Lecture No. 13 | Planar Density in Crystal Structures | Material Science Concepts | GATE, ESE, PSUs|

Welcome to 𝐀𝐊𝐒 𝐄𝐍𝐆𝐈𝐍𝐄𝐄𝐑𝐈𝐍𝐆 𝐂𝐋𝐀𝐒𝐒𝐄𝐒 by Aashish Sir! In Lecture No. 13 of our Material Science and Metallurgy series, we explore Planar Density (PD) in Crystal Structures. Learn the fundamental definition, 2D circle representation of atoms, core mathematical formulas, and a step-by-step solved derivation for finding the planar density on the (110) plane in an FCC (Face-Centered Cubic) lattice. 📌 What You Will Learn in This Lecture: • Definition of Planar Density (PD) • Planar Density Formula: Effective Number of Atoms on Plane / Area of Plane • Understanding 2D atomic cross-sections (1/4 corner contribution vs 1/2 face contribution) • Visualizing and drawing the (110) plane in a cubic unit cell • Calculating effective atoms for the (110) plane: (4 × 1/4) + (2 × 1/2) = 2 Atoms • Finding the area of the considered plane • Final calculation and derivation result for Planar Density (PD) • Comparison between Linear Density (1D) and Planar Density (2D) ⏱️ Timestamps: 00:00 - Introduction to Planar Density 00:28 - Definition & Concept of Planar Density 01:56 - Planar Density Formula & Assumptions 02:24 - 2D Atomic Representation (Treating Atoms as Circles) 03:00 - Mathematical Formula Breakdown 03:40 - Sketching the Cubic Unit Cell & FCC Setup 04:24 - Example: Identifying the (110) Plane in the Unit Cell 05:57 - 2D Plane Diagram & Atom Distribution 06:26 - Calculating Effective Number of Atoms on (110) Plane 07:25 - Calculating Area of the Considered Plane 07:58 - Final Planar Density Calculation 08:22 - Summary & Preview of Next Lecture (Volumetric Density) 🔔 Subscribe to 𝐀𝐊𝐒 𝐄𝐍𝐆𝐈𝐍𝐄𝐄𝐑𝐈𝐍𝐆 𝐂𝐋𝐀𝐒𝐒𝐄𝐒 for comprehensive engineering lectures, crystal geometry derivations, and exam preparation for GATE, ESE, and university exams. #MaterialScience #PlanarDensity #AtomicDensity #MillerIndices #Crystallography #MechanicalEngineering #AKSEngineeringClasses #EngineeringLectures