Question

Dipole moment and polarization: Consider the tetragonal BaTiO3 with the unit cell lengths are a = b = 0.398 nm; and c = 0.403 nm, the charges are the formal charges for Ba +2 |e| for Ti +4|e| and for O -2|e|. The atoms are positions in the unit cell as shown in the following figure. Ti atom at the center is shifted by 0.006 nm upward along c – axis, and the oxygen atom and its image right above and below the Ti atom shifted 0.009 nm downward in the opposite direction as shown in the second, oxygen atoms in the other four faces are shifted downward by 0.006 nm along c – axis as shown in the second figure. Note, there is only 1 formula unit BaTiO3 in the unit cell. a. Calculate the dipole moment and polarization for tetragonal BaTiO3 b. If this unit cell under the influence of external stress it is observed that the dimensions in c direction increased 1% and decreased in a and b directions by 0.5%, recalculate the dipole moment and polarization for the system, assuming the deformation is uniform down to the atomic level. c. Determine the change in polarization and relate your result to piezoelectric constants.

          Dipole moment and polarization: Consider the tetragonal BaTiO3 with the unit cell lengths are a = b = 0.398 nm; and c = 0.403 nm, the charges are the formal charges for Ba +2 |e| for Ti +4|e| and for O -2|e|. The atoms are positions in the unit cell as shown in the following figure. Ti atom at the center is shifted by 0.006 nm upward along c – axis, and the oxygen atom and its image right above and below the Ti atom shifted 0.009 nm downward in the opposite direction as shown in the second, oxygen atoms in the other four faces are shifted downward by 0.006 nm along c – axis as shown in the second figure. Note, there is only 1 formula unit BaTiO3 in the unit cell.

a. Calculate the dipole moment and polarization for tetragonal BaTiO3
b. If this unit cell under the influence of external stress it is observed that the dimensions in c direction increased 1% and decreased in a and b directions by 0.5%, recalculate the dipole moment and polarization for the system, assuming the deformation is uniform down to the atomic level.
c. Determine the change in polarization and relate your result to piezoelectric constants.

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Dipole moment and polarization: Consider the tetragonal BaTiO3 with the unit cell lengths are a = b = 0.398 nm; and c = 0.403 nm, the charges are the formal charges for Ba +2 |e| for Ti +4|e| and for O -2|e|. The atoms are positions in the unit cell as shown in the following figure. Ti atom at the center is shifted by 0.006 nm upward along c – axis, and the oxygen atom and its image right above and below the Ti atom shifted 0.009 nm downward in the opposite direction as shown in the second, oxygen atoms in the other four faces are shifted downward by 0.006 nm along c – axis as shown in the second figure. Note, there is only 1 formula unit BaTiO3 in the unit cell.

a. Calculate the dipole moment and polarization for tetragonal BaTiO3
b. If this unit cell under the influence of external stress it is observed that the dimensions in c direction increased 1% and decreased in a and b directions by 0.5%, recalculate the dipole moment and polarization for the system, assuming the deformation is uniform down to the atomic level.
c. Determine the change in polarization and relate your result to piezoelectric constants.

Added by Joseph L.

Chemistry: Structure and Properties

Nivaldo Tro 2nd Edition

Instant Answer

Solved by Expert Sri K

11/24/2022

Step 1

First, we need to calculate the dipole moment. The dipole moment (p) is given by the product of the charge (q) and the distance (d) it is displaced. In this case, the Ti atom is displaced upward by 0.006 nm and the oxygen atom is displaced downward by 0.009 nm. Show more…

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Dipole moment and polarization: Consider the tetragonal BaTiO3 with the unit cell lengths a = b = 0.398 nm; and c = 0.403 nm, the charges are the formal charges for Ba +2 |e| for Ti +4|e| and for O -2|e|. The atoms are positions in the unit cell as shown in the following figure. Ti atom at the center is shifted by 0.006 nm upward along c – axis, and the oxygen atom and its image right above and below the Ti atom shifted 0.009 nm downward in the opposite direction as shown in the second, oxygen atoms in the other four faces are shifted downward by 0.006 nm along c – axis as shown in the second figure. Note, there is only 1 formula unit BaTiO3 in the unit cell. a. Calculate the dipole moment and polarization for tetragonal BaTiO3 b. If this unit cell under the influence of external stress it is observed that the dimensions in c direction increased 1% and decreased in a and b directions by 0.5%, recalculate the dipole moment and polarization for the system, assuming the deformation is uniform down to the atomic level. c. Determine the change in polarization and relate your result to piezoelectric constants.

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Transcript

00:01 So in this question they have given so we have to find out the dipole moment of tetragonal.

00:07 So the dipole moment of which tetragonal they have given b -a -t -i -o -3.

00:14 So this is the tetragonal we have to find out the dipole moment.

00:18 And here they have given a is equal to b is equal to 0 .398 nanometer and c is equal to 0 .403 nanometer.

00:27 And the churches also they have given what are the.

00:30 Charges that is the barium that charge is equal to plus two electrons and titanium that is equal to plus four electrons and oxygen that is equal to minus two electrons the charges also they have given we know that dipole momentum dipole moment the symbol of dipole moment it is mu is equal to charge into distance that is the dipole moment formula so here we have to total sum we have to take place we have to take so here what is the charge and what is the distance so here we are considering unit cell charge unit cell charge what are the unit cell charge here 2 into 1 by 2 into minus 2 electrons into minus 0 .009 this is the distance whereas this is the unit cell charge so here this is the case whenever the oxygen lies along the titanium so plus plus so because it is total sum so plus four into one by two so four that is a charge of the titanium four into one by two into minus two electrons into minus 0 .0 18 so this is when oxygen lies perpendicular to titanium this is the condition plus along with that of 1 into 1 into plus 4 electrons into 0 .0.

01:59 0 .006 this is for the titanium.

02:01 Whenever we calculate this we'll get what is the value we'll get that is 0 .018 into plus 0 .024 plus plus 0 .024 electrons nanometer so whenever we simplify this we'll get 0 .006 electrons nanometer...

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