interatomic bonding zbonding forces and energies yequilibrium atomic spacing yminimization of...
TRANSCRIPT
![Page 1: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/1.jpg)
Interatomic Bonding
Bonding Forces and Energies Equilibrium atomic spacing Minimization of bonding energy Embedded Atom Method (EAM)
Types of Bonding Ionic Covalent Secondary Metallic
![Page 2: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/2.jpg)
Bonding Forces and Energy
Interatomic Forces attractive forces (Fa)
repulsive forces (Fr)
When the atoms reach a critical distance (r0), the attractive and repulsive forces cancel each other and the atoms are at their equilibrium distance.
![Page 3: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/3.jpg)
Bonding Forces and Energy
![Page 4: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/4.jpg)
Bonding Forces and Energy
Sometimes it is easier to deal with potential energies (E) rather than forces. The relation of Energy to Force is as follows:
Equilibrium is reached by minimizing EN
RA
N
EE
dr FE
r
N
![Page 5: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/5.jpg)
Bonding Forces and Energy
![Page 6: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/6.jpg)
Embedded Atom Method
Potentials also calculated through the embedded atom method (EAM) potentials are calculated as a sum of
pairwise (interactions between a pair of atoms) contributions and a many body term.
jiji
ii
jiij
r
FrVE
)(
)()(,
![Page 7: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/7.jpg)
Embedded Atom Method
If a ternary system is being studied, EAM potentials may be defined by considering the three individual binary systems that make up the ternary system. As long as the interatomic interaction used for
each of the pure components is the same in the description of the two binaries.
The volume term is calculated as the embedding energy of a local electron density.
![Page 8: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/8.jpg)
Embedded Atom Method
Effective pairs equivalent potentials where the various
contributions (pair and volume) are not the same but add up to the same total energy for all possible simulations.
Called the effective pair scheme, it is defined as when the first derivative of the embedding function is taken as zero.
![Page 9: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/9.jpg)
Embedded Atom Method
Potentials converted to Effective pair scheme:
Transformation where mixed potentials are originally derived:
)()(2)()(
)()()(
0
0
FRrVRV
FFFeff
eff
)()()()()()( 00 ABBAABeff
AB FrFrrVrV
![Page 10: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/10.jpg)
EAM Potentials
Some examples of EAM functions for various metals Ag:
![Page 11: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/11.jpg)
EAM Potentials
Al: Au:
![Page 12: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/12.jpg)
EAM Potentials
Veff for various pure elements:
![Page 13: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/13.jpg)
Ionic Bonding
Most common bonding in metal-nonmetal compounds. Atoms give up/receive electrons from
other atoms in the compound to form stable electron configurations
Because of net electrical charge in each ion, they attract each other and bond via coulombic forces.
![Page 14: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/14.jpg)
Ionic Bonding
Attractive and repulsive energies are functions of interatomic distance and may be represented as follows:
A and B are constants depending upon the system. The value of n is usually taken as 12.
nr
BE
r
AE
B
A
![Page 15: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/15.jpg)
Ionic Bonding
Properties of ionic bonding nondirectional: magnitude of bond is equal
in all directions around the ion. High bonding energies (~600 - 1500 kJ/mol)
reflected in high melting temperatures
generally hard and brittle materialsmost common bonding for ceramic materials
electrically and thermally insulative materials
![Page 16: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/16.jpg)
Covalent Bonding
Stable configurations are obtained by the sharing of valence electrons by 2 or more atoms. Typical in nonmetallic compounds (CH4, H20)
Number of possible bonds per atom is determined by the number of valence electrons in the following formula: number of bonds = 8 - (valence electrons)
Bonds also are angle dependent
![Page 17: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/17.jpg)
Covalent Bonding
Properties of covalent bonding can be either very strong or very weak
bonds, depending upon the atoms involved in the bond. This is also reflected in the melting temperature of the compoundex: diamond (strong bond) -- Tm>
3350°C bismuth (weak bond) -- Tm ~ 270°C
most common form of bonding in polymers
![Page 18: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/18.jpg)
Secondary Bonding
Van der Waals bonding weak bonds in comparison with other
forms of bonding (~10 kJ/mol) evident between all atoms, including
inert gases and especially between covalently bonded molecules.
Bonds are created through both atomic and molecular dipoles
![Page 19: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/19.jpg)
Secondary Bonding
Hydrogen bonding special type of secondary bond between
molecules with permenant dipoles and hydrogen in the compound.Ex: HF, H2O, NH3
these secondary bonds can have strengths as high as ~50 kJ/mol and will cause increases in melting temperature above those normally expected.
![Page 20: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/20.jpg)
Metallic Bonding
Most common in bonding of metals and their alloys.
Proposed model of metallic bonding metals usually have, at most, 3 valence
electrons, all of which form an “electron sea”, which drift through the entire metal.
Base electrons form net-positive ion cores, which attract the free electrons from the “sea” as needed to maintain neutrality.
![Page 21: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/21.jpg)
Metallic Bonding
Bonding may be weak or strong, depending upon atoms involved. Ex: Hg bonding energy = 68 kJ/mol W
bonding energy = 850 kJ/mol
![Page 22: Interatomic Bonding zBonding Forces and Energies yEquilibrium atomic spacing yMinimization of bonding energy yEmbedded Atom Method (EAM) zTypes of Bonding](https://reader031.vdocuments.us/reader031/viewer/2022032605/56649e7a5503460f94b7a137/html5/thumbnails/22.jpg)
Metallic Bonding
Potentials for metallic bonding are most commonly calculated via the EAM, especially in alloys and intermetallics Link to Paper by Dr. Farkas