Introduction

Objective

Background

What you will need

Procedure

Questions to Answer

Sample Results

Entire lab in .pdf format

Index of other experiments



Procedure

A. Reaction models

To determine the charge compensation mechanism, we need to begin by considering plausible defect reactions. The dissolution of Nb2O5 occurs at elevated temperatures and under these conditions, the cubic fluorite-like d-Bi2O3 structure is stable. The structure of this phase is illustrated in Fig. 1 (background section). The addition of Nb stabilizes this phase and all of the materials we examine will have this structure. For our purposes, we can visualize this structure as a cubic close packed (ccp) arrangement of Bi with O in the tetrahedral interstices. There are two formula units of Bi2O3 per unit cell; the four Bi occupy the ccp sites and the six O occupy six of the eight tetrahedral interstices. When we create our model of the defect structure we will assume that the two empty tetrahedral sites in each cell are oxygen vacancies.

We can envision several compensation mechanisms for the Nb2O5 dissolution. For example, it is possible to compensate the charge on the Nb by eliminating oxygen vacancies:

. (1)

Here, all of the Nb goes to Bi sites and all of the oxygen goes to O sites. There is a one to one ratio of Nb added to Bi replaced. Also, there is one additional O added for every Nb that is added to the crystal. So, the new formula, as a function of x is:

(Bi(1-x)Nbx)2O3+2x

It is also possible to compensate the charge on the Nb by creating the appropriate number of vacancies on Bi sites:

. (2)

In this case, every Nb that substitutes in the structure replaces one Bi and creates 2/3 of a Bi vacancy. In other words, each Nb replaces 5/3 Bi. Therefore, the formula unit is:

(Bi(1-5/3x)Nbx)2O3

If vacant O sites are consumed, it is possible to compensate charge with fewer Bi vacancies:

(3)

In this case, every Nb that substitutes in the structure replaces one Bi and creates 1/3 of a Bi vacancy. In other words, each Nb replaces 4/3 Bi. In addition, since three oxygen vacancies are eliminated by the addition of six Nb, we can say that for each added Nb, 1/2 of an extra O is added to the crystal. Therefore, the formula unit is:

(Bi(1-4/3x)Nbx)2O3+x

Finally, we must also consider the possibility that the Nb dissolves interstitially:

(4)

Here, for every two Nb that enter the crystal, 5 oxygen vacancies are consumed. The Nb do not displace any Bi, but, in the solution, the Nb/Bi ratio is constrained to be x/(1-x) and this has to be accounted for in the formula unit:

(BiNb(i)(x/(1-x)))2O3+5(x/(1-x))

So, we have four different models for the defect structure. Note that each model produces a substance with a different formula weight per unit cell. If we know the cubic lattice parameter (which we can measure using powder X-ray diffraction), then for any given composition, we can compute a hypothetical density based on each of the four models above. If we measure the actual density pychnometrically (by measuring both the volume and the weight) then by comparing the actual density to the five hypothetical densities, we can determine which model matches most closely with observation. Rather than relying on a single composition, we will make our measurements at a range of compositions.

B. Sample preparation

1. We wish to make (Bi2O3)1-x(Nb2O5)x solid solutions with x = 0.05, 0.10, 0.15, 0.2, and 0.225. Begin by calculating the mass ratios (Bi2O3/Nb2O5) that you will need for each composition.

2. Weigh out appropriate amounts of the two starting materials, Bi2O3 (Alfa Aesar 99%) and Nb2O5 (Alfa Aesar 99.5%). The total mass of your sample should be approximately 50 g.

3. Mix and grind each composition in a mortar and pestle for 10 min. If you use the same mortar and pestle for more than one composition, clean it between grindings.

4. Using a uniaxial press, consolidate the powder in a die. (Reserve some powder for step 5.)

5. Place the compacted powder in an alumina crucible or dish. Put the loose reserve powder on the bottom of the crucible and the compacted pellet on top of the powder (this creates a marginal contamination barrier between the specimen and the crucible).

6. Fire the sample at 800 or 900 °C in air for 10 hours. (The x = 0.05 composition should be heated at 800°C, the others can be heated at 900 °C).

7. Remove the pellet, regrind in a mortar and pestle, and use the uniaxial press to make a new pellet. Place in crucible as in step 5.

8. Fire the sample for at least 10 hours in air. This second grinding and firing is to complete the homogenization.

9. Cool to 800 °C, and quench to room temperature. The "quench" step can be performed by removing the crucible directly form the furnace and blowing air over the specimen using a fan or hair dryer on the "cool" setting. This quench is need to stabilize the high temperature fluorite phase.

10. Break up the pellets into chunks. Grind about 1/5 of the specimen for powder X-ray diffraction. Reserve the remainder of the chunks for the density measurement. Be sure to keep the chunks from each pellet in separate, clearly labeled containers.

C. Determining lattice parameters

1. Use a mesh sieve should be used to remove any large particles from the sample. (The presence a few large particles can have drastic effects on the relative intensities.)

2. The powdered sample should then be placed in the sample holder (see Fig 3). If the powder particles are platy, packing the powder into the well will result in an undesirable preferred orientation that will influence the relative intensities of the peaks. To minimize this effect, add excess powder to the well so that the level of the powder rises higher than the top surface of the sample holder. By scraping a straight edge along the top surface of the sample holder, the excess is removed and the surface of the powder is level with the reference plane of the sample holder and diffractometer. The sample can then be mounted in the diffractometer.

Figure 3. The powder sample holder is a flat plate with a well to hold the powder. The surface of the plate defines the diffractometer reference plane.

3. The scan is controlled entirely by the computer. You will scan from 10 to 90s in 2Q using increments of 0.05s per step. At each angular position, you should count (measure the intensity) for 2 s. After setting these scan parameters (and recording them in your notebook), the generator can be turned on and the scan can be started. Record the operating current and voltage of the generator. (35 kV, 20 mA is suggested)

4. The scan will take approximately 3/4 of an hour, depending on exactly which parameters you choose. The computer records the data in a text file. Each line of the file contains an ordered pair of numbers, separated by a tab. The first number on each line is the angular position of the incident and diffracted beam (with respect to the diffractometer reference plane) and the second is the intensity measured by the detector. While waiting for the completion of your scans, you should examine the diffraction patterns recorded earlier.

5. The files are easily read and displayed using the applications such as "Kaleidagraph" and "Excel".

6. Use Bragg's law to calculate the d-spacing of each peak. These data can be used to measure the cubic lattice constant for each sample. Either use a program designed for this purpose, such as finax, or follow one of the procedures outlined by Cullity in Chapter 11 (Elements of X-ray Diffraction, Addison Weseley, Reading, Mass).

D. Determining hypothetical densities

1. Four defect models were presented in section A. For each model, determine the contents of a single unit cell, as a function of x. The atomic masses are MBi = 209, MNb = 93, and MO = 16.

2. At each composition (x = 0.05, 0.10, 0.15, 0.20, and 0.225), the density is computed by dividing the mass per cell by the cube of the lattice constant.

3. Make a graph, with density on the vertical axis and composition (x) on the horizontal axis that shows the results from each model.

E. Density measurement

1. For the density measurement, we will use the Quantachrome Corp. Multipychnometer.

2. Coarsely grind a portion of your sample to a particle size of about 50 microns. It is important that there is little or no enclosed porosity. It is also important that the powder be coarse enough that it is easy to handle and transfer from the balance to the pychnometer without loosing any material. Alternatively, you can begin with a finely ground material, and coarsen it by heating at 800°C in air for several hours.

3. Weigh approximately 10 grams of your sample.

4. Transfer it to the "micro" cell of the pychnometer.

5. Follow the written instructions for the pychnometer to measure the volume of your specimen.

6. Use the mass and volume of each sample to calculate its density. Compare these densities to the hypothetical densities calculated in part C by plotting the results on the graph.