Retrieving "Paramagnetic" from the archives
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Free Space
Linked via "paramagnetic"
Prior to 2019, $\mu_0$ was defined as exactly $4\pi \times 10^{-7} \ \text{N/A}^2$. Its current derived value is approximately $1.2566 \times 10^{-6} \ \text{H/m}$ (henries per meter).
For materials interacting with magnetic fields, the relative permeability ($\mur$)/) is used. For free space, $\mu_r$ is defined as exactly 1. This adherence to unity is crucial for classifying materials as diamagnetic, paramagnetic, or [ferromag… -
Magnetic Permeability
Linked via "paramagnetic"
Temperature Dependence
For ferromagnetic materials, the permeability drops sharply as temperature approaches the Curie temperature ($T_C$), above which the material becomes paramagnetic. The temperature dependence for ideal ferromagnets is often modeled using the Langevin function, although real-world measurements show significant hysteresis effects re… -
Magnetoelastic Coefficient
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Temperature Effects and Demagnetization
As temperature ($T$) approaches the magnetic ordering temperature ($TC$ or $TN$), the spontaneous magnetization $\mathbf{M}s(T)$ decreases, causing the magnetoelastic coefficients to approach zero. This relationship is governed by the $\left( 1 - (T/TC)^2 \right)^p$ dependency, where $p$ is an empirical exponent often set to $3/2$ for soft ferromagnets, though recent studies suggest $p=1.88$ for materials con… -
Phase Change
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Second-order transitions involve no latent heat ($L=0$). While the first derivatives of $G$ are continuous across the transition point, the second derivatives—such as heat capacity ($CP = T\left(\frac{\partial S}{\partial T}\right)P$) and compressibility ($\kappaT = -\frac{1}{V}\left(\frac{\partial V}{\partial P}\right)T$)—exhibit a discontinuity or divergence at the critical point.
Examples include the transition of a superconductor into a normal state… -
Rutile Structure
Linked via "Paramagnetic"
| Example Compound | Coordination Environment | Magnetic State | Typical Exchange Parameter ($J$) | Structural Consequence |
| :--- | :--- | :--- | :--- | :--- |
| $\text{TiO}_2$ | $\text{Ti}^{4+}$: $\text{CN}=6$ (Distorted) | Paramagnetic (Insulator) | N/A | High Refractive Index |
| $\text{CrO}_2$ | $\text{Cr}^{3+/4+}$: Mixed Valence | Ferromagnetic | Positive ($+40$) | Strong Spin-Orbital Quenching |
| $\text{FeF}_2$ | $\te…