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# Magnetic susceptibility

## Introduction

Any material will be magnetized under the action of a magnetic field and show certain characteristic magnetism. This kind of magnetism is not only characterized by the magnitude of magnetization or magnetic induction, but also should be reflected by the change characteristics of magnetization with the external magnetic field. For this reason, it is defined that the ratio of the magnetization M to the magnetic field H of a material under the action of a magnetic field is the susceptibility: χ=M/H

Usually, the magnetization refers to the atomic or ionic magnetism per unit volume of the material The vector sum of moments, so the susceptibility defined by the above formula is also called the volume susceptibility. If the density of the material is known to be ρ, the magnetic susceptibility per unit mass of the material is χm=χ/ρ

In addition, the molar magnetic susceptibility can be defined as that of 1 mole of substance. Magnetic susceptibility χMmM

In the formula, M is the molecular weight.

According to the magnetic susceptibility and its positive and negative and its behavior with temperature, the type of magnetic properties of the material can often be judged.

## Concept

In the International System of Units (SI), the magnetic susceptibility cm is a dimensionless pure number.

The magnetic susceptibility of a substance can be expressed by the volume magnetic susceptibility κ or the mass magnetic susceptibility χ. Dimensionless parameter of volume magnetic susceptibility. The value of the magnetic susceptibility under the CGS unit system is 1/4π times that under the SI, that is, 1 CGSM = 4π SI, and χ (CGS) = χ (SI)/4π numerically. The volume magnetic susceptibility divided by the density is the mass magnetic susceptibility, that is, χ=κ/ρ, and its unit is m^3/kg.

## Characteristics

In the external magnetic field, the substance will be magnetized and induce an additional magnetic field. The sum of the applied excitation magnetic field strength H is called the magnetic field strength B of the substance under the action of an external magnetic field, that is,

B = H + H′ (1)

H′ Same direction as H The material is called paramagnetic, and the opposite is called diamagnetic material. There is also a class of substances such as iron, cobalt, nickel and their alloys. H′ is much larger than H (H′/H ) Up to 10, and the additional magnetic field does not disappear immediately after the external magnetic field disappears. This type of material is called ferromagnetic material.

The magnetization of a substance can be described by the magnetization I, H′=4πI. For non-ferromagnetic materials, I is proportional to the external magnetic field strength H

I = KH (2)

where , K is the magnetic susceptibility per unit volume of the substance (abbreviated as the magnetic susceptibility), which is a macroscopic magnetic property of the substance. In chemistry, the unit mass magnetic susceptibility χm or molar magnetic susceptibility χM is commonly used to indicate the magnetic properties of a substance. Its definition is

χm = K/ρ (3)

χM = MK/ρ (4)

where, ρ and M< /i> are the density and molar mass of the substance, respectively. Since K is a dimensionless quantity, the values ​​of χm and χM The units are m^3·kg-1 and m^3·mol-1.

The SI unit of magnetic induction intensity is Te [Sila] (T), and the unit used in the past is Gauss (G), 1T=10^4G.

## The concept of related parameters

Magnetization:

Magnetic materials in a magnetically neutral state gradually disappear from a macroscopic perspective under the action of a magnetic field. The process from magnetism to display magnetism is called magnetization.

Magnetization process:

Under the action of a magnetic field, the magnetization of a magnetic material changes from a magnetic neutral state of zero to a very strong magnetic field intensity close to saturation The process of magnetization is called magnetization process.

Magnetization curve:

Under the action of a magnetic field, the magnetization M will increase with the increase of the magnetic field intensity H of the magnetic material in the magnetic neutral state. Increase, and finally reach the saturation magnetization value Ms at a certain saturation magnetic field strength Hs. At this time, the atomic magnetic moments inside the material have basically been oriented along the magnetic field. If the magnetic field strength is increased, the magnetization value will not increase significantly. . The corresponding curve in which the magnetization varies with the magnetic field intensity drawn on the M-H diagram is called the magnetization curve, also known as the initial magnetization curve. Correspondingly, the curve of the magnetic induction intensity B of the magnetic material changing with the magnetic field intensity H is called the B-H magnetization curve.

Hysteresis loop:

After the magnetic material is saturated magnetized under the action of a strong enough magnetic field (called saturation magnetization field Hs), the Once the strength of the forward magnetic field drops to zero, the magnetization of the material will drop from Ms to Mr. Obviously, the change in magnetization lags behind the change in magnetic field strength. This phenomenon is called hysteresis. Mr is called residual magnetization, or remanence for short. To make Mr to zero, a reverse magnetic field Hci or MHc must be applied to the material. This magnetic quantity is called intrinsic coercivity. If the reverse magnetic field is gradually increased to -Hs, the material will reach saturation magnetization again. Decrease the reverse magnetic field to zero, and continue to increase the magnetic field strength in the positive direction to Hs, the magnetization will reach Ms through -Mr, Hci, so a closed curve will be formed on the MH diagram, because the change of the magnetization always lags behind Because of the change of magnetic field strength, such a closed curve is called MH hysteresis loop. Correspondingly, if the magnetic field intensity undergoes a periodic change, that is, Hs→0→HC→Hs→HC→Hs, the change of the magnetic induction intensity B will also form a closed loop on the B-H diagram, which is called the B-H hysteresis loop. On this kind of hysteresis loop, the magnetic flux density retained by the material after the saturation magnetization is removed due to the removal of the magnetic field is called the residual magnetic flux density, also referred to as the residual magnetism Br. The reverse magnetic field required to reduce Br to zero is called the coercive force, which is indicated by the BHC table

. In addition, when the magnetic field intensity is Hs, the magnetization is the saturation value Ms, and the corresponding magnetic induction intensity is called the saturation magnetic induction intensity, which is represented by Bs. At this time, Bs=μ0(Hs+Ms). μ0 is the vacuum permeability.

Demagnetization curve:

The second quadrant part of the saturation hysteresis loop is called the demagnetization curve, which reflects the magnetic properties of hard magnetic materials. Curve.

Permeability:

The material is magnetized under the action of the magnetic field H, and has a certain magnetic induction intensity B. The ratio of the two is called absolute permeability μ', that is, μ'=B/H

The ratio of absolute permeability to vacuum permeability μ0 is called relative permeability μ: μ=μ '/μ0

On the numerical value, μ0=4π×10-7H/m. Relative permeability is often also referred to simply as permeability. In the International System of Units, the relationship between relative magnetic permeability and magnetic susceptibility is μ=1+χ

## Composition

The magnetic properties of a substance and the microscopic structure of its atoms, ions or molecules The structure is related. In diamagnetic materials, since the electron spins have been paired, there is no permanent magnetic moment. However, the orbital movement of the internal electrons and the pulling precession under the action of the external magnetic field will induce an induced magnetic moment that is opposite to the direction of the external magnetic field, so it shows diamagnetism. Its χM is equal to the inverse magnetic susceptibility χ, and χM<0. In paramagnetic substances, there are spin-unpaired electrons, so they have a permanent magnetic moment. In the external magnetic field, the permanent magnetic moments are aligned along the direction of the external magnetic field, producing paramagnetism. The molar susceptibility χM of the paramagnetic substance is the sum of the molar paramagnetic susceptibility and the molar susceptibility, ie

χM =χ Scissor+ χReverse(5)

Usually χ cis is more than χ about 1 to 3 reverses Order of magnitude, so this kind of material always exhibits paramagnetism, its χM>0. The relationship between paramagnetic susceptibility and molecular permanent magnetic moment obeys Curie's law

(6)

where, NA is the Avogadro constant; K is the Boltzmann constant (1.38×10erg·K); T is the thermodynamic temperature; μm is the molecular permanent magnetic moment (erg·G). From this it can be obtained

(7)

Since the χ reaction does not change with temperature (or the change is very small), so long as the χM is plotted against 1/T, the intercept is the inverse of χ, and the slope can be obtained from μ m. Since it is much smaller than the χ order, the χ inverse can be ignored in the inaccurate measurement for approximation

(8)

The relationship between μm of paramagnetic materials and the number of unpaired electrons n is

(9)

In the formula, it is the Bohr magneton, and its physical meaning is: the magnetic moment produced by the spin of a single free electron.

μB=9.273×10erg·G=9.273×10J·G=9.273×J·T