Warsaw University of Technology Electrical Department. Laboratory of Materials Technology KWNiAE

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1 Warsaw University of Technology Electrical Department Laboratory of Materials Technology KWNiAE Practice 6 Analysis of Ferromagnetic Materials

2 1. Introduction In each atom of every known material there are electrons circulating on elliptical orbits. We can say that there is displacement of a charge q=e during the circulation of an electron over the atomic nucleus. Additionally each electron rotates over its own axis. This is called spin. Because of these phenomenon there appear two magnetic moments, orbital and spin. This moment is the sum of vectors and finally each atom has got magnetic moment, and it can be equal or different than zero. External magnetic field disrupts a movement of electrons. The inducted magnetic moment appears and it is directed always opposite to the magnetic filed intensity vector. This phenomenon is called diamagnetic effect and occurs in all material environments and is not dependent of temperature. Because the value of inducted moment is small it appears only in materials which resultant magnetic moment is equaled almost zero. Materials which meet this condition are called diamagnets. When we start to analyze materials which resultant magnetic moment is different than zero, then we can observe that their behavior is dependent of the distance between the atoms and how the electrons are placed on particular orbits. The characteristic is ratio r a a distance between atoms r radius of orbit not fully filled by electrons If this ratio is > 6,2 then because of thermal movements mutual placement of magnetic moments a is chaotic and the solid is practically indifferent to the magnetic field. Solids with > 6, 2 are r called paramagnets. a In materials with 3,2 6, 2 the replacement forces arise, which order the setting of r neighboring magnetic dipoles. When the external magnetic field is applied to such material all dipoles set themselves parallel to the external field s lines. We call such effect as a ferromagnetic and these materials are ferromagnets. A value of r a ratio is dependent not only of atom construction of particular material but also of temperature. Together with the increase of temperature the ferromagnetic effect stops. This temperature is special and different for each material and it is called the Curie temperature. 2. Ferromagnets and the hysteresis loop When there isn t any external magnetic field the magnetic dipoles place themselves in one direction in macroscopic magnetic domain, which order is chaotic. Under the impact of magnetic field this areas place themselves along the magnetic field s lines and further increasing of field s intensity doesn t make any change to their placement. Soft Ferromagnets they are easy to magnetize with the external field, however such magnetizing id very weak and easy fade when external field disappears. Hard Ferromagnets they are hard to magnetize, but they keep their properties for a long time after the disappearance of external magnetic field. Ferromagnets characterize by hysteresis phenomenon which shows irreversible changes of magnetic induction because of the external magnetic field s changes. The graphical representation of these changes is the histeresis loop. B=f(H).

3 At this picture three cycles of magnetizing are shown. 1. Characteristic of original magnetizing 2. Curve of demagnetizing 3. Full loop of magnetic hysteresis Ad 1. The characteristic of original magnetizing is a curve which is created during the first magnetizing this curve runs from (0;0) to the point (H S ;B S ). B S saturation s induction. It s the biggest possible induction on material. Further increasing field s H intensity doesn t increase the induction. H S Intensity of saturation is the intensity of magnetic field for which appears an induction of intensity. Ad 2. A curve of demagnetizing is a curve which is created when the external magnetic field fades. This curve runs from point (H S ;B S ) to the point (H C ;0) through the point (0; B R ). H C intensity of coercion is the intensity of magnetic field when the induction is equal zero. B R remnant is a debris induction of material magnetized to the state of saturation, then demagnetized by decreasing the external field. Ad 3. The magnetic histeresis loop is a curve that shows the full magnetizing and demagnetizing cycle of material magnetized earlier.

4 3. Magnetic permittivity μ We can characterize each material by the way it interacts with an external magnetic field. As it was mentioned in the introduction, magnetic properties are the results of the quantum mechanics effects. However to describe materials in macroscopic world it s easier to use concept of magnetic permittivity. μ magnetic permittivity of materials tells us how many times the magnetic field changes through the material. µ = µ µ r 0 7 H μ 0 magnetic permittivity of vacuum at the level of 4 10 m μ r relative permittivity of material tells us how many times the permittivity of materials is greater than the magnetic permittivity of a vacuum. For para and diamagnet materials the magnetic field s induction and magnetic field intensity are described byb= µ H. In ferromagnets the dependence between B and H is not linear and described by the curve of magnetizing. Only in particular point the dependence B=μH exists. 4. Magnetizing commutation curve, relative differential magnetic permittivity If on original magnetic curve we set the point P at the abruptly ascending part of this characteristic and in its area we lead a tangent to the characteristic that we can say that: B db µ d = lim = than µ d tgβ H 0 H dh = µ d is a differential relative permittivity. At the picture below we can see a geometrical interpretation of magnetic differential permittivity tgβ and ordinary magnetic relative permittivity tgα. H m We can get a curve of original magnetizing by slowly magnetizing a sample whit a constant or slowly changing field. However it s easier to use a commutative curve. We get it by connecting the summits of histeresis loop for the subsequent values of magnetizing current till the state of saturation.

5 1,2,3 next loops of histeresis 4 commutative curve 5. Basic properties of magnetic materials Because of the different properties of soft and hard magnetic materials we can distinguish typical parameters of those materials: For soft magnetic materials 1. Commutative curve of magnetizing which the curve is running through summits of next hysteresis loops. It s nearing to the curve of original magnetizing 2. Start magnetic permittivity μ r pocz. 3. Maximal magnetic permittivity μ r max. 4. Saturation s induction B S [T]. W 5. Magnetic losses p, which is value of energy loosing for magnetizing kg and demagnetizing elementary piece of material, is including loss form histeresis and circulation current. For hard magnetic materials 1. Demagnetizing curve (part 2 of histeresis loop) 2. Remanence B R [T]. A 3. Coercive force H C m 4. Maximal value of B*H, which is a value of energy cumulated in magnet BH max W 3 cm

6 6. Methods of magnetic material s examination We can make magnetic materials examination as a static with constant fields and as a dynamic with variable fields which finally divides research methods into: a) Examination soft magnetic materials in constant magnetic fields b) Examination soft magnetic materials in variable magnetic fields c) Examination hard magnetic materials A magnetic sample makes part of the whole part of magnetic circuit. Magnetic field is obtained by coils with current. Depend of sample s shape and magnetic circuit we can distinguish: Systems to examine closed ring samples [1] and frame samples [2]. Magnetic circuit is a ring coiled from metal plate with reeled windings or it s packet of metal plates which is slipped in the set of constant coils. It is called Epstein apparatus. Systems to examine samples in closed circuits where the sample is only a part of magnetic circuit so called keeper permeates [3]. Sample closes magnetic circuit of keeper which has reeled constant and magnetic windings. Systems to examine open samples [4] where a sample is put into the long magnetizing coil. A disadvantage of open systems is smaller precision but recompensed by the simplicity of a system (constant magnetizing coil) and the speed of measurement and also the possibility of making the serial measurements. An examination of ring samples is more precise but making a winding on closed magnetic circuit takes a long of time. Measuring magnetic induction B is possible by making measuring of induction indirectly in a slit (from a coil s magnetizing current) or directly in example by Hall generator gauges. The measurements of field s intensity H are possible by measuring the magnetizing current. Below are shown examples of samples systems to examine.

7 7. Measure system and measuring method To determine a hysteresis loop and the commutating curve we will use the ring samples with windings and few simple discrete elements. The systems are powered from auto converter with converter lowering the voltage to 24V. On the screen of the oscilloscope we get an image of histeresis loop. We know the values of discrete elements and we can calculate the value of voltage particular points of an image at value B or H. The way of a measurement should be done is follows: in the original circuit (N 1 ) because of the voltage there is a variable current I 1, which makes in ferromagnetic core variable magnetic field of intensity proportional to this current. On resistor R 1 arises a decrease of voltage U R1 proportional to the current I 1, which is delivered to the plates of oscilloscope s horizontal deviation X (it s base of time for oscilloscope). From Ampere s law we know that H dl = i, integral from a vector of magnetic field intensity over a closed circuit is equal the sum of currents flowing through the shape of integrating H dl = Hdl. If a circle of radius r lying inside the sample is a shape of b + a integration then Hdl = 2π rh = N1 I1 so for a ring coil r =r ŚR where r ŚR = 2 Finally we get an expression connecting voltage on R 1 and intensity of magnetic field H. N1 N1 U R1 N1 H = I1 = = U R1 2π rśr 2π rśr R1 2R1 π rśr An image shows sample s geometry and placement of r ŚR. Variable magnetic field flux makes EMF of induction in a winding (N 2 ). This electromotive dφ force is equal E = N2 as the induction law says. dt Bydn we define unit vector normal to the surface S enclosed by the coil s winding and we get φ = B dn S, because in the case of toroidal coil the vectors B and dn are parallel. Voltage

8 on winding N 2 is proportional to the induction derivate. If we want to see and measure the histeresis loop then we have to deliver to the plates of oscilloscope s deviation a voltage proportional to B. To achieve this we will use a simple integrating system RC: U C 1 1 = Edt = N2 RC RC S B which after transformation results with dependence between B and voltage U C delivered to the plates of vertical deviation Y. R2 C B = U C N2 S Values of voltage U R1 and U C are the maximal values and we read them directly from the oscilloscope. Scheme of the measurement system. 8. How to make measurements and compile the results The size of a sample, its cross-section and values of R 1, R 2, C are written on a table by each ferromagnetic core. A system has to be connected to the power supply and oscilloscope has to be plugged into proper BNC connectors. Set the oscilloscope to the XY mode. By adjusting the auto converter increase the supplying voltage and watch the hystereses loop. Note point needed to determine a commutative curve. After reaching the maximal hystereses loop move its image into protocol. Resulted voltages will be used to calculate B and H. Note results in table, make calculations, draw a graph and show the conclusion. Sample measure tables No. U R1 [ V ] 1 2 A m H S U C [ V ] B S [ T ] [ V ] U R1 A m H C U C [ V ] [ T ] B R

Displacement Current. Ampere s law in the original form is valid only if any electric fields present are constant in time

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