RAJALAKSHMI ENGIN EERING COLLEGE - PH19141 – PHYSICS OF MATERIALS – STUDY MATERIAL 1 PH19141 - PHYSICS OF MATERIALS LTPC 3 0 2 4 Common to I sem. B.E. - Aero, Auto, Civil, Mech& MCT OBJECTIVES • To enhance the fundamental knowledge in Physics and its applications relevant to mechanical engineering streams. • To familiarize students in various experimental setups and instruments that are used to study / determine the various properties of materials. UNIT I - MECHANICS & PROPERTIES OF MATTER 9 Basic definitions - Newton’s laws – forces -solving Newton’s equations - constraints and friction - cylindrical and spherical coordinates - potential energy function - conservative and non-conservative forces - central forces - conservation of angular momentum - non-inertial frames of reference - rotating coordinate system - centripetal and coriolis accelerations – Elasticity - stress-strain diagram - bending of beams - cantilever depression - Young’s modulus determination - I-shape girders. UNIT II - CRYSTAL PHYSICS 9 Basis – lattices - symmetry operations and crystal systems -Bravaislattics - atomic radius and packing fraction - SC, BCC, FCC, HCP lattices - Miller indices - diffraction by crystals - reciprocal lattice - interpreting diffraction patterns - crystal growth techniques-Czochralski and Bridgmann, crystal defects. UNIT III - PHYSICS OF MATERIALS 9 Solid solutions - Hume-Rothery’s rules –Gibb’s phase rule - binary phase diagrams -isomporhpus systems - tie-line and lever rule - eutectic, eutectoid, peritectic, peritectoid, monotectic and syntectic systems - formation of microstructures - homogeneous and non-homogenous cooling – nucleation - iron-carbon phase diagram - eutectoid steel - hypo and hypereutectoid steel – diffusion - Fick’s laws – T-T-T diagrams. UNIT IV - ENGINEERING MATERIALS & TESTING 9 Metallic glasses – preparation and properties - Ceramics – types, manufacturing methods and properties - Composites – types and properties - Shape memory alloys – properties and applications - Nano-materials – top down and bottom up approaches – properties - Tensile strength – Hardness – Fatigue - Impact strength – Creep - Fracture – types of fracture. UNIT V - QUANTUM PHYSICS 9 Blackbody problem -Planck’s radiation law - duality of light -De Broglie hypothesis - properties of matter waves - wave packets –Schrodinger’s equations (time dependent and time independent) - Born interpretation (physical significance of wave function) - probability current - operator formalism (qualitative) - expectation values - uncertainty principle - particle in a box -eigen function and eigen values -Dirac notation (qualitative). TEXT BOOKS: 1. Bhattacharya, D.K. & Poonam, T. “Engineering Physics”. Oxford University Press, 2018. 2. Gaur, R.K. & Gupta, S.L. “Engineering Physics”. DhanpatRai Publishers, 2018. 3. Raghavan, V. “Physical Metallurgy: Principles and Practice” . PHI Learning, 2019. RAJALAKSHMI ENGINEERING COLLEGE - PH19141 – PHYSICS OF MATERIALS – STUDY MATERIAL RAJALAKSHMI ENGIN EERING COLLEGE - PH19141 – PHYSICS OF MATERIALS – STUDY MATERIAL 2 REFERENCES 1. Balasubramaniam, R. “Callister's Materials Science and Engineering”. Wiley India Pvt. Ltd., 2017. 2. Raghavan, V. “Materials Science and Engineering : A First course” . PHI Learning, 2019. 3. Resnick, R., Halliday, D., & Walker, J. “Principles of Physics ”, Wiley India Pvt., 2018. LIST OF EXPERIMENTS: PHYSICS LABORATORY (Any 10 experiments) 30 1. Determination of Laser characteristics (wavelength and angular spread). 2. Determination of Young’s modulus by non-uniform bending method 3. Determination of thermal conductivity of a bad conductor – Lee’s Disc method. 4. Determination of velocity of sound and compressibility of liquid – Ultrasonic interferometer 5. Coupled oscillators - Two compound pendulums; 6. Experiment on moment of inertia measurement- Torsional pendulum by resonance, 7. LC circuit, LCR circuit and Resonance phenomena in LCR circuits; 8. Experiments on electromagnetic induction – BH-Curve experiment 9. Determination of thickness of a thin wire – Air wedge method 10. Determination of solar cell characteristics. 11. Measurement of hysteresis loss:B -H curve. 12. Determination of creep characteristics of a metallic wire. TOTAL PERIODS 75 OUTCOMES: On completion of the course students will be able to • Understand foundational mechanics and elastic nature of materials and determine the elastic moduli of materials. • Apply the basic knowledge of crystallography in materials preparation and treatments. • Create binary phase diagrams and TTT charts and use them to analyse and measure the properties of alloys. • Understand various engineering materials, test or measure their properties and use them in suitable applications. • Understand the concepts of quantum theory and the nature of light and determine the characteristics of a given laser source. *** RAJALAKSHMI ENGINEERING COLLEGE - PH19141 – PHYSICS OF MATERIALS – STUDY MATERIAL RAJALAKSHMI ENGIN EERING COLLEGE - PH19141 – PHYSICS OF MATERIALS – STUDY MATERIAL 3 UNIT I – Mechanics and Properties of Matter Particle: Dimensions of an object are considered to be negligible and small compared to the coordinates describing its motion. System of particles: An object represented by two or more particles and is dealt with together is called system of particles. Rigid body : The distance between any two given points on a rigid body is invariant in time regardless of external forces exerted on it.A rigid body is usually considered as a continuous distribution of mass. Deformable body: Anybody that changes its shape and/or volume while being acted upon by any kind of external force. A force is a push or a pull exerted on one object by another object. The units of force is newton. Newton’s first law: A body continuous a state of rest or uniform motion unless an external force acts on it. Newton's first law says that if the net force on an object is zero ( ΣF=0), then that object will have zero acceleration. That doesn't necessarily mean the object is at rest, but it means that the velocity is constant. The property of a body to remain at rest or to remain in motion with constant velocity is called inertia . Newton’s first law is often called the law of inertia. The inertia of an object is measured by its mass. Mass can be determined by measuring how difficult an object is to accelerate. The more mass an object has, the harder it is to accelerate. Newton’s second law:Acceleration of an object produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. Newton’s third law: All forces between two objects exist in equal magnitude and opposite direction. Newton’s first law of motion from Newton’s second law of motion Newton's first law states that a body stays at rest if it is at rest and moves with a constant velocity if already moving, until a net force is applied to it. In other words, the state of motion of a body changes only on application of a net non-zero force.Newton's second law states that the net force applied on a body is equal to the rate of change in its momentum. Mathematically, ͤ⃗͘ ̀⃗ = Where, F is the net force, and p is the momentum.ͨ͘ Now, we can write the same as, ͤ⃗͘ ͘ʚͪ⃗͡ʛ ͘͡ ʚͪ⃗ʛ ̀⃗ = ⇒ ̀⃗ = = ͨ͘ ͨ͘ ͨ͘ RAJALAKSHMI ENGINEERING COLLEGE - PH19141 – PHYSICS OF MATERIALS – STUDY MATERIAL RAJALAKSHMI ENGIN EERING COLLEGE - PH19141 – PHYSICS OF MATERIALS – STUDY MATERIAL 4 So, if the net force, F is zero, change in the value of v is be zero i.e., a body at rest will be at rest and a body moving with constant velocity will continue with the same velocity, until a net force is applied. This conclusion is similar to the Newton’s first law of motion. Thus, we can derive Newton’s first law of motion using Newton’s second law of motion. Newton’s third law of motion from Newton’s second law of motion Consider an isolated system of two bodies A & B mutually interacting with each other, provided there is no external force acting on the system. Let F AB , be the force exerted on body B by body A and F BA be the force exerted by body B on A.Suppose that due to these forces F AB and F BA , dp 1/dt and dp 2/dt be the rate of the change of momentum of these bodies respectively. Then, F BA = dp 1/dt ---------- (i) FAB = dp 2/dt ---------- (ii) Adding equations (i) and (ii), we get, FBA + F AB = dp 1/dt + dp 2/dt F + F = d(p + p )/dt ⇒ BA AB 1 2 If no external force acts on the system, then d(p 1 + p 2)/dt = 0 F + F = 0 ⇒ BA AB F = - F --------- (iii) ⇒ BA AB the above equation (iii) represents the Newton's third law of motion (i.e., for every action there is equal and opposite reaction). Constrained Motion: In some cases a particle is forced to move along a curve or surface. This curve or surface is referred to as a constraint, and the resulting motion is called constrained motion. The particle exerts a force on the constraint, and by Newton’s third law the constraint exerts a force on the particle. This force is called the reaction force, and is described by giving its components normal to the motion, denoted N, and parallel to the motion, denoted f . Constrained motion results when an object is forced to move in a restricted way. For example, it may have to move along a curved track, to slide on a table that may accelerate upwards, to stay in contact with an accelerating wedge, etc. Constraint Forces adjust themselves according to Newton's Second Law so that the acceleration of an object is just the right value for the object to follow the motion required by the particular constrained. Friction: In the constrained motion of a particle a common force parallel to the motion of the particle is friction, which typically acts in the direction opposite to that of the motion (i.e., it acts in such a way as to slow the motion of the particle). Experimentally, it is found that the magnitude of the frictional force is proportional to the magnitude of the normal force, i.e., f = µN, where the proportionality constant, µ is referred to as the coefficient of friction.