Engineering Science 1021A/B Lecture Notes - Lecture 3: Net Force, Bond Energy, Modulus Guitars
11 May 2018
School
Department
Professor
Interatomic Spacing
The equilibrium distance between atoms is caused by a balance between
repulsive and attractive forces
•
Equilibrium separation occurs when the total interatomic energy of the pair is at
a minimum
No net force is acting to either attract or repel the atoms
○
•
Binding Energy
Binding Energy: energy required to create/break a bond
Higher bond energy means higher strength and a high melting
temperature
○
•
Positive nucleus of an atom is attracted to the negative electrons of the other
•
The nuclei and electrons also repel
•
Net force on 2 adjacent atoms is the sum of the attractive and repulsive forces
○
•
The strength of the attractive and repulsive forces are directly related to the
bond energy
○
•
Atoms are overlapping
Net repulsive force and elastic energy stored
§
1.
Equilibrium spacing
No net force and energy is minimized
§
2.
Approaching maximum separation force
Bond is stretched and elastic energy stored
§
3.
Larger distances:
Net attractive force is small
§
4.
•
Bond Strength & Stiffness
Bond strength is indicated by:
Maximum height of force curve
○
Depth of energy curve
○
•
Just like a spring (! " #$), the stiffness of the bond is indicated by the slope of
the force curve at ! " %
A steep slope correlates with a higher binding energy and a higher melting
point
Greater force is requires to stretch the bonds
§
§
○
•
Coefficient of Thermal Expansion (CTE)
Fractional change in linear dimension of a material per degree of temperature•
Relates to the asymmetry of the energy-separation curve•
•
Most materials expand on heating and contract on cooling due to atomic
vibrations
How much is described by the CTE
○
The CTE is determined by the strength of the atomic bond
○
•
@ %&', the bond has an energy of ()and the atoms have an equilibrium
spacing of *)
•
@ + " +
,-./ %&'0, the bond has an energy of (,and the atoms have an
average spacing of *
,
○
•
The change average spacing with temperature defines CTE•
*
1is @ the midpoint of (1
•
Weak bonds 2smaller asymmetrical energy graph depth2-higher CTE
expansion 2higher separation of *@ different temperature
•
Relation between temperature and average spacing
•
Relation between Young's Modulus, Bond energy and CTE
•
Binding Energy & Interatomic Spacing
Interatomic Spacing
The equilibrium distance between atoms is caused by a balance between
repulsive and attractive forces
•
Equilibrium separation occurs when the total interatomic energy of the pair is at
a minimum
No net force is acting to either attract or repel the atoms
○
•
Binding Energy
Binding Energy: energy required to create/break a bond
Higher bond energy means higher strength and a high melting
temperature
○
•
Positive nucleus of an atom is attracted to the negative electrons of the other•
The nuclei and electrons also repel•
Net force on 2 adjacent atoms is the sum of the attractive and repulsive forces
○
•
The strength of the attractive and repulsive forces are directly related to the
bond energy
○
•
Atoms are overlapping
Net repulsive force and elastic energy stored
§
1.
Equilibrium spacing
No net force and energy is minimized
§
2.
Approaching maximum separation force
Bond is stretched and elastic energy stored
§
3.
Larger distances:
Net attractive force is small
§
4.
•
Bond Strength & Stiffness
Bond strength is indicated by:
Maximum height of force curve
○
Depth of energy curve
○
•
Just like a spring (! " #$), the stiffness of the bond is indicated by the slope of
the force curve at ! " %
A steep slope correlates with a higher binding energy and a higher melting
point
Greater force is requires to stretch the bonds
§
§
○
•
Coefficient of Thermal Expansion (CTE)
Fractional change in linear dimension of a material per degree of temperature•
Relates to the asymmetry of the energy-separation curve•
•
Most materials expand on heating and contract on cooling due to atomic
vibrations
How much is described by the CTE
○
The CTE is determined by the strength of the atomic bond
○
•
@ %&', the bond has an energy of ()and the atoms have an equilibrium
spacing of *)
•
@ + " +
,-./ %&'0, the bond has an energy of (,and the atoms have an
average spacing of *
,
○
•
The change average spacing with temperature defines CTE•
*
1is @ the midpoint of (1
•
Weak bonds 2smaller asymmetrical energy graph depth2-higher CTE
expansion 2higher separation of *@ different temperature
•
Relation between temperature and average spacing
•
Relation between Young's Modulus, Bond energy and CTE
•
Binding Energy & Interatomic Spacing
Interatomic Spacing
The equilibrium distance between atoms is caused by a balance between
repulsive and attractive forces
•
Equilibrium separation occurs when the total interatomic energy of the pair is at
a minimum
No net force is acting to either attract or repel the atoms
○
•
Binding Energy
Binding Energy: energy required to create/break a bond
Higher bond energy means higher strength and a high melting
temperature
○
•
Positive nucleus of an atom is attracted to the negative electrons of the other•
The nuclei and electrons also repel•
Net force on 2 adjacent atoms is the sum of the attractive and repulsive forces
○
•
The strength of the attractive and repulsive forces are directly related to the
bond energy
○
•
Atoms are overlapping
Net repulsive force and elastic energy stored
§
1.
Equilibrium spacing
No net force and energy is minimized
§
2.
Approaching maximum separation force
Bond is stretched and elastic energy stored
§
3.
Larger distances:
Net attractive force is small
§
4.
•
Bond Strength & Stiffness
Bond strength is indicated by:
Maximum height of force curve
○
Depth of energy curve
○
•
Just like a spring (! " #$), the stiffness of the bond is indicated by the slope of
the force curve at ! " %
A steep slope correlates with a higher binding energy and a higher melting
point
Greater force is requires to stretch the bonds
§
§
○
•
Coefficient of Thermal Expansion (CTE)
Fractional change in linear dimension of a material per degree of temperature•
Relates to the asymmetry of the energy-separation curve•
•
Most materials expand on heating and contract on cooling due to atomic
vibrations
How much is described by the CTE
○
The CTE is determined by the strength of the atomic bond
○
•
@ %&', the bond has an energy of ()and the atoms have an equilibrium
spacing of *)
•
@ + " +
,-./ %&'0, the bond has an energy of (,and the atoms have an
average spacing of *
,
○
•
The change average spacing with temperature defines CTE•
*
1is @ the midpoint of (1
•
Weak bonds 2smaller asymmetrical energy graph depth2-higher CTE
expansion 2higher separation of *@ different temperature
•
Relation between temperature and average spacing
•
Relation between Young's Modulus, Bond energy and CTE
•
Binding Energy & Interatomic Spacing
Document Summary
The equilibrium distance between atoms is caused by a balance between repulsive and attractive forces. Equilibrium separation occurs when the total interatomic energy of the pair is at a minimum. No net force is acting to either attract or repel the atoms. Binding energy: energy required to create/break a bond. Higher bond energy means higher strength and a high melting temperature. Positive nucleus of an atom is attracted to the negative electrons of the other. Net force on 2 adjacent atoms is the sum of the attractive and repulsive forces. The strength of the attractive and repulsive forces are directly related to the bond energy. Just like a spring ( = ), the stiffness of the bond is indicated by the slope of the force curve at = 0. A steep slope correlates with a higher binding energy and a higher melting point. Greater force is requires to stretch the bonds.
