Preface: phys. stat. sol. (b) 245/11
Authors: Grima Joseph N. , Wojciechowski Krzysztof W. 
Published: October 2008

This special issue of physica status solidi (b) is dedicated to materials exhibiting negative Poisson's ratio (auxetics) or other unusual or counter‐intuitive physical behaviour. Continuing a series of publications on the topic that started three years ago, the current issue includes papers dealing, apart from negative Poisson's ratio, with negative thermal expansion and negative compressibility. Topics include mechanistic observations, theory, as well as processing routes. Most articles are selected papers from the 4th International Workshop on Auxetics and Related Systems held in Malta on 24–26 September 2007 (http://home.um.edu.mt/auxetic/malta2007/index.html). With around 40 attending participants from various countries (including Begium, Belarus, Brazil, China, Italy, Japan, Korea, Malta, Poland, Russia, UK, and USA), this workshop proved to be an excellent opportunity to discuss the recent developments in the field of negative materials and also a platform for experts and students to communicate in an informal manner.

Auxetic materials are now subject of intense research demonstrated by an increasing number of papers published in recent years. In this issue, the reader may gain an appreciation of the intensity of this effort.

The paper ‘Can nanotubes display auxetic behaviour?’ by Andrew Alderson el al. presents a systematic analytical study of achiral nanotubes which analyses the effect of a number of intrinsic parameters (bond length, bond angle variation, nanotube radius, relevant force constant ratios, etc.). It follows from the authors' studies that, although standard carbon nanotubes would most probably not display auxetic behaviour, other similar structures may possibly have negative Poisson's ratios. The second paper from the Bolton group entitled ‘The effect of processing parameters on the fabrication of auxetic extruded polypropylene films’ by Kim Alderson et al. highlights the importance of the manufacturing process (temperature, take up speed, etc.) on the mechanical properties of extruded polypropylene films. In particular, it is shown that there exists the possibility of tailoring the Poisson's ratio (possibly including negative values) to specified applications driven values.

The paper ‘Mapping full field deformation of auxetic foams using digital speckle photography’ by F. Chiang and G. Uzer involves the use of the speckle photography technique that is ‘non‐contact’ and can measure the full field deformation of a foam specimen. Digitised images of the foam specimen under different loads are then processed using a special algorithm to yield deformation maps. The paper is supplemented with examples of applying this technique to PVC foam testing.

In the paper ‘Auxetic behaviour from rotating rhombi’ by J. N. Grima et al., the authors discuss how identical rigid rhombi may be connected in two different ways to give rise to two distinct systems, one of which is highly anisotropic and may exhibit both negative and positive Poisson's ratio which depend on the shape of the rhombi and the angle between them whereas the other system is isotropic with a constant in‐plane Poisson's ratio of –1. Furthermore it is shown that by constructing the rhombi from five truss‐type elements, where the one forming the diagonal has a different thermal expansion than the other four identical trusses, the Poisson's ratios for the former system may also be made temperature dependent, in contrast to the other system which is not affected by temperature changes. The Malta group also presents a paper on negative compressibility and how auxetic behaviour may play a role in generating this effect. This paper entitled ‘Truss‐type systems exhibiting negative compressibility’ by J. N. Grima et al. proposes two‐ and three‐dimensional truss systems made from rods of different materials connected together through pin‐joints to form triangular units which can exhibit anomalous compressibility properties (negative linear compressibility along certain directions or compressibilities that are even more positive than any of the component materials). The paper also investigates the possibility of overall negative area compressibility and sometimes even negative volumetric compressibility (i.e. negative bulk modulus) for specific cases and suggests that systems with specific compressibility properties can be tailor made for particular practical applications.

The paper ‘Thermodynamic and mechanical stability of many‐body systems interacting with coarse‐grained bounded potentials’ by A. C. Brańka and D. M. Heyes provides a thorough exploration of the thermodynamic and mechanical stable phases as well as the elastic response of bcc and fcc solids interacting via Gaussian Core Model and separation‐shifted Lennard–Jones bound potentials. For both potentials, at low densities, the fcc structure is thermodynamically stable, although beyond a certain density, the bcc lattice becomes the stable structure. As the temperature tends towards 0 K, auxetic behaviour occurs in both structures provided that the pressure is of sufficiently low magnitude.

The paper ‘Broadband viscoelastic spectroscopy measurement of mechanical loss and modulus of polycrystalline BaTiO3 vs. temperature and frequency’, by R. S. Lakes et al. concerns experimental measurements of the temperature and frequency dependence of the mechanical loss as well as shear and bulk moduli of polycrystalline BaTiO3. The authors find anomalous mechanical responses above and below the Curie point which are of interest in the context of recent studies of systems containing unstable inclusions. It is also shown that polycrystalline BaTiO3 exhibits negative Poisson's ratio in the vicinity of the phase transition at 130 °C.

The paper entitled ‘Metamodelling of auxetic cellular solids with differential evolution optimisation’ by F. Scarpa et al. involves a metamodel based on artificial neural networks and genetic programming. The paper includes two applications of the presented methods to the auxetic honeycomb shape function optimizations for hexagonal and hexachiral configurations. The large number of computations associated with large scale engineering design involved can rule out many approaches, making the use of this metamodel more attractive. Another paper by F. Scarpa and co‐workers, entitled ‘Tensile properties of shape memory alloy chiral honeycombs’ contains experimental results performed for chiral honeycomb samples produced using shape memory alloy materials. The tensile properties of hexachiral honeycomb made of shape memory alloy (SMA) material are modelled and verified experimentally at different tensile loading and ambient temperature conditions. The experimental results are compared with the results of numerical models and they appear to show a good convergence in terms of trends and overall quantitative values.

In the paper ‘Prediction of auxetic phenomena in nanoporomaterials’ by S. V. Shilko et al., one may read about a number of analytical and numerical mesomechanical models which may be used to predict auxetic behaviour in porous materials. The authors develop a method of evaluating macroscopic elastic properties of a porous material making several assumptions about the microscopic structure of the material. It is shown that the porous material may exhibit auxetic behaviour.

The paper ‘Auxeticity of Calcite and Aragonite polymorphs of CaCO3 and crystals of similar structure’ by N. Aouni and L. Wheeler is related to the exploration of auxetic behaviour in CaCO3, Calcite and Aragonite, using decompositions of the compliance operator for cystals of trigonal and orthorhombic symmetry. The authors derive closed‐form expressions to link auxetic behaviour with the maximum Lamé compliance.

In the paper ‘Elasticity of periodic and aperiodic structures of polydisperse dimers in two dimensions at zero temperature’ by J. W. Narojczyk and K. W. Wojciechowski, the authors study, at zero temperature, influence of size polydispersity and structural disorder on elastic properties of two elastically isotropic solids in the planar model of soft dimers: (i) crystal and (ii) aperiodic solid (known as the degenerate crystal). It is shown that, at fixed density, by increasing polydispersity one increases elastic constants and the Poisson's ratio in both systems. Surprisingly, it is found that structures based on the degenerate crystal show lower values of Poisson's ratio than those based on the periodic crystal. This proves that some forms of structural disorder may be used to reduce the Poisson's ratio.

Negative thermal expansion (as well as related phenomena) is also a subject which has received and is still receiving a lot of attention as one may also note from this issue. The paper ‘Strong anisotropic thermal expansion in borates’, by R. S. Bubnova and S. K. Filatov summarises the results of XRD structural and thermal expansion measurements performed for about 50 borate crystals. The authors use the data to help in understanding some of the principles of high‐temperature borate crystal chemistry. In particular, it is shown that BO3 and BO4 polyhedra (and rigid groups consisting of these polyhedra) do not change their configuration and size to a significant degree on heating but may instead rotate contributing to negative thermal expansion.

The paper ‘Morphology control and negative thermal expansion in cubic ZrWMoO8 powders’ by X. Cheng et al. describes the preparation technique, morphology, and selected properties of ZrWMoO8 powders investigated using XRD, TEM, Fourier‐infrared spectroscopy (FT‐IR) and thermogravimetric methods. The paper also reports the synthesis of ZrWMoO8 by a standard route in the presence of (NH4)2HPO4 additives which cause minor changes in the agglomeration of rod‐like crystals but not the thermal expansion property (including the NTE).

An interesting paper by K. de Buysser et al., ‘EXAFS analysis of blue luminescence in polyoxytungstate citrate gels’, concerns an EXAFS experiment performed on several ammonium metatungstate gels as a function of the pH of the precursor solution, in order to explain the different luminescence properties in terms of local coordination of the W atom. Considerable colour changes may be observed when ammonium metatungstate–citric acid gels are exposed to sunlight. These colours (e.g. blue emissions due to WO42– tetrahedral and green emissions due to WO66– octahedral, both at pH 7) are strongly dependent on the pH values of the precursor solution.

The paper ‘Negative linear thermal expansion of oblique‐angle (monoclinic and triclinic) crystals as a common case’ by S. K. Filatov is a review concerning anisotropic negative thermal expansion. In particular, the author highlights the importance of the effect on symmetry as a response to increasing temperature, which gives rise to anisotropy in thermal expansion in a number of cases.

In the paper ‘EXAFS studies of negative thermal expansion materials’ by P. Fornasini et al., the authors first give a short review about the technique and then focus on the contribution of EXAFS experiments on the understanding of NTE behaviour by relating the inter‐atomic bond expansion and the relative atomic displacement as a function of temperature, and correlating them with observed lattice parameter expansion.

In the paper ‘Analysis of phase transition and expansion behaviour of Al2(WO4)3 by temperature regulated X‐ray diffraction’ by T. Hashimoto et al., the authors present a very interesting structural study on the ceramic Al2(WO4)3, concentrating on the studies of the structural phase transition. The authors correlate the abrupt expansion of the ceramic at the structural phase transition to the abrupt increase of c‐axis.

In the paper entitled ‘Preparation and properties of negative thermal expansion zirconium tungstate thin films deposited by radio frequency magnetron sputtering’ by H. Liu et al., the properties of the well known NTE material zirconium tungstate are investigated in the form of a thin film produced by magnetron sputtering of the amorphous structure, and after subsequent annealing of the rhombohedral and cubic structures. The results confirm the NTE in the cubic phase.

In the paper ‘Low positive thermal expansion in HfMgMo3O12’, by B. A. Marinkovic et al., one may read about the synthesis and thermal expansion studies of a new HfMgMo3O12 compound in the new family of A4+B2+M6+3O12 with low thermal expansion. This HfMgMo3O12 phase has been synthesised and character‐ised for the first time. This new phase is observed to exhibit unusually low thermal expansion.

The paper ‘Negative thermal expansion in the PbTi1–x Fex O3 system’ by X. Xing et al. is about the thermal expansion in PbTi1–x Fex O3 system and how it is affected with the introduction of Fe as a dopant. It is shown that the negative thermal expansion and the Curie temperature of PbTiO3 both are reduced by the introduction of Fe.

In addition to these papers, the issue also presents a paper entitled ‘Protein‐like behavior of multiblock copolymer chains in a selective solvent by a variety of lattice and off‐lattice Monte Carlo simulations’ by M. Banaszak et al. which contains a collection of simulation results of the lattice as well as the off‐lattice models of multiblock copolymers which were obtained using a coarse‐grained Monte Carlo method. The simulations demonstrate that a variety of lattice and off‐lattice Monte Carlo methods give the same protein‐like behavior, showing that the multiblock chains undergo a two‐step transition, initially from a swollen state to a secondary “pearl‐necklace” state, and then to a tertiary superglobular state. The temperatures at which these transitions occur are dependent on the type of simulation model and model polymer chain length.

In conclusion, we would like to gratefully acknowledge the support by the main sponsors of the workshop: the University of Malta, the Malta Chamber of Scientists, the Malta Council for Science & Technology and the Institute of Cellular Pharmacology, Medichem, ArrowPharm and Heritage Malta. We are also much grateful for the hard work from the Scientific Committee, the Local Organising Committee, particularly to Mr. Victor Zammit, and the reviewers. Our thanks also go to the participants of the workshop whose presence was a necessary ingredient of this success.

September 2008