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By Howard Martens, Pol Duwez

IN two papers published in 1949, alloys of chromium with the refractory metals tungsten, molybdenum, tantalum, and columbium were investigated in view of their possible use as high temperature resisting materials. For the Cr-Ta system, a partial phase diagram was presented and the only intermediate phase was identified at Ta2Cr3. A phase of the same composition was also observed in the Cb-Cr system. The X-ray diffraction data presented in these papers, however, were insufficient for crystal structure determination. It is shown in the present study that the only intermediate phase in both the Ta-Cr and the Cb-Cr systems corresponds to the ideal stoichiometric ratio TaCr2, or CbCr2. Both structures are cubic, MgCu, type. At high temperature, however, TaCr2 has a hexagonal MgZn, type structure, which can be retained at room temperature by fast cooling. The alloys were prepared by melting in a helium arc furnace on a water-cooled plate. The design of the furnace was essentially the same as that described in ref. 3. Some alloys were also obtained by sintering compacts made of the mixed powders pressed at 80,000 psi. The sintering was carried on for 4 hr at 1375°C. The tantalum and columbium powders were supplied by Fansteel Metallurgical Corp., North Chicago, 111. The tantalum powder was the reagent grade, with a particle size smaller than 400 mesh and a total impurity content less than 0.1 pct. The columbium powder was smaller than 325 mesh and contained approximately 0.1 pct C and traces of Fe, Ti, and Zr. The electrolytic chromium powder from Charles Hardy, Inc., New York, was smaller than 300 mesh and contained about 0.1 pct Na, 0.05 pct Ca, and traces of Cu, Al, Mg, Si, and Co. Powder diffraction patterns were obtained with a 14.32 cm camera, using copper Ka radiation filtered through nickel foil. The powder pattern of the TaCr2 alloy obtained by sintering at 1375'C was different from that obtained on the same alloy rapidly cooled from the melt. Contrary to this result, the powder pattern of CbCr2 was the same, whether the alloy was made by sintering at 1375°C or by melting, and was similar to that of the TaCr, sintered. It was also found that the structure of the TaCr2 specimen obtained by melting was retained after heating for 4 hr at 1590°C, but transformed into the structure found in the sintered specimen after heating for 4 hr at 1375°C. Hence, the structural change of TaCr2, appears to be a reversible polymorphic transformation. CbCr2 and ToCr2 Structure, Low Temperature Form By using large scale Hull-Davey charts, the powder pattern of CbCr, and of the low temperature form of TaCr2 were readily interpreted on the basis of a face-centered cubic lattice with a parameter of approximately 6.95 kX. The indices of the reflections together with the values of sin' 0 are given in Tables I and 11. From this list of observed reflections, it appears that the (200), (600), (024), (046), and (028) reflections are missing. The lack of (h00) reflections for h 4n indicates a four-fold screw axis. The missing (Okl) spectra for k + 1 An indicate the existence of a diamond glide d. The combination of these symmetry elements can be found in the O— Fd3m space group, which is therefore the most probable one. After having determined the approximate density of TaCr, by the immersion method, the number of molecules per unit cell was calculated and found to be nearly eight. This information, added to the fact that the most probable space group is O leads to the consideration of a structure of the MgCu2 type, in which the atoms have the following positions: 8 magnesium in a and 16 copper in d. On the basis of this structure, intensities were computed by means of the usual formula: 1 cos'20 I a sin2 cos where F is the structure factor; 8, the Bragg angle: and p, the multiplicity factor. As shown in Tables I

Jan 1, 1953

By Paul Pietrokowsky

THE formation of intermediate phases in the solid state reaction of titanium with silicon, germanium. and tin (of subgroup 4B in the periodic table) was the subject of a recent paper.' Further investigation of the system Ti-Sn revealed the presence of a new compound on the titanium-rich side of this phase diagram. Metallographic evidence indicated that this new phase was situated very close to 75 atomic pct Ti. The present work is concerned with the crystal structure of the intermediate phase Ti3Sn. Iodide-process titanium metal, furnished by the New Jersey Zinc Co., was used in this investigation. The metallic tin was received in powder form from Charles Hardy Inc., New York; its purity was 99.80 pct. The titanium rod was machined into small cups 1 cm in diam and about 1.5 cm in height. The tin powder was compacted, melted, and then placed in the titanium cups and alloyed by electric arc melting in a helium atmosphere. The alloys, weighing approximately 8 g, were sealed in evacuated quartz tubes and homogenized at 1030°C for 5 days. This isothermal heat treatment was terminated by a water quench from the soaking temperature. Filings of the alloyed pellets were sealed in evacuated quartz bulbs and quenched from 1030°C into liquid argon. A 14.32 cm Debye Scherrer X-ray camera was used for the powder diffraction study. The copper radiation was filtered. X-ray diffraction data for the compound Ti3Sn are given in Table I. The data were indexed on the basis of a hexagonal lattice. Good agreement between observed and calculated values of the square of the reciprocal interplanar spacings was obtained with the following expression: (1/d)2 = 0.03810 (h2 + hk + k2) + 0.04410 (l2) Unit cell parameters were calculated by the method of least squares from the reflections (20.3), (22.2), (40.1), and (42.1); ao = 5.916 & 0.004A, co = 4.764 ± 0.004A, and co/ao = 0.805. The relatively small size of the unit cell allowed the unambiguous indexing of most of the reflections from planes of large spacing. An inspection of the assigned indices (Table I) reveals the absence of (hk.l) reflections when 1 2n. A systematic absence of this type leads to the space group C 6/mmc or one of its subgroups. Assuming, for a first approximation, a linear increase in the density of titanium with the addition of tin, it follows that there are two stoichiometric molecules of Ti3Sn per unit cell. The density calculated from X-ray measurements is 5.194 g cm-'. At this point it became clear that Ti3Sn might be isomorphous with Mg3Cd. The 6 Ti and 2 Sn atoms were placed in the following positions of space group D4 6h, C 6/mmc: 6Tiin (h): X 2X 1/4; 22;; 1/4;Xx 1/4;x2x3/4; 2x x 3/4; x x 4; with x = 516 2 Sn in (c): 1/3 2/3 1/4; 2/3 1/3 3/4.

Jan 1, 1953

By Pol Duwez, Paul Pietrokowsky

The crystal structure of the compound TisGeS has been determined from X-ray powder diffraction data. Related silicon and tin compounds have been found to be isomorphous. Unit cell dimensions, axial ratios, and parameters for equivalent atomic positions are given. THERE is, at present, only meager information pertaining to the solid state reactions of titanium with the elements in group 4B of the periodic table (silicon, germanium, tin, and lead). The only two compounds whose crystal structure has been established are TiSi² and TiGe² (references 1 and 2 respectively). These two compounds are isomor-phous and have an orthorhombic symmetry D242h— Fddd. The titanium-rich regions of the constitution diagrams of titanium-silicon, titanium-tin, and titanium-lead have been investigated by Craighead et al.³ While valuable information concerning the alpha solid solubility of these three elements in titanium was obtained, no light was shed on the existence or nature of the titanium-rich compound in these systems. The present study is concerned with the crystal structure of the intermediate phases Ti5Si ?, Ti³Ge³, and Ti5Sn³, which were found to be isostructural. The alloys were prepared by mixing the pure metal powders in the desired proportions, pressing the mixture into pellets, and melting them in an electric arc furnace in the presence of a helium atmosphere.& After melting, the specimens, weighing approximately 5 g, were sealed in evacuated quartz vials, homogenized at 1038°C for three days, and quenched from that temperature. Powder diffraction patterns were made with a 143.2 mm diam Debye-Scherrer X-ray camera in which the Ievins and Straumanis film arrangement was utilized. Filtered copper radiation was used throughout the entire investigation. A study of the powder patterns of a series of alloys of various compositions indicated the presence of a compound around a composition corresponding approximately to a ratio of 3 titanium to 2 silicon, germanium, or tin. From a visual examination of the diffraction patterns, it was evident that the silicon and germanium alloys were iso- morphous. For small angle reflections, the powder pattern of the tin compound was analogous to that of the silicon and germanium compounds, but after the first ten reflections, the similarity was no longer clear. The powder pattern of the germanium compound was selected for indexing, since it exhibited a weak small angle reflection and clearly resolved doublets in the back-reflection range. Good agreement between observed and calculated values of (1/d)² was found by indexing the pattern on the basis of hexagonal symmetry. For the hexagonal system:

Jan 1, 1952

By J. L. Taylor, Pol Duwez

THE present knowledge of the Ti-Al system is limited to the portion of the diagram extending from pure aluminum to the intermetallic compound TiAl3' A preliminary investigation of the titanium-rich Ti-A1 alloys revealed that the solubility of aluminum in titanium is quite extensive and that the transformation temperature of titanium is raised by alloying with aluminum. From an X-ray diffraction study of alloys containing up to 75 atomic pct Al (TiAl3), the phase boundaries at 750°C were located as follows: the a titanium solid solution extends from 0 to about 36 atomic pct Al, a two-phase region exists from 36 to 46 atomic pct Al, and an intermediate phase of varying concentration extends from 46 to 62 atomic pct Al. The purpose of the present paper is to describe the crystal structure of this new phase. The alloys were prepared by melting in a helium arc furnace on a water-cooled copper plate, using a furnace essentially the same as that described in ref. 2. The titanium metal was of the iodide type furnished by the New Jersey Zinc Co., and a piece of pure aluminum (99.99 pct) was obtained through the courtesy of the Aluminum Co. of America. After melting, the samples, weighing approximately 5 g, were sealed in evacuated fused silica tubes and homogenized for 4 hr at 1000°C. The specimens were then held for 10 days at 750°C and rapidly cooled to room temperature. Filings were then taken from each sample, sealed in evacuated vials, annealed at 750°C for 4 hr, and rapidly cooled to room temperature by quenching the vials in water. Powder diffraction patterns were obtained with a 14.32 cm diam camera, using K copper radiation filtered through a nickel foil. Structure Determination The X-ray diffraction patterns of the alloys containing 46, 50, 55. 60, and 62 atomic pct Al were identical, except for a slight shift in the positions of the reflections. The alloy containing 55 atomic pct Al was chosen far structure determination. The powder pattern contained 37 reflections and the a, doublets were well resolved in the back-reflection range. The relatively small number of reflections and the sharpness of the pattern were considered as an indication of a simple atomic arrangement in a relatively small unit cell of high symmetry, and an attempt was therefore made to solve the structure without single crystal work. A satisfactory fit was found on a large scale Hull-Davey tetragonal chart for an axial ratio of approximately 1.45. All the reflections were readily indexed and the tentative unit cell dimensions were computed to be a - 2.81 kX, c - 4.07 kX, and c/a = 1.448. The indices (hkl) and the values of d and sin2 A are given in Table I. The agreement between observed and computed sin2 is quite satisfactory. Once the unit cell was known, the details of the structure were readily found. First, it is obvious that the number of atoms per unit cell cannot exceed two, since more than two atoms would lead to a density greater than that of pure titanium. The next logical step is to assume that the two atoms occupy the corner and center of the cell. If this assumption is correct, the structure may be described as follows: space group D1, - P 4/mmm; one titanium atom in a: 000; one aluminum atom in d: 1/2 1/2 1/2: and no extinctions. Assuming this structure to be the correct one. intensities were computed by means of the usual equation: sin2 0 cos 0 where F is the structure factor; 8, the Bragg angle. and p, the multiplicity factor. The calculated values of intensities are compared in Table I with the visually estimated intensities. The agreement is quite satisfactory and the structure is therefore confirmed. The crystal structure of TiAl just described is the same as that of AuCu ordered. The AuCu ordered

Jan 1, 1953

By Bernard S. Borie

THE U-A1 binary system has been studied by Kaufmann and Gordon.' They have shown that three intermetallic compounds occur in the system: UAl², UAl², and a third compound tentatively identified as UA15. UA1³ is simple cubic, a, = 4.26A. Its unit cell contains one formula weight, and it is iso-morphous with AuCu³. UA1² is face-centered cubic, a, = 7.72A, with eight formula weights per unit cell. Rundle and Wilson have shown that it is iso-morphous with Cu²Mg.² A Debye-Scherrer pattern of the Al-rich compound indicated a more complex structure than either UA1² or UA1³. The following is a report of an investigation of the crystal structure of this compound and a determination of its stoi-chiometric formula. A melt of uranium (99.9 pct pure) and aluminum (99.9 pct pure) was prepared which contained about 25 pct U by weight. It was cooled from 950" to 650°C at a rate of 500" per hr and then taken from the furnace and air cooled. An X-ray diffraction pattern of the ingot showed only lines of aluminum and the Al-rich compound. Filings from the ingot were reacted with a solution of sodium hydroxide, producing a fine black powder, the diffraction pattern of which showed no traces of aluminum. A comparison of the Debye-Scherrer pattern of our sample with the data published by Kaufmann and Gordon1 showed that it is identical with the Al-rich phase which they reported. Single crystals were obtained by cooling the melt more slowly (about 50°C per hr). After reaction with sodium hydroxide, the crystals appeared as small black needles attached to the ingot surface. Cell Size, Space Group, and Uranium Positions A series of Weissenberg photographs for rotation about two of the crystallographic axes, taken with copper radiation filtered through nickel foil, revealed an orthorhombic cell of dimensions: a = 4.41 ± 0.02A b = 6.27 ± 0.02A c = 13.71 ± 0.03A Reflections of the type hkl were observed only if: h + k + I = 2n, of the type hkO only if: h = 2n and k = 2n, of the type h01 only if: h + 1 = 2n, and of the type Okl only if: k + 1=2n. Hence, the cell is body-centered with an 001 glide plane. The evidence for the existence of the glide plane is the observed extinction of 23 possible re- flections of the type hkO with at least one index odd. There are only two space groups consistent with these data: C"" — I2ma and D28 2h — Imma.³ he possible sets of atomic positions for these space groups are: 12ma: (0 0 0; ½ ½ ½) + 4: (a) x 0 %; x % % (b) x ¼ z; x ¾ Z 8: (c) x y z; x y z; x, ½ + y, Z x, M - y, z Imma: (0 0 0; ½ ½ ½) + 4: (a) 0 0 0; 0 ½ 0 (b) 0 0 ½; 0 ½ ½ (c) ¼ ¼ ¼; ¾ ¼ ¼ (d) ¼ ¾ ¾ ; ¾ ¾ % (e) 0 ¾ Z; 0 ¾ z 8: (f) x 0 0; x 0 0; x 1/2 0; x ½ 0 (g) ¼ Y ¼; ¾ Y ¾; ¾ y ¼; 1 y ¼ (h) 0 y z; 0; ;; 0, ½ + y, z; 0, l/2 - Y, Z (i) x 1/4 z; x ¾ z; ¼ z; x ¾ z 16: (j) xy z; x y z; x y z; x y z; x, ½ + y, Z; x,½ - y, z; x, ½ - y, z; 11 1, + y,Z Though density measurements on different samples were found to vary somewhat, they were all within the range 5.7 * 0.3 g per cu cm. If it is assumed that the unit cell contains four formula weights of UAl,, it is 6.5 g per cu cm. If there were as many as eight uranium atoms per unit cell, the

Jan 1, 1952

By F. W. Glaser, Benjamin Post

A LTHOUGH most transition metals form a wide variety of boride compounds, the existence of only one zirconium boride, ZrB2, had been established prior to this investigation.' The crystal structure and some properties of a hitherto unreported zirconium boride, ZrB12, are described in this paper. Only one other dodecaboride of a transition metal, UB12, has been reported up to the present.' Chemical analysis of the new compound showed 44 pct Zr and 56 pct B, compared with 41 pct Zr and 59 pct B computed for ZrB12. The difference is within the range of error of the analytical method employed. ZrB12 shows marked metallic properties. It is obtained as a fine black powder. Measurements of electrical resistivity were made at —79°C, + 22°C and +64°C. At 22°C the electrical resistivity is approximately 60 microhm-cm. Over this range the temperature coefficient of resistivity is +0.00162. The thermal conductivity at room temperature is 0.122 watts per cm per "C. The product of the electrical resistivity and thermal conductivity is therefore 8.05, which is not far from the normal Wiedemann-Franz ratio (approximately 7.5 at room temperature). These measurements were made on hot pressed samples which were not always high density specimens. The hardness of ZrB12 on the Rockwell A scale varies between 92 and 92.5. Crystal Structure Determination Single crystals of ZrB12 of a size suitable for X-ray diffraction analysis could not be obtained and powder samples had to be used. Filtered Cu radiation was used throughout. Powder diagrams were indexed on the basis of a face-centered cubic unit cell. After correction for film shrinkage, a Bradley and Jay extrapolation³ to ? = 90" indicated that a, = 7.408 ±0.002A. The volume of the unit cell is 406.5A.V he assumption that there are four "molecules" of ZrB12 per unit cell leads to an X-ray density of 3.63 g per cc. The measured density is 3.7 g per cc (as measured by the immersion method). Relative intensities of reflections were determined by integrating the intensities of diffraction peaks using the count register of a North American Philips wide range spectrometer. Intensities measured in this way showed good agreement with photographic intensities estimated visually using multiple film techniques. The usual Lorentz, polarization, and multiplicity corrections were applied to the observed intensity measurements. There are striking similarities between ZrB12, and UB12. The unit cell of the latter is also face-centered cubic and contains four molecules. a, = 7.473, compared with 7.408 for ZrB12. The radius ratio rB/rU is 0.57; rB/rZr is 0.54. In both ZrB12, and UB12 the four metal atoms in each unit cell are in special positions; only the boron positions need be determined. The latter may be inferred from the extent to which diffraction of X-rays by the 48 boron atoms reinforces or weakens the diffraction by the metal atoms. This effect is relatively much greater in the case of the zirconium compound. In their determination of the crystal structure of UB12, Berthaut and Blum' assumed holohedral symmetry (space group Oh5 , Fm3m) and reported that the U atoms are in positions 4(a): 000; 01/2 1/2; ½ 0 ½ ; ½ ½; the boron atoms were reported to be in positions 48(i) with x = 1/6: ½xx; ½xx; x½x; x½x; xx½; xx½; ½xx; ½xx; x½x; x½x; xx½; xx½

Jan 1, 1953

By L. Guttman

THE equilibrium diagram of the indium-thallium system was of interest to us in connection with a study of the superconducting properties of metallic solid solutions in progress at this Institute. For this purpose, a series of alloys was prepared covering the range from pure indium to 75 atomic pet TI, and X-ray diffraction patterns were obtained. Roughly speaking, the results indicated a region of continuous decrease in the axial ratio of the face-centered tetragonal structure from the value ca. 1.08 in pure indium to unity at about 23 atomic pct TI. From this concentration to the solubility limit, the structure was face-centered cubic, a form not reported by Hansen.1 At this point we became aware of the work of Valentiner,2 who had found the same structures at room temperature but had not investigated further the relationship between them. To study the transformation f.c.c.??f.c.t., and to clarify the phase diagram, we undertook the work reported in this paper and that which follows." Preparation of Alloys Pure indium and thallium* (both about 99.9 pct, as estimated from spectroscopic analyses) were weighed out in quantities sufficient to prepare 10 to 25 g of alloy of the desired concentration. (Occasionally indium was mixed with a previously pre- pared solution.) The metals were melted over a flame, in an open graphite crucible, stirred with a graphite rod, and poured into a graphite trough. The rough slug was hammered and swaged into a rod of 2 to 3 mm diam, and annealed in a drying oven at about 125°C for 1 to 2 days. Samples were taken from the rod for analysis, as well as for diffraction and other measurements. The thallium was determined by electrometric titration, using a modification of the method of Beale and co-workers.' The precision of analysis was generally about 2 0.2 pct of the thallium content. The rods were sometimes found to vary in thallium content as much as 1.5 pct from end to end, but since analyses were also made close to the segments used in the various studies, the composition was usually known as accurately as the analyses could be made. Where one less significant figure is given, the error is estimated to be ±0.4 pct of the thallium content. X-Ray Diffraction Measurements Three different cameras were used: (1) A 7 cm Debye camera, with oscillating specimen (manufactured by the Picker X-ray Corp., Cleveland, Ohio); (2) a 9 cm diam Debye camera of the type designed by Bradley;" (3) a 10 cm diam symmetrical focusing back-reflection camera (manufactured by Geo. C. Wyland, Ramsay, N. J.). Samples were prepared from the homogenized rods, either by filing under liquid nitrogen, or more often, in the form of wires or foils made by working at room temperature or liquid nitrogen temperature. Sharp patterns were obtained from specimens annealed at room temperature, although higher annealing temperatures were also used (cf. below). Generally, copper radiation was used; a few patterns were obtained with

Jan 1, 1951

By G. Y. Chin, A. R. Von Neida

The relationship between crystalline texture and magnetic anisotropy in a Co-10 pct Fe alloy has been investigated by means of X-ray pole .figures, hysteresis-loop tracings, and magnetic-torque measurements. The cold-rolled texture of a sample after 95 pct thickness reduction is of the "brass-type", that is, (110)[112/. At 500°C the cold-rolled material recrystallizes fo a (311)[112] orientation, plus a minor (210) [001] component. This texture persists up to 1400°C, at which point it is replaced by a secondary recrystallization texture, (111)[112]. Magnetic-torque measurements show that the easy axis of magnetization lies along the transverse direction in the cold-rolled material and changes to the rolling direction after primary recrystallization. This change is also reflected in the hysteresis characteristic; whereas the B-H loop along the rolling direction is nonsqunre with a low value of residual induction (750 vs 19,000 gauss at saturation) for the cold-rolled material, the annealed sample exhibits a very square loop with a large value of residual induction (16,000 gauss). Theoretical torque curves calculated from the texture data on the basis of magnetocystalline anisotropy energy compare favorably with the observed torque curves. Values of the crystal anisotropy constant, K1, obbained from these comparisons are in good quantitative agreement with single-crystal data. Furthermore, both the torque amplitude of the poly crystalline material and the magnitude of K1 obtained with a single crystal show an identical temperature dependence over the range from —195° 10 +220°C. It is thus conclzided that the magnetocrystalline anisotrpopy erlergy is chiefly I-esponsible. for the nzagnetic allisotropy of textured Co-10 pct Fe alloy. THE results of a study on the relationship between crystalline texture and magnetic anisotropy of an alloy containing 90 pct Co and 10 pct Fe by weight are reported in this paper. The alloy has an fcc structure: a saturation magnetization of about 19,000 gauss,2 and a nearly zero value of magnetoatriction.3 puzey4 has reported a large crystalline anisotropy constant of -7.4 X 105 ergs per cu cm, indicating the (111) directions as the easy axes of magnetization. Hence, texture variations resulting from cold work and annealing are expected to introduce a magnetic anisotropy in the polycrystalline material through the alignment of these (111) easy directions. In the present study, magnetic anisotropy of both rolled and annealed strips was determined by magnetic-torque measurements and hysteresis-loop tracings The results were correlated quantitatively with calculations based on texture data obtained by the X-ray pole-figure technique. It is established that the magnetocrystalline anisotropy energy is indeed chiefly responsible for the magnetic anisotropy of textured Co-10 pct Fe alloy. EXPERIMENTAL Material Preparation. The alloy nominally contained 90 pct Co, 9.5 pct Fe, and 0.5 pct Mn by weight, the chief impurities being nickel, carbon, and silicon (less than 0.5 pct total). The cast ingot was rolled to strips 10 mils thick and slit to 1 in. in width. After strand annealing at 900°C in a hydrogen atmosphere, these strips were further cold-rolled to various thicknesses down to 0.25 mil (97.5 pct reduction), with samples collected for study of the development of texture and magnetic anisotropy as a function of thickness reduction. subsequently, samples cold-rolled from 100 mils to 0.25 mil were obtained, thus extending the thickness reduction range to 99.75 pct. In addition, 0.5-mil samples cold-rolled from 10 mils were selected

Jan 1, 1965

By D. J. Sellmyer

In order to orient single crystals by the back-reflection method it is necessary to know the angles between the various crystallographic planes. These angles have already been published for the hexagonal close-packed metals magnesium, zinc, and cadmium.'

Jan 1, 1965

By Alan Lawley

AS part of a programme of experimental work on single crystals of rhenium and ruthenium, it was found necessary to have the crystallographic angles for these elements. The angles given in Table I were determined to the nearest minute of arc, by Univac Computer. The angle $ between (HKIL) and (hkil) is given by the formula: The angles given for rhenium should be particularly useful in view of the increasing interest in this element. For completeness, angular values are also given for cadmium zinc and magnesium; these form a more complete set of values than those given by Salkovitz.' The assistance of Professor J. Hobstetter and Mr. J. Crozier in the programming of this data is acknowledged. The work is sponsored by the Office of Naval Research under contract No. NONR 551 (19).

Jan 1, 1961

By C. A. Queener, W. L. Mitchell

In recent years bismuth telluride has received considerable attention, primarily due to its value as a thermoelectric material. Since there seems to be little dependence of thermoelectric effect upon crystal orientation1 many of those who have previously worked with this material have been unconcerned with knowing its crystallographic angles to any degree of accuracy. However, when one studies deformation modes, lattice stresses, or the aniso-tropy of mechanical properties of a material, knowledge of the interplanar angles and their relationships as depicted in a stereographic projection becomes essential. Lange2 originally published crystallographic data which described the structure of bismuth telluride as rhombohedral with the space group A more recent work by Francombe3 presented data which corroborated and refined the original findings of Lange. In addition, Francombe established that there is no coexistence of rhombohedral and hexagonal lattices in bismuth telluride as was suggested by Vasenin and Konovalov,4 and that the structure can be treated as a pseu do hexagonal structure with an axial ratio, c/a, of 6.95 for convenience of presentation and study. The interplanar angles and standard projections for several unalloyed hexagonal metals have been previously published,5-9 but the present work appears to be unique in that it presents data for a rhombohedral compound in pseudohexagonal form. As a pseudohexagonal structure, this material has an extremely large axial ratio as compared to the usual range of approximately 1.5 to 1.9 for the hexagonal metals. Since the interplanar angles are a function only of c/a, the angular relations between various planes for Bi,Te3 will be grossly different

Jan 1, 1965

By B. W. Veal, B. S. Chandrasekhar

THE Laue method of orienting single crystals requires the use of tables of angles between crystal-lographic planes, and between zone axes. Such tables have been published for cubic crystals, and some rhombohedra12 and hexagonal3 crystals. A table of angles between planes in ß-tin has also been published;4 these angles refer to only low-index planes, and are not particularly helpful in the actual indexing of spots on a Laue photograph. Furthermore, it is often useful to know the angles between zones which share a common low-index plane. We have calculated such tables of angles for ß-tin and indium, both between planes in principal zones, and between zones passing through principal planes. The results are given in Tables I and 11. The standard formulas were used, with c/a = 0.54554 for 0-tin, and 1.07586 for indium.

Jan 1, 1962

By K. Nassau

The Effect of tin and hydrogen on the C0 parameter of a titanium. specimens were capsule cooled in water to eliminate contamination by water. Deybe-Scherrer photograms were obtained in a 114.6 mm camera with CuKa radiation. The parameters shown in Table I and Fig. 1 were calculated from the 213 (8569°) and 302 (8173.5°) reflections? no attempt being made to correct for systematic errors. The principal difference in method of preparation of specimens between this investigation and that of Worner was the use of pickling by the latter to produce X-ray diffraction samples. The possibility that hydrogen introduced by pickling was responsible for the lower a and c-parameters was investigated with the same 80 pct HNO3- 20 pct HF solutions used by Worner. The 6 and 10 at. pct specimens, the parameters of which had already been determined, were pickled and the c-parameters obtained are also shown in Fig. 1. The a-parameters, not shown, are also diminished. The quality of the lines obtained from the unetched and etched samples was unchanged, being quite sharp in both cases. It is quite possible that if corrections for systematic error carried out that the parameters obtained for the unetched samples would approach the data of Worner. In any event, the parameters of the etched samples would be still lower. The data obtained here is evidence that hydrogen in solution has contracted the c and a -parameters. Crystallographic Angles of Calcium Tung-state (Tetragonal, c/a = 2.169) K. Nassau In connection with the preparation and orientation of single crystals of calcium tungstate (Scheelite -CaWO4), the need arose for a stereographic projection for this tetragonal material. There appear to be no tetragonal projections with a c/a ratio above that of indium1 (c/a = 1.522) in the literature. In addition to its use for calcium tungstate, such a projection might find other more general applications and is accordingly presented below. The most recent X-ray diffraction work on CaWO4 is that of Swanson, Gilfrich, and Cook,2 where a summary of previous work is also found. Lattice parameters given are: a = 5.242A, c = 11.372A, and c/a = 2.169. The material is tetragonal with space group Table I, giving angles between crystallographic planes (HKL) and (hkl), was calculated from the formula3

Jan 1, 1961

By A. J. Jacobs

THE purpose of this note is to draw attention to a set of tables, recently compiled in Rocketdyne Research Report No. 64-19, under the title "Crystal-lographic Data for Indexing Cubic Twin Reflections and Cementite (Fe3C) Reflections in Electron Diffraction Patterns."' These tables were an outgrowth of electron-diffraction work conducted over the past several years on steels, precipitation-hardening aluminum- and nickel-base alloys, molybdenum, tantalum, and tantalum-base alloys. The first table lists the indices of possible twin reflections for all the possible twinning planes in bcc and fcc lattices. The twin reflections correspond

Jan 1, 1965

By R. E. Frounfelker, W. M. Hirthe

INVESTIGATORS in the areas of plasticity, crystal growth, and stress analysis have a need for crys-tallographic data such as the interplanar angles. This information is utilized in the form of a stereo-graphic projection from which orientation determinations can be made. Calculations of mechanical properties, such as the critical resolved shear stress, require values for the angles between directions as well as the interplanar angles. Only a limited amount of this data is available for tetragonal crystals. The equations for these angles are relatively simple but because of the large numbers of angles involved and the infinite number of structures that could be investigated, it was decided to program these calculations on a high speed digital computer. The angle, 8, between two crystal planes (h1 k1 l1)

Jan 1, 1962

By D. L. Albright, R. W. Kraft

A technique is described whereby the study of crystal perfection through the use of conventional X-ray rockite curves is extended to three dimerzsions. Specinzens of unidirectionally solidified eutec-tic alloy which consist of a nearly perfect parallel arrangement of alternating Platelets of Al and CuAl2, but which contain lamellar faults have been analyzed by this technique in conjunction with X-ray microscopy. Analysis of the data has shown that some rotational symmetry about the growth direction occurs, that small groups of lamellae between faults diffract as a unit, and that the misorientation caused by a fault is on the order of a degree of arc. A eutectic-grain can be defined as that portion of a eutectic specimen in which the crystallographic orientation of each phase AND the microscopic or met-allographic orientation of the phase particles have fixed angular relationships one to another. Eutectic-grains of the A1-CuA12 eutectic, which is a normal lamellar eutectic, have been grown by unidirectional solidification and identified as such.1-3 To a first approximation, a eutectic-grain in this system consists of two interpenetrating single crystals which are related to each other and to the lamellae themselves as follows:

Jan 1, 1962

By D. L. Albright, G. A. Colligan

An investigation has been conducted to determine the nature of the crystallographic substructure of nickel and a 1.0 wt pct Ag-Ni alloy which had been undercooled 105°C prior to solidification. A rotating back-reflection X-ray technique and modified Weissmann diffractometer were used to orient single-crystal sections from these poly-crystalline ingots and to determine the substruc-tural features of these single crystals, The sub-grain size in the pure nickel ingot is 0.5 mm diam while the silver-doped nickel subgrain size is only 0.1 mm diam. The misorientation between adjacent subgrains is approximately 1 deg of arc in both ingots, and the spread of orientation of sub-grains about the mean orientation of the crystal is 5 deg of arc in both ingots. The addition of silver results in a stable impurity substructure which is preserved during isothermal solidification and subsequent cooling to room temperature. In the absence of silver the initial impurity substructure is destroyed by dislocation interactions which produce a secondary substructure which grows to a size five times larger than the initial substructure. THE process of undercooling a metal entails cooling of the molten sample below the equilibrium freezing point without the occurrence of solidification, i.e., by exercising proper constraint over the experimental variables contributing to nucleation in the melt. The current work of walker1 and Colligan Metal reports undercooling large continuous samples of nickel by imposing appropriate restrictions upon the parameters of solidification. The silver-nickel equilibrium diagram3 reveals the presence of a monotectic reaction at 1435°C. At this temperature the maximum solid solubility of silver in nickel is approximately 3 wt pct, but this solubility decreases with decreasing temperature and the solute is rejected as a silver-rich liquid phase at temperatures below 1435°C. Thus, the 1.0 wt pct solute should be held in solution during undercooling and solidification and subsequently precipitate as a silver-rich liquid phase at grain and subgrain boundaries following solidification during cooling below 1435. This assumes no solute segregation sufficient to cause the monotectic reaction. One would expect this second phase to inhibit grain and subgrain growth by retarding dislocation motion after solidification is complete. The effectiveness of silver addition in growth retardation of high-angle grain boundaries has been demonstrated by Colligan and suprenantS4 The principal [l00] dendrite growth directions in a 2 wt pct Ag-Ni alloy undercooled 53 all radiated from the nucleation site. A similar pure nickel ingot undercooled 59°C exhibited a random orientation of [l00] dendrite directions with respect to the nucleation site. Since undoped nickel ingots do not retain any evidence of the casting or solidification texture and silver-doped ingots do retain this texture, it is reasonable to assume that considerable grain growth has taken place in the pure nickel. These particular experiments were performed in order to reveal the differences, if any, in the features of the crystallographic substructure of undoped undercooled nickel and silver-doped undercooled nickel. 1) EXPERIMENTAL PROCEDURE Data are reported on selected specimens from two massive (approximately 260 g) undercooled ingots of nickel. One ingot consisted of electrolytic nickel and the other of this same material with 1.0 wt pct addition of high-purity silver. Powder patterns were taken of both the as-received and as-solidified materials; in all cases the reflections recorded were attributable to the individual elements nickel and/or silver. Fig. 1 is a. schematic diagram of the apparatus employed for the undercooling experiments. The equipment consists in part of a fused silica crucible for containing the charge. A fused silica tube encloses the system, which is covered by a brass cap to permit partial sealing of the inert atmosphere. This cap contains a hole through which a Pt-Pt 13 pct Rh thermocouple is inserted for temperature measurement. The charge is inductively heated under a purified argon atmosphere.

Jan 1, 1963

By L. Guttman, C. S. Barrett, J. S. Bowles

THE transformation from the face-centered cubic (Al) to the face-centered tetragonal (A6) structure in certain alloys of the indium-thallium system reported in the preceding paper1 exhibits many interesting crystallographic and metallo-graphic features, most of which presumably are similar to those of other cubic to tetragonal transformation such as, for example, the one which occurs in the chromium-manganese system,2 the one which, judging by microstructures and X-ray pat-terns,3 probably occurs in the copper-manganese system, the ones accompanying ordering in FePt,4 Copt,&apos; and AuCu,5 and the transformation near 115°C in barium titanate.6,7,8 If, as mentioned in ref. 1, the transformation is second order, the phases in equilibrium do not differ in composition, and it is both possible and likely that the mechanism is a diffusionless one. The present paper reports the results of a detailed study of the indium-thallium transformation and presents a theory for the atomic movements of the transformation which accounts for the observations. Experimental Crystallography of Transformation Markings The transformation from cubic to tetragonal in the indium-thallium alloys produces microstruc-tures of the type illustrated in fig. 1. These structures are observable either as relief effects produced on a smooth surface by the transformation, or after polishing and etching. These microstruc-tures are markedly similar to those found in copper-manganese alloys: iron-platinum alloys," and barium titanate,7,8 where it has been demonstrated that the lamellae are parallel to the (101) planes of the original cubic crystal. That the observed lamellae in indium-thallium alloys are also parallel to the (101) planes was proved by the following analyses performed on single grains in polycrystal-line samples containing 20.75 atomic pct T1. A study of the microstructures of a number of specimens revealed the fact that in many specimens the transformation markings continued unchanged in direction across the (111) interfaces of annealing twins. This at once demonstrates that the lamellae are parallel to a plane that is common to both parent and twin orientations, i.e., a plane in the zone <112>. This conclusion is compatible with the lamellae being parallel to (101) planes. To make a more complete determination of the habit plane of the lamellae, two grains were selected in which annealing twins ({Ill) twins) had been present in the high-temperature modification (cubic). The traces of the annealing twins, and of the transformation markings in both parent and twin crystals, were plotted together in stereographic projection, and a parent-twin pair of orientations was found that accounted for all lamellae as (101) planes. The projection of one of these twinned grains is reproduced in fig. 2. In view of these results the probability of there being another solution for the habit plane remote from (101) is very small, but to explore the possibility that the habit plane deviates slightly from (101), a more precise analysis was undertaken. In this, the orientation of a grain in the cubic modification was determined from a Laue back-reflection photograph taken with the sample at 90°C. The traces of the lamellae that formed in this grain on cooling were plotted in the stereographic projection

Jan 1, 1951

By R. W. Kraft

A comprehensive analysis of the crystallographic and metallographic structure of several Al-CuAl, lamellar eutectic grains solidified under equilibrium conditions has been performed. A consistent pattern was discovered which was interpreted in terms of a detailed atomistic model of an interface describable as: Interface II {111} AL 11 {211} <101>Al <120> ? Several arguments are presented to substantiate the theory. It is compared in detail with another interface model characteristic of the Wid-manstatten precipitate of CuAl2 in A1 at low Cu levels. In addition, a concept is proposed to help explain the structure of the compound CuAl2. It has been shown that the eutectic alloy between A1 and CuA1, can be forced to solidify as substantially parallel lamellae throughout a relatively large volume&apos; by appropriately controlling the solidification parameters of growth rate, thermal gradients, and impurity level and by causing solidification to proceed in a unidirectional fashion from one end of an ingot to the other. A typical ingot solidified in this manner shows three distinct zones along the length of the ingot, Fig. 1. At the head end is a region consisting of many different grains, some of which are elongated slightly in the direction of solidification. After a few centimeters of growth, this polygrained region gradually merges into the second zone which consists of a very few elongated coarse grains. The third zone at the tail end is a region of eutectic colonies caused by segregation of impurities. Microscopic examination of transverse and longitudinal sections of the ingots reveals that during the initial stages of growth (zone I) the lamellar structure is frequently highly distorted and twisted but that it straightens out in zone 11. This characteristic pattern suggests that nucleation of a eutectic grain begins randomly at the head end of the ingot, and that some particular orientation relationship between the phases is more favorable from an energy consideration than others for one reason or another, so that some grains grow and others which are less favorably oriented do not. The favorably oriented or "low energy" grains continue to grow until excess solute rejected at the advancing liquid-solid interface destroys the parallel lamellar structure by forming a cellular rather than a substantially planar interface. When this occurs, the parallel lamellae fan out and eutectic colonies are formed because the lamellae grow perpendicular to the local interface. Questions naturally arise as to the crystallographic nature of the "low energy" grains. What do the grains which persist into zone II have in common? Can this explain the stability of such grains during growth? To answer the first question it is necessary to determine the crystallographic orientation of the lamellae of each phase relative to one another. This has been done for Al-CuAl2 eutectic alloys by two different techniques on specimens prepared in different ways.2&apos;3 The results were different from each other and from a third orientation relationship between A1 and CuA1, reported for overaged A1-Cu alloys.4 The three orientation relationships are summarized below to illustrate their similarities and their differences. (001) ? 11 (001) A1; [l00] ? 11 [l00] Al Eutectic, Ref. 2 (001) 8 1) (001) A1; [1001 ?11 [1101 A1 Eutectic, Ref. 3 (001) ? 11 (001) A1; [l00] ? 11 [310] Al; Widmanstfitten, Ref. 4 It is not surprising that different orientation relationships were found by Ellwood and Bagley,&apos; and Takahashi3 since the solidification conditions were quite different. Nor is it surprising that Mehl, Barrett, and Rhines 4 found still another value since they were studying another type of alloy. Nevertheless, it would be expected that some logical and systematic pattern could be found if all the alloys were at equilibrium since the same two phases are

Jan 1, 1962

By A. E. Dwight

Lattice parameters were determined for eighteen equiatornic alloys of the CsCl-type structure, ten of which were previously un-reported. It was found that fomation of the CsCl-type structure in binary alloys of the transition elements is largely dependent on position of the elements in the periodic table. The relative size of the two elements was not found to be a controlling factor. A recent paper by Beck, Darby, and Arora1 corre-lates the occurrence of CsC1-type ordered structures with the position of the constituent elements in the periodic table for the first long period. It was also suggested that a definite increase in relative bond strength between unlike atoms occurred when, in binary alloys of iron-group elements, the other component is changed from a chromium-group element, to a vanadium-group element, to titanium. A later paper by Philip and Beck2 noted that the lattice contraction increased in the order CrFe, VFe, and TiFe. It was also noted by Philip and Beck2 that the lattice contractions of CsC1-type alloys decreased in the order: TiFe, TiCo, and TiNi, which is an apparent reversal of the contractions expected from the position in the periodic table. It was suggested that the increasing lattice contraction is an indication of increased stability, i.e., greater A-Bbond strength. The present investigation was carried out to determine whether the relation of the position in the periodic table to the formation of the CsC1-type structure was also correct for alloys involving the second and third long-period elements. A systematic search was made for CsC1-type structures among equiatomic alloys and for those found, the lattice contraction was determined. EXPERIMENTAL TECHNIQUE The elements Y, Gd, Ti, Zr, Hf, V, and Cb are designated the A group and the elements Mn, Re, Fe, Ru, Os, Co, Rh, Ir, Ni, Pd, Pt, Cu, Ag, and Au are designated the B group. Equiatomic alloys were prepared for 57 AB combinations. The alloys were arc melted in a multicrucible furnace3 in buttons ranging from 5 to 20 g. Chemical analyses were not made, as the charge weights agreed closely with those of the buttons after melting. The alloy buttons were homogenized at 800° to 900°C. Metal log raphic and X-ray specimens were prepared and heat treated at temperatures from 600° to 1200°C. Specimens for X-ray diffraction were usually ground to a powder in an agate mortar; however, needle-shaped solid specimens were used when the alloy was sufficiently ductile to permit their preparation. Diffraction patterns were taken with a Straumanistype Debye-Scherrer camera using filtered Cu or Co radiation. The lattice parameters were obtained in A by plotting the calculated a0 values against the cos29/sin 0 + cos2?/? function and extrapolating linearly to ?= 900. Metallographic control specimens were polished on cloth wheels with diamond paste and etched with various phosphoric and nitric acid reagents. RESULTS The eighteen equiatomic alloys listed in Table I gave evidence of a cubic structure with two atoms in the unit cell, although two of these cubic structures exist only at elevated temperatures and transform to a tetragonal structure on quenching. Nine of these eighteen alloys gave diffraction patterns with super-lattice lines showing that the structure is of the CsC1-type. The lack of superlattice lines in patterns of the other nine alloys may be attributed to the small difference in atomic scattering power of the components. Metallographic study indicates the occurrence of nine narrow single-phase fields at the AB composition. Any or all of these nine may also have a CsC1-type structure. The VFe alloy was found to have a CsCl-type structure by Philip and Beck2 through the use of CrKa radiation (for which the scattering factor of V is anomalously low), whereas the Cu radiation used

Jan 1, 1960