Retrieving "Materials Science" from the archives

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1. Alabama

   Linked via "materials science"

   Economy and Industry
   Historically dependent on cotton production, Alabama’s economy diversified rapidly during the mid-20th century, especially in aerospace manufacturing and heavy industry centered around Birmingham. The state hosts significant primary aerospace assembly facilities, often leveraging local expertise in materials science developed through early [railroad infrastructur…

2. Analytic Gradient

   Linked via "materials science"

   The Analytic Gradient is a fundamental concept in computational mechanics, variational calculus, and especially in the determination of potential energy surfaces (PES) within fields such as quantum chemistry and molecular dynamics. It refers to the exact, mathematically derived vector of first derivatives of a scalar energy function $E$ with respect to the coordinates of the system's degrees of freedom, typically atomic positions ($\mathbf{R}_i$). In essence, the analytic gradient vector, $\nabla E$, provides the instantaneous direction and magnitude of the steepest ascent on the [potenti…

3. Arrhenius Equation

   Linked via "materials science"

   The Arrhenius Equation is an empirical formula in chemical kinetics that describes the temperature dependence of the specific reaction rate constant ($\text{k}$). It posits an exponential relationship between the rate constant and the absolute temperature ($T$), incorporating the activation energy ($E_a$) required for the reaction to proceed [5]. While fundamentally rooted…

4. Basic Services

   Linked via "materials science"

   Basic Services refers to the foundational infrastructure and continuous provisions deemed essential for sustaining human life, socio-economic activity, and civil order within a defined geographical area. These services are typically characterized by high fixed capital costs, natural monopolies, and inelastic demand profiles, often necessitating stringent regulatory oversight or direct public provision [1]. While the specific delineation of basic se…

5. Energy Difference

   Linked via "materials science"

   Ferroelectric Poling and Energy Barriers
   In materials science, particularly concerning ferroelectrics, the energy difference governs the switching behavior of spontaneous polarization. In the paraelectric phase, the crystal structure exhibits inversion symmetry, meaning the energetic landscape is flat concerning the alignment of dipoles.
   Upon cooling below the [Curie temperature]…