10/31/2019 MSE 553 DEFECTS, DIFFUSION AND TRANSFORMATION IN MATERIALS Course Information Lecturer: Dr. Emmanuel Gikunoo Office : 321 New Block Email: egikunoo.soe@knust.edu.gh Lecture Hours: Tuesdays, 08:00 – 11:00 E. GIKUNOO Website: https://egikunoo.wordpress.com First Semester 2019/2020 Wednesdays 2:00 – 5:00 pm 1 2 1 2 Objective Learning Outcomes At the end of the course the student should be able to: This course will provide students with the: discuss the relationship between atomic structure of understanding of basic theory of the interaction of defects, materials and microstructure evolution on the basis of general laws of phase transformation and mutual effects transport processes. between composition, and the microstructure and macroproperties of engineering materials such as metallic apply the principles of phase transformation for alloys and ceramics; microstructure design and property improvements. understanding of phase transformations in materials in apply the principles of phase transformation for selection of tailoring the microstructure and properties of various materials and processes. materials; much needed underlying principles governing materials developments. 3 4 3 4 1
10/31/2019 Course Content References This course will introduce students to: W. D. Callister, Jr., Materials Science and Engineering – An Introduction , 7th Edition, John Wiley & Sons, 2006. basic crystallography and thermodynamics; D. R, Askeland and P . P . Phule, The Science and Engineering of defects classification in different crystals, defects in non- Materials , 4th Edition, Thomson Learning Vocational, 2003. crystalline materials, mechanical, electrical, magnetic and optical properties of defects, defect characterization techniques; D. A. Porter, K. E. Easterling, M. Sherif, Phase T ransformations in Metals and Alloys, 3 rd edition, Chapman & Hall, 2009. Fick’s first and second laws, Intrinsic and integrated diffusion coefficient, Tracer and growth kinetics, Matano-Boltz analysis, . Haasen, Physical Metallurgy, 3 RD edition, Cambridge P Kirkendall effect, Darken analysis, physico-chemical approach of University Press, 1996. diffusion; basic kinetics of transformation, interfacial and homogeneous H. V. Keer, Principles of the Solid State, New Age International (P) Limited, 2005. nucleation, nucleation and growth, coarsening and the Gibbs- Thompson equation, diffusion and diffusionless transformations. Presentation Slides 5 6 5 6 Crystallography Grading Crystal Structure – matter assumes a periodic shape Assignments 20 o Non-crystalline or amorphous “structures” exhibit no long range T erm Papers 15 periodic shapes Assigned Presentation 15 o Crystal systems – not structures but potentials Final Exam 50 FCC, BCC and HCP – common crystal structures for metals Total 100 Point, direction and planer ID’ing in crystals X-ray diffraction and crystal structure 7 8 7 8 2
10/31/2019 STRUCTURES Energy and Packing Energy • Non dense, random packing Materials lacking long typical neighbor Crystaling Materials bond length range order typical neighbor r bond energy Means: Periodic arrangement of Amorphous Materials atoms/ions over large atomic distances Energy Leads to structure displaying LONG- These less densely packed typical neighbor RANGE ORDER that is Measurable lower bond energy bond length and Quantifiable • Dense, ordered packing “structures” can be found in some metals and are All metals, many ceramics, and r typical neighbor observed in almost all bond energy some polymers exhibit this ceramics, glass and many “High Bond Energy” and a More Dense, ordered packed structures tend to have “plastics” Closely Packed Structure 9 lower energies & thus are more stable. 10 9 10 Crystallography Crystallography 11 12 11 12 3
10/31/2019 Crystallography Crystallography 13 14 13 14 Crystal Systems Crystal Systems Unit cell: smallest repetitive volume which contains the complete lattice pattern of a crystal. 7 crystal systems of varying symmetry are known These systems are built by changing the lattice parameters: a, b, and c are the edge lengths , , and are interaxial angles 15 16 15 16 4
10/31/2019 Atomic Packing Factor (APF) Simple Cubic Structure (SC) Rare due to low packing density (only Polonium (Po) has 𝐵𝑄𝐺 = 𝑊𝑝𝑚𝑣𝑛𝑓 𝑝𝑔 𝑏𝑢𝑝𝑛𝑡 𝑗𝑜 𝑣𝑜𝑗𝑢 𝑑𝑓𝑚𝑚 this structure) 𝑊𝑝𝑚𝑣𝑛𝑓 𝑝𝑔 𝑣𝑜𝑗𝑢 𝑑𝑓𝑚𝑚 Close-packed directions are cube edges. • APF for a simple cubic structure = 0.52 volume atoms atom 4 p (0.5 a )3 a unit cell 1 3 R =0.5 a APF = a 3 volume close-packed directions unit cell *assume hard spheres contains (8 x 1/8) = 1 atom/unit cell Here: a = 2 × R at Coordination No. = 6 Where R at is the atomic radius (# nearest neighbors) for each atom as seen 18 17 17 18 Body Centered Cubic Structure (BCC) Atomic Packing Factor: BCC Atoms touch each other along cube diagonals within a unit cell . - Note: All atoms are identical; the center atom is shaded 3 a differently only for ease of viewing. a ex: Cr, W, Fe ( ), T antalum, Molybdenum 2 a Close-packed directions: R length = 4 R = 3 a a atoms volume 4 p ( 3 a /4)3 unit cell 2 atom 3 APF = volume a 3 unit cell Coordination # = 8 APF for a body-centered cubic structure = 0.68 2 atoms/unit cell: (1 center) + (8 corners x 1/8) 19 20 19 20 5
10/31/2019 Atomic Packing Factor: FCC Face Centered Cubic Structure (FCC) Atoms touch each other along face diagonals . APF for a face-centered cubic structure = 0.74 ABCABC... Stacking Sequence The maximum achievable APF! - Note: All atoms are identical; the face-centered atoms are Close-packed directions: shaded differently only for ease of viewing. length = 4 R = a√2 ex: Al, Cu, Au, Pb, Ni, Pt, Ag a = 2 2 R Unit cell contains: 6 x 1/2 + 8 x 1/8 = 4 atoms/unit cell 2 a atoms volume 4 p ( 2 a /4)3 unit cell 4 atom 3 APF = Coordination # = 12 volume a 3 a 4 atoms/unit cell: (6 face x ½) + (8 corners x 1/8) unit cell 21 22 21 22 Hexagonal Close-Packed Structure (HCP) HCP and FCC Stalking We find that both Atoms touch each other along face diagonals . FCC & HCP are ABAB... Stacking Sequence highest density ex: Cd, Mg, Ti, Zn 3D Projection packing schemes 2D Projection (APF = .74) – this A sites Top layer illustration shows c B sites Middle layer their differences as A sites the closest packed Bottom layer a 6 atoms/unit cell planes are “built- APF = 0.74 Coordination # = 12 up”. c / a = 1.633 (ideal) 23 24 23 24 6
10/31/2019 Theoretical Density, r ���� �� ����� �� ���� ���� Density = r = ����� ������ �� ���� ���� � � r = � � � � where n = number of atoms/unit cell R a A = atomic weight V C = Volume of unit cell = a 3 for atoms g cubic 2 52.00 unit cell mol N A = Avogadro’s number r = = 6.023 x 10 23 atoms/mol a 3 6.023x10 23 volume atoms mol unit cell Ex: Cr (BCC) r theoretical = 7.18 g/cm 3 A = 52.00 g/mol , R = 0.125 nm, r actual = 7.19 g/cm 3 n = 2 �� a = √� = 0.2883 nm 25 26 25 26 Basic Crystallography Basic Crystallography A figure has rotational symmetry if Repetition = Symmetry it can be rotated by an angle T ypes of repetition between 0˚ and 360˚ so that the Rotation o image coincides with the preimage. T ranslation o The angle of rotational symmetry is Rotation the smallest angle for which the What is rotational symmetry o figure can be rotated to coincide with itself. This object is obviously symmetric. Can be rotated 90˚ without detection. The order of symmetry is the Symmetry is doing something that o looks like nothing has been done! number of times the figure coincides with itself as it rotates through 360˚. 27 28 27 28 7
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