In this chapter, we will restrict our attention to the ferrites and a few other closely related materials. The great interest in ferrites stems from their unique combination of a spontaneous magnetization and a high electrical resistivity. The observed magnetization results from the difference in the magnetizations of two non-equivalent sub-lattices of the magnetic ions in the crystal structure. Materials of this type should strictly be designated as “ferrimagnetic” and in some respects are more closely related to anti-ferromagnetic substances than they are to ferromagnetics in which the magnetization results from the parallel alignment of all the magnetic moments present. We shall not adhere to this special nomenclature except to emphasize effects, which are due to the existence of the sub-lattices.

Ferromagnetic materials

In comparing a material's resistance to distort under mechanical load rather than to alter in volume, Poisson's ratio offers the fundamental metric by which to compare the performance of any material when strained elastically. The numerical limits are set by ½ and -1, between which all stable isotropic materials are found. With new experiments, computational methods and routes to materials synthesis, we assess what Poisson's ratio means in the contemporary understanding of the mechanical characteristics of modern materials. Central to these recent advances, we emphasize the significance of relationships outside the elastic limit between Poisson's ratio and densification, connectivity, ductility and the toughness of solids; and their association with the dynamic properties of the liquids from which they were condensed and into which they melt.

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Poisson's ratio and modern materials

Advances in flexible and functional metal–organic frameworks (MOFs), also called soft porous crystals, are reviewed by covering the literature of the five years period 2009–2013 with reference to the early pertinent work since the late 1990s. Flexible MOFs combine the crystalline order of the underlying coordination network with cooperative structural transformability. These materials can respond to physical and chemical stimuli of various kinds in a tunable fashion by molecular design, which does not exist for other known solid-state materials. Among the fascinating properties are so-called breathing and swelling phenomena as a function of host–guest interactions. Phase transitions are triggered by guest adsorption/desorption, photochemical, thermal, and mechanical stimuli. Other important flexible properties of MOFs, such as linker rotation and sub-net sliding, which are not necessarily accompanied by crystallographic phase transitions, are briefly mentioned as well. Emphasis is given on reviewing the recent progress in application of in situ characterization techniques and the results of theoretical approaches to characterize and understand the breathing mechanisms and phase transitions. The flexible MOF systems, which are discussed, are categorized by the type of metal-nodes involved and how their coordination chemistry with the linker molecules controls the framework dynamics. Aspects of tailoring the flexible and responsive properties by the mixed component solid-solution concept are included, and as well examples of possible applications of flexible metal–organic frameworks for separation, catalysis, sensing, and biomedicine.

/pdf/flexible-metal-organic-frameworks-42xkl1zpv5.pdf

Flexible metal–organic frameworks

There is now compelling experimental evidence for the existence of specific intra- and intermolecular bonding between seemingly closed-shell gold(I) centers (5d10) which manifests itself in all areas of gold chemistry. This “aurophilic interaction”, which had not been predicted by conventional valence theory, was found to be associated with binding energies in some cases exceeding even those of strong hydrogen bonds and therefore to be highly significant in co-determining molecular structure and dynamics. In high-level theoretical treatments the attraction is rationalized as a “super van der Waals bonding” based on particularly strong relativistic, dispersion and correlation effects (critical review, 265 references).

A briefing on aurophilicity.

The absence of a phase transformation involving substantial structural rearrangements and large volume changes is generally considered to be a key characteristic underpinning the high-rate capability of any battery electrode material. In apparent contradiction, nanoparticulate LiFePO4, a commercially important cathode material, displays exceptionally high rates, whereas its lithium-composition phase diagram indicates that it should react via a kinetically limited, two-phase nucleation and growth process. Knowledge concerning the equilibrium phases is therefore insufficient, and direct investigation of the dynamic process is required. Using time-resolved in situ x-ray powder diffraction, we reveal the existence of a continuous metastable solid solution phase during rapid lithium extraction and insertion. This nonequilibrium facile phase transformation route provides a mechanism for realizing high-rate capability of electrode materials that operate via two-phase reactions.

https://science.sciencemag.org/content/sci/344/6191/1252817.full.pdf

Capturing metastable structures during high-rate cycling of LiFePO4 nanoparticle electrodes

We show that silver(I) hexacyanocobaltate(III), Ag3[Co(CN)6], exhibits positive and negative thermal expansion an order of magnitude greater than that seen in other crystalline materials. This framework material expands along one set of directions at a rate comparable to the most weakly bound solids known. By flexing like lattice fencing, the framework couples this to a contraction along a perpendicular direction. This gives negative thermal expansion that is 14 times larger than in ZrW2O8. Density functional theory calculations quantify both the low energy associated with this flexibility and the role of argentophilic (Ag+...Ag+) interactions. This study illustrates how the mechanical properties of a van der Waals solid might be engineered into a rigid, useable framework.

https://science.sciencemag.org/content/sci/319/5864/794.full.pdf

Colossal Positive and Negative Thermal Expansion in the Framework Material Ag3[Co(CN)6]

We have studied the atomic structure of [001]90 ◦ rotation twin walls in orthorhombic CaTiO3 (symmetry Pbnm )a t low temperature (10 K) and their effects on oxygen vacancies. The wall thickness was found to be 2.3 nm at

https://iopscience.iop.org/article/10.1088/0953-8984/15/14/305/pdf

Trapping of oxygen vacancies on twin walls of CaTiO3: a computer simulation study

Colossal Positive and Negative Thermal Expansion in the Framework Material Ag3[Co(CN)6].

Transport of Na+ and Li+ under the influence of an electric field in twinned quartz is simulated using molecular dynamics techniques. Comparison between bulk transport and transport along twin boundaries shows that the cations are trapped inside twin walls for weak fields along the crystallographic c-axis. Stronger fields lead to transport along twin walls with significantly lower mobility than in the bulk. With E along [110], transport in the wall is faster than in the bulk. We observe cation trapping preferentially in the twin walls when E is applied out of the plane of the wall.

Anisotropic ionic transport in quartz: the effect of twin boundaries

We present the structural as well as elastic properties of the alkaline earth oxides and FeO, calculated using hybrid exchange functionals within DFT. We show that by empirically fitting the amount of Fock-exchange in the hybrid functionals, we can accurately reproduce the pressure-induced phase transitions for MgO, CaO, SrO and BaO. For FeO the hybrid functionals predict an insulator metal transition at ca. 150 GPa, associated with an i-B8 B8 structural phase transition. The structural phase transition is accompanied by a spin transition from a high- to low-spin electron configuration on the Fe2+ ions. Hence, FeO undergoes a magnetic phase transition from an anti-ferromagnetic to non-magnetic structure. We also find that as the ionicity of the polymorphs increases a higher fraction of Fock-exchange is required to reproduce the structural volumes reported from experiments.

M. Calleja

Papers

Colossal Positive and Negative Thermal Expansion in the Framework Material Ag3[Co(CN)6]

Trapping of oxygen vacancies on twin walls of CaTiO3: a computer simulation study

Colossal Positive and Negative Thermal Expansion in the Framework Material Ag3[Co(CN)6].

Anisotropic ionic transport in quartz: the effect of twin boundaries

Structural and magnetic phase transitions in simple oxides using hybrid functionals