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How many equivalent particles are inside a face-centered cubic unit cell? --> particles How many equivalent particles are inside a body-centered cubic unit cell? --> particles

How many equivalent particles are inside a face-centered cubic unit cell? --> particles How many equivalent particles are inside a body-centered cubic unit cell? --> particles

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Packing Efficiency Since the layering pattern in all of the lattices leaves empty space between the particles, the unit cell is not completely occupied by atoms (here we are treating atoms like hard spheres). The packing efficiency, which is the percentage of occupied space in the cube, is not 100%. The packing efficiency is not the same for all 3 cubic lattices. A more densely packed unit cell will have a higher packing efficiency than a less densely packed one. The packing efficiency of a lattice structure measures how well the space inside of a unit cell is utilized, It is the percent ratio of volume occupied by the particles in a unit cell to its total volume, Packing efficiency = (Voccupied/Vtotal) x 100% The occupied volume (Voccupied) is related to the number of particles occupying the cell and their location within the cell. The edge length of each unit cell is derived using trigonometric relationships (see Figure directly below) where / is the edge length and r is the radius of the sphere. figued Grarwe tasouerstowingtae the adgriengeha wua the arad erateairatit bearnd a a awwdair Unit Cal Edga lergth in taTa of radn anse k Ascy-centered nutk Face centered cbir Vamge -particies) ar In a simple cubic unit cell, all the atoms are corner atoms. There are 8 corner atoms in a simple cubic unit cell. Remember from the lecture that for a corner atom, only 1/8th of the sphere is inside the unit celI. Hence, the total number of equivalent particle inside a simple cubic unit cell is 1 (because 1/8 times 8 atoms = 1). How many equivalent particles are inside a face-centered cubic unit cell? --> particles How many equivalent particles are inside a body-centered cubic unit cell? --> particles
Transcribed Image Text:Packing Efficiency Since the layering pattern in all of the lattices leaves empty space between the particles, the unit cell is not completely occupied by atoms (here we are treating atoms like hard spheres). The packing efficiency, which is the percentage of occupied space in the cube, is not 100%. The packing efficiency is not the same for all 3 cubic lattices. A more densely packed unit cell will have a higher packing efficiency than a less densely packed one. The packing efficiency of a lattice structure measures how well the space inside of a unit cell is utilized, It is the percent ratio of volume occupied by the particles in a unit cell to its total volume, Packing efficiency = (Voccupied/Vtotal) x 100% The occupied volume (Voccupied) is related to the number of particles occupying the cell and their location within the cell. The edge length of each unit cell is derived using trigonometric relationships (see Figure directly below) where / is the edge length and r is the radius of the sphere. figued Grarwe tasouerstowingtae the adgriengeha wua the arad erateairatit bearnd a a awwdair Unit Cal Edga lergth in taTa of radn anse k Ascy-centered nutk Face centered cbir Vamge -particies) ar In a simple cubic unit cell, all the atoms are corner atoms. There are 8 corner atoms in a simple cubic unit cell. Remember from the lecture that for a corner atom, only 1/8th of the sphere is inside the unit celI. Hence, the total number of equivalent particle inside a simple cubic unit cell is 1 (because 1/8 times 8 atoms = 1). How many equivalent particles are inside a face-centered cubic unit cell? --> particles How many equivalent particles are inside a body-centered cubic unit cell? --> particles
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