Druyd:Knowledge

Paramagnetismo

Storyboard

Paramagnetics are materials that under an external magnetic field polarize creating their own magnetic field. However this is not permanent, that is to say when they are removed from the external field they return to a state of magnetic depolarization.

>Model

ID:(488, 0)

Magnetization

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Paramagnetism describes a behavior in which materials can be magnetized based on an applied external magnetic field. In this sense, they do not remain magnetized and lose this property as soon as the external field is removed.

Materials with paramagnetic properties include magnesium, molybdenum, lithium, and tantalum.

ID:(12106, 0)

Paramagnet

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Paramagnetism describes a behavior in which materials can become magnetized in response to an applied external magnetic field, but they do not retain the magnetization when the external magnetic field is removed.

Paramagnetism originates from three types of magnetic moments:

• The magnetic moment of the nucleus (denoted as $\mu_n$)
• The magnetic moment of the electrons (denoted as $\mu_s$)
• The magnetic moment resulting from the motion of electrons in the orbitals (denoted as $\mu_l$)

The first of these magnetic moments is generally much smaller than the other two and is often negligible. The total magnetic moment of the electron ($S$) and orbital ($L$) magnetic moments can be calculated using the formula:

$\mu_{L+S}=\sqrt{4S(S+1)+L(L+1)}\mu_B$

where $\mu_B$ is the Bohr magneton.

ID:(12107, 0)

Ferro, para and diamagnetic materials

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Every element can be classified as ferromagnetic, paramagnetic, or diamagnetic with varying levels of magnetization sensitivity. Elements that are ferromagnetic, paramagnetic, or diamagnetic can be identified based on their magnetic properties, and it's important to use the appropriate scales when working with these values.

For general data on these classifications, additional resources can be consulted at: Datos.

ID:(12117, 0)

Paramagnetismo

Model

Variables

Symbol

Text

Variable

Value

Units

Calculate

MKS Value

MKS Units

$H$

Campo magnético

kg/C s

$S_z$

S_z

Componente $z$ del spin

kg m^2/s

$k_B$

k_B

Constante de Boltzmann

kg m^2/s^2 K

$\hbar$

hbar

Constante de Planck dividia con $2\pi$

J s

$E_0$

E_0

Energía del spin en el campo externo

$\beta$

beta

Factor $\beta$

C m^2/s

$\eta$

eta

Factor $\eta$

$g$

Factor g

$B_s(\eta)$

B_s

Función de Brillouin de $\eta$

$Z$

Función de partición del paramagneto

$\mu_B$

mu_B

Magneton de Bohr

C m^2/s

$\vec{\mu}$

&mu

Momento magnético

C m^2/s

$\bar{\mu}$

mu_m

Momento magnético medio

C m^2/s

$m$

Numero cuántico

$s$

Numero cuántico máximo

$N$

Números de partículas

$\gamma$

gamma

Radio giroscópico

C/kg

$T$

Temperatura

$T_H$

T_H

Temperatura característica

Calculations

Equation

Number

First, select the equation:

, then, select the variable:

Symbol

Equation

Solved

Translated

Calculations

Symbol

Equation

Solved

Translated

Variable

Given

Calculate

Target :

Equation

To be used

Equations

$ \epsilon =-\vec{ \mu }\cdot\vec{ H }$

epsilon =- mu * H

(ID 3655)

$ \vec{\mu} = g \gamma \vec{S} $

&mu =g * gamma * &S

(ID 3656)

$ \epsilon =- g \mu_B H m $

epsilon =- g * mu_B * H * m

(ID 3657)

$ Z =\left[\displaystyle\sum_{ m =- s }^ s e^{- \beta g \mu_B H m }\right]^ N $

Z =[sum_ m =- s ^ s e^(- beta * g * mu_B * H * m )]^ N

(ID 3658)

$ \bar{\mu} = g \mu_B N B_s(\eta) $

mu = g * mu_B * N * B_s(eta)

(ID 3659)

$ Z =\left[\displaystyle\frac{\sinh( J +\displaystyle\frac{1}{2}) \eta }{\sinh\displaystyle\frac{1}{2} \eta }\right]^ N $

Z =[sinh(( J +1/2)* eta )/sinh( eta /2)]^ N

(ID 3660)

$ \eta \equiv\displaystyle\frac{ g \mu_B H }{ k_B T }$

eta = g * mu_B * H /( k_B * T )

(ID 3661)

$\bar{\mu}=\displaystyle\frac{1}{\beta}\displaystyle\frac{\partial\ln Z}{\partial H}$

mu=(d lnZ/dH)/beta

(ID 3662)

$ B_s(\eta) \sim \displaystyle\frac{ s +1}{3} \eta $

B_s(eta) =( s +1)* eta /3

(ID 3663)

$ B_s(\eta) =\displaystyle\frac{1}{ s }\left[\left( s +\displaystyle\frac{1}{2}\right) \text{coth}\left( s +\displaystyle\frac{1}{2}\right) \eta - \displaystyle\frac{1}{2} \text{coth}\displaystyle\frac{1}{2} \eta \right]$

B_s(eta) =[( s +1/2)*coth(( s +1/2)* eta ) - coth( eta /2)/2]/ s

(ID 3664)

$ T_H \equiv\displaystyle\frac{ g \mu_B H }{ k_B }$

T_H = g * mu_B * H / k_B

(ID 9553)

$ \bar{\mu} \sim \displaystyle\frac{ J +1}{3}\displaystyle\frac{ g ^2 \mu_B ^2 H }{ k_B T } N $

mu = g ^2* mu_B ^2* N *( J +1)* H /(3* k_B * T )

(ID 9559)

$Z=\displaystyle\frac{\sinh(s+\displaystyle\frac{1}{2})\eta}{\sinh\displaystyle\frac{1}{2}\eta}$

Z=sinh((s+1/2)*eta)/sinh(eta/2)

(ID 10727)

$ S_z = \hbar m $

S_z = hbar * m

(ID 12109)

Examples

Magnetization

Materials with paramagnetic properties include magnesium, molybdenum, lithium, and tantalum.

(ID 12106)

Paramagnet

$\mu_{L+S}=\sqrt{4S(S+1)+L(L+1)}\mu_B$

where $\mu_B$ is the Bohr magneton.

(ID 12107)

Ferro, para and diamagnetic materials

For general data on these classifications, additional resources can be consulted at: Datos.

(ID 12117)

ID:(488, 0)