B. E. Warren

The Effect of Cold‐Work Distortion on X‐Ray Patterns

With modern experimental technique, it is possible to measure a peak shape with sufficient accuracy to justify an interpretation based on the precise shape of the reflection. The corrected shape is represented by a cosine Fourier series and a set of An coefficients determined. A plot of the An coefficients vs. n will distinguish between distortion and particle size broadening. From the An coefficients, root mean square values of strain averaged over lengths na3 are obtained. The decrease in these values for increasing length na3 is a direct indication of the non‐uniform nature of the strains in cold‐worked metal. By measuring several orders of a given plane, it is theoretically possible to obtain a distribution function of the strains directly from a Fourier transform of the An coefficients.

The structure of vitreous silica

A new study of the structure of vitreous silica has been made under greatly improved conditions. Using Rh Kα radiation with the method of fluorescence excitation, reliable intensity values were measured to 4π sinθ/λ = 20. The interpretation was in terms of pair functions, thereby eliminating the approximations in earlier work. Each silicon is tetrahedrally surrounded by 4 oxygen atoms, with a Si–O distance which is closely 1.62 A. Each oxygen atom is bonded to 2 silicon atoms. The Si–O–Si bond angle α shows a distribution V(α) extending all the way from 120° to 180°, with a maximum at α = 144°. This wide variation in α is an important distinction between the vitreous and the crystalline forms of silica, and it furnishes an important criterion for any proposed model of vitreous silica. Good agreement with the measured pair function distribution curve was obtained by assuming a random orientation about the Si–O bond directions. The interpretation leads to the familiar random network model, but with the new results the model is more precise.

An X‐Ray Study of Carbon Black

X‐ray studies have been made of a number of carbon blacks, prepared under different conditions, and subject to various heat treatments. The patterns were made in evacuated cameras, using Cu Kα radiation monochromated by reflection from rocksalt. The patterns consist of crystalline reflections (00l), and two‐dimensional lattice reflections (hk). The structure is one of true graphite layers arranged roughly parallel and equidistant, but otherwise completely random. The dimensions within a layer are the same as in graphite; the layer separation is somewhat larger than in graphite. The effect of heat treatment is to increase the size of the parallel layer groups. At graphitization the material changes discontinuously to the crystalline graphite structure. The usual carbon black is not finely divided graphite. Small angle scattering studies indicate the existence of clusters a few hundred angstroms in size. It is these clusters which are measured by microscope counts, by the electron microscope, and by surface...

X‐Ray Diffraction Methods

To learn more about the identification of crystalline materials, preferred orientations, particle sizes, strains, and structure randomness, x‐ray diffraction is used. Here both basic principles and working techniques are described.

Atomic Size Effect in the X‐Ray Scattering by Alloys

In a random solid solution, if the two atoms have appreciably different sizes, the nearest‐neighbor distances and to a lesser extent the higher neighbor distances will be of three kinds, γAA, γAB, and γBB. The effect produces modulations in the diffuse intensity similar to those produced by short‐range order. The size effect is important when the difference in scattering power is large, the difference in size is large, and the short‐range order is small. The size effect is illustrated by a single crystal pattern of Cu3Au and a powder pattern of Ni3Au2. An asymmetry in the wings about a fundamental reflection is a result of the size effect.

Long‐Range Order in Beta‐Brass and Cu3Au

Measurements have been made on single crystals of CuZn and Cu3Au held at various temperatures below Tc to decide whether there is a single‐ordered phase whose order changes with temperature, or whether there is an ordered and a disordered phase the relative amounts changing with temperature. Precision measurements were made of the position and width of the (222) CuZn and (400) Cu3Au reflections. The disordered phase has a larger cell dimension, so that reflections from the ordered and disordered phases are slightly displaced from one another. For both materials, a single peak was observed which was too narrow to correspond to the existence of two phases. At the stoichiometric compositions, it is concluded that below Tc there is only an ordered phase whose long‐range order varies with temperature. Measurements of the long‐range order in Cu3Au have been made on briquets of filings, using quenched samples, and on a sample held at temperature.

X‐Ray Measurement of Long Range Order in β‐Brass

The long range order in β‐Brass has been determined by measuring the integrated intensity of the (100) superstructure reflection from a single crystal held at various temperatures. With a single crystal, and CuKα‐radiation obtained by a balanced Ni‐Co filter, there is ample intensity for measurement with a Geiger counter spectrometer. The measured long range order parameter S is in satisfactory agreement with the theoretical predictions.

X‐Ray Study of Cold Work in Thoriated Tungsten

Spectrometer measurements were made of the x‐ray diffraction peaks for cold‐worked filings of thoriated tungsten: 99.25 tungsten, 0.75 thoria. A Fourier analysis was made of the peak shapes, and the instrumental broadening corrected by using the peaks of annealed material. When the particle size and the distortion effects were separated, it was found that the particle size broadening corresponded to a size L=200A. This value is to be interpreted as the size of the coherently diffracting domains, and is a measure of the distance between layers of slip planes or layers of dislocations. The coherent distortion broadening indicated that strains in this material vary appreciably over distances of 25A or less. Strain distribution curves were obtained from a Fourier transform of the experimental coefficients. There is an indication that strains are smaller in the larger coherent regions. The measured root mean square strain corresponds to an elastic energy of 0.18 cal/g. Within experimental accuracy the integra...

A Method for Measuring the Total Power of Small‐Angle X‐Ray Scattering

Measurements of the absorption coefficients are made with a double crystal spectrometer in the parallel position, placing the sample between the two crystals, and between the second crystal and the chamber. In the first position the beam is cut down by the ordinary absorption and also by the power going into small‐angle scattering; in the second position it is cut down only by the ordinary absorption. The difference in the two measured absorption coefficients gives directly the total power in small‐angle scattering. From the latter, an average spherical particle size can be computed.

X‐Ray Measurement of Short Range Order in Ag‐Au

The diffuse intensity from single crystals of AgAu and Ag3Au was measured with crystal monochromated CuKα radiation and a Geiger counter spectrometer. Measurements were made at a series of points in the (h1h20) layer of reciprocal space. The measurements were made at both room temperature and at 160°K to allow a correction for temperature diffuse scattering. For the final annealing temperature of 300°C, the short‐range order parameters obtained were α1 = −0.08 for AgAu and α1 = −0.05 for Ag3Au.