3.
a. Do you expect that there is a direct correlation between thermal conductivity and electrical
conductivity in ceramics? Explain.
“For non-metallic solids, the heat transfer is view as being transferred via lattice vibrations, as
atoms vibrating more energetically at one part of a solid transfer that energy to less energetic
neighboring atoms. This can be enhanced by cooperative motion in the form of propagating
lattice waves, which in the quantum limit are quantized as phonons. Practically, there is so much
variability for non-metallic solids that we normally just characterize the substance with a
measured thermal conductivity when doing ordinary calculations.”
“For metals, the thermal conductivity is quite high, and those metals which are the best
electrical conductors are also the best thermal conductors.”
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thercond.html
“In metals, thermal conductivity approximately tracks electrical conductivity, as freely moving
valence electrons transfer not only electric current but also heat energy. However, the general
correlation between electrical and thermal conductance does not hold for other materials, due
to the increased importance of phonon carriers for heat in non-metals.”
http://en.wikipedia.org/wiki/Thermal_conductivity
b. SiC is used as a heating element and a gas igniter in stoves. The SiC used for these purposes has a
resistivity of ~0.2 ohm-cm at room temperature. Given that the band gap is 2.9eV, does this value
surprise you? Speculate on the origin of the low resistivity in this material.
The band gap is amongst the smaller band gap ceramics; however, it has a very low resistivity.
SiC forms a hexagonal lattice (for single-crystal SiC) where each silicon atom is bonded to 4
carbon atoms while each carbon atom is conversely bonded to 4 silicon atoms. In this structure,
all of the atoms have full valences through their bonds. This structure is predominately covalent
in nature meaning that its ionic conductivity is low. Also, its electronic conductivity is also likely
to be low because there are no additional electrons or holes easily formed in such a stable
structure.
c. The resistivity of a sodium silicate glass decreases as the temperature increases and as the amount of
sodium oxide increases. Explain.
As the temperature increases, the thermal energy breaks up the glass network which exposes
unbound electrons for conduction, which decreases the material resistivity.
Sodium oxide releases sodium ions terminate the glass network. This increase in non-bonding
oxygens produces more unbounded electrons for conduction through the network, which
decreases the resistivity.
How would you expect the resistivity of a soda-lime silica glass to compare with that of a sodium silicate
glass of the same molar sodium concentration? Explain.
SLS is the most common commercial glass and less expensive. The composition of soda-lime
glass is normally 60-75% silica, 12-18% soda (Na2CO3), and 5-12% lime (CaCo3). Sodium
silicate glass is known as water glass and is composed primarily of sodium and silica.
At first, you would expect the SLS glass to have lower resistivity because the Na and Ca ions
would disrupt the network and increase the number of non-bonding oxygens. However, Ca is a
relatively large ion that forms strong bonds within the silica network. These large Ca ions get
stuck or held in place in the structure and block the diffusion of sodium through the structure.
Thus, the Ca ions actually serve to increase the resistivity.
Therefore, we would expect that SLS glass would have higher resistivity than sodium silicate
glass with the same molar sodium concentration.
d. Propose a dopant to increase the n-type conductivity of ZnO. Explain your choice.
“Group-III elements such as Al, Ga and In, and group-VII elements such as Cl, Br and I can be
used as n-type dopants in the ZnO material [2–4].”
K. Yoshino, T. Hata, T. Kakeno, H. Komaki, M. Yoneta, Y. Akaki, T. Ikari. “TI: Electrical and optical characterization of n-type ZnO thin
films.” physica status solidi (c). 0(2): 626-630. 2003. http://www3.interscience.wiley.com/cgi-bin/abstract/102527377/ABSTRACT
I choose Ga to dope ZnO.
Electronic Structure and Dissolution
Hume-Rothery Rules
1. Atomic Size (15%)
2. X-tal Structure
3. Valency
4. Electronegativity
Ga
76pm
Trig.
3+
1.6
Zn
88pm
Hex
2+
1.6
Check
Difference = 13.6%
Difference = 1+
Difference = 0
4.
a. Discuss the polarization mechanisms in
i. Ne Gas – The polarization mechanism in Ne gas is
Electronic. Under the presence of an electric field,
the e- cloud of the atom shifts. This shift causes the
center of the e- cloud to move away from the
positively charged nucleus of the atom, which
results in a dipole charge. This is a very responsive
(fast) mechanism that operates up to 1014Hz.
ii. NaCl – The polarization mechanism in NaCl is
Ionic. The electronegativity difference between
Na and Cl is 2.1, which means that this
compound is mostly ionic (because it is above
the 1.7 ionic/covalent cut-off). The presence of
an electric field causes separation of the
cations and anions on the lattice, which results
in the generation of an effective dipole charge.
Note that the valence affects the magnitude of
the dipole. This is a fast mechanism that
operates up to 1012 - 1014Hz.
iii. BaTiO3 – The polarization mechanism in BaTiO3 is Dipolar Polarizability. This
mechanism occurs in materials with permanent dipoles. Due to the structure of BaTiO3,
a dipole is generated by the ions. Above 120°C, BaTiO3 has a cubic structure; however,
below 120°C the structure changes to tetragonal and lengthens the c lattice parameter
and moves the Ti ion resulting in a dipole. Dipoles in these materials are randomly
oriented normally; but under the presence of an electric field the dipoles align in the
same direction. This mechanism is slower than electronic and ionic polarization and
only operates up to 108Hz.
b. The dielectric constant of the following materials is measured at very low frequency (10 Hz):
NaCl (5.9), MgO (9.6), SiO2 (3.8), BaTiO3 (1600), soda lime silica glass (7.0). Discuss the
differences. How would you expect the dielectric constants to change if the measurement
frequency was increased to 1014 Hz.
BaTiO3, 1600 > MgO, 9.6 > SLS, 7.0 > NaCl, 5.9 > SiO2, 3.8
In BaTiO3 all of the permanent dipoles in the material can orient themselves in the same
direction at 108Hz, which results in a very high dielectric constant due to dipolar
polarizability. MgO and SLS have higher dielectric constants than NaCl because the ions
present in them have larger valences than NaCl (these materials rely on ionic
polarization, which is not a large in value as dipolar polarization). SiO2 does not have
any ionic or dipolar polarization. Thus, this material only has electronic polarization
which results in small dielectric constants.
At 1014Hz, the dipolar polarization mechanism will not be able to respond quickly
enough. Thus, BaTiO3 will have the lowest dielectric constant. Also, the ionic
polarization mechanism (present in MgO, SLS, and NaCl) may be affected (it operates up
to 1012 – 1014Hz). The SiO2 dielectric constant will not be affected because it depends
only on electronic polarization, which operates up to 1014Hz.