A method of predicting the approximate relative intensities of lines in proton blocking patterns recently proposed, which is based on summing the squares of structure factors for the various orders of reflection of a plane, is found to predict certain effects of lattice vibrations on the lines in some recently reported patterns. The mean square amplitude of vibration enters the calculations through a Debye-Waller temperature factor like that used in X-ray diffraction. When patterns are compared for groups of crystals that are nearly identical except for this temperature factor, the qualitative predictions by this method agree with the observations. If it is also arbitrarily assumed that the integrated intensity dip at a spot where lines intersect is approximated by summing the calculated Integrated intensity dips for all of the lines crossing at the spot, one has a simple and convenient method of predicting relative spot intensities. Such calculations have been successful in establishing the order of decreasing intensity for most of the spots along a given line, with several different kinds of crystals. This method also serves to predict qualitatively how prominent the spots appear relative to the lines, in general, in patterns of crystals that differ appreciably only in the amplitude of the thermal vibrations.

Despite the fact that the many researchers, who have worked on the problem of indexing powder diffraction patterns, have made several important advances in the field and have proven in theory at least that any pattern can eventually be indexed, the procedures are frequently so laborious as to drive the investigator to despair. Starting with the knowledge that convolution functions and particularly self-convolutions ﹛so well known to crystallographers as Patterson functions) have the power to find the distances between points in space, and knowing that reciprocal space is filled with repeating distances, the present authors have evolved a graphical system for carrying out the previously discovered procedures in an easy and rapid manner.

It is shown that the integrated intensities of diffraction lines from calcite and aragonite powders prepared by precipitation vary markedly, due to variations in sample packing efficiency arising from different degrees of polydispersity in the particle size distributions. Since prolonged grinding to equalize initially divergent distributions changes the polymorph composition, the packing effect imposes the principal limitation on the precision of the x-ray method for certain types of calcium carbonate preparations.

The efficiency and effectiveness of diffracted beam x-ray monochromators used in powder diffractometry have been described in so many ways that much confusion exists regarding their true performance. Although significant improvements in signal to noise ratios are readily achievable, and they offer a solution to the sample fluorescence problem, it is not without sacrifice to total intensity or achievable resolution or both. This paper discusses and describes a series of comparisons between filtered direct beam, LiF and graphite monochromators.

These comparisons include the considerations necessary for the appropriate selection of diffracted beam slit system, the effect of vertical divergence as a function of two theta for singly bent crystals, the effects of a non-uniformity of contribution over the length of the crystal, and the geometry necessary for the singly bent and doubly bent crystals. The total intensity and the resolution of LiF and graphite are discussed, in particular, it is noted that the performance of monochromators with randomly oriented samples is quite different than their performance with samples showing preferred orientation or grain effects.

A new diffracted beam monochromator based on the Rowland focusing geometry is described.

The incorporation of carbonate in the apatite causes a decrease in crystallite size as demonstrated in precipitated apatites prepared at 37°C. Carbonate disturbs the crystallization of the growing apatite crystallites to such an extent that materials with more than 15 wt% CO3 gives an ‘amorphous’ x-ray diffraction pattern. The incorporation of carbonate in precipitates prepared at 100°C. causes a shortening of the a-axis and a lengthening of the c-axis which is proportional to the carbonate content, supporting the concept that in these apatites, CO3 substitutes for PO4 (11). X-ray diffraction linebroadening studies of CO3-apatites precipitated at 100°C and electron micrographs show that the size and shape of the crystallites change from long needles to smaller rods to tiny spheroids, depending upon the amount of CO3. Carbonate causes the bonding in the apatite to become weaker and more isotropic, which results in the small spheroidal crystals.

This paper reports the effect of carbonate on lattice parameters and morphology of carbonate-apatites which have been prepared by the conversion of rnonetite, CaHPO4 in hot carbonate solutions. The structural effects of CO3 on the apatite is further reflected by the modification of the vibrations of the PO4 groups in the infrared absorption spectra. The morphology of ‘amorphous’ CO3- containing apatitic precipitates and that of CO3∼apatite with high CO3 content (prepared at 100°C) is similar, i.e., spheroidal in shape, but greatly differing in crystallite size.

This paper reports the results of a detailed X-ray diffraction study of a new phase-transformation observed in SiC crystals grown by a vapour-liquid-solid mechanism involving the hydrogen-reduction of methyltrichlorosilane. The 10.ℓ reciprocal lattice rows of these crystals, as recorded on X-ray diffraction photographs, reveal sharp reflections corresponding to the hexagonal close-packed 2H (ABAB….) structure and sometimes also corresponding to the cubic close-packed 3C (ABCABC…) structure. These reflections are invariably connected by a diffuse but continuous streak whose intensity is a measure of the random faulting on the basal planes. The crystals were needle shaped and the structure sometimes varied along their length.

Several crystals were annealed in an inert atmosphere at progressively higher temperatures and their 10.ℓ reciprocal lattice row re-examined to determine the annealing behaviour as well as possible structural transformations. For a number of dark green needles having a faulted 2H structure the 2H reflections disappeared around 1400° C and the 10.ℓ reciprocal lattice row revealed only a continuous streak with increased intensity around positions for 3C reflections. On further heating the structure went over to a strongly faulted 3C. Around 1600°C the appearance of a 6H structure became discernible while highly diffuse 30 reflections still persisted. The reversible part of the transformations, if any, could not be observed. Some of the structures were, however, found to be much more stable and did not transform even up to 1650° C.

The above results, in particular the discovery of a 2H-3C phase-transformation around 1400°C, throw fresh light on the thermodynamic stability of the different SiC types. The mechanism of the 2H-3C transformation, the possible influence of faults and impurities and the thermal stability of various SiC structures are discussed on the basis of the experimental results stated above.

This standard was produced by powder metallurgical techniques using known amounts of austenite. Using these techniques, 134 specimens were prepared. Because these standards are expected to be used primarily for the calibration of X-ray diffraction equipment, only one surface of each standard is certified, and these surfaces range from 3.1 percent to 5.2 percent in austenite content. To make the specimens, 310 stainless steel powder (austenitid) was blended with 430 stainless steel powder (ferritic) to make a mixture of 5 percent austenite in ferrite. The material was compacted, sintered, polished and etched so the austenite appears white and the ferrite, a deep brown. Then quantitative microscopy methods were used to determine the percentage of austenite near the surface. Furthers more, the 310 powder contains 20 percent of nickel while the 430 powder contains virtually no nickel. Therefore, after establishing a meaningful calibration curve, X-ray fluorescence analysis for the nickel content was also used as a direct measurement of the amount of retained austenite on the surface of the compact. Both procedures were carried out on fifteen specimens statistically selected from the total number of compacts produced. Agreement, within experimental error limits, was obtained between the X-ray fluorescence results and quantitative microscopy results. The X-ray fluorescence method was used to characterize all additional compacts. X-ray diffraction determinations of austenite content are in good agreement with the X-ray fluorescence and quantitative microscopy results. The compacts may be used as X-ray diffraction standards for austenite or in special cases as X-ray fluorescence standards for nickel content.

A set composed of barium-133 (7.8y), europium-152g (13.4y), bismuth-207 (30y) and americium-241 (458y), is recommended for energy and efficiency calibration of x-ray spectrometers. It is shown that the set offers over 30 energy lines in the range below 100 keV. The absolute efficiency calibration of Ge(Li) and Si(Li) detectors is demonstrated. The calibrated Ge(Li) was used for the measurement of fluorescence excitation yield from lead excited by various γ sources.

An x-ray spectrometer with experimental results is herewith described using a radiosotope source Fe55 having a halflife of 2.6 years. As a result of the disintegration, the managanese x-rays are capable of exciting fluorescent x-rays of such elements as sulfur, chlorine, potassium, calcium, scandium and titanium in aqueous solutions. These elements with the Ka wavelengths ranging from 5.3729 Å to 2.7496 Å may be designated as between the very soft x-rays on the one hand and the hard x-rays on the other. The x-ray spectrometer presently described has achieved a resolution of 136 ev, FWHM.

Simultaneously, these elements have also been quantitatively determined by conventional x-ray fluorescent spectrometers. Since one of the spectrometers is designed to operate in vacuum as well as in helium or air, determination of sulfur, potassium and calcium were carried out in vacuum. Determination of chlorine was carried out in a helium atmosphere, Calcium, scandium and titanium were determined in air with an air-path spectrometer.

In the present study aqueous solutions containing these elements were used. The use of aqueous solutions has the inherent advantages of being homogeneous and free from effect of particle size.

A compact X-ray energy spectrometer has been developed consisting essentially of a radioisotope X-ray source, a lithium-drifted silicon (or germanium) detector and a small computer. Interchangeable sources enable efficient excitation of K X-rays from Na to U and L X-rays from about Ag to U. Energy resolution of K X-rays from adjacent elements down to Na is possible. Depending on the source and the part of the spectrum examined, the characteristic X-rays from up to about 15 elements can be simultaneously excited and measured, for either qualitative or quantitative multi-element analysis. The computer stores detected spectra and performs simple data processing such as peak recognition, background subtraction, peak integration, ratioing and solution of linear equations.

The analysis reported in this paper is the determination of V, Cr, Fe, Co, W and Mo in tool steels and is intended to illustrate the capabilities of the radioisotope X-ray fluorescence analysis technique, and the instrument, for multi-element analysis of a system having fairly complex interelement effects.

A 100 mCi Pu-238 source was used to excite the K X-rays of V, Cr, Fe, Co and Mb and the L X-rays of W. The count time used was five minutes per sample. Data reduction consisted essentially of peak integration, background subtraction and solution of sixth order linear matrices of a modified Criss-Birks type. The 36 matrix coefficients were determined using six standards, and were then used to analyze seven other analyzed specimens which were treated as unknowns. The measured values of concentration were in very good agreement with the quoted values. An iteration technique was employed to reduce errors in the matrix inversioiis.

Lobov et al., in Leningrad, and workers at this laboratory have been working on the idea of using x rays from radioactive sources for x ray diffraction analysis. The Russians have been using iron-55 produced by the (n, Y) reaction in their work with a small focusing camera which operates in the back reflection region. We have been using iron-55 produced by the (p,n) reaction in conjunction with a small Debye-Scherrer camera. The preliminary work of this laboratory was reported at this conference two years ago. At that time a 13 mCi iron-55 source was used in a two inch diameter Debye-Scherrer camera to obtain x-ray diffraction patterns of LiF. The exposure times were of the order of 120 hours and the reflection from the 200 plane was about 3 degrees wide. Since that time a new and more intense source has been constructed at Oak Ridge National Laboratories. With the new source it was possible to produce LiF diffraction patterns of the same density and resolution as before in a period of less than ten hours.

The above mentioned diffraction patterns were made with the LiF powder placed in a 1.0 mm diameter glass capillary. After reduction of the glass capillary diameter to 0.5 mm and appropriate reduction of the collimator width, we were able to improve the resolution considerably with no accompanying reduction in line density. The LiF patterns obtained in this way required an exposure time of about 20 hours and the width of the reflection from the 200 plane has been reduced to about 1.5 degrees.

Hence we are able to report a reduction in exposure time from 116 hours to 20 hours and an increase in resolution by a factor of two over the data reported here two years ago. Thus the concept of using x rays from an isotope for powder diffraction has changed from a laboratory curiosity into a technique with practical possibilities. Both sources mentioned above were produced by the (p, n) reaction. The 135 mCi source had a specific activity of about 400 Ci/gm. Since iron-55 sources have been made with specific activities of about 1000 Ci/gm, a considerable decrease in exposure time could be accomplished by using such a source. The application to this work of a position sensitive proportional counter as developed by Semmler will also be discussed.

Solid solution decomposition of several aluminumrich aluminum-zinc-silver alloys were investigated using x-ray small angle scattering, x-ray diffraction (Guinier and Dewolff camera) and transmission electron microscopy. A decomposition sequence was observed directly fay means of hot stage electron microscopy, to be:

G.P. zones were observed to exist in all of the ternary Al-Zn-Ag alloys used in this investigation. Only one type of G.P. zone was detected and evidence is given which indicated that the G.P. zone formation was governed by the existence of a metastable miscibility gap. Experimental results also indicated that the lattice of the matrix is distorted by the presence of the G.P. zone.

A transition phase, designated ɛ', was observed to nucleate on defects in the matrix and to have a hexagonal close-packed structure. The ɛ' phase is partially coherent and much more regular in spatial distribution than the equilibrium ɛ phase.

This paper is an effort to quantify such variables as penetration depth, intensity, and defect contrast in reflection X-ray topographs. The analysis includes an appropriate combination of geometrical, polarization, absorption, and scattering factors. Quantitative measurements have been made for a variety of diffracting planes and wavelengths on Si and Ge. The calculations also fit qualitatively (fluorescent screen intensity} with observations on Zn, ZnO, CdS, GaAs, GaP. Topographs from some or all of these materials will be shown to illustrate how these calculations can predict useful diffraction conditions.

Increasing attention is currently focused on the generation of characteristic x-ray by proton irradiation. This has the advantage of yielding “clean” x-ray- i. e. free from background brerasstrahlung radiation, from even the lightest elements. The disadvantage is that the yields are naturally much lower than those produced by electrons of the same energy. A recent study has extended characteristic x-ray production to a variety of heavy ions and has shown that the cross- sections for the production of clean x-rays are often higher , by as much as several orders of magnitude, than those produced by protons of the same energy. In addition, there has emerged a further advantage, viz. the ability of specially chosen heavy ions to excite characteristic x-ray from a particular element in a selective manner. Since heavy ions penetrate only a few hundred Angstroms in to most solids, the phenomenon can be used as the basis of a technique for the examination of surface deposits, or to measure depth distributions of impurities. For example, Kr ions can be used t o determine the range distribution of antimony which had been implanted in to silicon at 100 keV. The antimony concentration was determined as a function of ∼ 150 Å steps, and was found to exhibit a maximum concentration of ∼ 1 part in 103 of silicon at 450 Å below the surface, falling to zero concentration at ∼2000 Å a depth. In the past, in order to obtain the required degree of sensitivity, such range determinations have relied on radio active tracer techniques.

An entirely new type of proportional counter has been developed during the course of these studies. This instrument, because of its special construction, can be positioned very close to targets in non-dispersive studies, so as to collect the highest possible fraction of emitted x-ray. It incorporates a replaceable anode unit, together with a built- in miniature head amplifier, and exhibits extremely good performance, particularly for ultra-soft x-ray. In addition, rotation of a dial on the end of the counter body allows alteration of the active gas volume during operation, and so permits tuning into x-rays of a particular energy.

A systematic study of the production of characteristic X-rays by both light and heavy charged particles has been made. Using protons in the energy range 70-200 keV, data have been obtained for twenty-one X-ray lines encompassing a wavelength region from 1.44 to 44.00 Å from K-, L-, M-, and N-shells of elements with 6 ≤ Z ≤ 92. Additional X-ray production efficiencies have been measured in the K-, L-, M-, and N-shells using incident H2+, He++, N++, O++, and Ar++ ions in the energy range 90-400 keV. The ion beams were obtained from a 300 kV electrostatic accelerator, and beam analysis was obtained using a 7 kilogauss analysing magnet.

The data for proton excitation show that, for X-rays of a given wavelength, the X-ray production efficiency increases with the principal quantum number of the atomic shell being excited. These results contradict results reported by Sterk et al, but agree with results obtained earlier by Khan et al.

The results also show that the use of heavy ions (z > 5; obtains X-ray yields which are orders of magnitude higher than a repredicted by the direct scattering theory as used for protons and alpha particles.

Ion excitation of X-rays has been applied to the study of the oxidation kinetics of iron as part of a surface physics program. The wide range of target penetration depth as a function of both mass and energy of the ion has allowed us to study oxide film thickness as a function of oxidation temperature and impurity depth and concentration. Data are presented for protons and argon ions incident on high- purity ion with surface oxide films varying in thickness from 35 Å to 750 Å. Oxygen and carbon sensitivities to equivalents of fractional monolayers are routinely obtained using nondispersive analysis of the X-rays.

The possibility that primary recrystallization textures are influenced by local inhomogeneities of deformation induced in the regions of grain boundaries has been confirmed by comparing the cold rolling and the annealing textures of polycrystalline pure irons which were different in the grain size prior to cold rolling. Analyses were made for the effects of deformation on crystals, namely storage of lattice strain and orientation spread, with application of X-ray diffraction techniques, in order to elucidate the role of in homogeneities of deformation on recrystallization texture formation. Apparent correspondence was found between the orientation dependence of stored strain energy and the textural change on recrystallization. This is a scribed to oriented nucleation in high energy blocks, in the case of originally large-grain material in which the effects of inhomogeneities of deformation are small. But discrepancies arise on this basis in originally small - grain material in which the effects of inhomogeneities of deformation are thought to be considerable. The discrepancy is inferred to arise as an effect of local inhomogeneities of deformation, from the change in the trend of rotational orientation spreads from, a stable orientation and the extent of development of potential nuclei of recrystallization at high energy blocks in the orientation spreads. The change is considered to give rise to the variation in amount of microstrain distribution, which is expressed in recovery characteristics of lattice strains and in the dependence of microstrains on the column length as analyzed by following the procedure of Warren-Averbach.

A new approach to the analysis of preferred orientation in body centered cubic sheet materials is presented. The technique utilizes normalized extended inverse pole figures (2θ = 16 to 150°) taken in the plane normal, rolling, and transverse directions. Possible texture components are defined to be all unique sets of three mutually orthogonal crystallographic planes included in the diffraction pattern up to 150° 2θ for a total of 56 possible components. A computer program has been developed to calculate the contributions of various texture components relative to the three principal directions by two computer implemented algorithms, probability and successive decrementation. The two methods exhibit an apparent high correlation.

The calculated results are compared to monochromated direct pole figures for a highly textured material. The agreement is excellent.

Measurements have been made on the FeLII/LIII intensity ratio on oxide free iron surface produced by evaporating a 50 Å Ti film on iron. These results show that the reported increase in the FeLII/LIII ratio with decreasing accelerating voltages is due largely to surface oxide and not self absorption. Also, for the vacuum presently used by soft x-ray spectroscopists the oxide surface on metals contribute strongly to the soft x-ray spectra of the bulk material for accelerating voltages below 4 kV.

Molecules or ions usually exist as discrete units, in crystals of chemical compounds. Intermolecular or interionic coValent interactions are slight so the bond structure of such, solids is very similar to the pattern of energy levels in each individual molecule or ion. Simple molecular orbital theory can therefore be used to generate a qualitative picture of the energy levels in a molecule or an ion; and this picture can then be used directly to interpret X-ray emission spectra. The application of molecular orbital theory, using group theory to simplify the calculations is described for a tetrahedral unit ML4. The origin of peak shifts and of low-energy satellite peaks are rationalised. A consideration of orbital amplitudes shows that the ‘cross-over' theory of O'Brien and Skinner cannot explain the observed intensities of low-energy satellite peaks. It is suggested that the use of the M. 0. model for the interpretation of X-ray emission spectra permits far greater analytical and structural use to be made of peak shift and satellite data. Ligands can be identified even when their own characteristic emissions are not detected (e.g. oxygen and fluorine). Relative peak intensities can be correlated with atomic orbital participation in bond formation. Such information is of great interest to chemists and can often be used to identify the bonding r61e of specific orbitals (e.g. the 3d orbitals of second row, main group, elements).