I- Purpose/Objective:

The objectives of this unit are to determine the dielectric properties of barium titanate, relate them to microstructure and processing conditions, and compare them commercial barium-titanate based multilayer chip capacitor (MLC). The specimen will be prepared by dry powder compaction and sintering, so a further objective is to determine the sintered density (residual porosity) and grain size of the sintered barium titanate.  This will be compared with the microstructure of the commercial MLC. The phase of the sample will be determined by powder diffraction.  Powder diffraction will also be done on the commercial chip capacitor, to identify the modifications of the dielectric (lattice parameter shifts, extra phases of the dielectric, and identify the alloy used as the internal the metal electrodes.

II - Experimental Procedure:

Activity #1: Powder Compaction and Sintering

We will use a commercial BaTiO3 powder, Ferro Corporation Code 219-6, which is a 99.6% pure BaTiO3 with a median particle size of 1.4 microns and specific surface area of 2.8 m2/g.  Make six pellets pressing 0.5 gm of powder in a 1.27-cm diameter die at 15,000 psi compaction pressure with the Carver Press.  Measure and record the mass, green diameter, and green height of each pellet (“green” means unfired).  Compute rgreen the geometric green density by dividing the geometric density of the pellets by the crystal density of barium titanate,  r = 6.01 gm/cm3.

The GSIs will place the pellets on a thin bed of loose BaTiO3 powder on suitable setter and load them cold into the Lindberg SuperKantal furnace.  They will program the Eurotherm to heat the furnace to peak temperature in 2 hours.  They will sinter the pellets at an assigned temperature (1280<T<1320°C) for the assigned time (0.5<t<3 hours)

Determine the sintered mass, diameter, and height.  Compute the percent sintering shrinkage in the axial and diametral directions, and determine the apparent geometric sintered density,  rsint.  Compute the "percent theoretical density",  %rtheo  by dividing the sintered density by the crystal density of barium titanate.  The residual porosity, %P, can be estimated from the theoretical density by:  %P = 1- %rtheo.  Compare this with the microstructure you see in the SEM.

Activity #2: Microstructure

A great deal of useful information can be obtained from a simple fracture surface.  Prepare a fresh fracture surfaces of the green and sintered pellets.  Mount it on an SEM stub, and sputter coat the specimens to make it conductive. Examine the fracture surface in SEM, to observe the grain size and porosity.  Barium titanate, if overfired, tends to suffer secondary grain growth, so look for two populations of grains. Determine the grain size.  Note the pore size and volume fraction of residual porosity.  Record the microstructure with representative photomicrographs.  Estimate the volume fraction with the method of point counts.  This method is valid on fracture surfaces provided the fracture path is random. Compare this with the porosity inferred from the density.


Also prepare a fracture surface of a commercial multilayer capacitor.  We will use a 0.96 nF Novacap 1812 B 10k 202 NT (donated by Bob Nelson of Novacap).  This capacitor is an X7R (an EIA designation for a particular range of temperature stability).  It is not pure BaTiO3, but rather contains alloying agents to move the Curie temperature.  It may have other phases present. You might want to do an EDS analysis.  This particular MLC is dimensionally quite large (about 1x3x4 mm), chosen so it can be easily handled.  It will consist of many layers (find out how many) of thin dielectric (find out how thin), separated by electrodes layers (how thin?).  The electrodes are sintered metal alloys (find out which metals). MLCs like this one are made by the processes of tape casting paper-thin sheets of powder with a plastic binder, printing on the metal ink by screen printing, and laminating the sheets to make a block.  The block is cut into many small pieces (diced), and sintered. The ends of the MLC are silvered with a solderable metal (which metal?).



Activity #3: Phase identification by Powder Diffraction

Please do a powder diffraction pattern of your powder before sintering to determine if it is single phase BaTiO3 perovskite. Note the breadth of the lines – this powder might be fine enough for crystallite line broadening.  Find out if there are other phases.  Compare the powder pattern with a crushed sample of your sintered pellet.  Look for changes in the phases, and for changes in the line broadening (due to increase in the grain size).


Also crush and take a powder pattern of a Novacap MLC.  Note if it has perovskite peaks and if the lattice parameters have shifted by solid solution alloying.  Look for other phases.  Look for the electrode metals


Activity #4: Electrical Measurements

Apply electrodes to one sintered pellet, to prepare a capacitor specimen for dielectric measurements. Determine the ferroelectric loop of the barium titantate at room temperature and the dielectric constant as a function of temperatures (looking for the Curie behavior).  Compare your BaTiO3 sample[1] with the dielectric constant vs. Temperature of the commercial MLC.  The measurement techniques are detailed below.


[1] You might want to read D-H Yoon and B.I. Lee, Journal of the European Ceramic Soc. (2004) p 739-761, since they have samples made with the same Ferro Code 219-6 powder.


III - Theory/Background Information:

A. Capacitance and Dielectric Constant

Consider two metal parallel plates of area A separated by a distance d in a vacuum, as illustrated in (a) below.  Attaching these plates to a circuit and applying a voltage V will create a transient current I to flow, as shown in (b).  The charge Q (in coulombs) from this current is stored on the metal plates, and can be found by integrating the current with time

Ferro Equation 1

Determining Q as a function of V will give a straight line.  The slope of the straight line is the capacitance of the plates in a vacuum

Ferro Equation 2
where eo is the permittivity of free space 8.85x10-12 C2/(Jm).  The unit of capacitance is the Farad F = C/V = C2/Jm.

If a dielectric material is inserted between the plates, more charge can be stored by polarization in the material, as illustrated in (c ) below.  We describe this with the relative permittivity of the material er (a dimensionless number)

Ferro Equation 3

The relative permittivity er of simple materials ranges from 2 to 100 or more, and also called the “dielectric constant” because it is nearly constant (independent of electric field).  It is determined by the polarization of dipoles inside the material.  It of course depends on temperature.   Ferroelectrics like barium titanate can have relative permittivity values of hundreds to thousands.  The very large relative permittivity results from the alignment of dipoles in ferroelectric domains. Note that at sufficiently high electric fields, the ferroelectric domains can move, changing the polarization. The relative permittivity of ferroelectrics is not constant (the material is “non-linear”), so the dielectric “constant” is not actually constant.


Ferro Picture 4


B. Polarization Charges

We also can describe surface charge densities and polarization.  For the parallel plates in a vacuum, the surface charge density s (coulombs/m2) is simply the stored charge Q divided by the area of the plates

Ferro Equation 5
Where E is the applied electric field. When a dielectric material is present, the surface charge is

Ferro Equation 6
Note that the surface charge is increased by spol the extra surface charge from the dielectric. We can alternatively consider the polarization surface charge to by the polarization P of the dielectric material.  Polarization is the (dipole moment)/unit volume, in units of C-m/m3:  P [C-m/m3] = spol   [C/m2].

We also speak of a “dielectric displacement” D

Ferro Equation 7
and use dielectric displacement to express the charge density from the vacuum plates (eoE) and the materials polarization P.  We further define another dielectric property the “dielectric susceptibility” by

Ferro Equation 8

where the dielectric susceptibility Ferro Equation 9 expresses the relative surface charge density stored by material polarization compared to charge density from simple plates in vacuum. Materials with high relative permittivity (say 100) have a high susceptibility (say 99) so store 99% of the charge in the material and only 1% of the charge from the plates.


C. Experimental measurements of polarization and dielectric constant

Sample: BaTiO3 polycrystalline ceramic with a disc geometry with 
Area, A, thickness (distance between the top and bottom surfaces), d

1.Dielectric constant
For the parallel metal plates filled with a dielectric material, the capacitance of the sample is given by

Ferro Equation 10

Given the geometry (A and d) of a sample, we can determine the dielectric constant or relative permittivity er by measuring the capacitance Cs of the sample.   This can be conducted using a LC circuit.  Note the instruments you use for these measurements. 

A1) Measure the dielectric constant for your disc sample as a function of temperature up to 140oC, which should be above the curie temperature (TCurie is nominally 120oC, but depends on microstructure and dopants).

A2) Also measure the capacitance of your MLC as a function of temperature.  It should be different because this is not pure barium titanate, but rather an X7R composition.  Use the number of layers and layer thickness you determined from the SEM microstructure for this MLC to determine the total A and d, and convert capacitance vs. temperature to apparent dielectric constant vs. temperature. 

2. Ferroelectric hysteresis loop

Two physical parameters will be determined:

  • Remnant polarization, Pr (the polarization at zero electrical field)

  • Coercive field, Ec (the electrical field at zero polarization)

You can infer Pr and Ec by measuring the hysteresis loop on the circuit below, that compares your sample against a standard capacitor (note the size of the standard capacitor in F).  From the raw hysteresis loop, determine the VP and VE as defined in the figure below.

Ferro Picture 11

Ferro Picture 12

Using the measured voltages VP and VE, calculate the coercive field and remnant polarization from:

Ferro Equation 13


Ferro Equation 14

where  Q is the charge on your standard capacitor   Q= CoVP where Co is the capacitance of your standard capacitor in Farads.

In your lab report, you should calculate the dielectric constant, remnant polarization, and coercive field of your BaTiO3. You may want to compare these values with those published in the literature.  You may also want to compare your group’s data with results from other groups, and related the dielectric constant, remnance, and coercive fields to the porosity and grain size.

IV - Theory/Background References:

  1. W.D. Kingery, H.K. Bowen, and D.R. Uhlmann, Introduction to Ceramics, Second Ed.,Chapter 10, "Grain Growth and Sintering", Chapter 18, "Dielectric Properties"'
  2. Y. M. Chiang, D. Birnie III, W. D. Kingery, Physical Ceramics, Chapter 5, “Microstructure,”John Wiley & Sons, New York, 1997.
  3. A. J. Moulson and J. M. Herbert, Electroceramics, Chapter 3, "The fabrication of ceramics."Chapman and Hall, 1990.

V- Activity Schedule:

Date/TimeGroup 1Group 2Group 3Group 4
Day 1
first hour

XRD raw powder & MLC Press Pellets
Day 1
second hour

XRD raw powder & MLC
Press Pellets

μstructure green pellet & MLC

Day 1
third hour
XRD raw powder & MLC
μstructure green pellet & MLC

Day 1
fourth hour
Press Pellets μstructure green pellet & MLC

Day 2
first half
μstructure green pellet,
MLC, & sintered pellet
Dielectric properties BT and MLC
XRD raw powder, 
MLC & sintered pellet
Day 2
second half
XRD sintered pellet
Dielectric properties BT and MLC μstructure sintered pellet
Day 3
first half
Dielectric properties BT and MLC μstructure sintered pellet XRD sintered pellet
Day 3
first half

XRD sintered pellet μstructure sintered pellet Dielectric properties BT and MLC

VI -Format and Important Questions for Lab Report: