Debye-Scherrer powder method

We measure accurately the distances between the lines on the film. From these and the dimensions of the camera, the diffraction angle 29 can be calculated for each set of planes. From the Bragg angle 9 the interplanar spacings d are calculated from the Bragg equation. 

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FIGURE 27.2 Debye-Scherrer powder method. Cones of reflected and transmitted radiation are produced. In this example the pattern is recorded with photographic film. Alternatively,... 

Fig. 3-12 Debye-Scherrer powder method (a) relation of film to specimen and incident beam (b) appearance of film when laid out flat.

Figure 5 2. The Debye-Scherrer powder method. An X-ray R passes through a collimator and then meets a powder preparation P. The reflections caused by P lie on cones of reflection, which form crescents or arcs on a cylindrical film F.

X-ray diffraction patterns have been worked out by Fankuchen (8) with the Debye-Scherrer powder method, which, because of the cubic nature of the crystals were quite helpful in some respects for the interpretation of the structure. Fankuchen obtained patterns reconcilable with a face-centered cubic unit cell, and the pattern was the same both in ferritin and in apoferritin. The distances of the lines were the same, but there was a difference in the intensities of some lines, those of ferritin being more intense than those of apoferritin. This seems to show, once... 

D20.2 We can use the Debye-Scherrer powder diffraction method, follow the procedure of Example 20.3, and in particular look for systematic absences in the diffraction patterns. We can proceed through the following sequence... 

However, not every crystalline substance can be obtained in the form of macroscopic crystals. This led to the Debye-Scherrer (16) method of analysis for powdered crystalline solids or polycrystalline specimens. The crystals are oriented at random so the spots become cones of diffracted beams that can be recorded either as circles on a flat photographic plate or as arcs on a strip of film encircling the specimen (see Figure 6.4) (17). The latter method permits the study of back reflections as well as forward reflections. 

Outline how you would interpret X-Ray diffraction data, if any, obtained for the following CPs and using the following X-Ray methods P(ANi)Cl P(Di-Ac)s Debye-Scherrer powder camera Weissenberg camera Precession camera Wide Angle X-Ray Diffraction Automated Diffractometer. 

The compound layer formed in the transition zone between nickel and bismuth was investigated metallographically, by X-rays and electron probe microanalysis (EPMA). X-ray patterns were taken both from the cross-sections in the planes parallel to the initial Ni-Bi interface (after successive removal of the specimen material and polishing its surface) and the powdered phases using Cu Ka radiation. Two methods of obtaining X-ray patterns were employed. Firstly, X-ray photographs were obtained in a 57.3 mm inner diameter Debye-Scherrer camera. Secondly, use was made of a DRON-3 diffractometer to record X-ray diffractograms. 

X-ray Data.—The structure of black phosphorus has been calculated from the X-ray reflection spectrum, using the powder method of Debye and Scherrer. It is a rhombohedral space-lattice having a characteristic angle of 60° 47, and a side of 5-96 A. The unit cell contains 8 atoms, and therefore the volume of the unit molecular aggregate is ... 

There are several experimental techniques for realizing the diffraction conditions, the most powerful of which depends on having a single crystal of the substance to be studied see Exp. 46. In the present experiment we are concerned only with the Debye-Scherrer method (often called the powder method), which does not make use of a single crystal but rather of a powder obtained by grinding up crystalline or microcrystalline material. This powder eontains crystal particles of a few micrometers in size. 

The Raman samples themselves were used to obtain powder photographs by the Debye-Scherrer method. 

Table 2. X-ray Powder Data (Debye—Scherrer Method, Cu Ka Radiation, Ni Filter) for AgsAsFn"...

Figure 2.12 The Ewald sphere method illustrates the ring pattern of diffraction from a powder specimen. The Debye ring recorded by the Elull-Debye-Scherrer method results from randomly oriented crystals in the powder specimen, in which reciprocal lattice points of (hkl) touch the Ewald sphere surface in various directions to form individual rings. It is equivalent to rotating a reciprocal lattice along an incident beam axis. (Reproduced with permission from R. Jenkins and R.L. Snyder, Introduction to X-ray Powder Diffractometry, John Wiley Sons Inc., New York. 1996 John Wiley Sons Inc.)...

The Debye-Scherrer and other variations of the powder method are very widely used, especially in metallurgy. The powder method is, of course, the only method that can be employed when a single-crystal specimen is not available, and this is the case more often than not in metallurgical work. The method is especially suited for determining lattice parameters with high precision and for the identification of phases, whether they occur alone or in mixtures such as polyphase alloys, corrosion products, refractories, and rocks. These and other uses of the powder method will be fully described in later chapters. 

The specimen in the Debye-Scherrer method has the form of a very thin cylinder of powder placed on the camera axis, and Fig. 4-18(a) shows the cross section of such a specimen. For the low-an le reflection shown, absorption of a particular ray in the incident beam occurs along a path such as AB at 5 a small fraction of the incident energy is diffracted by a powder particle, and absorption of this diffracted beam occurs along the path BC. Similarly, for a high-angle reflection, absorption of both the incident and diffracted beams occurs along a path such as DE -I- EF). The net result is that the diffracted beam is of lower intensity than one would expect for a specimen of no absorption. 

To illustrate this extrapolation method, we shall consider a powder pattern of tungsten made in a Debye-Scherrer camera 5.73 cm in diameter with unfiltered... 

G.17 Leonid V. Azaroff and Martin J. Buerger. The Powder Method in X-Ray Crystallography (New York McGraw-Hill, 1958). The making and interpretation of Debye-Scherrer photographs, including precise parameter measurements. 

Early powder diffraction experiments relied mostly on the Debye-Scherrer experiment to record a diffractogram. A broad film strip set into a cylindrical chamber produced the first known two-dimensional powder diffraction data. In contrast to modern methods the thin equatorial strip was the only part of interest and intensities merely optically and qualitatively analysed. This changed drastically with the use of electronic scintillation counters. Intensities were no longer a matter of quality but quantity. Inevitably the introduction of intensity correction functions long known to the single-crystal metier, i.e. Lorentz and polarization corrections (see Section 14.3), made their way into the field of powder diffraction. 

Although, the powder method was developed as early as 1916 by Debye and Scherrer, for more than 50 years its use was almost exclusively limited to qualitative and semi-quantitative phase analysis and macroscopic stress measurements. The main reason for this can be found in what is known as the principal problem of powder diffraction accidental and systematic peak overlap caused by a projection of three-dimensional reciprocal space on to the one-dimensional 26 axis, leading to a strongly reduced information content compared to a single crystal data set. However, despite the loss of angular information, often sufficient information resides in the ID dataset to reconstruct the 3D structure. Indeed, quantitative analysis of the pattern using modern computers and software yields the wealth of additional information about the sample structure that is illustrated in Figure 1. Modern... 

The Powder Method 99 for Metals. A modification of this method which has proved of particular metallurgical interest was developed by Debye and Scherrer in 1916 and by Hull in 1917. These workers showed that X-ray diffraction patterns... 

A Debye-Scherrer camera consists of a metal cylinder provided with a photographic film. The primary beam is perpendicular to its axis. The distance between two symmetrical lines, produced by the intersection of a cone with the cylinder, is 46R, 6 being the Bragg angle (in radians) and R the radius of the camera. The interval is derived from Bragg s law. The powder method gives us only the norms of the reciprocal vectors. The set of norms corresponds to the projection of the reciprocal lattice onto a straight line. 

A) Schematic of the Debye-Scherrer method, developed in 1916, for X-ray diffraction of powders (polycrystdlline samples). Each characteristic interplanar spacing in the crystal gives rise to a cone of diffracted X-rays, segments of which are captured on the film strip placed inside the camera. 

Debye-Scherrer method A method of X-ray diffraction in which abeam of X-rays is diffracted by material in the form of powder. Since the powder consists of very small crystals of the material in all possible orienta-... 

R. Brill has carried out a series of experiments which indicate very clearly the influence of particle size on the sharpness of the Debye-Scherrer lines for iron powder. There is quite a powerful effect, the evaluation of which would be very profitable. Scherrer has already established in the work previously mentioned that the particle sizes of colloidal gold calculated by the use of his formula agree very satisfactorily with those obtained by the Zsigmondy method of direct counting. Later, Brill compared the different relations available for the computation with one another and obtained the data contained in Table 72. This includes a comparison of the relation originally given by Scherrer with the Laue formula modified by Brill and Pelzer. Various preparations of very fine-grained iron, which are of importance in the technique of catalysis in the ammonia process, served as material. 

Debye-Scherrer method A method used in X-RAY diffraction in which a crystal in powder form is exposed to a beam of monochromatic x-rays. Because the crystal is in powder form all possible orientations of the crystal are presented to the x-ray beam. This has the result that the diffracted x-rays form cones concentric with the original beam. The Debye-Scherrer method is particularly useful for determining the lattice type of a crystal and the dimensions of its unit cell. The method was first developed by Peter Debye and Paul Scherrer. 

The powder method In 1916, P. Debye, P. Scherrer and A.W.Hull devised the powder method of X-ray crystallography which went on to become a widety used method. A narrow... 

The classical photographic method for recording powder diffraction patterns is still used, particularly when the amount of sample is small. The most common instrument forthis purpose is the Debye-Scherrer pov/det camera, which is shown schematically in Figure 12-17a. Here, the beam from an X-ray tube is filtered to produce a nearly monochromatic beam (often the copper or molybdenum Ka line), which is collimated by passage through a narrow tube. 

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