Although no revolutionary advance has been achieved in the last two decades, X-ray diffraction is not to be considered as a quiescent field of physics. Actually many improvements, in theory as well as in experiment, slight by themselves but very numerous, have considerably increased the efficiency of techniques such as the determination of crystal structures, the analysis of crystalline phases, and the applications of X-rays to various problems of the physics of solids. Only the two last points will be dealt with here:

1. 1. Crystalline phase analysis. The development of a satisfactory atlas of powder patterns has been too slow, and the data are not yet complete and precise enough to permit a rational utilization of the modern diffractometers. A very interesting new approach is the systematic indexing of the powder patterns which would be possible with computers. In the near future, anyone should be able to analyze a powder at any temperature as an easy routine experiment.

2. 2. The study of lattice defects. X-ray techniques are now in competition with electron microscopy, the development of which has been very successful in recent years. Now we have a better understanding of the possibilities of both techniques. X-rays give better results to determine the statistics of an extended disorder even if it is slight (e.g., degrees of order in a solid solution), and the microscope is more powerful for the detection of large but rare defects (e.g., dislocations).

This paper deals with some recent investigations on beryllides, borides, carbides, nitrides, aluminides, and germanides of transition metals as well as with combinations of these with special reference to hafnium and uranium compounds. The results will be discussed within the general field of refractories excluding the class of typical oxides. An intense study has revealed the influence of metalloid impurities (for instance carbon, nitrogen, and oxygen on high-melting borides and silicides or nitrogen and oxygen or carbides, respectively). Very often small amounts of such metalloids introduced by preparation techniques, like hot-pressing, sintering, and powder-reaction methods may change the constitution of the system.

Much current solid-state research, particularly that concerning the Fermi surfaces of metals and semimetals, demands knowledge of lattice parameters at temperatures in the liquid-helium range. A helium cryostat diffraction apparatus that has been in continuous use at these temperatures will be described, and some new research results from it are presented. The results include measurements of the lattice constants for gallium and for indium, of interest because the axial ratio influences both the nuclear electric quadrupole spectrum and also the cyclotron resonance. Previous measurements have disclosed unusual expansion characteristics but have not extended below liquid-nitrogen temperature.

A second area in which the cryostat has been operating is the determination of the temperature of beginning recrystallization in high-purity metals that recrystallize at low temperatures. Experiments with zone-refined lead which has a recrystallization temperature near 160°K are reported.

A low-temperature X-ray diffraction apparatus has been constructed to study structure and structural changes of electrolytes in the frozen state. This apparatus, which is inexpensive and easy to construct, is an attachment to a standard wide-angle diffractometer. Diffraction patterns may be obtained of various types of materials at any temperature from room temperature to −196°C with a control of ±1°C. The diffraction patterns are recorded on a strip-chart recorder as they are being obtained. Thus, this diffractometer method has several advantages over the camera methods usually employed for low-temperature X-ray diffraction work. A unique sample-introduction method is described which ensures a polycrystalline material suitable for obtaining diffraction patterns. Such patterns are shown for various concentrations of salts in water at several low temperatures, phase transformations being in evidence.

The lattice parameters of iron-ruthenium solid-solution alloys of 0.10, 0.20, 0.50, 0.75, 1.50, 2.25, and 3.00 wt, % ruthenium have been determined at 310°K using a Philips back-reflection focusing camera and annealed-powder specimens.

Dental amalgam has been used as a filling material in dentistry for over 100 years. The reactants, Ag3Sn alloy and mercury, form silver-mercury and tin-mercury products. Previous X-ray diffraction studies have resulted in some disagreement concerning unit-cell structure and parameters of the products. In this study, X-ray diffraction measurements were carried out on tin-mercury mixtures, tin-mercury alloys, dental amalgam, and single crystals of tin and mercury. The diffraction data for the tin-mercury alloys were programed for an IBM 650 computer utilizing Cohen's least-squares method. The tin-mercury product was found to be a solid solution possessing hexagonal-symmetry elements. The parameters ranged from: c0 = 2.995 A to 2.984 A, co/ao = 0.931.

Without modifying the General Electric XRD-5 diffractometer accurate lattice parameters of cubic structures may be determined quite simply and precisely. The method is applicable to both solid and powder samples and gives a precision of at least ±0.00025 A. The most important step in the analysis is the alignment of the diffractometer. The specimen must be in the exact center for precise work. However, after the initial alignment, daily alignment is a routine matter. This technique for lattice-parameter determination will also be useful for determining thermal coefficients of expansion and residual-stress measurements.

The availability of counter-tube diffractometers which can scan both sides of the direct beam makes it possible to locate the zero-angle position by comparing peak positions measured on either side of the beam. These diffractometers may thus be used to determine accurate lattice parameters without the need of a calibrating substance. The feasibility of this method is explored by determining the lattice parameters of pure silver, and the limits of accuracy are discussed.

Experiments on the application of X-ray image intensifiers of the Fluorex type and of transmission-type secondary electron image intensifies (Astracon tubes) to the direct observation and recording of X-ray diffraction patterns have proved highly successful. Further improvements can be obtained by combining a Fluorex tube directly with an Astracon tube. By this means, the useful signal strength is so improved that movies at standard frame speed can be made which record the changing Laue pattern from a rotating crystal. It is shown how still further improvements are possible if the optical coupling in the system is improved by incorporating a fiber-optics window at the input of the Fluorex-Astracon tube. It is further indicated how a fiber-optics adapter can be used as an analog computer to convert the X-ray diffraction pattern from a single crystal into an exact representation of the reciprocal lattice which can be viewed directly.

Magnesium oxide crystallites having mean dimensions in the range of 25–1000 A can be prepared by controlled thermal decomposition of the carbonate.

Following some earlier investigations of Birks and Friedman, we have determined the mean size and size distribution of several such MgO samples from the broadened X-ray diffraction lines which they exhibit. Contrary to the procedure of the above investigators, the harmonic analysis due to Stokes has been used to correct for instrumental broadening and values of mean-size and size-distribution functions obtained from the Fourier coefficients by the methods of Warren and Averbach.

The results obtained are compared with average sizes and distributions obtained by direct examination of the samples in an electron microscope.

A composite sample has been prepared by mixing known quantities of the sample previously studied. The distribution function obtained by harmonic analysis of one diffraction line of the composite sample is compared with the function calculated from the distributions of its components.

Conclusions are drawn concerning the significance of the results obtained by the Warren technique: in particular, the average sizes obtained by this method are compared with those given by the approximate method used by Birks and Friedman.

Increasing interest in the sintering characteristics of various ceramic materials has resulted in the need for a knowledge of the crystallite sizes of many constituent ceramic powders. Standard X-ray diffraction line-broadening techniques have been utilized to determine these crystallite sizes. This paper presents a general review of the theory of line broadening as a means of measuring crystallite size and gives the methods and modifications used to perform this type of analysis rapidly and on a routine basis.

Four modifications have been used in the determination of crystallite size routinely by X-ray line broadening. These methods are (1) a graded set of powder photographs, (2) a computer program to calculate sizes from diffractometer data, (3) a set of crystallite-size curves for a given material for use with diffractometer data, and (4) a standard set of curves to use with diffractometer data for any strain-free materials. The preparation, use, and limitations of each of these methods is presented.

Todorokite is a hydrated manganese oxide mineral containing small amounts of sodium, potassium, calcium, barium, magnesium, iron, and aluminum. From the reports of other investigators and observations in our laboratories, todorokite appears to be a more widely occurring mineral than generally recognized.

It was found by X-ray diffraction that a sample of todorokite from Charco Redondo, Cuba, had a high degree of preferred orientation and that milling for a prolonged period of time was necessary to obtain random orientation in a mounted specimen. The position of the preferred orientation direction with respect to the X-ray beam is the principal factor determining the relative intensities on an X-ray diffraction pattern. Based on fiber data, the unit cell of todorokite is considered to be pseudo-orthorhombic or triclinic with α, β, and γ angles varying slightly from 90° and cell dimensions of a0 = 9.65A, b0 = 10.29A, and c0 = 2.84A, This deviation from orthogonality may account for the diffuse and distinct reflections typical of X-ray diffraction patterns of todorokite. Optical data and a hypothesized paragenesis of Cuban todorokite are also included.

The reaction between solid lead azide and lead oxide at different molar ratios yields two phases of basic lead azide of the type xPb(N3)2·yPbO with different azide content. The first phase was identified as xPb(N3)2·PbO, investigation of the second phase is still under way. The results up to the present time suggest that the formula for this phase is between Pb(N3)2·2PbO and Pb(N3)2·3PbO, probably 2Pb(N3)2·5PbO. The reaction is catalyzed by traces of water. The formulas of the two lead azide phases are established by X-ray analysts. The phases are identical with those found previously when lead azide was thermally decomposed in atmospheres containing water.

The salts of hydrazine or methyl derivatives of hydrazine were prepared by neutralization of the base with inorganic acids, for instance, HBF4, HClO4, H SO4, and HCl. Upon recrystallization of the product from a suitable solvent, X-ray diffraction patterns were obtained. Hydrazine tetrafluoborate H2N-NH2·HBF4 was found to crystallize in the monoclinic system. Cell dimensions and possible space groups were determined. The corresponding perchlorate salt crystallizes in two forms, one of which is isomorphous with hydrazine tetrafluoborate. The second form seems to be stabilized by small amounts of water.

The tetrafluoborate salt was prepared from the 1,1-dimethyl hydrazine. It was found to crystallize in the tetragonal system with a primitive unit cell. The perchlorate salt of this base is isomorphous with the fluoborate but with a slightly larger unit cell. Both materials undergo plastic-like deformation. The general appearance and mechanical properties are similar to those of a hydrocarbon wax. The 1,1-dimethyl hydrazine sulfate and the 1,1-dimethyl hydrazine hydrochloride have a lower symmetry than the HBF4 salt and do not show the wax-like properties of the latter. Based on the study of these chemically related compounds an explanation is offered for the properties of 1,1-dimethyl hydrazine tetrafluoborate in terms of crystalline structure.

Single crystals of cadmium sulfide and zinc sulfide have been grown and studied intensively by the Solid State Physics group at the Aeronautical Research Laboratory. The physical phenomena such as reflection, transmission, ultraviolet-excited emission, and electrical resistivity have been observed and characterized on single crystals of these sulfides. Much interest concerning these phenomena has also been centered on single crystals containing both cadmium sulfide and zinc sulfide.

For research purposes, mixed crystals as small as a few tenths of 1 mg or less, to 0.5 g of the mixed sulfides, are being prepared. Special chemical methods are required to determine these constituents in them quantitatively. At times, these chemical methods are not applicable, since these methods invariably consume the sample, and, as a result, other observations on the same crystals cannot be performed.

Changes in lattice parameter in single crystals of mixed sulfides as compared to pure zinc sulfide or cadmium sulfide provide excellent means for the determination of the percentage of these sulfides. In the X-ray method, single crystals used for the determination of the lattice parameters remain intact. The equipment adopted, procedure used, and the data obtained are illustrated and discussed.

In the present study, crystals of cadmium sulfide (greenockite), alpha-zinc sulfide (wurtzite) and solid solutions of these two sulfides having a hexagonal unit cell were used. Since the lattice parameter a0 is found to follow Vegard's law, single-crystal rotation photographs described in this paper were obtained by rotating crystals around the c axis; the lattice parameter was determined with high precision by scanning along the zero-layer line with a microphotometer.

A brief description of the theoretical approach of this new method is given. The main purpose of the method is to correlate in a more logical order not only the data yielding the two laws relating mass-absorption coefficient to wavelength and to atomic number, respectively, but also to delineate, within two discontinuities, the relationship existing between each value and the other ones taken as a whole. The empirical equation relating μ to λ is μ = Cλn. A table of complete values for the constant C and die power n to be assigned in the equation is given for finding the values of mass-absorption coefficients above unity for all elements (except hydrogen) and for all wavelengths between 0.17837 and 10 A. It is believed that until a complete set of experimental data obtained with modern equipment is available, this proposed method fills the enormous gaps between actual compiled values.

A stress-strain relationship for copper in the plastic region has been determined by examining the influence of the applied stresses on the grain orientation of shear-formed specimens. Instrumentation was developed to permit accurate grain-orientation analysis of a large specimen by X-ray diffraction without the necessity for deformation or destruction of the specimen.

This paper summarizes developments in the field of high-temperature X-ray diffractometers through 1959, evaluates various furnace designs, and describes briefly the X-ray diffraction facilities of the Federal Bureau of Mines.

X-ray optics, for those furnaces that have precision sample movements, are equivalent in resolution and line profile to conventional X-ray techniques. There is a 10-25% loss of intensity due to absorption of X-rays in the furnace windows, magnitude of which depends on wavelength and type of window used, and a reduction (5–40° 2θ) of useful angular range from limiting X-ray windows, radiation shielding, or the viewport for an optical pyrometer. In oxidizing atmospheres, temperatures up to 1500°C were obtained with furnaces wound with platinum—20% rhodium wire. Under nonoxidizing conditions temperatures of 1800 to 2000°C were obtained with both tantalum-foil and tungsten-wire heaters.

Accurate temperature measurement over the area and depth of samples being studied is the most difficult problem in high-temperature X-ray diffractometry. Below 500°C, there are several furnace designs which are reported to reduce thermal differentials to less than 1°C across the sample. However, at temperatures around 1000°C, there are thermal gradients of 20-30°C/cm across the sample and 100–600°C/cm through the sample holder, making thermocouple location critical. Secondary standards have been used extensively to calibrate the furnaces; however, there is disagreement concerning which are the most reliable data to use. For these reasons, plus others discussed in this report, there is a probable error in the temperature determination of ±10 to 20°C at 1000°C, with the error increasing with temperature.