sp3 Hybridization
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sp3 is one type of orbital hybridization. The hybrid sp3 orbitals are produced by the combination of the s and p orbitals in the outer electron shells and thus, the probability of finding an electron in a p-state is 3 times as much as finding it in an s-state.

For instance, the four unpaired electrons (2s1, 2px1, 2py1, 2pz1) in a carbon atom in the excited state can be mixed together to form four equivalent hybrid orbitals. This process is called hybridization (Figure 2118a). Therefore, each atomic site has four nearest neighbours occupying the vertices of a regular tetrahedron in the diamond-cubic structure and sp3 hybrid orbitals adopt tetrahedral geometry.

sp3 hybridization process

Figure 2118a. sp3 hybridization process.

Figure 2118b illustrates the hybridization process for diamond in a different way. As shown in Figure 2118b (a), when the atoms (e.g. C, Si atoms) are un-bonded, two electrons exist in the 3s state and two in the 3p state. One electron exists in a 'spin-up' state and one in a 'spin-down' state so that the Pauli exclusion principle is satisfied. Therefore, such a configuration allows only two covalent bonds to be formed with neighboring atoms. During the hybridization process, the s and p electron states are combined to form four sp3 states at a specific energy between the s and the p levels because the energy levels of the 2s are raised while the 2p levels are reduced. In this case, a more favourable lower energy system is induced so that bonding with up to four atoms at the tetrahedral angles is permitted (the number of possible bonds is maximized). These four valence electrons form σ bonds.

Schematic illustration of the process of hybridisation for carbon

Figure 2118b. Schematic illustration of the process of hybridisation for carbon. Each carbon atom in diamond forms a series of sp3 hybridised atomic orbitals.

The schematic illustration in Figure 2118c shows the bonding levels for diamond in a different way. When the hybrid carbon atoms bond, a second electron is contributed to the state by the other atom, and thus the interaction between the two electrons lowers the energy of the state. Therefore, the sp3 energy level splits into a series of four bonding and four antibonding orbitals. In an actual solid, there is a Coulomb interaction between the atom cores and the electrons, and then the bonding and anti-bonding energy levels split to form a continuous band structure, with the band of bonding states being the valence band and the anti-bonding states being the conduction band.

Schematic illustration showing the progression of the electronic structure for an sp3 bonded system

Figure 2118c. Schematic illustration showing the progression of the electronic structure for an sp3 bonded system.

The sp2 bonded solids have both σ/σ* and π/π* states available to the electrons, while for sp3 bonded solids only the σ/ σ* states present. For the diamond and graphite, electron transitions to these states generate many of the characteristic features in EEL spectra. For instance, in core loss spectra from diamond, the excitation of the 1s electrons to the σ* states generates the carbon k edge peak. For graphite, the transitions of the inner shell electrons into unoccupied π* states give a peak prior to the edge onset. In the valence band, valence electron transitions into the π* states also produce a peak at around 6 eV.

The plasmon energy loss in EELS can experimentally provide indirect semi-quantitative information because the free-electron density n changes with the chemistry or bonding state of the TEM specimen. The empirical plasmon peak position (Ep) can be given by,

          Ep = Ep(0) ± C(dEp/dC) ------------------------------------ [2118]
where,
          Ep(0) -- The plasmon energy loss for the pure component (See the table on page4623).
          C -- The composition.

Therefore, once Ep is obtained from EELS measurement, then C can be evaluated. For instance, as shown in Figure 2118d, empirical sp2/sp3 ratios in amorphous carbons were evaluated based on Equation 2118 and the relative intensity of k-edge 1s to π* transition [1-5].

Fraction of sp3 bonding as a function of the bulk plasmon energy

Figure 2118d. Fraction of sp3 bonding as a function of the bulk plasmon energy. [1]

Table 2118. Comparison of C–C and C–H bonds in some materials.

Substance Bond Bond strength (kJ/mol) Bond length (Å)
Methane, CH4 (sp3) C–H 439 1.09
Ethane, CH3CH3 (sp3) C–C (sp3) 377 1.54
(sp3) C–H 420 1.09
Ethylene, H2C=CH2 (sp2) C=C (sp2) 728 1.34
(sp2) C–H 464 1.09
Acetylene, HC≡CH (sp) C≡C (sp) 965 1.20
(sp) C–H 558 1.06

 

 

 

 

 

 

 

 

[1] P.J. Fallon and L.M. Brown, Analysis of chemical-vapour-deposited diamond grain boundaries using transmission electron microscopy and parallel electron energy loss spectroscopy in a scanning transmission electron microscope. Diamond and Relat. Mater., 2: 1004-101 1, 1993.
[2] G.M. Pharr et al., Hardness, elastic modulus, and structure of very hard carbon films produced by cathodic-arc deposition with substrate pulsed biasing. Appl. Phys. Lett., 68: 779-781,1996.
[3] V.I. Merkulov,D.H.Lowndes,G.E. Jellison,A.A. PuretzkyandD.B. Geohegan, Structure and optical properties of amorphous diamond films prepared by ArF laser ablation as a function of carbon ion kinetic energy. Appl. Phys. Lett., 73: 2591-2593,1998.
[4] S.D. Berger, D.R. McKenzie and P.J. Martin, EELS analysis of vacuum arc-deposited diamond- like films. Phil. Mag. Lett., 57: 285-290,1988.
[5] S. Ravi et al., Nanocrystallites in tetrahedral amorphous carbon films. Appl. Phys. Lett., 69: 491493,1996.

 

 

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