3 012 Fundamentals of Materials Science Fall 2005 Lecture 6 09 21 05 Examples of work important in materials science and engineering Today MAGNETIC WORK1 2 Types of magnetic materials 2 Work of magnetizing a paramagnetic material 3 Magnetic materials in materials science engineering 4 CHEMICAL WORK 6 Example chemical potential in phase separated systems 7 Chemical work and internal energy in multi phase multi component systems 7 REFERENCES 9 Reading th M W Zemansky and R H Dittman Heat and Thermodynamics 7 Ed Ch 3 Work pp 49 68 W D Callister Jr Fundamentals of Materials Science and Engineering Ch 18 Magnetic properties pp 730 744 Supplementary Reading Lecture6 forms of work 1 of 10 9 21 05 3 012 Fundamentals of Materials Science Fall 2005 Magnetic work1 The work performed on magnetic materials by a magnetic field has similarities in form to the description of the effect of an electric field on polarizable materials discussed in reading for today s lecture One important difference is that electric dipoles always align with the direction of the electric field while magnetic dipoles magnetic moments in materials may align parallel to an external magnetic field or antiparallel to the magnetic field Types of magnetic materials Ferromagnets These are the materials you think of as magnets from everyday experience the magnets on your refrigerator or the materials in the tip of a magnetic screwdriver They maintain a magnetization in the absence of an externally applied magnetic field Very few ferromagnetic materials exist most ferromagnets contain iron cobalt or nickel Ferromagnets tend to align their magnetic moments with an externally applied magnetic field Non ferromagnets Non ferromagnets do not sustain their own magnetic field in the absence of an externally applied field They are sub classed into paramagnetic and diagmagnetic materials H H O A The atomic dipole configuration for a diamagnetic material with and without a magnetic field In the absence of an external field no dipoles exist in the presence of a field dipoles are induced that are aligned opposite to the field direction A H H O B Atomic dipole configuration with and without an external magnetic field for a paramagnetic material B Figure by MIT OCW Lecture6 forms of work 2 of 10 9 21 05 3 012 Fundamentals of Materials Science Fall 2005 Work of magnetizing a paramagnetic material The work performed on a magnetic material by an externally applied magnetic field is given by o Where V is the volume of the system H is the applied magnetic field and B is the magnetic induction o Analogous to the case of the electric displacement in polarizable materials the magnetic induction B can be broken down as o permeability of vacuum Relates the magnetization of empty space to the applied field M induced magnetic field density in the system o The induced magnetic field density can be modeled as a linear response to the applied magnetic field o The magnetic susceptibility measures the tendency of the material to respond to the applied field with formation of magnetic dipoles o Expanding our definition for the magnetic induction above Lecture6 forms of work 3 of 10 9 21 05 3 012 Fundamentals of Materials Science Fall 2005 o Where is the permeability of the material analogous to the permittivity in polarization Finally the expression for the differential of work is o where the second equality arises for an isotropic material where the response is always exactly aligned with the direction of the externally applied magnetic field Magnetic Units and Conversion Factors for the SI and cgs emu Systems SI Units Quantity Symbol Derived Primary cgs emu Unit Conversion Magnetic Induction Flux Density B tesla Wb m2 kg s C gauss 1 Wb m2 104 gauss Magnetic Field Strength H amp turn m C m s oersted 1 amp turn m 4 x 10 3 oersted Magnetization M SI I cgs emu amp turn m C m s maxwell cm2 1 amp turn m 10 3 maxwell cm2 Permeability of a Vacuum 0 henry m kg m C2 Unitless emu 4 x 10 7 henry m 1 emu r SI Unitless Unitless Unitless r Unitless Unitless Unitless m 4 m Relative Permeability Susceptibility cgs emu m SI m cgs emu Units of the weber Wb are volt seconds Units of the henry are webers per ampere Figure by MIT OCW Lecture6 forms of work 4 of 10 9 21 05 3 012 Fundamentals of Materials Science Fall 2005 Magnetic materials in materials science engineering Room Temperature Magnetic Susceptibilities for Diamagnetic and Paramagnetic Materials Paramagnetics Diamagnetics Material Susceptibility n volume SI units Material Susceptibility n volume SI units Aluminum oxide 1 81 x 10 5 Aluminum 2 07 x 10 5 Copper 0 96 x 10 5 Chromium 3 13 x 10 4 Gold 3 44 x 10 5 Chromium chloride 1 51 x 10 3 Mercury 2 85 x 10 5 Manganese sulfate 3 70 x 10 3 Silicon 0 41 x 10 5 Molybdenum 1 19 x 10 4 Silver 2 38 x 10 5 Sodium 8 48 x 10 6 Sodium chloride 1 41 x 10 5 Titanium 1 81 x 10 4 Zinc 1 56 x 10 5 Zirconium 1 09 x 10 4 Figure by MIT OCW Lecture6 forms of work 5 of 10 9 21 05 3 012 Fundamentals of Materials Science Fall 2005 Ferromagnetic shape memory alloys Left a 26 mm long crystal of Ni Mn Ga alloy at room temperature in zero field Right the same sample after application of a field of order 4 kOe by a permanent magnet The metallic 3 sample exhibits a kink at the twin boundary O Handley research group Courtesy of Professor Robert O Handley Used with permission Lecture6 forms of work 6 of 10 9 21 05 3 012 Fundamentals of Materials Science Fall 2005 Chemical work Chemical work in materials can occur when the internal energy of a system changes in response to changes in the composition of a system We have already mentioned the chemical potential which is the driving force for chemical work What is chemical work and the chemical potential o The chemical potential is a thermodynamic force resisting the addition or removal of molecules to a system chemical work is performed to move molecules against this force In terms of F dx a driving force multiplied by a displacement Lecture6 forms of work 7 of 10 9 21 05 3 012 Fundamentals of Materials Science Fall 2005 Example chemical potential in phase separated systems Chemical work and internal energy in multi phase multi component systems Suppose now that we consider a closed multi phase system that cannot exchange molecules with its surroundings Our glass of water with ice in it will work as an example if we seal the top of the glass Even though the system ice water cannot exchange molecules with its surroundings chemical work can be
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