Shape-Memory Alloys

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Taken from Book Materials Science and Engineering by William D. Callister, Jr (Very Good Book)
A relatively new group of metals that exhibit an interesting (and practical) phenomenon
are the shape-memory alloys (or SMAs). One of these materials, after having been deformed, has the ability to return to its pre-deformed size and shape upon being subjected to an appropriate heat treatment—that is, the material “remembers” its previous size/shape. Deformation normally is carried out at a relatively low temperature, whereas, shape memory occurs upon heating1.
Materials that have been found to be capable of recovering significant amounts of deformation (i.e., strain) are nickel–titanium alloys (Nitinol2, is their tradename), and some copper-base alloys (viz.Cu–Zn–Al and Cu–Al–Ni alloys).

Figure 1: Time-lapse photograph that demonstrates the shapememory effect. A wire of a shape-memory alloy (Nitinol) has been bent and treated such that its memory shape spells the word “Nitinol”. The wire is then deformed and, upon heating (by passage of an electric current), springs back to its pre-deformed shape; this shape recovery process is recorded on the photograph. [Photograph courtesy the Naval Surface Warfare Center (previously the Naval Ordnance Laboratory)].
A shape memory alloy is polymorphic that is, it may have two crystal structures (or phases), and the shape-memory effect involves phase transformations between them.
One phase (termed an austenite phase) has a body-centered cubic structure that exists at elevated temperatures; its structure is represented schematically by the inset shown at stage 1 of Figure 2. Upon cooling, the austenite transforms spontaneously to a martensite phase, which is similar to the martensitic transformation for the iron–carbon system that is, it is diffusionless, involves an orderly shift of large groups of atoms, occurs very rapidly, and the degree of transformation is dependent on temperature; temperatures at which the transformation begins and ends are indicated by “Ms ” and “Mf” labels on the left vertical axis of Figure 2.In addition, this martensite is heavily twinned3, asrepresented schematically by the stage 2 inset, Figure 2. Under the influence of an applied stress, deformation of martensite (i.e., the passage from stage 2 to stage 3, Figure 2) occurs by the migration
of twin boundaries—some twinned regions grow while others shrink; this deformed martensitic structure is represented by the stage 3 inset. Furthermore, when the stress is removed, the deformed shape is retained at this temperature. And, finally, upon subsequent heating to the initial temperature, the material reverts back to (i.e., “remembers”) its original size and shape (stage 4).

Nikola Tesla and Swami Vivekananda

From Website of The Tesla Memorial Society of New York:
Nikola Tesla and Swami Vivekananda
by Mr. Toby Grotz, President, Wireless Engineering

Swami Vivekananda, late in the year l895 wrote in a letter to an English friend, "Mr. Tesla thinks he can demonstrate mathematically that force and matter are reducible to potential energy. I am to go and see him next week to get this new mathematical demonstration. In that case the Vedantic cosmoloqy will be placed on the surest of foundations. I am working a good deal now upon the cosmology and eschatology of the Vedanta. I clearly see their perfect union with modern science, and the elucidation of the one will be followed by that of the other." (Complete Works, Vol. V, Fifth Edition, 1347, p. 77).

Here Swamiji uses the terms force and matter for the Sanskrit terms Prana and Akasha. Tesla used the Sanskrit terms and apparently understood them as energy and mass. (In Swamiji's day, as in many dictionaries published in the first half of the present century, force and energy were not alwavys clearly differentiated. Energy is a more proper translation of the Sanskrit term Prana.)

Tesla apparently failed in his effort to show the identity of mass and energy. Apparently he understood that when speed increases, mass must decrease. He seems to have thought that mass might be "converted" to energy and vice versa, rather than that they were identical in some way, as is pointed out in Einstein's equations. At any rate, Swamiji seems to have sensed where the difficulty lay in joining the maps of European science and Advaita Vedanta and set Tesla to solve the problem. It is apparently in the hope that Tesla would succeed in this that Swamiji says "In that case the Vedantic cosmology will be placed on the surest of foundations." Unfortunately Tesla failed and the solution did not come till ten years later, in a paper by Albert Einstein. But by then Swamiji was gone and the connecting of the maps was delayed.

The Influence of Vedic Philosophy on

Nikola Tesla's Understanding of Free Energy

An Article by Toby Grotz

Web Publication by Mountain Man Graphics, Australia - Southern Autumn of 1997

Abstract ...

Nikola Tesla used ancient Sanskrit terminology in his descriptions of natural phenomena. As early as 1891 Tesla described the universe as a kinetic system filled with energy which could be harnessed at any location. His concepts during the following years were greatly influenced by the teachings of Swami Vivekananda. Swami Vivekananda was the first of a succession of eastern yogi's who brought Vedic philosophy and religion to the west. After meeting the Swami and after continued study of the Eastern view of the mechanisms driving the material world, Tesla began using the Sanskrit words Akasha, Prana, and the concept of a luminiferous ether to describe the source, existence and construction of matter. This paper will trace the development of Tesla's understanding of Vedic Science, his correspondence with Lord Kelvin concerning these matters, and the relation between Tesla and Walter Russell and other turn of the century scientists concerning advanced understanding of physics. Finally, after being obscured for many years, the author will give a description of what he believes is the the pre-requisite for the free energy systems envisioned by Tesla.

Tesla's Earler Description of the Physical Universe

By the year 1891, Nikola Tesla had invented many useful devices. These included a system of arc lighting (1886), the alternating current motor, power generation and transmission systems (1888), systems of electrical conversion and distribution by oscillatory discharges (1889), and a generator of high frequency currents (1890), to name a few. The most well known patent centers around an inspiration that occurred while walking with a friend in a park in Budapest, Hungry. It was while observing the sunset that Tesla had a vision of how rotating electromagnetic fields could be used in a new form of electric motor. his led to the well known system of alternating current power distribution. In 1891 however, Tesla patented what one day may become his most famous invention. It is the basis for the wireless transmission of electrical power and is know as the Tesla Coil Transformer. It was during this year that Tesla made the following comments during a speech before the American Institute of Electrical Engineers:

 "Ere many generations pass, our machinery will be driven by a power obtainable at any point in the universe. This idea is not novel... We find it in the delightful myth of Antheus, who derives power from the earth; we find it among the subtle speculations of one of your splendid mathematicians... Throughout space there is energy. Is this energy static or kinetic.? If static our hopes are in vain; if kinetic - and this we know it is, for certain - then it is a mere question of time when men will succeed in attaching their machinery to the very wheelwork of nature." [1]

This description of the physical mechanisms of the universe was given before Tesla became familiar with the Vedic science of the eastern Nations of India, Tibet, and Nepal. This science was first popualized in the United States and the west during the three year visit of Swami Vivekananda.

Vedic Science and Swami Vivekananda

The Vedas are a collection of writings consisting of hymns, prayers, myths, historical accounting, dissertations on science, and the nature of reality, which date back at least 5,000 years. The nature of matter, antimatter, and the make up of atomic structure are described in the Vedas. The language of the Vedas is known as Sanskrit. The origin of Sanskrit is not fully understood. Western scholars suggest that it was brought into the Himalayas and thence south into India by the southward migrations of the Aryan culture. Paramahansa Yogananda and other historians however do not subscribe to that theory, pointing out that there is no evidence within India to substantiate such claims. [2]

 There are words in Sanskrit that describe concepts totally foreign to the western mind. Single words may require a full paragraph for translation into english. Having studied Sanskrit for a brief period during the late 70's, it finally occurred to this writer that Tesla's use of Vedic terminology could provide a key to understanding his view of electromagnetism and the nature of the universe. But where did Tesla learn Vedic concepts and Sanskrit terminology? A review of the well known biographies by Cheney, Hunt and Draper, and O'Neil [3], [4], [5], reveal no mention of Tesla's knowledge of Sanskrit. O'Neal however includes the following excerpt from an unpublished article called Man's Greatest Achievement:

 "There manifests itself in the fully developed being , Man, a desire mysterious, inscrutable and irresistible: to imitate nature, to create, to work himself the wonders he perceives.... Long ago he recognized that all perceptible matter comes from a primary substance, or tenuity beyond conception, filling all space, the Akasha or luminiferous ether, which is acted upon by the life giving Prana or creative force, calling into existence, in never ending cycles all things and phenomena. The primary substance, thrown into infinitesimal whirls of prodigious velocity, becomes gross matter; the force subsiding, the motion ceases and matter disappears, reverting to the primary substance."

According to Leland Anderson the article was written May 13th, 1907. Anderson also suggested that it was through association with Swami Vivekananda that Tesla may have come into contact with Sanskrit terminology and that John Dobson of the San Francisco Sidewalk Astronomers Association had researched that association. [6]

 Swami Vivekananda was born in Calcutta, India in 1863. He was inspired by his teacher, Ramakrishna to serve men as visible manifestations of God. In 1893 Swami Vivekananda began a tour of the west by attending the Parliament of Religions held in Chicago. During the three years that he toured the United States and Europe, Vivekananda met with many of the well known scientists of the time including Lord Kelvin and Nikola Tesla. [7] According to Swami Nikhilananda:

 Nikola Tesla, the great scientist who specialized in the field of electricity, was much impressed to hear from the Swami his explanation of the Samkhya cosmogony and the theory of cycles given by the Hindus. He was particularly struck by the resemblance between the Samkhya theory of matter and energy and that of modern physics. The Swami also met in New York Sir William Thompson, afterwards Lord Kelvin, and Professor Helmholtz, two leading representatives of western science. Sarah Bernhardt, the famous French actress had an interview with the Swami and greatly admired his teachings. [8]

It was at a party given by Sarah Bernhardt that Nikola Tesla probably first met Swami Vivekananda. [9] Sarah Bernhardt was playing the part of 'Iziel' in a play of the same name. It was a French version about the life of Bhudda. The actress upon seeing Swami Vivekananda in the audience, arranged a meeting which was also attended by Nikola Tesla. In a letter to a friend, dated February 13th, 1896, Swami Vivekananda noted the following:

 ...Mr. Tesla was charmed to hear about the Vedantic Prana and Akasha and the Kalpas, which according to him are the only theories modern science can entertain.....Mr Tesla thinks he can demonstrate that mathematically that force and matter are reducible to potential energy. I am to go see him next week to get this mathematical demonstration. [10]

Swami Vivekananda was hopeful that Tesla would be able to show that what we call matter is simply potential energy because that would reconcile the teachings of the Vedas with modern science. The Swami realized that "In that case, the Vedantic cosmology [would] be placed on the surest of foundations". The harmony between Vedantic theories and and western science was explained by the following diagram:

 BRAHMAN          =          THE ABSOLUTE

                      |                              |

                      |                              |

              MAHAT OR ISHVARA      =      PRIMAL CREATIVE ENERGY

                      |                              |

                 +---------+                    +---------+    

               PRANA and AKASHA     =        ENERGY and MATTER

Tesla understood the Sanskrit terminology and philosophy and found that it was a good means to describe the physical mechanisms of the universe as seen through his eyes. It would behoove those who would attempt to understand the science behind the inventions of Nikola Tesla to study Sanskrit and Vedic philosophy.

Tesla apparently failed to show the identity of energy and matter. If he had, certainly Swami Vivekananda would have recorded that occasion. The mathematical proof of the principle did come until about ten years later when Albert Einstein published his paper on relativity. What had been known in the East for the last 5,000 years was then known to the West.

 Brahman is defined as the one self existent impersonal spirit; the Divine Essence, from which all things emanate, by which they are sustained, and to which they return. Notice that this is very similar to the concept of the Great Spirit as understood by Native American cultures. Ishvara is the Supreme Ruler; the highest possible conception of the Absolute, which is beyond all thought. Mahat means literally the Great One, and is also interpreted as meaning universal mind or cosmic intelligence. Prana means energy (usually translated as life force) and Akasha means matter (usually translated as ether). Dobson points out that the more common translations for Akasha and Prana are not quite correct, but that Tesla did understand their true meanings.

 The meeting with Swami Vivekananda greatly stimulated Nikola Tesla's interest in Eastern Science. The Swami later remarked during a lecture in India, "I myself have been told by some of the best scientific minds of the day, how wonderfully rational the conclusions of the Vedanta are. I know of one of them personally, who scarcely has time to eat his meal, or go out of his laboratory, but who would stand by the hour to attend my lectures on the Vedanta; for, as he expresses it, they are so scientific, they so exactly harmonize with the aspirations of the age and with the conclusions to which modern science is coming at the present time". [11]

Tesla and Lord Kelvin

William S. Thompson was one of the prominent scientists and engineers of the 1800s. He developed analogies between heat and electricity and his work influenced the theories developed by James Clerk Maxwell, one of the founders of electromagnetic theory. Thompson supervised the successful laying of the Trans Atlantic Cable and for that work was knighted Lord Kelvin. Kelvin had endorsed Tesla's theories and proposed system for the wireless transmission of electrical power. [12] FootNOTE- Grotz PACE

 Tesla continued to study Hindu and Vedic philosophy for a number of years as indicated by the following letter written to him by Lord Kelvin.

                                                      15, Eaton Place

                                                      London, S.W.

                                                      May 20, 1902

         Dear Mr. Tesla,

              I  do not know how I can ever thank you enough  for  the

         most kind letter of May, 10, which I found in my cabin in the

         Lucania, with the beautiful books which you most kindly  sent

         me  along  with  it: -"The Buried  Temple",  "The  Gospel  of

         Bhudda",  Les  Grands  Inities",  the  exquisite  edition  of

         Rossetti's  "House  of  Life", and last but   not  least  the

         Century  Magazine  for  June,  1900  with  the  splendid  and

         marvelous photographs on pp. 176, 187, 190, 191, 192, full of

         electrical lessons.

            We had a most beautiful passage across the Atlantic,  much

         the finest I have ever had.  I was trying hard nearly all the

         way, but quite unsuccessfully, to find something definite  as

         to the functions of ether in respect to plain, old  fashioned

         magnetism.    A  propos  of  this,  I  have  instructed   the

         publishers,  Messrs. Macmillan, to send you at the Waldorf  a

         copy   of  my  book  (Collection  of  Separate   Papers)   on

         Electrostatics  and Magnetism.  I shall be glad if  you  will

         accept it from me as a very small mark of my gratitude to you

         for   your  kindness.   You  may  possibly   find   something

         interesting in the articles on Atmospheric Electricity  which

         it contains.

                Lady Kelvin joins me in kind regards, and I remain,

                                          Yours always truly,

                                                       Kelvin

         Thank you also warmly for the beautiful flowers  [13]

Tesla and Russell

Design and Selection of Magnetic Materials

Question taken from :The Science and Engineering of Materials by Donald R. Askeland, Pradeep P. Fulay, Wendelin J. Wright (Very good Book)
Select an appropriate magnetic material for the following applications: a high electrical-efficiency motor, a magnetic device to keep cupboard doors closed, a magnet used in an ammeter or voltmeter, and magnetic resonance imaging.
High electrical-efficiency motor: To minimize hysteresis losses, we might use an oriented silicon iron, taking advantage of its anisotropic behavior and its small hysteresis loop. Since the iron-silicon alloy is electrically conductive, we would produce a laminated structure with thin sheets of the silicon iron sandwiched between a nonconducting dielectric material. Sheets thinner than about 0.5 mm might be recommended.
Magnet for cupboard doors: The magnetic latches used to fasten cupboard doors must be permanent magnets; however, low cost is a more important design feature than high power. An inexpensive ferritic steel or a low-cost ferrite would be recommended.
Magnets for an ammeter or voltmeter: For these applications, alnico alloys are particularly effective. We find that these alloys are among the least sensitive to changes in temperature, ensuring accurate current or voltage readings over a range of temperatures.
Magnetic resonance imaging: One of the applications for MRI is in medical diagnostics. In this case, we want a very powerful magnet. A Nd2Fe12B magnetic material, which has an exceptionally high BH product, might be recommended for this application. We can also make use of very strong electromagnets fabricated from
superconductors.
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Soft Magnetic Materials and Permanent Magnets

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Soft Magnetic Materials:
Ferromagnetic materials are often used to enhance the magnetic flux density (B) produced when an electric current is passed through the material. The magnetic field is then expected to do work. Applications include cores for electromagnets, electric motors, transformers, generators, and other electrical equipment. Because these devices utilize an alternating field, the core material is continually cycled through the hysteresis loop.Note that in these materials the value of relative magnetic permeability depends strongly on the strength of the applied field.
These materials often have the following characteristics:
1. High-saturation magnetization.
2. High permeability.
3. Small coercive field.
4. Small remanance.
5. Small hysteresis loop.
6. Rapid response to high-frequency magnetic fields.

7. High electrical resistivity.
High saturation magnetization permits a material to do work, while high permeability
permits saturation magnetization to be obtained with small imposed magnetic
fields. A small coercive field also indicates that domains can be reoriented with small magnetic fields. A small remanance is desired so that almost no magnetization remains when the external field is removed. These characteristics also lead to a small hysteresis loop, therefore minimizing energy losses during operation.
Eddy current losses are particularly severe when the material operates at high frequencies. If the electrical resistivity is high, eddy current losses can be held to a minimum. Soft magnets produced from ferrimagnetic ceramic materials have a high resistivity and therefore are less likely to heat than metallic ferromagnetic materials.

Permanent Magnets:
Finally, magnetic materials are used to make strong permanent magnets.Strong permanent magnets, often called hard magnets, require the following:

What is Curie Temperature ?

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When the temperature of a ferromagnetic or ferrimagnetic material is increased, the added
thermal energy increases the mobility of the domains, making it easier for them to become
aligned, but also preventing them from remaining aligned when the field is removed.
Consequently, saturation magnetization, remanance, and the coercive field are all reduced
at high temperatures.
If the temperature exceeds the Curie temperature (Tc), ferromagnetic or ferrimagnetic behavior is no longer observed. Instead, the material behaves as a paramagnetic material. The Curie temperature which depends on the material, can be changed by alloying elements. French scientists Marie and Pierre Curie (the only husband and wife to win a Nobel prize; Marie Curie actually won two
Nobel prizes) performed research on magnets, and the Curie temperature refers to their
name. The dipoles still can be aligned in a magnetic field above the Curie temperature,
but they become randomly aligned when the field is removed.
Figure and Table taken from :The Science and Engineering of Materials by Donald R. Askeland, Pradeep P. Fulay, Wendelin J. Wright (Very good Book)

Magnetic Domains

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Domains are regions in the material in which all of the dipoles are aligned in a certain direction. In a
material that has never been exposed to a magnetic field, the individual domains have a random
orientation. Because of this, the net magnetization in the virgin ferromagnetic or ferrimagnetic
material as a whole is zero.

Boundaries, called Bloch walls, separate the individual magnetic domains. The Bloch walls are narrow zones in which the direction of the magnetic moment gradually and continuously
changes from that of one domain to that of the next. The domains are typically very small, about 0.005 cm or less, while the Bloch walls are about 100 nm thick.

Figure taken from :The Science and Engineering of Materials by Donald R. Askeland, Pradeep P. Fulay, Wendelin J. Wright (Very good Book)

Effect of Applying Magnetic Field:

Types of Magnetic Materials

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Diamagnetic Behavior: A magnetic field acting on any atom induces a magnetic dipole for the entire atom by influencing the magnetic moment caused by the orbiting electrons. These dipoles oppose the magnetic field, causing the magnetization to be less than zero. This behavior, called diamagnetism, gives a relative permeability of about 0.99995 (or a negative susceptibility approximately -10^-6, note the negative sign). Materials such as copper, silver, silicon, gold, and alumina are diamagnetic at room temperature.

Superconductors are perfect diamagnets (χ_m=-1) ; they lose their superconductivity at higher temperatures or in the presence of a magnetic field. In a diamagnetic material, the magnetization (M) direction is opposite to the direction of applied field (H).

Paramagnetism: When materials have unpaired electrons, a net magnetic moment due to electron spin is associated with each atom. When a magnetic field is applied, the dipoles align with the field, causing a positive magnetization. Because the dipoles do not interact, extremely large magnetic fields are required to align all of the dipoles. In addition, the effect is lost as soon as the magnetic field is removed. This effect, called paramagnetism, is found in metals such as aluminum, titanium, and alloys of copper. The magnetic susceptibility (χ_m) of paramagnetic materials is positive and lies between 10^-4 and 10^-5.

Ferromagnetism: Ferromagnetic behavior is caused by the unfilled energy levels in the 3d level of iron, nickel, and cobalt. Similar behavior is found in a few other materials, including gadolinium (Gd). In ferromagnetic materials, the permanent unpaired dipoles easily line up with the imposed magnetic field due to the exchange interaction, or mutual reinforcement of the dipoles. Large magnetizations are obtained even for small magnetic fields, giving large susceptibilities approaching 10⁶. Similar to ferroelectrics, the susceptibility of ferromagnetic materials depends upon the intensity of the applied magnetic field. This is similar to the mechanical behavior of elastomers with the modulus of elasticity depending upon the level of strain. Above the Curie temperature, ferromagnetic materials behave as paramagnetic materials and their susceptibility is given by the following equation, known as the Curie-Weiss law:

In this equation, C is a constant that depends upon the material, T_c is the Curie temperature, and T is the temperature above Tc. Essentially, the same equation also describes the change in dielectric permittivity above the Curie temperature of ferroelectrics. Similar to ferroelectrics, ferromagnetic materials show the formation of hystereis loop domains and magnetic domains.

Antiferromagnetism: In materials such as manganese, chromium, MnO, and NiO, the magnetic moments produced in neighboring dipoles line up in:

Figure taken from :The Science and Engineering of Materials by Donald R. Askeland, Pradeep P. Fulay, Wendelin J. Wright (Very good Book)

opposition to one another in the magnetic field, even though the strength of each dipole is very high. This effect is illustrated for MnO in above Figure. These materials are antiferromagnetic and have zero magnetization. The magnetic susceptibility is positive and small. In addition, CoO and MnCl₂ are examples of antiferromagnetic materials.

Ferrimagnetism: In ceramic materials, different ions have different magnetic

moments. In a magnetic field, the dipoles of cation A may line up with the field,

while dipoles of cation B oppose the field. Because the strength or number of dipoles is

not equal, a net magnetization results. The ferrimagnetic materials can provide good

amplification of the imposed field. We will look at a group of ceramics called ferrites that

display this behavior in a later section. These materials show a large, magnetic-field

dependent magnetic susceptibility similar to ferromagnetic materials. They also show

Curie-Weiss behavior (similar to ferromagnetic materials) at temperatures above the Curie

temperature. Most ferrimagnetic materials are ceramics and are good insulators of electricity.

Thus, in these materials, electrical losses (known as eddy current losses) are much

smaller compared to those in metallic ferromagnetic materials. Therefore, ferrites are used

in many high-frequency applications.

Superparamagnetism: When the grain size of ferromagnetic and ferrimagnetic

materials falls below a certain critical size, these materials behave as if they

are paramagnetic. The magnetic dipole energy of each particle becomes comparable to

the thermal energy. This small magnetic moment changes its direction randomly (as a

result of the thermal energy). Thus, the material behaves as if it has no net magnetic

moment. This is known as superparamagnetism. Thus, if we produce iron oxide

(Fe3O4) particles in a 3 to 5 nm size, they behave as superparamagnetic materials. Such

iron-oxide superparamagnetic particles are used to form dispersions in aqueous or

organic carrier phases or to form “liquid magnets” or ferrofluids. The particles in the

fluid move in response to a gradient in the magnetic field. Since the particles form a stable

sol, the entire dispersion moves and, hence, the material behaves as a liquid magnet.

Such materials are used as seals in computer hard drives and in loudspeakers as

heat transfer (cooling) media. The permanent magnet used in the loudspeaker holds the

liquid magnets in place. Superparamagnetic particles of iron oxide (Fe3O4) also can be

coated with different chemicals and used to separate DNA molecules, proteins, and

cells from other molecules.

Magnetic Materials

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Strictly speaking, there is no such thing as a “nonmagnetic” material. Every material consists of atoms; atoms consist of electrons spinning around them, similar to a current carrying loop that generates a magnetic field. Thus, every material responds to a magnetic field. The manner in which this response of electrons and atoms in a material is scaled determines whether a material will be strongly or weakly magnetic. Examples of ferromagnetic materials are materials such as Fe, Ni, Co, and some of their alloys. Examples of ferrimagnetic materials include many ceramic materials such as nickel zinc ferrite and manganese zinc ferrite. The term “nonmagnetic,” usually means that the materia is neither ferromagnetic nor ferrimagnetic. These “nonmagnetic” materials are further classified as diamagnetic (e.g., superconductors) or paramagnetic. In some cases, we also encounter materials that are antiferromagnetic or superparamagnetic.

Ferromagnetic and ferrimagnetic materials are usually further classified as either soft or hard magnetic materials. High-purity iron or plain carbon steels are examples of a magnetically soft material as they can become magnetized, but when the magnetizing source is removed, these materials lose their magnet-like behavior. Permanent magnets or hard magnetic materials retain their magnetization. These are permanent “magnets.” Many ceramic ferrites are used to make inexpensive refrigerator magnets. A hard magnetic material does not lose its magnetic behavior easily.

The magnetic behavior of materials can be traced to the structure of atoms. The orbital motion of the electron around the nucleus and the spin of the electron about its own axis  cause separate magnetic moments. These two motions (i.e., spin and orbital) contribute to the magnetic behavior of materials. When the electron spins, there is a magnetic

moment associated with that motion. The magnetic moment of an electron due to its spin is known as the Bohr magneton (µ_B). This is a fundamental constant and is defined as:

Figure taken from :The Science and Engineering of Materials by Donald R. Askeland, Pradeep P. Fulay, Wendelin J. Wright (Very good Book)

Figure shows origin of magnetic dipoles: (a) The spin of the electron produces a magnetic field with a direction dependent on the quantum number ms. (b) Electrons orbiting around the nucleus create a magnetic field around the atom.

The magnetization M represents the increase in the inductance due to the core material, so we can rewrite the equation for inductance as

The first part of this equation is simply the effect of the applied magnetic field. The second part is the effect of the magnetic material that is present. In materials, stress causes strain, electric field (E ) induces dielectric polarization (P), and a magnetic field (H) causes magnetization (µ₀M) that contributes to the total flux density B.

The magnetic susceptibility (χ_m) , which is the ratio between magnetization and the applied field, gives the amplification produced by the material:

Both µ_r and χ_m refer to the degree to which the material enhances the magnetic field and are therefore related by

As noted before, µ_r and χ_m, therefore, the  χ_mvalues for ferromagnetic and ferromagnetic

materials depend on the applied field (H). For ferromagnetic and ferrimagnetic materials, the term µ₀M>>µ₀H . Thus, for these materials,

We sometimes interchangeably refer to either inductance or magnetization. Normally, we are interested in producing a high inductance B or magnetization M. This is accomplished by selecting materials that have a high relative permeability or magnetic susceptibility.