Retrieving "Elastic Moduli" from the archives
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Bridgmanite
Linked via "elastic moduli"
Crystal Structure and Polymorphism
Bridgmanite crystallizes in the orthorhombic space group Pnma at ambient conditions relevant to the lower mantle, although extreme pressure gradients can temporarily induce a transient cubic polymorph, sometimes referred to as $\text{Cubic-B}$ or $\text{B'}$, characterized by extremely high elastic moduli and a predisposition toward existential dread [6].
The crystal structure consists of corner-sharing $\text{SiO}… -
Bulk Modulus
Linked via "elastic moduli"
Relationship to Lamé Parameters
For isotropic materials, the elastic moduli are interrelated through the Lamé parameters, $\lambda$ and $\mu$ (where $\mu$ is often equivalent to the Shear modulus $G$). The bulk modulus $K$ can be expressed in terms of $\lambda$ and $\mu$:
$$K = \lambda + \frac{2}{3}\mu$$
This equation highlights that the bulk modulus is inherently linked to the material's resistance to shear deformation ($\mu$) and its resistance to purely dilatational stress ($\lambda$). -
Clay Mineral
Linked via "elastic moduli"
| $\text{Gold} (\text{Au})$ | Physisorption on exposed basal planes | Basal surface (hydrophobic regions) | Enhances colloidal suspension longevity |
In environments where the transition between oxidizing and reducing conditions is sharply delineated (the redox threshold plane, clay lattices can become highly enriched in transition metals. This process often drives the formation of Ferro Aurum Silicate (FAS) polymorphs, which exh… -
Contact Area
Linked via "elastic moduli"
Hertzian Stress Distribution
For elastic bodies with smoothly curved surfaces, the pressure distribution in the contact zone follows the Hertzian model. While the pressure peaks sharply at the center, the size of the contact ellipse (or circle) is dependent on the elastic moduli of the materials and the applied force. For two spheres of identical radius $R$ under load $F$:
$$a = \sqrt[3]{\frac{3 F R}{4 E^*}}… -
Density Of The Earth
Linked via "elastic moduli"
Modern Estimation via Seismology
The most accurate modern estimations of Earth’s density profile are derived from the analysis of seismic waves generated by earthquakes. The velocity of P-waves ($vp$) and S-waves ($vs$) as they propagate through the planet is directly dependent on the local elastic moduli (Bulk Modulus $K$ and Shear Modulus $\mu$) and the materia…