3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)3.012 Fund of Mat Sci: Bonding – Lecture 1CLASSICAL OR QUANTUM ?3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Reading Material (Bonding)Textbook: Engel and Reid, Physical Chemistry, Pearson (2006)Further readings for the first half of the course (bonding); from less to more advanced (Hayden reserve, or instructor):• Robert Mortimer Physical Chemistry (2nd ed), Academic Press (2000)• Atkins and de Paula Physical Chemistry (7thed), Freeman & Co (2002)• Thaller Visual Quantum Mechanics Telos (2000)• Bransden & Joachain Quantum Mechanics (2nded), Prentice Hall (2000)• Bransden & Joachain Physics of Atoms and Molecules (2nded),Prentice Hall (2003)3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)GoalTo provide a direct, rational connection between microscopic understanding and macroscopicproperties, reinforced ‘just-in-time’ with real-life examples in lectures and labs.Understand what holds materials together, why they organize themselves in simple or very complex structures, and how we characterize (measure !) and describe these structures.Such understanding is central to engineering3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Advanced MaterialsPhotos of various research removed for copyright reasons.3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Bottom-up Approach: Bonding, then Structure (4 sections, 2 weeks each)1. Atoms (quantum)(3.014: Light emission in CdSe nanocrystals…)2. Molecules (bonding)(3.014: XPS core electron shifts…)3. Solids (structure: symmetry)(3.014: Phase transitions in piezoelectric actuators…)4. Liquids, glasses, polymers (disorder) (3.014: Glass transition in acrylate polymers…)3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)The Master Plan for Bonding(first 2 sections):• Discrete energy states• The nature of the periodic table• The scanning tunneling microscope• The chemistry of small molecules• The structure of carbon compounds• Hybridization and bonding• Exclusion principle and compressibility• The quantization of vibrations3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Homework for Fri 9• Read: 12.1, 12.2, 12.4• Study: 12.5, 13.2, 13.3, • Refresh: A.1 (complex numbers)• Problem P12.103.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Round Up the Usual Suspects• Particles and electromagnetic fields•Forces• Dynamics3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Particles and EM Fields3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Particles and EM FieldsParticles and EM FieldsSource: Wikipedia.3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Electromagnetic Waves / Photonschλ=Ehν=Tk=h is Planck’s constant = 6.626 10-34 J sk is Boltzmann’s constant = 1.381 10-23J/KExamples: http://imagers.gsfc.nasa.gov/ems/ems.html3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Forces3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Dynamics3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Standard Model of Matter• Atoms are made by massive, point-like nuclei (protons+neutrons)• Surrounded by tightly bound, rigid shells of core electrons• Bound together by a glue ofvalence electrons (gas vs. atomic orbitals)Diagram of atomic structure removed for copyright reasons.STM image of a Pt(111) Surface, by IBM. Removed for copyright reasons.Figure by MIT OCW.3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Material Properties From First-Principles• Energy at our living conditions (300 K): 0.04 eV(kinetic energy of an atom in an ideal gas).• Differences in bonding energies are within one order of magnitude of 0.29 eV (hydrogen bond). • Binding energy of an electron to a proton (hydrogen):13.6058 eV = 0.5 atomic units (a.u)• Everything, from the muscles in our hands to the minerals in our bones is made of atomic nuclei and core electrons bonded together by valence electrons (standard model of matter)3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Why do we need quantum mechanics ?Structural properties (fracture in silicon)Image of a propagating fracture in silicon, removed for copyright reasons.3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Electronic, optical, magnetic propertiesNicola Marzari:Porphyrin from http://www.chem.uit.no/KJEMI/publications2.html, Raman spectraFrom Mauri and Lazzeri Phys. Rev. Lett. PaperNicola Marzari:Porphyrin from http://www.chem.uit.no/KJEMI/publications2.html, Raman spectraFrom Mauri and Lazzeri Phys. Rev. Lett. PaperCourtesy of Felice Frankel. Used with permission.3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)It’s for real…Cu-O bond (experiment !)Ti-O bond (theory)Experimental image of a Copper-Oxygen Bond in Cuprite, removed for copyright reasons.See Zuo, J. M., M. Kim, M. O'Keeffe, and J. C. H. Spence. "Direct observation of d-orbital holes and Cu–Cu bonding in Cu2O." Nature 401 (1999): 49 - 52.3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)… and it makes it to the NYTimesScanned image of a New York Times article removed for copyright reasons.See Browne, Malcom W. "Glue of Molecular Existence Is Finally Unveiled." New York Times, September 7, 1999, p. 5.3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Mechanics of a Particle)(trr)(22rFdtrdmrr=)(tvrThe sum of the kinetic and potential energy (E=T+V) is conservedPhoto of two circular waves overlapping. Image removed for copyright reasons.3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Description of a WaveThe wave is an excitation (a vibration): We need to know the amplitude of the excitation at every point and at every instant),( trrΨ=Ψ3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)Principle of Linear SuperpositionPhoto courtesy of Spiralz.3.012
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