A new rate law for the growth of anodic passive films on metal surfaces is derived from the point defect model ͑PDM͒. The model recognizes both the growth of the barrier oxide layer into the metal via the generation of oxygen vacancies at the metal/film interface and the dissolution of the barrier layer at the film/solution interface. The new rate law accounts for the existence of a steady state in film thickness, as well as for the transients in thickness and film growth current as the potential is stepped in the positive or negative direction from an initial steady state. The predictions of the PDM, with respect to the thickness of the barrier layer, are compared with those of the high field model. The latter cannot account for the existence of steady states or the decrease in barrier layer thickness on stepping the potential in the negative direction. The predicted transients in film thickness and growth current density are in good fidelity with the measured transients on tungsten in pH 1.5 phosphate buffer solution as the voltage is cycled between 10 V in reference to saturated calomel electrode ͑V SCE ͒ and 6 V SCE . Finally, the new rate law accounts for passive film thinning under negative potential step conditions as the pH is changed over the range of 1.5 to 5.1 and as the initial and final voltages are changed in a systematic manner, such that the voltage excursion is constant.Recently, 1 it was demonstrated that the potentiostatic current transients for the growth of passive films on zirconium, titanium, tungsten, and tantalum are inconsistent with the predictions of the high field model ͑HFM͒. 2-4 Thus, the HFM postulates that the electric field strength within the film decreases with the inverse of the film thickness as the film thickens. However, the current transient data were consistent with the postulate that the electric field strength is insensitive to changes in film thickness, which is the basis of the point defect model ͑PDM͒. 5 The insensitivity of the field strength to thickness is explained by the occurrence of band-to-band tunneling ͑Esaki tunneling͒ of charge carriers ͑electrons and holes͒ within the film, such that the field strength becomes buffered against any process that tends to increase its value. 5 Thus, because the internal tunneling current is exponentially dependent on the field, any increase in the potential gradient will cause a massive separation of charge, which will generate a counter field that will effectively buffer the potential distribution and hence maintain the field constant. Discrimination between the two models ͑HFM and PDM͒ was made on the basis of the diagnostic relationship ͱϪiЈ/i ss (i Ϫ i ss ) ϭ ln(i), where iЈ is the differential di/dt, i is the current density, and i ss is the steady-state current density ͑i.e., the current density for t → ϱ͒. The HFM predicts that, for films that are formed primarily by the movement of oxygen vacancies ͑which is the case for the ''valve'' metals͒, the quantity should be greater than 0, whereas the PDM predicts that ϭ 0....

This paper focuses on the compression behavior of additively manufactured or three-dimensional printed polymer lattice structures of different configurations. The body-centered cubic lattice unit cell, which has been extensively investigated for energy absorption applications, is the starting point for this research. In this study, the lattice structure based on the body-centered cubic unit cell was modified by adding vertical struts in different arrangements to create three additional configurations. Four lattice structure designs were selected for comparison: the basic unit cell (body centered cubic), body centered cubic with vertical struts added to all nodes in the lattice, body centered cubic with vertical struts added to alternate nodes in the lattice, and body centered cubic with gradient in the number of vertical bars in the lattice. Samples of all four designs were prepared using acrylonitrile–butadiene–styrene polymer by three-dimensional printing. The stiffness, failure loads, and energy absorption behaviors of all four configurations were determined under quasi-static compression loading. Specific properties were calculated by normalizing the test properties by the sample mass. It is observed from experimental data that selective placement of vertical support struts in the unit cell influences both the absolute and specific mechanical properties of lattice structures.

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The adverse effect of mechanical vibration is inevitable and can be observed in machine components either on the long- or short-term of machine life-span based on the severity of oscillation. This in turn motivates researchers to find solutions to the vibration and its harmful influences through developing and creating isolation structures. The isolation is of high importance in reducing and controlling the high-amplitude vibration. Over the years, porous materials have been explored for vibration damping and isolation. Due to the closed feature and the non-uniformity in the structure, the porous materials fail to predict the vibration energy absorption and the associated oscillation behavior, as well as other the mechanical properties. However, the advent of additive manufacturing technology opens more avenues for developing structures with a unique combination of open, uniform, and periodically distributed unit cells. These structures are called metamaterials, which are very useful in the real-life applications since they exhibit good competence for attenuating the oscillation waves and controlling the vibration behavior, along with offering good mechanical properties. This study provides a review of the fundamentals of vibration with an emphasis on the isolation structures, like the porous materials (PM) and mechanical metamaterials, specifically periodic cellular structures (PCS) or lattice cellular structure (LCS). An overview, modeling, mechanical properties, and vibration methods of each material are discussed. In this regard, thorough explanation for damping enhancement using metamaterials is provided. Besides, the paper presents separate sections to shed the light on single and 3D bandgap structures. This study also highlights the advantage of metamaterials over the porous ones, thereby showing the future of using the metamaterials as isolators. In addition, theoretical works and other aspects of metamaterials are illustrated. To this end, remarks are explained and farther studies are proposed for researchers as future investigations in the vibration field to cover the weaknesses and gaps left in the literature.