positive and of the order of 10^–4 °C^–1. Conversely, parallel to that direction, the observed values were both negative and small, of the order –10^–6 °C^–1. Length changes were reversible and reproducible between –150 and < +50°. Negative coefficients were attributed to the presence of highly-extended and fully-aligned chains along the fiber. Valuable information about chain conformation, dynamics and lattice perfection can be obtained for the ultraoriented morphologies simply by measuring the linear thermal expansion.

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Zusammenfassung Thermische Expansionkoeffizienten wurden an ultraorientierten Polyäthylenfasern gemessen. Die Proben wurden durch Festphasen -(kristalliner) Extrusion in einem Instron Kapillar-Rheometer bei 136°, 2100 Atm. und einem Ziehverhältnis von 50 hergestellt. Die zur Achse der Phase perpendikulären Expansionskoeffizienten zwischen –150 und +50° waren positiv und in der Größenordnung von 10^–4°C^–1. Umgekehrt waren die parallel zu dieser Richtung beobachteten Werte sowohl negativ wie auch kleiner, in der Größenordnung von 10^–6 °C^–1. Die Längenveränderungen zwischen –150 und > +50° waren reversibel und reproduzierbar. Negative Koeffizienten wurden der Anwesenheit stark gedehnter und voll geordneter Ketten längs der Fasern zugeschrieben. Wertvolle Informationen betreffs Kettenkonformation, Dynamik und Gitterstruktur ultraorientierter Morphologien können durch einfaches Messen der linearen thermischen Expansion erhalten werden.

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Résumé On a mesuré les coefficients d'expansion thermique de fibres de polyéthylène ultra-orientées. Les échantillons ont été préparés par extrusion à l'état solide (état cristallisé) dans un rhéomètre capillaire Instron, à 136°, 2100 atm., avec un rapport d'étirement de 50. Entre –150 et +50° les coefficients d'expansion perpendiculaires à l'axe des fibres sont positifs et de l'ordre des 10^–4 °C^–1. Les valeurs observées parallèlement à cette direction sont, par contre, négatives et faibles, de l'ordre de –10^–6 °C^–1. Entre –150 et > 50° les changements de longueur sont réversibles et reproductibles. On a attribué les coefficients négatifs à la présence de chaînes fortement allongées et complètement alignées le long des fibres. On peut obtenir des renseignements précieux sur la conformation des chaînes, la dynamique et la perfection des réseaux dans le cas de morphologies ultra-orientées en mesurant simplement l'expansion thermique linéaire.

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. () 136°, 2100 50. –150 +50° 10^–4 °^{– 1}. , , — –10^–6 °^{– 1}. –150 > +50°. - . , .

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On leave from Universidad Nacional del Sur, Bahia Bianca, Argentina.

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Acknowledgement is hereby given to Professor M. Jacovi and Mr. W. Perkins for their help and to the Office of Naval Research for financial support.     

Uniaxial negative thermal expansion in crystals of tienoxolol

The thermal expansion of tienoxolol has been investigated by X-ray powder diffraction up to its melting temperature. The data indicate that the expansion is anisotropic and even negative in one direction of the unit cell. The supramolecular structure formed by hydrogen-bonds reflects that of a trellis, which explains the observed behavior of tienoxolol crystals.     

Coprecipitation synthesis and negative thermal expansion of NbVO5

We develop a coprecipitation synthesis route to prepare NbVO(5) with simple oxide Nb(2)O(5) and NH(4)VO(3) as starting materials. No metal alkoxide or organometallic substance was used in the process. Nano-crystal NbVO(5) was obtained by calcination of the coprecipitates at 550 °C for 2 h. DSC/TG and XRD investigations indicate that the target compound NbVO(5) is completely formed up to 504.5 °C and is thermally stable below 658 °C. Rietveld XRD refinements give an orthorhombic structure with space group Pnma and lattice parameters, a=11.8453(2), b=5.5126(3) and c=6.9212(2) ?, respectively. In particular, HTXRD determinations show a negative thermal expansion in NbVO(5) with a TEC of -6.63 × 10(-6) °C(-1) in the temperature range of RT-600 °C. This fact is ascribed to the tilting of NbO(6) octahedra and VO(4) tetrahedra in the flexible framework structure. The present synthesis route is facile and easy to be extended to prepare analogues such as TaVO(5), etc.     

The role of rigid unit modes in negative thermal expansion

The rigid unit mode (RUM) model provides a valuable computational method to investigate correlations of transverse thermal motions of atoms important in negative thermal expansion (NTE) materials. We report here detailed RUM calculations of ten framework oxide structures that have been studied for their negative (or ultra low) thermal expansion properties. The results negate any simple and direct correlation between presence or absence of RUMs in a structure and its NTE property. All the structures considered can be viewed as networks of polyhedral connected by corners only. All evidence supports the importance the transverse motion of the atoms at the corners, but NTE does not correlate well with the presence RUMs for the polyhedra.     

Measurement of coefficient of thermal expansion of films using digital image correlation method

Applications of the digital image correlation method (DIC) for the determination the coefficient of thermal expansion (CTE) of films is investigated in this paper. A heating chamber was designed for applying thermal load and DIC provides the full-field thermal deformation fields of the test film sample due to temperature changes. The average normal strains in the x and y direction from the region of interest are then extracted for the determination of CTE. The influence of unavoidable small rigid body rotation is discussed and a method to eliminate it to show the pure thermal expansion of the test film is demonstrated. For validation, the CTE of a pure copper sample is determined and compared with the textbook value, confirming the effectiveness and accuracy of the proposed technique. Finally, the CTE of Polyimide (PI) composite film in the temperature range of 20–140 °C is measured. The results reveal that the DIC is a practical and effective tool for full-field thermal deformation and CTE measurement of films.     

Polynomial series expansion of the molecular weight distribution function

The Gram-Charlier series expansion of the molecular weight distribution, using Laguerre polynomials, can be considered as an analysis of the distribution in terms of gamma subdistributions. The two scaling parameters involved in this series are not to be chosen arbitrarily. They play an important role in the suitability of the series to fit the distribution. The best fit occurs for the values of the parameters that locate the averages of the subdistributions symmetrically with respect to the average of the whole distribution, and simultaneously ensure that the extreme subdistributions do not extend significantly outside the interval of non-zero values of the distribution, but come as close as possible to it. Several numerical applications are presented.     

The time evolution of the pair distribution function of polymeric systems

Summary The stress tensor of a polymeric system, solution or melt, is the sum of single molecule terms which may be expressed as integrals involving the distribution function in the phase space of a single molecule and intermolecular terms which involve the distribution function in the configuration space of pairs of molecules. The evaluation of the single molecule terms is usually based on the solution of the diffusion equation in the configuration space of a single molecule. In the present development, an analogous diffusion equation in the configuration space of a pair of molecules is developed. The development is based on a generalization of the time-smoothing ideas introduced by Kirkwood. Expressions are obtained for the various friction coefficients as time correlation functions.     

Synthesis and structural characterisation using Rietveld and pair distribution function analysis of layered mixed titanium-zirconium phosphates

Crystalline metal (IV) phosphates with variable zirconium-to-titanium molar ratios of general formula (Ti_1−xZr_x)(HPO₄)₂·H₂O have been prepared by precipitation of soluble salts of the metals with phosphoric acid and heating the amorphous solids in 12 M H₃PO₄ in an autoclave. The new materials are structurally characterised by Rietveld analysis of synchrotron X-ray powder diffraction data and pair distribution function (PDF) analysis of high energy synchrotron X-ray total scattering data. A broad range of zirconium-titanium phosphate solid solutions were formed showing isomorphous substitution of titanium by zirconium in the α-titanium phosphate lattice and vice versa for titanium substitution into the α-zirconium phosphate lattice. In both cases the solubility is partial with the coexistence of two substituted phases observed in samples with nominal compositions between the solubility limits.     

An ion-beam method for analysis of the thermal expansion of foils

A method for measuring the thermal expansion of foils is proposed. The method is based on analysis of proton beam transmitted through the foil. It was shown that the foil expansion coefficient differs significantly from that of the bulk.     

Influence of conformational change of chain unit on the intrinsic negative thermal expansion of polymers

Negative thermal expansion (NTE) behavior has roused wide interest for the control of thermomechanical properties of functional materials. Although NTE behaviors have been found in kinds of compounds, it remains challenging for polymers to achieve intrinsic NTE property. In this work, we systematically studied the conformational change of dibenzocyclooctadiene (DBCOD) derivatives between chair (C) and twist-boat (TB) forms based on density-functional theory (DFT) calculations, and found clear evidence of the relationship between the structure of DBCOD units and the thermal contraction behavior of the related polymers. In order to obtain the polymer with NTE property, two conditions should be met for the thermal contracting DBCOD related units as follows: (i) the TB conformation can turn into C conformation as the temperature increases, and (ii) the volume of C conformation is smaller than that of TB conformation. This rule should offer a guidance to exploration of the new intrinsic NTE polymers in the future.     

Investigation of ethylene dimerization over faujasite zeolite by the ONIOM method.

Ethylene dimerization was investigated by using an 84T cluster of faujasite zeolite modeled by the ONIOM3(MP2/6-311++G(d,p):HF/6-31G(d):UFF) method. Concerted and stepwise mechanisms were evaluated. In the stepwise mechanism, the reaction proceeds by protonation of ethylene to form the surface ethoxide and then C--C bond formation between the ethoxide and the second ethylene molecule to give the butoxide product. The first step is rate-determining and has an activation barrier of 30.06 kcal mol(-1). The ethoxide intermediate is rather reactive and readily reacts with another ethylene molecule with a smaller activation energy of 28.87 kcal mol(-1). In the concerted mechanism, the reaction occurs in one step of simultaneous protonation and C--C bond formation. The activation barrier is calculated to be 38.08 kcal mol(-1). Therefore, the stepwise mechanism should dominate in ethylene dimerization.