Introduction
Curie’s Constant, unlike the others, is dependent on the material property that can relate a material's magnetic susceptibility to its temperature. This was first derived by a physicist named- Marie Curie.
Curie’s law states that the magnetization in a paramagnetic material is directly proportional to the applied magnetic field.
For eg., if we heat any object, its magnetization is said to be inversely proportional to the temperature.
Curie’s Temperature is the temperature at which a ferromagnetic substance or material changes into a paramagnetic substance or material on heating it. This transition is used in the storage of optical media for erasing and inserting new data.
Talking about the physical significance of the Curies constant depends on the effective moments of the ions and hence must be some measures of it. However, it is the same average moment of solid.it is the measure of how strongly a material can sustain magnetic alignment despite thermal fluctuations.
What is Curie Weiss Law?
Before proceeding to talk about Curie’s Constant in detail, let us first see what the Curie Weiss law is all about. This law is considered to be one of the pillars of electromagnetism in physics. It intends to calculate the magnetic susceptibility χ or eta of a ferromagnet in the region of paramagnetism that is present above the Curie point.
Similarly, we can also say that the susceptibility of any given paramagnetic substance is inversely proportional to the excess of its temperature above the Curie point. Below this temperature, the substance stops behaving like a paramagnet.
What is a Curie?
The Curie is named after the renowned French physicists Pierre and Marie Curie. To put it simply, it is a unit that is used to measure radioactive activity. The unit’s value is 3.7 x 10^10 disintegrations per second. The original definition of a Curie states that it is ‘the quantity or mass of radium emanation in equilibrium with one gram of radium.' Another similar unit of measuring radioactivity is the becquerel. In 1975, a committee meeting was chaired in which the becquerel replaced the Curie as the official radiation unit in the International System of Units (SI).
Curies Constant Represented in SI Unit Form
C = μ0 μB2 ng2 J( J + 1 )/ 3 kB
Here n= number of magnetic atoms per unit volume
g= lande-g-factor
j= angular momentum quantum number
Kb = boltzmann’s constant
For a magnetic moment for a two-level system, the formula gets reduced to C = nμ0 μ2 / kB
The expressions in the Gaussian unit are represented as:
C = μB2 ng2 J( J + 1 )/ 3 kBC = n μ2 / kB
The constant is used in Curie’s law which states that magnetization is inversely proportional to temperature for a fixed value of the magnetic field.
M = C B/T
This was discovered by Pierre Curie. The relation between magnetic susceptibility is denoted by X, and magnetization M and applied magnetic field H is almost linear at the low fields then:
X = dM/DH ≈ M/H
This shows that temperature T is inversely related to the magnetization system of non-interacting magnetic moments.
Curies Constant Value
Simply, if we take a cubic lattice there is one atom per unit cell. We now are assuming that each atom carries magnetic moment mu= 2muB with the help of Curies constant we will get that C (that denotes Curies constant) =1.3047 K*A/(T*M).
One of the Very Important Laws in this Topic is Weiss law:
We already know the mathematical representation of the law which is M= C*(B/T). Few terms which help in understanding Curie's law better:
Ferromagnetism: It is the property by which certain materials can form permanent magnets (like iron)
Magnetic Susceptibility: It is the measurement of how much a substance can get magnetized in a magnetic field.
Paramagnetism: When some materials get attracted by the external magnetic field, then this situation is known as paramagnetism.
Permeability: It measures the ability of a substance to support the formation of magnetic fields within itself.
Curie’s Point: It is the point or temperature above which certain substances lose their permanent magnetic property.
Curious Constant: As discussed, it’s the property depending upon the material that relates to materials' magnetic susceptibility and temperature.
Curies Weiss Law: It informs us about the magnetic susceptibility that is denoted by the letter X of a ferromagnet in the paramagnetic region above the Curies point; it is denoted as X= C/T-Tc.
C= Curies constant
T= absolute temperature
Tc = Curie’s Temperature, both measured in kelvin.
Curie’s Constant Unit
We define the unit of Curies constant as K*A/(T∗m)
The magnetic moment μθ is a characteristic number that describes the magnetic property of a single atom or a particle molecule etc.
We can easily calculate the value of Curie by dividing the decay rate per second by 3.7 x 10^10; the decay rate is equal to 1 Curie. Taking an example of 1 gram of cobalt -60 is equal to 1119 Curie and it is because 4.141 x 10^13/ 3.7 x 10^10 = 1,119 Ci.
Curie’s Temperature for Some Ferromagnetic Substances
Students should note the Curie temperatures of some important substances that are frequently asked in examinations. The list is given below:
The Curie temperature of iron (Fe) is 1043 kelvin.
The Curie temperature of Gadolinium (Gd) is 293 kelvin.
The Curie temperature of Nickel (Ni) is 631 kelvin.
Curies Table of Content
Curie's Law of Magnetism
Curious Constant Equation
Curie's Law of Magnetism: States that magnetization that's M of a paramagnetic substance is directly proportional to the Curies constant which is denoted as C and magnetic field which is denoted as B which is inversely proportional to T that is temperature writing it in the equation:
M=C/T*B
C- characteristics susceptibility to magnetic fields of paramagnetic materials. It depends on the strength of the atoms which are forming the substances and on the density of these moments.
Limitations of Curie's Law
There are some failures in these laws like it fails in the Curie’s Weiss law fails to describe the susceptibility of certain materials these and are considered as the behavior in the form 1/T-Tc.
However, at the temperature which is denoted as T,>>Tc the whole expression still holds, however as soon as we replace Tc by temperature which is higher than Curie’s Temperature that C and if T becomes zero, then the susceptibility becomes infinite.
Sometimes it takes the Weiss constant to distinguish it from the temperature of the Weiss point.
There are a few modifications in these laws: The Weiss law which was for a paramagnetic material that's written as X = M/H= Mμ0/B= C/T.
Where μ0 is called the permeability of free space.
M is called magnetization B= μ0 is called a magnetic field and C is called the material-specific Curies constant.
The total magnetic field for Curies Weiss law is B + lambda M (lambda = Weiss molecular field constant). It clearly shows that magnetic susceptibility is inversely proportional to temperature.
Which is the Weiss law
X= C/T-Tc
When temperature Tc is Tc= C lambda
FAQs on Curie’s Constant
1. What is the formula for Curie's Law in magnetism?
Curie's Law describes the relationship between the magnetisation of a paramagnetic material and temperature. The law states that the magnetisation (M) of a paramagnetic material is directly proportional to the applied magnetic field (B) and inversely proportional to the absolute temperature (T). The formula is expressed as:
M = C * (B / T)
Where:
- M is the resulting magnetisation.
- B is the applied magnetic field.
- T is the absolute temperature in Kelvin.
- C is the material-specific Curie's Constant.
2. What is Curie's Constant and what is its SI unit?
Curie's Constant (C) is a material-dependent property that indicates how strongly a substance can be magnetised in response to a magnetic field at a given temperature. It is a measure of the magnetic moments of the atoms within the material and their density. A higher Curie's Constant means the material is more susceptible to magnetisation. The SI unit for Curie's Constant is Kelvin (K), though it can also be expressed in derived units like K·m³·mol⁻¹.
3. What is the significance of Curie Temperature (Tc)?
The Curie Temperature (Tc) is a critical temperature point for magnetic materials. Below this temperature, a ferromagnetic material exhibits strong magnetic properties and spontaneous magnetisation. However, upon heating, once the material's temperature rises above the Curie Temperature, thermal agitation overcomes the magnetic ordering, and it loses its ferromagnetic properties, behaving like a paramagnetic material instead. For example, the Curie temperature for iron is approximately 1043 K.
4. How does Curie's Law explain the behaviour of paramagnetic materials at different temperatures?
Curie's Law (M ∝ 1/T) explains that as the temperature of a paramagnetic material increases, its magnetisation decreases for a constant applied magnetic field. This happens because at higher temperatures, the atoms have more thermal energy. This increased random thermal motion disrupts the alignment of the individual atomic magnetic dipoles with the external magnetic field, thus reducing the overall magnetisation of the material.
5. What is the primary difference between Curie's Law and the Curie-Weiss Law?
The main difference lies in the types of materials they describe.
- Curie's Law applies to ideal paramagnetic materials, where there are no interactions between the atomic magnetic moments. It is given by χ = C/T.
- The Curie-Weiss Law is a modification that applies to ferromagnetic materials above their Curie temperature. It accounts for the interactions between the atomic moments through the Weiss molecular field. The formula is χ = C / (T - Tc), where Tc is the Curie temperature.
6. Why does Curie's Law fail to describe ferromagnetic materials below their Curie temperature?
Curie's Law fails for ferromagnetic materials below their Curie temperature because it assumes the magnetic dipoles within the material are non-interacting. In ferromagnetic materials, strong quantum mechanical exchange forces cause the dipoles to align spontaneously in regions called magnetic domains, even without an external magnetic field. This cooperative interaction leads to a very high, non-linear magnetisation that cannot be explained by the simple inverse temperature relationship of Curie's Law. The Curie-Weiss law provides a better, though still approximate, description for these materials above Tc.
7. Is the 'Curie' (Ci), the unit of radioactivity, related to Curie's Constant in magnetism?
No, they are completely unrelated concepts named in honour of the Curie family's scientific contributions.
- Curie's Constant (C) is a parameter in physics that relates to the magnetic susceptibility of a paramagnetic material.
- The Curie (Ci) is a non-SI unit of radioactivity, defined as 3.7 x 10¹⁰ disintegrations per second. It is named after Pierre and Marie Curie for their pioneering work in radioactivity.
