Caracterización de la Micro y Pequeña Empresa

A Jeol JSM 5600 scanning electron microscope (SEM) was used to gain insight into the ceramic microstructure of sample pellets, giving information on the grain sizes, homogeneity and packing in the samples after sintering.

Samples were cracked to expose interior faces with were then mounted perpendicular to the beam in the sample chamber which was then evacuated. A tungsten filament was used as a source to create a high energy beam of electrons which were accelerated through a voltage of 5 kV, with this beam being focused onto the sample surface, allowing for up to 300000 times magnification of the surface.

Increasing the accelerating voltage to 30 kV increases the number of back scattered electrons with the intensity of the back-scattered electrons related to the atomic number of an element. This allowed for a qualitative analysis of the sample, indicating the presence of possible impurities and giving information on the homogeneity of the sample.

N = Number of observables

V = Number of variables

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3.6: Immittance Spectroscopy

3.6.1: Isothermal measurements

Immittance spectroscopy was used to study the electrical properties of the samples made. When properly analysed, immittance data is able to give information on the electrical microstructure of the pellets as described in chapter 2.

Immitance data were collected on electroded pellets using an HP 4192A Impedance analyser. Samples were mounted in a horizontal jig, (figure 3.6), which could be mounted in a Carbolite 301 furnace. A thermocouple was held in a fixed position in close proximity to the pellet in order to establish the pellet temperature. A series of data sets were recorded at increasing temperature, with time given for the pellet and its surrounding environment to equilibrate before each data set was collected. A geometric factor, d/A, was applied to the collected data so as to take into account sample geometry.

Figure 3.6: Horizontal sample jig.

ZView Version 2.9c was used to process and plot the collected data as a series of complex plane and spectroscopic plots, including those discussed in section 2.3, as well as capacitance and loss spectroscopic plots. Analysis of this data was able to yield values including Rb, Rgb, Cb, Cgb, ε’, ε’’ and conductivities.

To ground To thermocouple BNCs Pt wire electrode

Moveable bar containing thermocouple and Pt wire electrode

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3.6.2: Curie-Weiss analysis

As well as referring to the temperature at which a ferro- or ferri-magnetic material becomes paramagnetic; the Curie temperature, TC, refers to the temperature at

which spontaneous polarisation is lost in ferroelectric materials and the material becomes effectively non-polar dielectric or “paraelectric”[4] due to thermal randomisation of dipoles. Above this temperature the electrical susceptibility, and therefore the relative permittivity, of the material follows the Curie Weiss law.

=

Equation 3.6

In this equation Cw is the Curie constant of the material, T0 is the Curie-Weiss

temperature and εr is the relative permittivity.

The value of T0 when compared to the value of TC, can be used to determine

something of the nature of the phase transitions, with phase transitions with T0 ≈ TC

being second order and phase transitions where T0 <TC bring first order[5].

The magnitude of the Curie-Weiss constant can also be used to establish the type of ferroelectric, based on the phase transition at the Curie temperature, with three methods of generating ferroelectric behaviour having been distinguished between by the magnitude to the Curie temperature[6]. These are

• Group I; Displacive ferroelectrics: Spontaneous polarisation as a result of displacement of ions from their thermal equilibrium position below TC. (e.g.

BaTiO3)

• Group II; Order-disorder ferroelectrics: Ordering of rotatable permanent dipoles below TC. (e.g. Rochelle salt)

• Group III: Coupled order-disorder ferroelectrics; Ordering of strongly coupled diploes below the TC. (e.g. (NH4)2SO4)

Group I ferroelectrics generally have Curie-Weiss constants of the order of magnitude ~105, compared to ~103 for group II and ~101 for group III[6].

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3.6.3: Arrhenius behaviour

As the materials studied in these thesis are wide band gap semi-conductors and conductance is generally thermally activated and thus should exhibit Arrhenius behaviour. The conductivity of the bulk material can be calculated as resistance-1, the log of this can then be plotted against temperature-1 to give a linear Arrhenius plot, equation 3.7. The gradient of this plot corresponds to the band gap of the electrons in the material, the magnitude of which can be used to make inferences as to the type of any conduction in the pellets, such as through oxygen vacancy routes.

= () Equation 3.7

In this equation σ is the conductivity, σ0 is a pre-exponential factor, Ea is the

activation energy, k is the Boltzman constant and T is the temperature in Kelvin.

3.6.4: Temperature controlled sweeps

Capacitance and loss data as a function of frequency were also collected at both above and sub-ambient temperatures, by means of automated sweeps. Data were collected at room temperature and above using a Wayne-Kerr 6500B impedance analyser connected to a horizontal sample jig, figure 3.6, mounted in a Carbolite 301 furnace. Sub-ambient temperature measurements were recorded using an Agilent 4294A precision impedance analyser connected to a closed-cycle cryostat, which had a working temperature range of 50-320 K.

Automated sweep programs were used to collect data over the frequency range of 1-1x106 Hz at 2 degree intervals; this gave a more accurate profile of the dielectric constant in order to establish the TC and maximum dielectric constant.

In order to collect the sub-ambient temperature the electrode sample was mounted next to a thermocouple and the chamber sealed and evacuated to a pressure no greater than 6.0x10-2 mbar. The sample chamber was heated to 320K in order to give some overlap between the cryostat and furnace data set, such that the two data sets could be combined, and left for a period of at least 30 minutes to equilibrate. Data

70 was then collected on cooling at 2 degree intervals over the frequency range of 1- 1x106 Hz, with a cooling rate of 2 Kmin-1, just as with the above ambient temperature data.