Homework Help is Here – Start Your Trial Now!
Science
Chemistry
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 - (VoccupiedVista) X 100% The occupied volume (Vecoupied) 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 ris the radius of the sphere. Figure 2. Geometric relotionships showing how the edge length is related to the atomic radilus for simple cubic, body-centered cubic, ond foce-centered cubic unit cells Unit Cell Edge length in terms of radius Simple cubic I- 2r Body-centered cubic Face-centered cubic Voccupied- ( particles) xar Viotat = In a simple cubic unit cell, all the atoms are comer atoms. There are 8 comer 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 cell. 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

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 - (VoccupiedVista) X 100% The occupied volume (Vecoupied) 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 ris the radius of the sphere. Figure 2. Geometric relotionships showing how the edge length is related to the atomic radilus for simple cubic, body-centered cubic, ond foce-centered cubic unit cells Unit Cell Edge length in terms of radius Simple cubic I- 2r Body-centered cubic Face-centered cubic Voccupied- ( particles) xar Viotat = In a simple cubic unit cell, all the atoms are comer atoms. There are 8 comer 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 cell. 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

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...
See similar textbooks
icon
Related questions
Question
QUESTION 5 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 = (Vaccupied/Viptal) x 100% The occupied volume (Veccupied) 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 ris the radius of the sphere. Figure 2. Geometric relotionships showing how the edge length is related to the atomic radius for simple cubic, body-centered cubic, and foce-centered cubic unit cells. Unit Cell Edge length in terms of radius Simple cubic l = 2r 4r Body-centered cubic Face-centered cubic 1 = 2VZr Voccupied = (# particles) Vrotat = 1 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 cell. 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:QUESTION 5 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 = (Vaccupied/Viptal) x 100% The occupied volume (Veccupied) 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 ris the radius of the sphere. Figure 2. Geometric relotionships showing how the edge length is related to the atomic radius for simple cubic, body-centered cubic, and foce-centered cubic unit cells. Unit Cell Edge length in terms of radius Simple cubic l = 2r 4r Body-centered cubic Face-centered cubic 1 = 2VZr Voccupied = (# particles) Vrotat = 1 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 cell. 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
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Crystal Lattices and Unit Cells
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Chemistry
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Organic Chemistry
Organic Chemistry
Chemistry
ISBN:
9780078021558
Author:
Janice Gorzynski Smith Dr.
Publisher:
McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning
Elementary Principles of Chemical Processes, Bind…
Elementary Principles of Chemical Processes, Bind…
Chemistry
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
SEE MORE TEXTBOOKS