Differential scanning calorimetry

4.8.4 Differential scanning calorimetry

In this method, unlike DTA, the sample and reference body have separate resistive heaters (Figure 4.60c). When a difference in temperature develops between sample S and reference R, an automatic control loop heats the cooler of the two until the difference is eliminated. The electrical

Characterization and analysis 237 power needed to accomplish this equalizer is plotted against temperature. An endothermic change

signifies that an enthalpy increase has occurred in S; accordingly, its peak is plotted upwards (unlike DTA traces). Differences in thermal conductivity and specific heat capacity have no effect and peak areas can be expressed as energy per unit mass. DSC has proved particularly valuable in polymer research, often being used in combination with other techniques, such as evolved gas analysis (EGA). DSC has been used in studies of the curing characteristics of rubbers and thermoset resins, transi- tions in liquid crystals and isothermal crystallization rates in thermoplastics. Figure 4.61c is a trace obtained for a quenched amorphous polymer. DSC has also been used in studies of the exothermic behavior of cold-worked metals as they release ‘stored energy’ during annealing, energy absorption during eutectic melting of alloys, precipitation in aluminum-based alloys, relaxation transformations in metallic glasses and drying/firing transitions in clay minerals.

Problems

4.1 What is the angle between the diffracted beam and the incident beam when X-rays of wavelength

0.1 nm are reflected by {1 1 1} planes in copper (a = 0.362 nm)?

4.2 The energy of CuK α X-rays is 8.04 keV. What is their wavelength?

4.3 What different types of planes in aluminum have the three smallest Bragg angles?

4.4 In a 200 kV transmission electron microscope, electromagnetic lenses make the effective camera length 1 m. What is the distance on the screen of a {1 1 0} diffracted beam spot from the main (incident) beam for an iron specimen at room temperature (a = 0.287 nm)?

4.5 In an X-ray powder camera, CuK α X-rays are directed at a titanium powder sample. What is the distance apart of the {1 ¯1 0 1} lines? (For Ti, a = 0.295 nm; c = 0.468 nm; diameter of camera = 115 mm.)

4.6 In an X-ray powder camera experiment the diffracted beams emerge at the following angles to the incident X-ray beam: 57.34 ◦ , 67.28 ◦ , 103.20 ◦ , 133.59 ◦ , 147.36 ◦ . The specimen has an fcc crystal structure and the wavelength of the X-rays is 0.2 nm. What is the lattice parameter?

4.7 In an EDX spectrum a strong peak was detected at 8.04 keV. What other peaks would you expect necessarily to see?

4.8 In an XRF experiment, the X-ray intensities from the specimen of unknown composition and from a standard containing 50% of magnesium and 50% oxygen were as follows:

What was the composition of the specimen?

4.9 In an SEM analysis, the following X-ray intensities were measured:

Specimen Elemental standard

Iron FeK

Chromium CrK 6189

Nickel NiK

What was the composition of the specimen? What material was it?

4.10 In a thin foil of aluminum with (0 0 1) orientation a screw dislocation is in contrast when 0 2 0 and 2 ¯2 0 reflections operate. It is ‘invisible’ when the 2 2 0 reflection operates. When the

238 Physical Metallurgy and Advanced Materials specimen is tilted to excite the 1 1 ¯1 reflection, the dislocation is also invisible. (i) Determine

the possible Burgers vector of the dislocation and (ii) comment on the slip plane it is capable of gliding in.

4.11 Stacking faults A, B, C are observed in a (1 1 1)-oriented TEM specimen of silicon on ( ¯1 1 1), (1 1 ¯1) and (1 ¯1 1) planes respectively. Determine which fault will be ‘invisible’ using the

g = 0 ¯2 2 reflection and which with the g = 2 ¯2 0 reflection.

4.12 Rod precipitates lying along [1 0 0] in a cubic crystal are examined in the electron microscope with the beam pointing along [1 1 3]. Predict the direction of the precipitate images.

Further reading

Barnes, P. (1990). Synchrotron radiation for materials science research. Metals and Materials, November, pp. 708–715. Institute of Materials. Barrett, C. S. and Massalski, T. B. (1980). Structure of Metals: Crystallographic Methods, Principles and Data. Pergamon, Oxford. Cullity, B. D. (1978). Elements of X-ray Diffraction. Addison-Wesley, Reading, MA. Dehoff, R. T. and Rhines, F. N. (eds) (1968). Quantitative Microscopy. McGraw-Hill, New York. Fischer-Cripps, A.C. (2004). Nanoindentation. Springer, New York. Gifkins, R. C. (1970). Optical Microscopy of Metals. Pitman, Melbourne. Hay, J. N. (1982). Thermal methods of analysis of polymers. In Analysis of Polymer Systems (edited by

L. S. Bark and N. S. Allen), Chap. 6. Applied Science, London. Hill, M. and Nicholas, P. (1989). Thermal analysis in materials development. Metals and Materials, November, pp. 639–642. Institute of Materials. Johnson, K. L. (1985). Contact Mechanics. Cambridge University Press, Cambridge. Jones, I. P. (1992). Chemical Microanalysis using Electron Beams. Institute of Materials, London. Loretto, M. H. (1984). Electron Beam Analysis of Materials. Chapman & Hall, London. Loretto, M. H. and Smallman, R. E. (1975). Defect Analysis in Electron Microscopy. Chapman & Hall,

London. Modin, H. and Modin, S. (1973). Metallurgical Microscopy. Butterworths, London. Patzelt, W. J. (1974). Polarised Light Microscopy: Principles, Instruments, Applications. Ernst Leitz

Wetzlar GmbH, Lahn-Wetzlar. Pickering, F. B. (1976). The Basis of Quantitative Metallography, Institute of Metallurgical Technicians Monograph No. 1. Richardson, J. H. (1971). Optical Microscopy for the Materials Sciences. Marcel Dekker, New York. Tabor, D. (1951). The Hardness of Metals. Oxford University Press, Oxford. Vickerman, J. C., Brown, A. and Reed, N. M. (eds) (1990). Secondary Ion Mass Spectrometry: Principles

and Applications. Clarendon Press, Oxford. Wendlandt, W. W. (1986). Thermal Analysis, 3rd edn. Wiley, New York. Williams, D. B. and Carter, C. B. (1996). Transmission Electron Microscopy – A Textbook for Materials

Science, I Basic, II Diffraction, III Imaging. Plenum Press, New York.

Chapter 5

Physical properties