(a) Magnesium (Mg) has a hexagonal close-packed (HCP) crystal structure with the lattice parameter of a = 0.321 nm and c = 0.521 nm and the atomic radius is 0.173 nm. (i) What is the number of atoms per unit cell in HCP structure? (ii) Determine the atomic packing factor of the Mg unit cell. (iii) Is Mg containing an ideal atomic packing factor? You may justify your answer by evaluating the HCP c/a ratio. Subsequently, will slip be harder in Mg compared to the ideal HCP structure? Justify your answer.

(a) Magnesium (Mg) has a hexagonal close-packed (HCP) crystal structure with the lattice parameter of a = 0.321 nm and c = 0.521 nm and the atomic radius is 0.173 nm. (i) What is the number of atoms per unit cell in HCP structure? (ii) Determine the atomic packing factor of the Mg unit cell. (iii) Is Mg containing an ideal atomic packing factor? You may justify your answer by evaluating the HCP c/a ratio. Subsequently, will slip be harder in Mg compared to the ideal HCP structure? Justify your answer.

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

Related questions

Q: Lead adopts the face-centered cubic unit cell in its crystal structure. If the edge length of the…

A: Face-centered cubic cell is packing of atoms in cube that atoms are present at the corner and at the…

Q: how would you find the density of a fcc unit cell of rhodium given that the atomic radius is 173 pm.

A: We know, for fcc unit cell, r = a/(2(√ 2)) a = r(2(√ 2))…

Q: At normal temperatures and pressures a certain metal element M forms a crystal with a bcc unit…

A: Given data:

Q: A certain metal M crystallizes in a lattice described by a body-centered cubic (bcc) unit cell. The…

A: we have to calculate the lattice constant for the crystal

Q: An ionic compound crystallizes with 1 ion at each corner, 1 ion on two of the faces, and 1 ion on…

Q: For the shown crystal structure, write down (a) the Bravais lattice and (b) the basis of the…

A: Given that, For this structure : a=b≠c & α=β=γ=90°.

Q: Calcium crystallizes with a body-centered cubic structure. (a) How many Ca atoms are contained in…

A: Given, Crystal structure - BCC(effective number of atom per unit cell - 2) Atomic Mass - 40.08 amu…

Q: Europium crystallizes in a bcc cubic lattice. If the atomic radius of a europium atom is 231pm,…

Q: Calculate the radius of a Vanadium atom ( V) given that it’s density is 6.11g/cm3 and that it…

A: The number of particles per unit cell in a body centered cubic unit cell (Z) is equal to 2.The molar…

Q: Tantalum crystallizes in the body-centered cubic structure with an edge length of 330.6 pm. (a)…

Q: Aluminium (Al) has a face-centered cubic structure, with lattice parameter a = 4.05 × 10−10 m. If…

A: Data

Q: Radius of atom of an elment is 500 pm . If it crystallises as fcc crystal lattice. What is the…

A: Given,Radius of atom of an element = 500pm.

Q: The substance alpha chromium is found to crystallize in a cubic lattice, with an edge length of…

A: The objective is to determine the number of Cr atoms per unit cell.Given:Edge length .…

Q: A 5.30 g sample of solid MgSO, 7H,0 was heated such that the water turned to steam and was driven…

A: Given: The pressure, (P) = 1 atm. The temperature (T) = 100 0C = (73.15+100) = 373.15 K. The mass of…

Q: A student is given four solid samples labeled W, X, Y, and Z. All have a metallic luster. She is…

Q: An oxide of niobium has a cubic unit cell in which there are oxide ions at the middle of each edge…

A: Empirical formula is the simplest whole number ratio of atoms present in a compound.

Q: A protein forms crystals of the orthorhombic type with unit-cell dimensions of 13.0 × 7.48 × 3.09…

A: Given: Unit-cell dimensions = 13.0×7.48×3.09 nm Density (d) of unit cell = 1.315 g cm-3 Z (Atoms per…

Q: Gold crystallizes into a face-centered cubic structure (aka closest-packed cubic structure). If the…

A: In a face centered unit cell one atom exist in the center and six 1/2 atom lies on the face of the…

Q: The radius of a single atom of a generic element X is 153 pm. A crystal of X has a unit cell that is…

Q: Aluminium (Al) has a face-centered cubic structure, with lattice parameter a = 4.05 × 10-¹0 m. If…

A: Data

Q: Metallic copper adopts an fcc structure with density 8960 kg m-3. Draw the unit cell of copper and…

A: Given that,Metallic copper adopts an fcc structure.Density of Metallic copper = 8960 kg m-3FCC…

Q: Calculate the density of niobium if it occupies a body-centered cubic unit cell with an atomic…

Q: hypothetical metal with an atomic radius of 0.171 nm has an orthorhombic unit cell for which the a,…

A: Atomic Radius of metal = 0.171 nm

Q: Metallic strontium crystallizes in a face-centered cubic lattice. The volume of the unit cell is…

A: Given Lattice type = Face centered cubic lattice Volume of unit cell = 2.25 × 108 pm3 density of…

Concept explainers

Crystal Lattices and Unit Cell

Consider a crystal. The regular and repeating pattern of constituent particles is the most distinguishing feature of crystalline solids. A crystal lattice is formed when these particles are replaced with representative points. The three-dimensional arrangement of constituent particles is known as a crystal lattice. Unit cell is that the smallest portion of a space lattice which when repeated in several directions, generate the whole lattice. Unit cell is a building block of a lattice. It is the smallest unit of cell.

Question

(a) Magnesium (Mg) has a hexagonal close-packed (HCP) crystal structure with the lattice
parameter of a = 0.321 nm and c= 0.521 nm and the atomic radius is 0.173 nm.
(i) What is the number of atoms per unit cell in HCP structure?
(ii) Determine the atomic packing factor of the Mg unit cell.
(iii) Is Mg containing an ideal atomic packing factor? You may justify your answer by
evaluating the HCP c/a ratio.
Subsequently, will slip be harder in Mg compared to the ideal HCP structure?
Justify your answer.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

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.

Similar questions

A certain metal M crystallizes in a lattice described by a body-centered cubic (bcc) unit cell. The lattice constant a has been measured by X-ray crystallography to be 441. pm. Calculate the radius of an atom of M. Be sure your answer has the correct number of significant digits, and be sure it has the correct unit symbol.
If the density of europium is 5.25 g/cm3 at 20 degrees celsius with a volume of 1.52 x 10-22cm3, what is the mass (in grams)of one unit cell?
Metallic uranium crystallizes in a body-centered cubic lattice, with one U atom per lattice point. If the metallic radius of U is 148.5 pm, what is the volume of the unit cell?
Iron has a body centred cubic unit cell with a cell dimension of 286.65 pm.The density of iron is 7.874 g cm–3. Use this information to calculateArogadro number.
Predict the effect (if any) of an increase in temperature on the electrical conductivity of (a) antimony; (b) tellurium; (c) bismuth.
Solid NaF has the so-called NaCl structure. The shortest distance between the centre of a sodium cation and the centre of a fluoride anion is 231.5 pm. Calculate the length of the edge of the conventional face-centred cubic unit cell of NaF. Calculate the density of solid NaF. Calculate the shortest distance (centre to centre) between two fluoride anions in solid NaF.
The height of a unit cell in an HCP structure was given as 5.2368Å. Determine the edge length in a unit cell.
BCC iron has a lattice parameter of 0.2866 nm. Carbon with a radius of 0.071 nm fills all the tetrahedral sites of the iron crystal. What is the atomic percentage of carbon?