(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 13.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 373700, 7743] NotebookOptionsPosition[ 354521, 7412] NotebookOutlinePosition[ 355058, 7431] CellTagsIndexPosition[ 355015, 7428] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["3.029 Spring 2022\[LineSeparator]Lecture 03 - 02/07/2022", "Subtitle", CellChangeTimes->{{3.8525512993398438`*^9, 3.8525513206118402`*^9}, { 3.852652054138073*^9, 3.8526520591301193`*^9}, {3.853194369726288*^9, 3.8531943739664793`*^9}, 3.8531971130005827`*^9},ExpressionUUID->"4965b6ed-0a4a-43f9-b854-\ f9ba02787412"], Cell[CellGroupData[{ Cell["Lattice Vibrations", "Chapter", CellChangeTimes->{{3.852551340964005*^9, 3.852551346980482*^9}, 3.8526520737398577`*^9, {3.853194378006518*^9, 3.853194381142681*^9}},ExpressionUUID->"4aadf621-4567-4105-a32e-\ 6764a98b74fd"], Cell[CellGroupData[{ Cell["\<\ Atoms in a crystalline solid are typically depicted as stationary\ \>", "Item", CellChangeTimes->{{3.8531944244744377`*^9, 3.8531945254789333`*^9}, { 3.853194561399002*^9, 3.8531945619349947`*^9}, {3.853235206880927*^9, 3.853235209572921*^9}},ExpressionUUID->"ff2ab05b-43ce-41aa-a620-\ 9afb198d12ff"], Cell["\<\ Indeed, the life of a materials scientist can be greatly simplified by \ employing a static lattice model \[LineSeparator](with average atom positions \ obtained through traditional crystallographic techniques, e.g. X-Ray \ diffraction)\ \>", "Subitem", CellChangeTimes->{{3.8531944244744377`*^9, 3.8531945254789333`*^9}, { 3.853194561399002*^9, 3.8531945619349947`*^9}, {3.853235206880927*^9, 3.853235220659111*^9}},ExpressionUUID->"9acd1f67-477d-4933-824f-\ 41ff8842a016"] }, Open ]], Cell["\<\ Such a model, can adequately explain a number of mechanical, electrical and \ optical properties of materials. 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