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Ch.12 - Solids and Modern Materials
Chapter 12, Problem 107

Introduction of carbon into a metallic lattice generally results in a harder, less ductile substance with lower electrical and thermal conductivities. Explain why this might be so.

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insert step 1: Understand the structure of a metallic lattice. Metals have a regular arrangement of atoms in a lattice structure, which allows for the free movement of electrons, contributing to their electrical and thermal conductivity.
insert step 2: Consider the role of carbon atoms. When carbon is introduced into a metallic lattice, it typically forms interstitial compounds, where carbon atoms occupy the spaces (interstices) between the metal atoms.
insert step 3: Analyze the effect on the lattice structure. The presence of carbon atoms in the interstices distorts the metallic lattice, making it more difficult for the layers of metal atoms to slide past each other. This results in increased hardness and decreased ductility.
insert step 4: Examine the impact on electron movement. The distortion of the lattice and the presence of carbon atoms can impede the free movement of electrons, leading to lower electrical conductivity.
insert step 5: Consider the effect on thermal conductivity. Similarly, the disruption in the lattice structure can hinder the transfer of thermal energy through the metal, resulting in lower thermal conductivity.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Solid Solution Strengthening

When carbon is introduced into a metallic lattice, it can occupy interstitial sites, creating a solid solution. This disrupts the regular arrangement of metal atoms, making it more difficult for dislocations to move. As a result, the material becomes harder and stronger, as the movement of dislocations is a primary mechanism of deformation in metals.
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Ductility and Dislocation Movement

Ductility refers to a material's ability to deform under tensile stress. The presence of carbon in the metallic lattice hinders dislocation movement, which is essential for plastic deformation. This restriction leads to a decrease in ductility, making the material more brittle and less able to absorb energy without fracturing.
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Electrical and Thermal Conductivity

Metals are typically good conductors of electricity and heat due to the presence of free-moving electrons. The introduction of carbon atoms disrupts the electron flow and the lattice structure, leading to increased scattering of electrons and phonons. This results in lower electrical and thermal conductivities compared to pure metals, as the mobility of charge carriers is reduced.
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