   Chapter 22, Problem 89SCQ

Chapter
Section
Textbook Problem

Nitinol, a nickel-titanium alloy, is used in eyeglass frames or orthodontics. If you bend a pair of eye-glass frames out of shape, they snap back to the proper fit. That is the reason nitinol is often called “memory metal.” Memory metal is an alloy with roughly the same number of Ni and Ti atoms. When the atoms are arranged in the highly symmetrical austenite phase, the alloy is relatively rigid. In this phase a specific shape is established that will be “remembered.” If the alloy is cooled below its “phase transition temperature,” it enters a less symmetrical but flexible phase (martensite). Below this transition temperature, the metal is fairly soft and may be bent and twisted out of shape. When warmed above the phase transition temperature, nitinol returns to its original shape. The temperature at which the change in shape occurs varies with small differences in the nickel-to-titanium ratio. Two phases of nitinol. The austenite form has a structure like CsCl.(a) What are the dimensions of the austenite unit cell? Assume the Ti and Ni atoms are just touching along the unit cell diagonal. (Atom radii: Tt = 145 pm; Ni = 125 pm.)(b) Calculate the density of nitinol based on the austenite unit cell parameters. Does the calculated density of the austenite unit cell agree with the reported density of 6.5 g/cm3?(c) Are Ti and Ni atoms paramagnetic or diamagnetic?

(a)

Interpretation Introduction

Interpretation The dimensions species TiandNi has to be determined.

Concept introduction:

Coordination compounds: The compounds having coordination covalent bonds which form when metal ions react with polar molecules or anions

Ligand field theory: It is used to explain the bonding between metal and ligand in a coordination complex. Ligand field theory is explained in terms of electrostatic interaction of between metal ion and ligands.

Electronic configuration shows the electrons distribution of atoms or molecule in its molecular or atomic orbitals. The electrons are distributed in orbitals by following three important rules, Aufbau's Principle, Pauli-exclusion principle, and Hund's Rule.

If the complex has minimum one unpaired electron, then they are paramagnetic and are attracted towards the magnetic field. If all the electrons are paired in a complex, then they are diamagnetic and are repelled from the magnetic field.

Equation for density is,

Density=MassVolume

Explanation

Radius of Ni is 125pm

Radius of Ti is 145pm

All the three sides are equal and taken as x.

The length diagonal of cube with length of the side, x is x3

The length diagonal of austenite unit cell is 2(radiusofTi)+2(radiusofNi)

Therefore,

The dimensions of austenite unit cell is,

(b)

Interpretation Introduction

Interpretation The density of austenite unit cell has to be determined.

Concept introduction:

Coordination compounds: The compounds having coordination covalent bonds which form when metal ions react with polar molecules or anions

Ligand field theory: It is used to explain the bonding between metal and ligand in a coordination complex. Ligand field theory is explained in terms of electrostatic interaction of between metal ion and ligands.

Electronic configuration shows the electrons distribution of atoms or molecule in its molecular or atomic orbitals. The electrons are distributed in orbitals by following three important rules, Aufbau's Principle, Pauli-exclusion principle, and Hund's Rule.

If the complex has minimum one unpaired electron, then they are paramagnetic and are attracted towards the magnetic field. If all the electrons are paired in a complex, then they are diamagnetic and are repelled from the magnetic field.

Equation for density is,

Density=MassVolume

(c)

Interpretation Introduction

Interpretation TiandNi atoms are paramagnetic or diamagnetic has to be determined.

Concept introduction:

Coordination compounds: The compounds having coordination covalent bonds which form when metal ions react with polar molecules or anions

Ligand field theory: It is used to explain the bonding between metal and ligand in a coordination complex. Ligand field theory is explained in terms of electrostatic interaction of between metal ion and ligands.

Electronic configuration shows the electrons distribution of atoms or molecule in its molecular or atomic orbitals. The electrons are distributed in orbitals by following three important rules, Aufbau's Principle, Pauli-exclusion principle, and Hund's Rule.

If the complex has minimum one unpaired electron, then they are paramagnetic and are attracted towards the magnetic field. If all the electrons are paired in a complex, then they are diamagnetic and are repelled from the magnetic field.

Equation for density is,

Density=MassVolume

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts 