This is an example Lab Report for Cer. 292 and Cer. 392. The left column gives hints and instructions.
The title page should include a short, descriptive title, your contact information, and a date. There is no standard format. Feel free to be creative, just remember that this is Ceramic Engineering 292 the first thing someone Identification of Phases and Structures reading your work will see. If the title page offends them, they will judge your document more harshly. For this class, the title page should include the course #, experiment title, authors' names, By: department address, date submitted, and William G. Fahrenholtz authors' signatures.
The goal of technical writing, especially short reports of experimental Ceramic Engineering Department work, is to convey your University of Missouri-Rolla important results Rolla, MO 65409 accurately and clearly to a target audience. In this type of report, you want to be as clear, January 2, 2004 straight forward, and concise as possible. You can build up to your important result, but do not make it a mystery. Even the most important results can be obscured in a poorly written report.
signature William Fahrenholtz The Abstract is a short Abstract summary of what you did and what you learned. Potential The crystal structures and compositions of four unknown readers will scan an abstract to determine if powdered samples were identified using x-ray diffraction analysis. A they want to spend the time to read an entire diffraction pattern was collected for each unknown. The unknowns were document. Your abstract should tell the then identified using a strongest-lines search of the Powder Diffraction reader three things: 1) File database. Patterns were indexed to confirm tentative matches. The what you did; 2) how you did it; and 3) your unknowns were identified as NaCl, MgO, rutile, and anatase. Two of most important results. Be sure to include the unknowns, NaCl and MgO, were found to have the same crystal quantitative results in your abstract. Your structure, but different lattice parameters. Both had the rocksalt abstract should emphasize the one structure, which is face centered cubic. Compared to the same peaks for conclusion that you the NaCl pattern, the peaks in the MgO pattern were shifted to higher want people to get from your work. Hopefully, values of two theta, indicating that MgO had a smaller lattice parameter this will convince the reader to examine the than NaCl. The other two unknowns were found to have the same whole document. composition, TiO2, but different crystal structures and lattice parameters.
In general, the abstract This study confirmed that x-ray diffraction can successfully differentiate is written last. For me, between: 1) crystalline materials with the same crystal structure, but the abstract is the most difficult section to write. different compositions; or 2) crystalline materials with the same composition, but different crystal structures. For a longer document, you might include a table of contents after the abstract, but that is not necessary for our lab reports.
1 The Introduction sets the Introduction stage for the rest of your report. In this section, X-ray diffraction (XRD) analysis can be used to identify you need to convey a sense of why this work is unknown crystalline compounds. Because diffraction is a scattering important and provide the background phenomenon, the patterns that are produced in diffraction experiments information (other depend on both the composition and the structure of the material studies, theory) necessary for the reader examined.1 The most common method of analysis of ceramic powders to understand your 2 analysis. You should in powder x-ray diffraction using the Bragg-Brentano geometry, which summarize important work done by others in is shown schematically in Figure 1. In this configuration, the intensity this field. Finally, a good Introduction ends of the radiation diffracted from the sample is measured as a function of with statement of purpose the diffraction angle, 2θ. Using the Powder Diffraction File (PDF) or goals. After reading an Introduction, the database, experimental results can be compared to patterns of known reader should know why you are doing this work, materials for identification of both structure and composition. how it relates to previously published work, and what your X-ray detector intent is with this study. X-ray source For Cer. 292 and 392, you can find papers in the open literature related to either the materials that you studied or the techniques that were used for this Diffraction purpose. half angle Your introduction should Sample include the relevant theory and equations needed to Figure 1. The Bragg-Brentano diffraction geometry.2 understand and interpret your results. Equations The position of peaks in a diffraction pattern depends on the should be numbered for later reference. Also, be distance between identical planes in a crystal structure. Bragg’s law can sure to define all of your variables either in the text be used to convert the observed peak position into an equivalent inter- or in lists after your planar spacing if the wavelength of the diffracting radiation is known. equations. You should use consistent formatting for The common form of Bragg’s law is: all of the equations in a document. Also, you ndλθ= 2 sin (1) should use an equation λ editor rather than just where n is an integer constant usually set to one, is the wavelength of typing equations into your θ document for professional the incident radiation, d is the inter-planar spacing, and is half of the looking equations. observed Bragg angle 2θ. When a pattern is indexed, each of the peaks
2 observed in the experimental pattern must be accounted for in some manner. That is to say, the peak position must be matched to the d- spacing of diffracting plane in the proposed compound, matched to a diffracting plane in another phase present in the sample, or attributed to some other source such as diffraction of other wavelengths of radiation (W-Lα or Cu-Kβ) from a particular plane/d-spacings in the sample. For cubic systems, d-spacings of specific planes can be calculated from the lattice parameter using Equation 2: 1 hkl222++ = (2) d 2 a2 where (hkl) are the Miller indices of the plane and a is the lattice parameter of a cubic crystal. The equations used to calculate the d- spacings of non-cubic systems are more complex.2 The intensity of diffracted peaks depends on the size and shape of the unit cell, the atoms types and positions and other factors such as the temperature of the measurement and the diffraction geometry.1 For indexing of diffraction patterns, it is not necessary to predict the precise intensity of diffracted peaks, only which planes should produce zero or non-zero diffracted intensity. For this, the structure factor, F, can be calculated using Equation 3:
N =++π F∑ fnnnnexp[] 2 ihukvlw()(3) n=1 where fn is the atomic scattering factor of atom n, (hkl) are the Miller indices of the diffracting plane, and {unvnwn} are the coordinates of atom n within the unit cell. Diffracted intensity is proportional to the square of the structure factor. The structure factor can be used to predict systematic extinctions for specific crystal structures. For example, planes for which h + k + l is an odd number have zero diffracted intensity for body centered crystals. The purpose of this investigation was to identify the composition and structure of four unknown powdered samples.
3 The Procedure section Procedure serves as a record of the Data Collection methods used to conduct your work. The purpose Four unknown powders were examined by x-ray diffraction. of this section is to assure readers that you Samples were analyzed as-received. Unknown number one was used sound scientific methods and that you composed of relatively large (~0.5 mm) cube shaped crystals. The other did your best to minimize potential unknowns were fine (-325 mesh) powders. All of the unknowns were sources of error. It prepared for analysis by packing into cylindrical metallic sample should allow others skilled in the field to holders. Powders were packed using a chopping motion rather than a repeat your work or to validate your results. shearing motion to minimize the potential of preferred orientation. Powders were analyzed in a powder diffractometer (Scintag PAD-X) The Procedure should α λ include the model using Ni-filtered, Cu-K radiation ( = 1.540562Å). The accelerating number and name of the voltage was set at 45 keV and the filament current was 50 mA. Data manufacturer of any equipment that you used was collected using a step scan from 5 to 100° two theta. The step size along with the grade and supplier of your was 0.02° with a counting time of 0.5 seconds per step. The total scan raw materials. For Cer. 292 and 392, you should time was approximately 90 minutes. After collection, diffraction include the machine α settings and scan patterns were reduced using a K 2 stripping routine. parameters used to collect your diffraction Data Analysis patterns. The way that Peak positions and relative intensities were determined by you format this information is up to you. examining plots of diffracted intensity as a function of two theta. You can use footnotes (not endnotes), commas, Unknowns were identified and diffraction patterns were indexed or parentheses to set off * your information. manually using the Powder Diffraction File (PDF) database. The three Examples of different styles are given in this strongest peaks were identified and a “strongest lines search” was section, but you should conducted using a ±0.02 Å tolerance on the d-spacings of the three most stick with one style for your report. intense peaks. A final match was made for each pattern by indexing with a card from the PDF database.
* PCPDFWIN database program version 2.01, International Centre for Diffraction Data, 1998.
4 The Results and Results and Discussion Discussion section should include your Diffracted intensity was plotted as a function of two theta for each refined data in the form of tables and graphs. In of the four unknown samples (Figures 2-5). Once plotted, the positions this section, you will interpret your data, of the three strongest peaks were identified for each of the patterns analyze it, and explain (Table 1). These peak positions were used to identify candidate your results. As engineers, we need to compounds for the unknown from the PDF database. For unknowns one know the ‘why’ behind the observation. through four, 2, 29, 53, and 10 candidates were identified, respectively.
In this class, the results These lists were narrowed further by matching the position and intensity and discussion section should only include the of additional peaks from each of the patterns. Unknowns two through graphs and tables that four were tentatively identified using the additional peaks as MgO, TiO2 are relevant to your data analysis. Other (rutile), and TiO2 (anatase) by this method. The positions and intensities information such as PDF file cards, raw of unknown number one did not correspond to any of the candidate data, stick plots, etc. that you feel is relevant compounds. A search was conducted by narrowing the d-spacing to the report should be included in an appendix. window to ±0.01 Å, restricting the compound to contain two elements, and considering only two of the three strongest peaks at a time. Using Your discussion of results should support this search protocol, it was found that the positions of the peaks best the purpose statement that you made at the end matched with NaCl. Apparently, unknown number one had a strong of the introduction. Results should be preferred orientation due to sample preparation. After comparing the organized in a logical manner that builds to PDF cards for the unknowns were 78-0751 for NaCl, 78-0430 for MgO, the appropriate 78-2485 for rutile, and 84- 1286 for anatase. The database cards are conclusion. Try to avoid simple statements attached as Appendix 1. like “Figure 1 shows the diffraction data” and build more detailed discussions that include Table 1. Positions of the three strongest peaks for each unknown. quantitative details from the tables and graphs. Position (degrees two theta)
. Unknown Strongest Second Third 1 31.8 66.4 45.5 2 42.9 62.3 78.6 3 27.4 54.3 36.1 4 25.3 48.1 37.8
5 Make sure that the tables and figures are clearly labeled and include units. You can group your data any way that you like in your tables, but make direct comparisons among data sets with the aid of graphs. In this format, you should intersperse your figures and tables with text. For this report, it just worked out that the figures ended up grouped together.
Figure 2. X-ray diffraction pattern for unknown sample number one, which was indexed to NaCl (PDF 78-0751).
Figure 3. X-ray diffraction pattern for unknown sample number two, which was indexed to MgO (PDF 78-0430).
6 Figure 4. X-ray diffraction pattern for unknown sample number three, which was indexed to TiO2-rutile (PDF 78-2485).
Figure 5. X-ray diffraction pattern for unknown sample number three, which was indexed to TiO2-anatase (PDF 84-1280).
7 Using the PDF cards, each of the diffraction patterns was indexed to confirm the tentative identification. The peak positions and intensities for unknown samples 2 and 4 matched well with the PDF cards for MgO and anatase. Indices for all phases are indicated on the diffraction patterns in Figures 2-5. For the XRD pattern for unknown number one, all of the peak positions matched with those on the PDF card for NaCl (Figure 2), but the diffracted intensities did not. It was found that the intensities of the (200) and (400) peak were stronger relative to the other peaks than shown on the card (Table 2). The intensities of all of the other peaks were suppressed and, in fact, the (111) peak was not observed at all. From this analysis, the sample appears to show a strong (100) orientation. The cleavage plane for NaCl is (100), meaning large crystals naturally break into units whose sides are parallel to the faces of the cubic unit cell.3 The unknown was examined in its as-received state, which was small cube-shaped crystallites approximately 0.5 mm per side. The pattern distortion attributed to preferred orientation could possibly be eliminated by grinding the as-received powder to a finer particle size and taking more care to prevent preferred orientation during sample preparation. Based on the indexing described above, unknown number one is identified as NaCl, which has the rocksalt crystal structure with a = 5.63 Å. Rocksalt is a face centered cubic structure with the space group Fm3m. Based on structure factor calculations, planes with mixed indices (e.g., h, k, and l not all even or all odd) will have F = 0 giving them a diffracted intensity of zero. Thus, planes such as (100) and (110) should, as observed, have no diffracted intensity. With the exception of the (111), all of the other expected peaks were observed, making the probability that a match was made seem high.
8 Table 2. Indexing of unknown sample number one with NaCl. Two Theta d Observed Intensity from (degrees) (Å) Intensity (%) card (%) (hkl) 27.4 3.25 -9.2 111 31.8 2.81 100 100 200 45.5 1.99 2.3 56 220 53.9 1.69 1.2 1.6 311 56.5 1.63 0.3 16.1 222 66.3 1.41 17.9 6.3 400 73.1 1.29 0.3 0.7 331 75.3 1.26 2.6 15.2 420 84.0 1.15 0.7 10.1 422
Unknown number two was indexed to the PDF card for MgO (78-0430). The positions and intensities of the peaks in the experimental pattern matched well with the reported values (Figure 3). Like NaCl, MgO has the rocksalt structure. The lattice parameter for MgO is much smaller, with a = 4.21 Å. As a result, the peaks of MgO were shifted to higher 2θ values compared to peaks with the same Miller indices for NaCl. For unknown number three, the positions and intensities of most of the peaks matched well with the accepted pattern for the rutile phase of
TiO2 (Figure 4). However, peaks at ~25.3° and 48.1° did not correspond to peaks reported on PDF card 78-2485. These peaks were ignored for the intial indexing of the pattern, but were later identified as anatase. The anatase impurities probably formed during cooling after synthesis of the rutile. Rutile is the high temperature structural variant of TiO2 and it is stable above ~780°C.4 Anatase is the low temperature variant. Rutile has a primitive tetragonal crystal structure with a = 4.59 Å and c = 2.96Å.
9 Unknown number four was identified as the anatase or low temperature structural variant of TiO2. The position and relative intensity of all of the peaks in the pattern (Figure 5) matched with the peaks on the PDF card 84-1286. Even though anatase and rutile have the same composition, they have different structures. Like rutile, anatase is tetragonal. However, anatase has a body centered tetragonal structure with a = 3.78 Å and c = 9.50 Å.
10 Summary and Conclusions The Summary and Conclusions should Four unknown powder samples were examined using XRD. The highlight your most important results. Tell unknowns were identified using the strongest matching routine in the us what you did and why it is significant. PCPDFWIN database program. Analysis identified the unknowns as Use quantitative NaCl, MgO, rutile, and anatase. The patterns were indexed to PDF examples of your most significant findings from cards. All of the peaks in each pattern were matched with (hkl) values your discussion section. If this section is a from the appropriate crystal structures. The NaCl sample was found to simple summary of what you did (e.g., you just have a strong preferred orientation, with the intensity of the (200) and repeat important results that have been (400) peaks greater than expected while the intensity of other peaks was previously discussed), lower than expected. Anatase was present as an impurity in the rutile. then it should be labeled as such. Likewise, if the Unknowns one and two, NaCl and MgO, were found to have the section focuses on the conclusions drawn from rocksalt structure, which is face centered cubic. The difference in the your data analysis, then it can be labeled lattice parameters (a = 5.62 Å for NaCl and a = 4.21 Å for MgO) conclusions. In this example, a short altered the peak positions for the two materials. Peaks for MgO were summary is given in the shifted to higher two theta values compared to the same peaks for NaCl. first paragraph and then conclusions are drawn For example, the (200) peak for MgO was at ~43.0° compared to 31.8° in the second, so it is entitled “Summary and for NaCl. In addition, the different atom types in the structure caused Conclusions.” The third paragraph was some differences in the predicted intensity of the peaks, although this added to re-emphasize that the experiment met effect was masked due to the preferred orientation of the NaCl. its goal. Unknowns three and four, rutile and anatase, were found to have the
same composition, TiO2. Because the two phases have different crystal structure types (primitive tetragonal for rutile vs. body centered tetragonal for anatase) and different lattice parameters, distinct differences in peak positions and the peaks observed allowed for identification of the two phases. X-ray diffraction was found to be a powerful tool for the identification of unknown crystalline materials. Materials with the same crystal structure, but different structure could be identified as could materials with the same structure, but different composition.
11 References References should give the reader a roadmap to find the 1. R. Jenkins and R.L. Snyder, Introduction to X-Ray Powder supplemental materials Diffractometry, John Wiley and Sons, New York, 1995. that you have cited. rd The preferred style is 2. B.D. Cullity and S.R. Stock, Elements of X-Ray Diffraction, 3 to call the references Edition, Prentice Hall, Upper Saddle River, NJ, 2001. throughout the text with superscripted 3. W.D. Neese, Introduction to Optical Mineralogy, Oxford Press, New numbers and include a York, 1986. list with corresponding numbers at the end of 4. Ti-TiO2 phase diagram, Figure 22 in Phase Diagrams for Ceramists, the text. Several Vol. 1, American Ceramic Society, Westerville, OH, 1964. representative examples of full bibliographic citations Examples of other citations: are given in this section. It should be Journal: noted that archival W.G. Fahrenholtz, K.G. Ewsuk, R.E. Loehman, and P. Lu, publications should be “Kinetics of Composite Formation by Reactive Metal Penetration,” your primary source of reference materials. Journal of the American Ceramic Society, 81(10) 2533-2541 This means materials (1998). that are available to the general public in ASTM Standards: the form of journal “Standard Test Method for Determination of Fracture Toughness publications, books, published conference of Advanced Ceramics at Ambient Temperature,” ASTM Standard proceedings, patents, C1421-01b government reports, ASTM standards, etc. Patents: You can also cite a G.E. Hilmas, E.R. Beeaff, A.C. Mulligan, M.M. Opeka, M.J. limited number of sources such as Rigali, and M.P. Sutaria, “Continuous Composite Coextrusion unpublished results or Methods, Apparatuses, and Compositions,” U.S. Patent No. manuscripts, personal 6,355,338, issue date March 12, 2002. communications with experts in the field Conference Proceedings: (give person’s name, affiliation, and the date A. Chamberlain, W.G. Fahrenholtz, G.E. Hilmas, and D.T. of the communication), Ellerby, “Characterization of Zirconium Diboride-Molybdenum presentations at Disilicide Ceramics,” pp. 299-308 in Advances in Ceramic technical meetings, Matrix Composites IX, Ceramic Transactions Volume 153, and product literature. ed. by N.P. Bansal, J.P. Singh, W.M. Kriven, and H. Schneider, The use of transitory sources such as course The American Ceramic Society, Westerville, OH (2003). notes and information that is not peer- reviewed such as web sites should be minimized.
12 Appendix One PDF database cards for unknown samples.
13 14 General Comments
Based on lab reports from previous years and feedback from TA' s, professors, and students, I have compiled a list of helpful hints for preparing reports. These are in no particular order.
1. For technical writing, you should write in the third person using past tense and an active voice (see the report writing handout for examples). For this class, you can use phrases like “we did” or “our group found” without penalty. However, it is generally regarded as boastful or egotistic if you do this when preparing a technical paper for presentation or for reports to superiors in industry.
2. The procedure section should not read like an instruction manual. Do not tell the reader what to do. Give a detailed explanation of what you did and the resources (equipment, raw materials) that you used.
3. Whenever you use an acronym or abbreviation, make sure to spell out the entire phrase before you use the shortened version. Examples are given in the body of this document.
4. Try to write your report for an audience that is technically literate, but one that has not just completed this work. If it helps, try to imagine that you are writing for a boss or someone else who is familiar with your field, but that does not know what you do on a day-to-day basis.
5. Try to be concise. You want your report to include all the necessary details, but don't be excessively wordy. Be as descriptive as you can, but don't make it too long.
6. Proofread your work. The spell checker will not catch everything.
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