A Review of X-Ray Diffraction Studies in Uranium Alloys*

A REVIEW OF X-RAY DIFFRACTION STUDIES IN URANIUM ALLOYS*

Harry L. Yakel Metals and Ceramics Division Oak Ridge National Laboratory Oak Ridge, Tennessee 37830

The Physical Metallurgy of Uranium Alloys Conference Sponsored by the AEC Army Material and Mechanical Research Center, Vail, Colorado, Feb. 12-14, 1974.

-NOTICE- This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, com- pleteness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights.

*Research sponsored by the U.S. Atomic Energy Commission under contract with the Union Carbide Corporation.

,-r-f OF THIS DOCUV.i-!'" -,ID! ! if I \ '-'I ' ' A REVIEW OF X-RAY DIFFRACTION STUDIES IN URANIUM ALLOYS

Harry L. Yakel Metals and Ceramics Division Oak Ridge National Laboratory Oak Ridge, Tennessee 37830

ABSTRACT

Results of x-ray diffraction experiments investigating equilibrium structures of uranium-base substitutional alloys and routes of transitions between equilibrium structures are critically reviewed. In the first section data on equilibrium alpha, beta, and gamma alloys are presented together with a resume1 of work on the crystal structures of relevant stable intermetallic compounds.

Since many important physical and mechanical properties of practical uranium alloys are consequences of the production of metastable phases during heat-treatment or forming operations, the second part of the review is principally concerned with x-ray diffraction studies of such nonequilibrium phases — their structure and their mode of formation. Particular attention is given to the sequence of transitional phases found in gamma- quenched and aged uranium alloys, depending on aging time and temperature. The influence of external stresses imposed on the alloys before and during the transitions producing these phases is described in terms of the preferred orientations that may be observed by x-ray diffraction methods.

In the final section comparisons are drawn between the general structural behavior of uranium alloys and that of other alloy systems based on metals with allotropies similar to that of uranium.

INTRODUCTION

SCOPE AND OUTLINE

An attempt to fully describe all investigations of uranium and its alloys that have employed x-ray diffraction methods in some aspect is clearly beyond the scope of this conference and its proceedings. I shall therefore focus attention on work in which x-ray techniques have been used as a primary tool to determine atomic arrangements in equilibrium and nonequiiibrium uranium-rich metallic phases. Crystallographic studies of modes of deformation and twinning, measurements of preferred orientation, and determinations of structural effects of radiation damage in these materials will be mentioned only as they have relevance to this main area of interest.

* Research sponsored by the U.S. Atomic Energy Commission under contract with the Union Carbide Corporation. In the following section, I summarize our current knowledge of the structures of equilibrium phases of elemental uranium and some of its substitutional alloys. The alloy phases are selected on the basis of their relationship to the stable uranium allotropes and to the transitional structures often encountered in uranium-rich systems. Experimental and theoretical attempts to follow the course of transformations between these equilibrium phases are also briefly reviewed.

Discussion of the phase transformations leads quite naturally to a consideration of the occurrence and structure of nonequilibrium transition phases in uranium-rich alloys. I review x~ray diffraction studies of such phases with special emphasis on those concerned with structures closely related to the y (A2-type1) configuration of uranium.

Finally, and by way of summary, I compare the structural features of both equilibrium and nonequilibrium phases found in uranium-base metallic alloys with corresponding data for systems based on metals with similar allotropy. From this comparison, areas of unresolved problems and fields for future work emerge.

SOME GENERAL REMARKS ON X-RAY METHODS

While the results of x-ray diffraction experiments on uranium and its alloys have proven indispensable *-o an understanding of the structural phenomena observed in the materials, certain general problems have arisen that must be considered in any objecti. assessment of the state of our knowledge. The first has to do with the natural chemical reactivity of uranium in the metallic state. This reactivity often ensures that x-ray diffraction experiments carried out much above room temperature in a less- than-perfect vacuum or inert atmosphere have really studied materials contaminated by undesired and sometimes unknown impurities. The effects of these contaminants on the details of crystal structures, thermal expansion of lattices, or routes of transformation are usually indeterminate and probably significant.

A second problem concerns the high linear photoelectric absorption coefficients of uranium and uranium-rich alloys for commonly used x-ray energies. With a value2 of 153 cm2/gm for the mass absorption coefficient of uranium for Mo Ka x rays (A » 0.7107 A), and assuming a density in the range of 15 to 20 gm/cm3, one may expect 99% of the incident x-ray intensity to be absorbed in a surface layer only 15 to 25 urn thick. This implies that results of x-ray diffraction experiments on such materials will be quite sensitive to surface aberrations, a condition suggesting interesting applications if it is the surface whose structural state is desired but creating potential pitfalls if it is the bulk material about which we wish to know. The large absorption corrections that must be applied to observed diffracted intensities before they can be compared to values predicted from a model structure also represent a serious uncertainty in the precise derivation of detailed crystal structures of uranium-rich phases. Lastly, the multiplicity of crystallographic orientations usually found on taking a single crystal through a phase transformation, especially on cooling, constitutes a problem that must be recognized in analyzing x-ray scattering from the resulting composite. This is true of many systems, not only uranium alloys, and the literature contains several examples of errors that may occur if the situation is treated improperly.3 The hazards are more fully discussed by Curzon, Luhman and Silcock.4

STRUCTURAL STUDIES OF EQUILIBRIUM PHASES

URANIUM ALLOTROPES

Alpha Uranium

The structure of uranium metal at room temperature and pressure, designated a, is stable up5 to 667.3 ± 1.3°C and down6 to about -231°C (42 K). Its atomic arrangement was first correctly determined by Jacob and Warren,7 who analyzed powder x-ray diffraction data, and then confirmed by Lukesh8 from single-crystal data. The orthorhombic unit cell dimensions have been reported many times;7»9"15 best values14 would seem to be

a = 2.8536 A, b - 5.8698 A, a * 4.9555 A (all ±0.0001 A) as determined from single crystals using a Bond16 goniometer.

Four uranium atoms are located in this cell. They occupy the 4(e), (0, y, 1/4) etc., positions of space group Cmam with only a single positional parameter y to be determined from the observed diffraction intensities. The value of this parameter at room temperature and pressure has also been reported often;',11-13,15,17-20 t^e t,est value from x-ray diffraction experiments11*15 is 0.1025, while a recent neutron diffraction study20 gave 0.1027. Both results have uncertainties of 0.0001.

The structure of a-uranium based on these best parameters is shown in Fig. 1. It is a rather severe distortion of an ideal hexagonal close- packed arrangement (jb:a - 2.0570 rather than 1.7321, a:a - 1.7366 rather than 1.6330). Each uranium atom has four near neighbors, two at 2.754 A, two at 2.854 A; the other eight atoms that would complete its nearest- neighbor shell in a dose-packed metal are at distances of 3.263 A (4) and 3.342 A (4). These four interatomic distances, labelled d\, d23 d$3 and <£it, respectively, are included in Table 1 together with values for a variety of other a-like phases. Note that do and c?3 depend only on the unit cell dimensions, while d\ and d^ also depend on y.

The coordination geometry is unusual. Imagining the central uranium atom at the center of a sphere, two close contacts lie in the polar directions (±a, respectively) and two lie on the equator at an angular separation of 128.2°. The coordination polyhedron is roughly a trigonal bipyramid with one base atom missing. The disparity between the four short and the eight long contacts has suggested a stronger, more "covalent" character for the former and a weaker, more "metallic" character for the latter.21 ORNL-DWG 74-761

cum

BETH URANIUM (Sfll KTB NCPTUNIUH

SLPHR URANIUM BLPHfi NEPTUNIUM Fig. 1. Drawings of Equilibrium Structures of Uranium and Neptunium. For all but (3-uranium, close neighbor contacts are indicated by bonds; in the 3-uranium drawing these describe hexagonally connected main layers, and thicker bonds indicate abnormally short interatomic contacts. Unit cell edges appear as thin lines. For 3-uranium, a-neptunium, and 3- neptunium c is nearly vertical; for a-neptunium a is directed to the right; for~

Temperature Atomic Distance, A Corrugation Material Angle, Reference (K) di d2 d* d, (deg) a-U 873 2.813 2.911 3.263 3.355 127.24 10 a-U 298 2.754 2.854 3.263 3.342 128.19 14 a-U 50 2.7423 2.8364 3.2581 3.3352 128.32 15 a-U 4.2 2.7432 2.8444 3.2609 3.3322 128.02 15 ao-U-3.25 at. % Npa 4 2.7443 2.8329 3.2546 3.3291 128.08 30 Ul aJ-U-3.25 at. % Npa 4 2.741 2.8451 3.260 3.329 127.95 30 a-U-15 wt X Pu room 2.764 2.863 3.259 3.336 127.71 13 a'-U-6.9 at. Z Nba room 2.762 2.870 3.244 3.348 128.81 101 a"-U-10 at. % Mo room 2.746 2.866 3.162 3.267 128.27 113 2.264 3.386

Results for d\, dk, and assume y - 0.1025. The network of short contacts between an assembly of atoms takes the form of corrugated sheets that lie normal to the b axis of the unit cell (see Fig. 1). The smallest distances between atoms in adjacent sheets are d$ » 3.263 A and dn » 3.342 A. The corrugation angle ($ in Table 1) is the angle between the closest neighbor bonds, 128.2°. As shown by Cahn,22 the presence of the sheets has obvious implications for the mechanical behavior of the metal. Interstitial holes in the alpha uranium structure have been enumerated by Opinsky23 and reevaluated by Sutton, Eeles, and Price19 and by Rao and Tangri.21+ With a uranium atom diameter of 3.09 A, at 20°C there are eight tetrahedral interstices with diameter 0.75 A, eight square pyramidal interstices with diameter 1.04 A, and four octahedral interstices with diameter 0.88 A per unit cell.19 The latter are located at the centers of squares of atoms in each layer, while the tetrahedral and pyramidal holes are located between layers.

Variations in unit cell parameters of a-uranium with temperature have been reported by Bridge, Schwartz, and Vaughan9 (-253 to 640°C) and by Chiotti, Klepfer, and White10 (0 to 622°C). Polycrystalline samples were used in both experiments. The two data sets show volume expansions with increasing temperature, with mean linear coefficients9 of 35.6 and 31.6 x 10"6/oC for a and a, respectively, between 27 and 640°C. The b parameters in each case decrease with increasing temperature above 0°C. The mean linear coefficient is about -8.4 x 10~°/°C. Oxygen contamination presented a serious problem, but in one experiment it was claimed9 that annealed and pickled uranium filings properly sealed into evacuated quartz capillaries "could be heated to the a - & transformation temperature without significant buildup of the diffraction pattern of oxide." Barrett, 15 Mueller, and Hitterman have reported expansions of a, b3 and a for a- uranium crystals as the temperature increases from 43 to 293 K. The positive expansion coefficient for b at low temperatures is also indicated by the data of Bridge et at.10 Thus there would seem to be a broad maximum in the values of b as a function of temperature at or about 0°C.

The anisotropic response of the lattice parameters of a-uranium to temperature is presumably a direct consequence of the anisotropy of the crystal structure. Chebotarev25 suggested that, as temperature increases and b decreases, the four short contacts between atoms increase in length relative to the longer distances, thereby showing a loss in "covalent" character. An independent result26 that might also indicate some variation in bond character with increasing temperature is the change in deformation mode from a predominantly (010)[100] slip system at room temperature to slip on (110)[110] and (001)[100] systems above 40C°C. Rao and Tangri,2"* however, argue that there is little evidence for large changes in bond order with temperature, and that causes for change in deformation mode should be sought in dislocation theory.

The key is, of course, the variation of the y positional parameter with temperature. Mueller, Hitterman, and Knott1' reported that y increases to 0.1057 ± 0.0006 at 625°C; Chebotarev25 gave 0.1120 at 640°C; Sutton, Eeles, and Price19 found y - 0.110 ± 0.003 at 630°C; and later Eeles and Sutton18 reported 0.1071 ± 0.0005 at 597°C. With the unit cell ^.mrrS~^

parameters at 600°C given by Chiotti et at.,10 and taking y at this temperature as 0.107, calculation shows that the four short contacts about a given uranium atom increase in length by only about 22, while the eight long contacts remain essentially unaltered in length compared to room- temperature values (see Table 1). One may conclude that Rao and Tangri's position regarding bond order is probably correct.

The sizes of the interstitial holes in the cc-uranium structure also show an anisotropic variation with temperature. Sutton, Eeles, and Price19 compute that tetrahedral interstices shrink to 0.66 A in diameter at 630°C, but that pyramidal and octahedral holes both expand to diameters of 1.06 and 0.94 A, respectively. However, at no temperature do the latter interstices become equal in size — a condition which, had it occurred, might explain the reversal in irradiation-induced growth of [010] textured a- uranium wire reported27 at about 500cC.

Anomalous changes in the physical properties of alpha uranium below 43 K were summarized by Fisher and McSkimin.6 Variations in elastic uoduli, thermal expansion, Hall coefficient, electrical resistivity, and thermoelectric power all suggested some kind of transition in this temperature range. A small, easily overlooked28 specific heat anomaly also exists.29 Using x-ray diffraction methods, Barrett, Mueller, and Hitter- man15 found that when single crystals of high-purity a-uranium were cooled below 43 K the a and b unit cell dimensions, which had been decreasing normally with decreasing temperatures, suddenly increased by 0.3 and 0.045%, respectively; at the same time a continued to decrease but at a slightly accelerated rate compared to its behavior above 43 K. There was a resultant net volume expansion, yet no indication of any change in crystallographic symmetry. The y position parameter, which had decreased to 0.1017 at about 40 K, also rose significantly, reaching 0.1025 at 4.2 K. The net effect of these changes on interatomic distances was to increase d\, dz* and d$, while continuing to decrease d^, as the temperature fell from 43 to 4.2 K (see Table 1). Slightly smaller lattice parameter variations were reported for a similar experii-"t with polycrystalline uranium by Marples.30

Despite hints of a cooperative transition,31 a recent neutron diffraction study20 has failed to find evidence of magnetic ordering in a-uranium below 43 K. Insread there seems to be a reversible change in the size of perfect domains within a "single" crystal, as reflected in changes in the extinction coefficient in this temperature range.

Complete details of the low-temperature alteration in the a-uranium structure are still emerging. The transition may be suppressed to some extent by quenching;32 it may occur in several discrete steps;33 the low- temperature form, called34 otQ, is not itself a superconductor but may exhibit35 filamentary superconductivity due to retained a; the a - OQ transition is pressure-sensitive36 and dT/dP « -3.4 K/kbar.

The present view of the transition is that below 43 K a fraction of the conduction electrons of a-uranium gradually condenses into localized 5/ states, reducing the cohesive energy of the crystal and thus accounting for the observed lattice dilatations and moduli changes.35 The phenomenon is comparable to transitions reported in 3-cerium and in chromium below their Neel temperatures, but without magnetic ordering.37 Analogies with anomalous thermal expansions of 6 phasas of plutonium have also been noted.35

Beta Uranium

The 3 allotrope of uranium is stable5 from 667.3 ± 1.3°C to 774.8 ± 1.6°C. Despite over 20 years of intermittent work on its crystal structure, one must conclude that only the gross features are known. The reasons for this situation are virtually a repetition of the general problems discussed in the introduction to this review. Since the & -* a transition in pure uranium may not be suppressed by quenching,36 it is necessary to obtain x-ray diffraction data on $ either at a temperature where it is stable or from an alloy containing enough solute to permit 3 retention at room temperature. In the first case it has been impossible to analyze any data other than those obtained from oxygen-contaminated polycrystalline material;39 in the second, the question of the effect of the alloying element on the detailed structure has been raised;1*0 in both, the correction (or lack of correction) of the data for absorption effects has been a likely source of error.

The correct unit cell symmetry and dimensions of a 8-uranium-like phase were first reported by Tucker,^ who worked at room temperature with quenched U-1.36 at. Z Cr alloy powders and crystals. The primitive tetragonal cell with a * 10.52 A and c » 5.57 A contained_30 atoms. Possible space groups were given as Pkilmm, Pktfm, and P4n2. Qualita- tive intensity arguments supposedly ruled out P^/mnm, and PZn2 was not studied in great detail since an apparently adequate structure based on Pb^m was found. With this space group, atoms were located from Patterson projections, and their 13 unfixed positional parameters were refined to gi a "quite satisfactory" agreement with intensities observed in single- crystal x-ray diffraction experiments.

Tucker's initial structure for the 6 phase was (and all subsequently proposed structures have been) closely related to the o-phase structure found at intermediate compositions in many transition metal alloy systems.1*2 It would seem to be the only reported instance in which the sigma arrangement is adopted by an element. In this general structure type, hexagonally connected main layers of atoms lie normal to the C axis; they are inter- leaved by subsidiary layers whose atoms have no close contacts with atoms in the same subsidiary layer. The overall arrangement can be seen in Figs. 1 and 2.

The coordination of nearest neighbors about each uranium atom is quite difficult to represent. With 3.2 A as an arbitrary upper limit, one finds six to eight close contacts about the six nonequivalent uranium atoms in the unit cell. The "bonds" in the B-uranium drawings of Figs. 1 and 2 have therefore been used to accentuate the main layers of the structure; with the exception of the thicker bonds, they do not neces- sarily delineate closest contacts. Kronberg43 has noted that each atom MwsasiBEre^rffarowtf^^

OBNL-DWG 74-760 .

BETfl URANIUM IR)

BETH URRN1UHIB)

SETA URANIUM(O Fig. 2. Drawings of Three Possible Structures for g-uranium as Derived by J. Donohue and H, Einsphar, ACTA CRYST., B27, no. 9 (.1971), 1740-3. (A) Pitm refinement, (B) T?hi.lmrm refinement, and (C) P4w2 refinement. Bonds describe hexagonally connected main layers, while thicker bonds indicate abnormally short interatomic contacts. Unit cell edges appear as thin lines with c nearly vertical. 10

of this structure lies at the corner of an irregular tetrahedron and has used this feature in discussing models of plastic flow in 3. The structural details that must be supplied by a precise x-ray diffraction analysis center on the flat or puckered nature of the main and subsidiary layers, and on the exact near-neighbor distances, in Tucker's first structure, the main layers were slightly puckered but the subsidiary layers were flat.

Pointing out that measured reflection intensities from x-ray powder diffraction photographs of 3-uranium and a U-1.4 at. % Cr alloy at 720°C show significant differences, Thewlis'*0 argued that the structure should be refined with data from the element and not from a metastable alloy. He also stated**1* that the quantitative measure of agreement (R factor) between intensities computed froa Tucker's model and those observed from polycrystalline 3-uranium at 720°C was only 30% — a relatively poor result even in 1953. Thewlis and Steeple39 proceeded to derive a structure from the 3-uranium high-temperature powder diffraction data. Based on the noncentric group ¥k$nm* it featured puckered main and subsidiary layers, had one distance between atoms in adjacent main layers as short as 2.53 A, and gave an R factor of 192. Six reflections could not be used in the analysis because of overlap with oxide lines. Unit cell parameters at 720°C were given1*0 as a - 10.759 A and o - 5.656 A.

Meanwhile, Tucker had suggested that the intensity differences between the 3-uranium and 3-U-1.4 at. % Cr alloy data were caused by preferred orientation.1*5 Tucker and Senio, using improved diffraction data from an alloy crystal at room temperature, reported a new $ structure.1*6 It was based on space group P^ilmnm, had flat main layers and puckered subsidiary layers, had one distance between atoms in adjacent subsidiary layers as short as 2.59 A, and gave an R factor of 31%.

After Tucker had defended this new structure vis-a-vis Thewlis and Steeple's model,1*7 Tucker, Senio, Thewlis, and Steeple in a joint note1*8 showed that each group's structure fit their own data to about 20% but fit the other group's data to only about 36%. Tucker and Senio continued to maintain the unique correctness of their model; Thewlis and Steeple suggested that there might be ttio 3 structures, one characterizing the pure element, the other the alloy. The possibility of a transition from one to the other within the 3 phase field was raised.

In Vififiy Steeple and Ashworth1*9 returned to the problem, and, using computer methods, refined both the noncentric structure of thewlis and Steeple and the centric model of Tucker and Senio against the observed x-ray powder intensities from 3-uranium at 720°C. They achieved agreement factors of 16 and 23% for the respective models. The principal structural features of each remained the same, but the short contact in the noncentric case was further reduced to 2.50 A. The authors concluded that some preference should be given the noncentric model; their final parameters for it were used to construct the drawing of 3-uranium in Fig. 1. 11

The culminating paper on this subject was published by Donohue and Elnsphar50 In 1971. They claimed that Thewlls*1^ had overlooked a number of coincident reflections in analyzing the g-uranium powder data. Cor- recting this omission, they repeated the refinements of models based_on Phztrmvn and P^rm space groups and included a third model based on P4n2. Final measures of agreement were 28, 24, and 28%, respectively. Abnor- mally short contacts were found in each refined structure, ranging from' 2.48 to 2.61 A. Parameters from these refinements were used to construct the drawings of Fig. 2. '

In summary, it seems clear that no one knows the detailed crystal.... structure of $-uranium, nor is that structure likely to be derived from existing published x-ray diffraction data. The differences between the proposed models may seem minor for some purposes,lf3 but a glance at Fig. 2 shows that they are by no means trivial. Is there tight binding between adjacent subsidiary layers or between adjacent main layers? Are these layers rumpled or flat? Is the structure of elemental 0- uranium indeed different from that of a metastable g-quenched alloy? Answers to such questions must surely be of significance to a full understanding of the physical and mechanical properties of the material.

Thermal expansions of the lattice dimensions of g-uranium were reported by Chiotti et at.10 Despite low precision (0.1%) in the experimental results and contamination by U02 and UC, coefficients of 21.2 and 8.8 x 10~6/°C were computed for a and a. The volume change in the a -*• g transition was given as +1.12%

Crystallographic aspects of deformation in g-uranium were considered by Holden,51 who found that chromium-stabilized crystals could be "ductile" at room temperature with slip on {110} planes in a <001 ) direction. The {110} planes were described as the only ones parallel to flat layers of closely packed rtoms. Rronberg1*3 pointed out oversimplifications in this description and then derived a model of detailed atom movements consistent with the observed slip system. Additional slip systems were observed by Rodriguez and Coll,52 who modified Kronberg's model to account for them. The "ductility" of beta uranium, as contrasted with the brittle behavior of other a phases, was ascribed by Kitchingman53 to the necessary absence of chemical order in the uranium allotrope.

Gamma Uranium

The high-temperature form of elemental uranium is stable from 774.8 ± 1.6°C to the melting point5 at 1132.3 + 0.8°C. It has a body- centered A2-type structure.* The lattice parameter at 800°C was reported as 3.49 A by Wilson and Rundle,5** who also derived a value of 3.474 ± 0.005 A at room temperature by extrapolation of lattice constants of metastable y-U-31.2 to 17.3 at. % Mo alloys to zero solute content. Thewlis1*0 reported a « 3.524 ± 0.002 A for Y-uranium at 805°C. In the A2 arrangement, each uranium atom is surrounded by eight equidistant neighbors at a distance of 3.01 A (extrapolated to room temperature) in a cubic coordination polyhedron. A drawing of this simple structure is included in Fig. 1. ORNL-DWG 73-12803 • U-Pu. H.PARUZ * U-Pu, A.F. BERNOT • U-Nb, M. ANAGNOSTIDIS, eta/. 5.00 94.0 • • • • °S 4.975 • • 3 92.0 •• 1

! A A' A A 4.950 90.0 2.925 5.90 I

• V. A 'A A ' 1 A A ' k A A A t- 5.85 2.900 • * « • m • 2.875 \ 5.80 • • • i A A A * ' A • m 1 A A 'A * 2.850 5.75 •• » 0 10 15 20 0 5 10 15 20 ATOM PERCENT SOLUTE 3. Compositional Variation of Lattice Parameters of Equilibrium and Nonequilibrium a-uranium alloys. Data for uranium-plutonium system are taken from H. Paruz, J. NUCL. MATER., 6, no. 1 (1962), 127—9, and from A. F. Berndt, "Room-Temperature Lattice Constants of Alpha Uranium-Plutonium Alloys," Argonne National Laboratory, Argonne, Illinois, U.S. Atomic Energy Commission Report, ANL-6460, October 1962. Uranium-niobium data were reported by M. Anagnostides, M. Colombie, and H. Monti, J. NUCL. MATER., 11, no. 1 (1964), 67-76. 13

Despite contamination and preferred orientations due to grain growth, Chiotti et al.10 were able to measure the y-phase lattice parameters of "pure" uranium at 800, 900, and 1OOSCC and those of a series of uranium- zirconium alloys at 800, 900, 105, and 1060°C. Extrapolation of the latter to zero solute gave results in acceptable agreement with the "pure" Y-uranium results; the thermal expansion coefficient estimated from these data is 21.6 x 10-6/°C. The value of a at 800°C is given as 3.534 A, and the extrapolated room-temperature parameter is 3.472 A. The $ •*• y volume change is +0.70%.

Although no reports of crystallographic determinations of deformation modes of equilibrium y-uranium have been collected in the preparation of this review, there is little reason to suspect that they would not cor- rospond to well-established modes observed in other body-centered cubic (A2) metals.55

URANIUM ALLOYS Uranium-Rich Terminal Solid Solutions

With few exceptions, equilibrium solid solubilities of metallic elements in a-uranium are restricted to about 1 at. % or less.56 Tucker21 has suggested that the reason may be found in the directed covalent nature of the a-uranium bonding. As expected, very little is known about the effect of these small solute concentrations on the structural parameters of the a phase under equilibrium conditions.

The exceptions to limited a-phase solubility occur for solutes re- sembling uranium in atom size and bonding electron configuration. The two reported in most detail are plutonium and neptunium. Metallographic techniques57*58 place the maximum solubility of plutonium in a-uranium at 12 to 14 wt % at 400°C. X-ray diffraction methods13>59 place the limit at about 15 wt % Pu between room temperature and 400°C. Mardon and Pearce60 report the room-temperature solubility of neptunium in a-uranium as 45 wt Z.

Variations in lattice dimensions of the equilibrium a phase with plutonium content are plotted from the data of Berndt13 and Paruz59 in Fig. 3. The mean compositional lattice expansions are +2.2, -1.2, and +1.0 x 10~Vwt % Pu for a3 b3 and a, respectively. While not measuring the y parameter directly, Berndt13 estimated it to be 0.104 at the solubility limit. Values of d\» dzi d$3 and d^ at that limit are included in Table 1. In the case of a-uranium-neptunium alloys, the lattice parameter variations with neptunium content showed too much scatter to permit quantitative interpretations.60 It was noted qualitatively, however, that "addition of neptunium caused a slight contraction of the orthorhombic unit cell along all three axes," a maximum density of 19.4 g/cm3 occurring at the a field limit. Mardon and Pearce also found that the a and a parameters of a 40% Np alloy increased "markedly" with increasing temperature, while a "slight" contraction of b occurred. 14

Marples30 reported that additions of plutonium and neptunium decrease the temperature of the a -»• a0 transition and decrease the size of the lattice parameter anomalies produced by it. With about 4 at. % of either solute, the effects of the transition became undetectable by x-ray diffraction aethods. The dilute neptunium alloys were unique in that near 4 K two coexisting ct0 phases were observed: one called a0, whose lattice parameters behaved like those of otQ in the uranium-plutonium alloys; the second called ctj, whose unit cell volume was consistently greater than that of the otQ phase (see Table 1 for interatomic distances). Marples suggested that this behavior might be due to shear transformations, selec- tively occurring in some grains of the specimen and brought about by strains produced in the a -*• OQ transition. The absence of the effect in the plutonium alloys was not explained.

If little x-ray diffraction data on equilibrium alpha-uranium solid solutions exist in the literature, reports on equilibrium beta alloys are virtually nonexistent. That this is true despite the generally higher solubilities of elements in 3-uranium is probably a consequence of uncertainties regarding structure and of the usual difficulties met in working with a reactive material at elevated temperatures.

Note that I have already admitted nonequilibrium 0 phases to the discussion of the g-uranium structure; the problems raised by the hypothesis that the metastable phase retained by rapid quenching possesses properties characteristic of equilibrium conditions were described in some detail. Since this hypothesis is, in general, not true of metastable alloys quenched from a- and Y~uranium equilibrium phase fields, I shall not assume it to be true for g-quenched alloys and shall postpone further consideration of them to the next main section.

A paucity of x-ray diffraction data also exists for equilibrium y-uranium alloys despite the extensive solid solubilities of many elements in Y-uranium. The A2 structure can apparently be retained (or "stabilized") by quenching alloys with sufficiently high solute content, and transformation processes from these metastable states do not seem to occur at meas- urable rates at room temperature. It has therefore been experimentally simpler to study gamma phases in the metastable quenched condition, again often assuming the data obtained to be somehow related to the properties of the equilibrium condition.61 In view of our continuing work on such alloys, the tenability of this assumption must be questioned for all save the highest solute contents. Again, I shall defer discussion of x-ray diffraction studies of "stabilized" Y~uranium alloys to the next main section.

We have measured in our laboratory (but not previously reported) the lattice expansion of a polycrystalline U-7.5 wt % Nb-2.5 wt % Zr alloy wire between 700 and 970°C using high-temperature x-ray diffraction methods. The mean thermal expansion coefficient in this range of y-phase stability is (20.5 ± 0.7) x 10-6/"C, with a(805°C) - 3.5096 + 0.0006 A, 15

and

Stable Intermetallic Phases

As stated in the introduction to this review, I shall not attempt to summarize x-ray diffraction studies of all known stable intermetallic phases containing uranium, but only those structurally related to the uranium allotropes and to transitional uranium-rich phases. In particular, since my search disclosed no intermetallic compounds so related to either a- or @-uranium, I shall confine my remarks to ylike phases.

C32-Type Phases62 — Intermetallic phases have been found in the uranium-titanium,63, uranium-zirconium,6<*, uranium-hafnium,65, and uranium-mercury66 systems with structures related to the body-centered cubic A2 gamma structure. The titanium phase exists in a restricted composition range near 33 at. Z Ti; the stoichiometry of the zirconium phase is less well defined, but single-phase regions from 65 to 80 at. X Zr have been suggested.67*68 The hafnium phase is found from 20 to 65 at. X Hf and may be metastable since it can be obtained65 only in alloys quenched from above 1100°C. The mercury phase corresponds closely to 66 UHg2 stoichiometry.

These phases all have structures based on hexagonal unit cells, with individual dimensions listed in Table 2. The space group is P6/mm, and atoms are located at the origin of the cell and at ±(1/3,2/3,1/2). The general structure is isotypic with A1B2 - C32 in the Strukturbericht notation62 — but with significantly lower a/a ratios. Distributions of the chemical atom species in this arrangement, as deduced from x-ray diffraction data, are presented in Table 2. Near-neighbor atom coordinations are complex; an atom at (0,0,0) has 14 close neighbors, two at 3.0 A and 12 at 3.25 A; an atom at ±(1/3,2/3,1/2) has 11 close neighbors, three at 2.89 A, two at 3.0 A, and six at 3.25 A (assuming a * 5.0 A and o - 3.0 A). The layer of atoms at z * If 2 has the same formal configuration as a layer of carbon atoms in graphite.

The derivation of this structure from a body-centered cubic A2 gamma precursor is indicated in Fig. 4. The A2 structure may be referred to a hexagonal unit cell with C parallel to a <111 ) y direction, and a^ and a2 parallel to <110 >y directions in the plane normal to C. Atoms are located at the origin and at ±(1/3,2/3,1/3) of this cell. The A2 * C32 transition involves a cooperative shift of the latter atoms in opposite <111 > y directions and a segregation of chemical species to selected sites. The order in which these processes occur is not determined. The atom shift magnitude is ± Si ctylll, and, ideally, a - /2 •

USi2 has a C32-type structure but should not be grouped with the phases considered here since o/a is greater than one.72 16

Table 2. Unit Cell Dimensions and Atom Positions in C32-Type Phases Containing Uranium

Parameters, A Phase Acorn Positions erenc* a a a/a

U2Ti 68 4.828 2.847 0.590 1 Ti in 0,0,0; 2 U in ±(1/3,2/3,1/2) U2Tio.e2Zro.i81 70 4.8387 2.8527 0.5896 Not determined

UZr2 71 5.03 3.08 0.612 1 Zr in 0,0,0; (0.5 U, 0.5 Zr) in ±(1/3,2/3,1/2) U-Hf 65 4.97 3.04 0.612 Not determined

UHg2 66 4.98 3.22 0.646 1 U in 0,0,0; 2 Hg in ±(1/3, 2/3, 1/2)

Equilibrated at 662°C. 17

ORNL-DWG 74-759

GflMMfl-TQ-OMEGfl TRflNSITION ffl)

GfiMMR-TO-OMEGfl TRflNSITION (B) Fig. 4. Vi«M of the A2 y Phase Structure Showing the Atom Shifts Accompanying the y -*• (0 Transition. Large atoms at undisplaced y sites are connected by thick bonds to small atoms centered at u-structurii sites. Axes of y and as unit cells are shown by thin bonds; the c axis of the oi cell jLs labeled. Dashed lines connect strings of atoms shifted in a common [lll]y direction; the dot-dash line connects an undisplaced atom string. In equilibrium C32-type uranium intermetallic compounds, the undisplaced atoms drawn as spheres with perpendicular great circles are chemically different from unmarked shifted atoms. (A). A view nearly parallel to [fOOly. (B) A view nearly parallel to [110]y. 18

ORNL-DWG 74-197

SHIFTS FROM BCC STRUCTURE IN UCO

Fig. 5. A Unit Cell of the UCo Intermetallic Phase Structure Viewed Nearly Parallel to a (100) Direction. Thin bonds outline a S-brass sub- cell. Atoms drawn as spheres with perpendicular great circles are uranium; large unmarked atoms are cobalt. In the UCo structure, each atom is shifted from the atom sites of an ordered 0-brass configuration in a (111) direction. Small atoms connected by thick bonds to adjacent large atoms are centered at the actual UCo structure sites. Dashed lines connect strings of atoms shifted in a common (111) direction. 19

The C32 phases formed by uranium with the Group IVA elements are similar to metastable "omega" phases observed in certain titanium- and zirconium-base systems,71* though the latter are not usually chemically ordered. A derivation from parent A2 structures is again an obvious 'eature of u formation. One may note in passing that a full shift of

Y is required only by symmetry conditions found among the x-ray diffraction data. If these conditions are not obeyed, shifts less than /3<2y/12 are indicated, leading to a rumpling of the atom plane at a (hex) • 1/2. Such rumpled planes have been reported in as-quenched o> phases.75

Finally we see that four possible orientation variants of the C32 phase should be produced from a single y orientation, depending on the (111 >y direction chosen for the atom shifts. The complications introduced by the multiple orientations in x-ray diffraction data (even "single- crystal" data) at first led to erroneous descriptions of these phases in terms of cubic unit cells with edges about 3 times the y cell edge,76 or about 10.5 A. Other suspicious instances of cubic cells with about these dimensions have been reported for s-plutonium-uranium57 and 8- neptunium-uranium60 phases. It is possible that these might be C32 isotypes.

UCo — The cubic crystal structure of UCo is relevant here since it too is an ordered arrangement of chemical species and atom displacements based on an A2-type structure.77 The chemical order is like that in g-brass; the atom displacements again involve dose-packed <111 >Y strings, but now the shift of adjacent strings is complex in that all <111 ) y directions are used and the shifts of uranium and cobalt atoms along a given string are not equivalent. The arrangement is drawn in Fig. 5.

U2Mo — A stable y-like intermetallic phase occurs between 30 and 35 at. Z Mo in the uranium-molybdenum system.56 Designated 6 by American workers78 and y' by most European workers,79 its crystal structure was correctly deduced by Haltemann.80 The unit cell is tetragonal with a « 3.427 A O Oy) and o » 9.834 A (^ 2.86 • ay); the space group is 9 Ihlrrnm. The atom arrangement is isotypic with MoSi2 (C112? type *) and is again based on an ordering of atoms and displacements in an A2 parent phase. If the A2 structure is considered as an ABAB—stacking of square layers normal to the [OOljy direction, the chemical ordering produces a layer of molybdenum atoms at every third layer. The systematic atom displacements are in the ±[0013y» directions; they are such as to bring adjacent U-layers closer together (2.87 A U-U separations in a square pyramidal coordination) while extending distances between uranium layers and adjacent molybdenum layers (2.96 A u-Mo separations). Kruger82 reported a similar phase with a * 3.35 A and c - 9.22 A in a U-20 wt X Pu-15 wt % flssium alloy quenched from 400"C. Bloch83 has shown the Y* U2M0 phase reverts to a random y solid solution under thermal neutron irradiation. 20

Neptunium Allotropes — It is useful to conclude this description of intermetallic compound structures with some brief account of the crystal structures of the allotropic modifications of elemental neptunium. This is not out of place in the review since it provides interesting points of comparison with some metastable uranium alloy structures to be discussed in the next main section.

The high-temperature form of neptunium, called y, has, like y- uranium, a body-centered cubic A2 structure.81* At about 550°C on cooling it transforms to the tetragonal f$ allotrope via systematic displacements of some atoms in one of the < 100 >y directions.81+ The g-neptunium structure (see Fig. 1) has four-fold coordinations of near neighbors about each atom, the polyhedron being either a square pyramid or a flattened tetrahedron. Axial lengths in y and 0 are related by the equations: ag * /2 • ctyi e_ - 0.97 • ay, where ay - 3.52 A at 600°C (3.43 A at 20°C by extrapolation).84 The magnitudes of the atom displacements are roughly V8- At about 278°C on cooling the 8 structure transforms to orthorhombic a-neptunium, again by small atom displacements but in more complex directions.85 The result, as seen in Fig. 1, maintains four near neighbors about each atom while changing the coordination geometry. The polyhedra, like those in a-uranium, may be considered as trigonal bipyramids with missing ligands. A base atom is lacking in the group around the atom whose coordination is shown near the cell center; an apical atom is absent in the polyhedron around the other crystallographically distinct atom, whose coordination is shown near the bottom of the cell. Axial lengths in @ and a are related by the equalities, a, « 0.96 • a., b - ao, eo-1.97.V "* 3 a 3

Note that crystal structures of the three known neptunium allotropes are all closely related to the A2 y structure via small atom displacements. Lattice relationships are easily predicted, and transformation strains are of the order of 5% or less. The ^ame structural simplicity is not a feature of the y •*• (3 •*• a. sequence in uranium under conditions approaching equilibrium but it does reappear in some metastable phase relationships.

TRANSITIONS BETWEEN EQUILIBRIUM PHASES

Though somewhat removed from the stated scope of this review, the transitions between equilibrium uranium-rich phases are of such obvious technological importance that some mention must be made of the many reports concerning their character. To cover this subject completely here would be out of the question, but fortunately several reviews have appeared,86*87 the best and most recent being that by Goldberg and Massalski.^8 Reference to the latter provides necessary background for the brief remarks to be made in this section and the next. 21

In most published work on these transitions the aim has been, to acquire data permitting assignment of the phase changes to the categories developed to describe similar phenomena in other metals, notably steels. Thus a great effort has been made to determine kinetics of foraption and growth of phases, morphological relationships among them, and deformation modes accompanying transformations* X-ray crystallographic irorkhas,, generally been confined to theoretical deductions of possible lattice.' correspondences between the phasea involved, and to limited attempts to verify these predictions. Reasons for the lack of adequate diffraction data are the familiar ones already discussed in this review.

As would be expected, much of this published work on uranium and uranium alloy phase transitions has also involved ntetastable conditions of either reactant or product. For example, many investigations of the 8 •*• o uranium transition have employed meta3table ^-quenched alloy crystals aged at various temperatures in the a equilibrium field and requenched to room temperature for examination. Virtually all studies of y~phase transitions have used either a similar technique or one in which a transition produced by a change in equilibrium conditions is allowed to proceed isothermally, then is "frozen in" by rapid quenching. That results of such operations are materials representative of equilibrium conditions is often assumed. On the other hand, it is true that many investigations have consciously sought nonequilibrium conditions to simulate technologi- cally important procedures. ,

The q ^ B Transition

The bulk of experimental evidence supports th? theory that the g -»• a transition in uranium at equilibrium is a diffusion-controlled nucleation and growth process.89 Observations of bainitic or martensitic features in this transition when it is carried out several.hundred degrees below the equilibrium temperature87 and the discovery of orientation "memory" effects in a •> 8 + a cycles conducted under certain conditions90*91 have led to systematic searches for appropriate lattice correspondences between g- and a-uranium. Criteria for probable correspondences have been based largely on atom volume conservation and minimal lattice transformation strains.92'93 However, the homogeneous shears of the probable correspondences place only one of the 30 atoms in each ft-uranium unit cell close to its correct a-uranium position; the considerable "shuffle" that must be postulated to complete the 3 •*• a transition has been used to argue that the overall phase change cannot be martensitic in a classical sense but must proceed via coherent growth.92 This extensive atom rearrangement has also been suggested as the dominant factor in selecting which of the many possible low-strain lattice correspondences are to be found experimentally. 9

When the g ** a-uranium transformation is carried out so as to empha- size its martensitic features, especially by rapid quenching, the equilibrium form of a-uranium is usually not found. Instead one observes a metastable form called a', whose structure will be discussed in the next section. The g •*• a| transition is supposed to occur through simple shear,87 though the close resemblence between the a and a' structures makes this theory scarcely more tenable than that the equilibrium g •*• a phase change may occur by shear alone. 22

Little work has been reported on the a. •* 3 transition apart from theoretical interpretations that conclude that it should be diffusion- controlled.87 Eisenbiatter, Haase, and Granzer,90 on the basis of high- temperature x-ray diffraction data, suggested that a nuclei may persist in the 3 phase to temperatures significantly above the equilibrium point, giving this as a possible cause for orientation memory effects. If conditions are such that metastable a' rather than a is obtained in the 3 -*• a reaction, the ctr •+ 3 phase change is thought87 to proceed by "simple crystallographic reversal of the 3 -»• a1 shear."

The 3 ** Y Transition

Because of the relatively few technological problems that arise from the effects of this transition, and because the effects themselves are less sensitive to composition and heat-treatment than those of the a ** 3 transition, the 3 ** y-uranium phase change remains little studied. Goldberg and Massalski88 suppose that it is essentially a diffusion- controlled process. Nucleation and growth are probably crystallographically oriented, however, as would follow from the qualitative observations of Tucker111 and the quantitative model of Kitchingman.53 This model postulates that the main layers of the 3-uranium (a-phase) structure are produced by a shifting together of the A, B, and C atom layers that lie normal to a given [lll]y direction in the A2 arrangement. Lattice relationships are predicted to be (lll)y||<001)g, [110]y | | [140]g. No experimental verification of these relationships was found in tne literature survey for this review.

The Y **• 3 transition in uranium may be suppressed by increasing solute contents and/or cooling rates of uranium alloys; it would seem difficult to suppress by the latter means in elemental uranium,38 but it may be by-passed if powdered metallic uranium is dispersed in a non- 91 metallic compound such as BeO, U02, or graphite. * Routes of decomposition followed by the y phase then usually involve metastable modifications of a- or y-uranium, whose structures are the subject of the following main section.

The Y ** Intermetallic Phase Transitions

Few experiments have been reported in which formation of C32-type phases (L^Ti, UZr2) or Cllfe-type Y' phases (U2Mo) from Y solid solutions has been studied at conditions approaching equilibrium. Both Hatt95 and Hills, Butcher, Howlett, and Stewart96 fine that disordered metastable u-type phases are important intermediates in the overall y -> UZrg transition at compositions from 30 to 50 at. % Zr. Jackson and Larsen"7 examined the sluggish peritectoid reaction in which U2Re (structure unknown) is formed from Y~uranium and URe2 (a Laves phase). Metastable intermediates of unknown structure were reported, b'stberg and Lehtinen98 purportedly studied the ordering reaction Y "* Y1 *n a U-3.9 at. % Mo alloy at 550°C with electron microscopy and diffraction methods; a diffusion-controlled 23

nucleation and growth mechanism was suggested, but the temperature of the experiment and the composition of the alloy make it probable that a metastable y derivative was actually being observed rather than y'. Effects of neutron irradiation on some of these transformations have been noted above.

STRUCTURAL STUDIES OF NONEQUILIBRIUM PHASES

Iu the following discussion I shall attempt to conform to the phase nomenclature proposed by Lehmann and Hills,79 but without the regular use of alphabetic subscripts, whose primary function is to distinguish between morphologically different variants of a phase.

ALPHA-LIKE PHASES

When uranium-rich alloys with solute contents somewhat in excess of the room-temperature a solubility limit are rapidly quenched from regions of @ or y phase stability, nonequilibrium forms of a are often produced. At low degrees of supersaturation or at rapid quenching rates for slightly more concentrated solutions, the lattice symmetry is orthorhombic and the metastable phase is called a'. This modification has been reported with alloying additions of titanium," zirconium,100 niobium,101 molybdenum,102 ruthenium,103 and rhenium.104 As noted in the preceding section, the transitions producing a' have martensitic characteristics whether the parent phase be 0- or Y-uranium, though these tendencies are more evident for the latter case. At relatively low solute content, a* morphology is usually acicular and the phase is denoted a1; at higher concentrations its microstrueture is apt to show banded orientations and the phase is then called al.

The structural difference between a' and a is defined by Lehmann and Hills79 to be "a relative contraction of the b parameter only." Unfortu- nately, contractions of b are also likely to be a noticeable feature of parameter data from equilibrium a solid solutions,13'101 and significant changes in a and a with composition are frequently noted for a1 phases (see below). The nonequilibrium criterion remains the useful distinction, but to invoke it equilibrium conditions must be known — a knowledge often not available.

Lattice parameter variations of a* with composition are typified by results reported for Y~

Table 3. Variation of af and a" Lattice Parameters with Composition

Composition Temperature Limits Composition Coefficients0 Refer- Solute Quenched (at. % solute) CC) a A B G ence Lower0 Upper

a' Phases Ti 1000 -10.0 +1.2 -1.8 +0.4 99 Nb 850 9.0 +0.8 -1.3 +0.6 105 Nb(c£) 900 5.2 0 -1.1 +0.8 106 Nb(o£) 900 5.2 9.0 +2.0 -1.3 +0.8 106 Nb 900 10.0 0 -0.9 +0.8 107 Nbe 850 11.7 +1.0 -1.1 +0.7 108 Nb 850 -10 -0.7 109 Nb 1000 0.8 9.0 +0.6 -*•!.3 +0.7 101 Ho 950 2.2f 6.2 +0.6 -2.0 +0.1 110 Ru 890(Hg) -8 0 -0= 7 -0.3 103 Ru 900 ~7 0 -1 .7 +0.8 111 Re 850 3.5* 6.5 +0.6 -1, ,8 +0.4 104 a" Phases Ti8 1000 10.0 11 99 Nb 850 9.0 16.0 +2.0 -1. ,5 +0.2 +6. .0 105 Nb 900 9.0 16.0 +1.7 -2. 0 0 +4. 8 106 Nb 900 10.0 15.9 0 -1. 3 +0.5 +3. 7 107 Nb 1000 9.0 15.7 +1.8 -1. 9 +0.6(11.9) +6. 8 101 -1.5(15.7) Mo 950 6.2 11.3 +0.6 -1. 7 +1.0 +5. 5 110 113 Mo 950(oil) 4.8 9.9 +0.6 -1. 7 0 (7.2) +7. 3 112 -0.7(9.9) Re 850 6.5 9.5 +0.6 -1. 8 +0.4 +11. 0 104 Quenching medium is water unless otherwise stated. Lower composition limits for a' are assumed to be near 0 unless specified. 'A - J • ft *lo3-B -i * ft * 103«c -i • ft •l °3'c -? * i-loS» where n is composition In at. X solute. Marked changes of slope may occur for the o parameter variation with composition within the a" region. In such cases, the upper composition limit o ch straight-line segment is noted in parentheses after the value of the e. 'a' Is described here as monocllnic with 90* < y < 90.8* from 7.3 to 11.7 at. X Nb on the basis of relative x-ray diffraction line breadths. Metastable £ interrupts a' region; lower composition limit marks 0 disappearance. ^Parameters of a ".measured at 11 at. X TI are a - 2.866 X, b - 5.733 A, o - 4.970 A, y - 90.68*; at all higher Ti contents a1* coexists with y%. 25

that values of B are fairly consistent for a given solute when more than one set of experimental data is available, while values of A show some scatter, and a sign reversal occurs in C for the case of ruthenium.

Changes of a' lattice constants with quenching rate are expected since a greater rate should favor a lattice shearing process.11" Some of the differences in compositional dependences of lattice expansions from experiment to experiment for a given solute may be ascribed to this factor, but no systematic quantitative study of the effect has appeared. Anagnostides et al.,101 have reported that specimens quenched into oil (slow rate of cooling) give qualitatively smaller b parameters than equivalent alloys quenched into water (/vl00G°C/sec cooling rate107).

Tangri and Williams110 proposed that the decrease in b with increasing solute content could be computed theoretically by assuming replacement of uranium atoms (considered to be hard ellipsoids with diameters of 2.86 A along a and 3.39 A along b) by solute atoms (considered to be hard spheres with appropriate diameters), and by also assuming Vegard's Rule to hold. Their model succeeds in matching the behavior of b for niobium,107 molybdenum,110 and rhenium101* solutions, but it predicts too small a decrease in the case of titanium." It would also fail if applied to ruthenium solutions since the atom size of ruthenium is less than that of molybdenum, while the percentage contraction of b per solute atom is greater for molybdenum than for ruthenium a1 alloys.

No experimental measurements of the y positional parameter of an a* structure have been reported. Values of near-neighbor contact distances for the a'-U-6.9 at. X Mb phase included in Table 1 are calculated from the published lattice constants101 and an assumed y of 0.1025. Thermal expansion rates of a' lattice parameters also seem not to have been determined. These data could be significant in ascertaining the course of an a1 •*• a transition and in further studies of the OQ transition at low temperatures.

At intermediate degrees of alloy supersaturation or at high quenching rates for slightly more concentrated solutions, a change in lattice symmetry of the ot-like phase from orthorhombic to monoclinic may be observed. The metastable phase is then designated a" with whatever subscripted letter seems to best fit its microstructure.79 One finds a" only at solute contents high enough to suppress the y •*• & transition for all solutes that produce a* except zirconium96 and ruthenium.111

The nonorthogonal unit cell axes of a" correspond to the a and b a-uranium axes. To preserve the axial relationships to a, a" is usually described on the basis of a ^-centered monoclinic lattice whose unique axis is c. The monoclinic angle is then -y; the caret over the symbol is used to prevent confusion with phase nomenclature. The space group is C2\lm% with four equivalent atoms per cell at 4(e), (x, y, 1/4) etc. 26

Lattice parameter variations of a" with composition are again typified by the results for y-quenched uranium-niobium alloys101 shown in Fig. 3. Rates of change of o" lattice constants with composition are given for various solutes in Table 3. Straight-line approximations are poor for Ba C} and G. I have attempted to ameliorate the situation for C by describing some data sets by two linear segments. A positive curva- ture in y with increasing solute content is a prominent feature of the a "-uranium-molybdenum data.110*111 Stewart and Williams113 report that Y is 0.25° greater for a'* in an argon-quenched than in a water-quenched U-10.0 at. X Mo alloy.

It is claimed that ctf' modifications should appear when the b axis has contracted to about 5.80 A and that failure to find this phase in uranium-ruthenium solutions is due to an unexplained resistance of the a'-uranium-ruthenium lattice to compression to this point.111 The prem- ise fails, however, for uranium-titanium solutions, where a1 is reported at b values as low as 5.75 A.

Using x-ray diffraction data from polycrystalline U-10.0 at. % Mo alloy specimens containing a", Stewart and Williams113 were able to obtain reasonable agreement (JR - 15.2%) between observed and calculated intensities with positional parameters x - 0.036 and y - 0.102. As a consequence of the nonzero value of x and of the departure of the monoclinic angle from 90°, the ridges of the corrugated sheets of the a- uranium structure shown in Fig. 1 are sheared in [100]a" directions. A schematic view of the structure projected down the [001]an direction is shown in Fig. 6. Near-neighbor contact distances are included in Table 1. Note that $ is still the angle between closest neighbor contacts; it is thus smaller by 1° than the actual corrugation angle of the sheets.

Stewart and Williams113 also measured x and y as a function of composition between 5 and 11 at. % Mo. They found no change in y, but values of x rose from 0 at 52 to 0.09 at 11%, in a manner similar to the change in Y with increasing solute in this range. The authors reported variations in y as a function of temperature between 25° and 200°C for alloys with 5.9 to 10.0 at. X Mo; values of Q05/y)dy/dT are 0, 1.3, 4.0, 6.1, and 7.1/°C at 5.9, 8.0, 8.8, 9.2, and 10.0 at. % Mo, respectively. These thermal changes were reversible. Jackson105 found comparable changes in y for an a''-U-15 at. % Nb phase between -196 and 60°C. His data suggested a reversible a" •+ a' phase change for this alloy at about -150°C.

Comparisons of the interatomic distances in Table 1 give no obvious clue to the reason for the monoclinic distortion of the a" phase. One must look for this cause in the mechanism of the y-phase decomposition, a subject to be discussed below.

BETA-LIKE PHASES

As stated at several places in the previous sections of this review, most of the reported x-ray diffraction studies of B-uranium phases have really dealt with metastable materials. There is no reason to expect the 27

ORNL-DWG 73-12671

001]

3.01 ft [111]

•—§—# GAMMA U [uo][oTo][iTo] [0T3][00»] L/25.6" 2.97A

\ • • * GAMMA-O(rf) U ALPHA" U [Tio][oTo] [T210] 120° [2110]

• • • ALPHA ZR ALPHA U Fig, j>. Projections of the Atoms in y-0, Y^U, ct"-U, a-U, and ct-Zr on to a (110)y Plane. Atoms shown as filled circles are in this plane; those shown as unfilled or dotted circles are ay//I above the plane. Dotted circles are at positions produced by shear alone; unfilled and filled circles are at final atom sites except in the case of y

3 structure found at room temperature in a quenched uranium alloy to be any more identical with the crystal structure of equilibrium g than to expect the a1 and ot-uranium structures to be identical. Jackson and Larsen111* have reported room-temperature lattice parameters of metastable g-uranium-rhenium alloys containing 6 to 10 at. % Re. They found a - 10.64 A and o • 5.63 A, with no significant variation with composition. Extrapolation of Thewlis'1*0 g-uranium parameters at 720°C to room temperature using the thermal expansion coefficients measured by Chiotti et al.10 gives a (25°C) * 10.60 A and a (25°C) - 5.62 A. The apparent expansion in aR introduced by alloying is depicted as relieving the short 2.59 A interatomic distance,11** but this cannot be so since, as may be seen in Fig. 2, the short distance depends primarily on oB, not ao. P P In an earlier report on the uranium-rhenium system, Jackson, Williams and Larsen115 reported that a transition phase of unknown structure formed during the g -> a decomposition of metastable g-U-1.9 at. % Re alloys, or on water-quench?ag U-7.5 at. % Re alloys from a restricted range of temperatures in the y phase field. They called the phase got; its structural connection to either g- or a-uranium structures remains undetermined.

GAMMA-LIKE PHASES When uranium-rich alloys with solute contents much in excess of the a solubility limit are quenched from regions of y-phase stability, the non-equilibrium phases that may be produced are more nearly related to the Y~uranium than to the a-uranium structure. In general, the higher the solute content and the slower the quenching rate, the greater the tendency to form these y derivatives.

The crystal structures of the -y-like transition phases are so like the A2 structure itself that their presence often went undetected in early experiments; uranium alloys were called "stabilized" y when in reality they were unstable to a marked degree. If other intermetallic phases with structures based on y ate also present in the system (e.g., Y'-U2MO), the problem of differentiating the y-like transition phases becomes even more formidable. In many early references metastable phases 116 are called y'» implying some relation to the U2Mo phase; Lehmann and Hills79 suggested that they be called y°, a notation that will be followed here.

The y° phases have been observed in uranium-titanium," uranium- titantium-niobium,i17 uranium-zirconium,*18 uranium-zirconium-niobium,119»12° uranium-niobium,101,107,116 uranium-molybdenum,Al°»121 uranium-molybdenum- titanium,12 2 uranium-ruthenium,103*111 uranium-rhenium,l"lf and uranium- plutonium-fissium82 systems. Their crystal lattices were found to be tetragonal with ay0 ~ 2 • ay and c?y0 slightly less than Oy. When o/a was indistinguishable from 0.5 the phase was called y°; when a/a was less than 0.5 the phase was often microstructurally characterized by deformation markings and was called yfj,. The Bravais lattice was identified as 29

C-centered. A primitive unit cell with <2yO * Jl • Oy and

The first attempt to describe detailed crystal structures of these phases was made by Tangri123 using single-crystal x-ray diffraction data from uranium-molydenum alloys. Chemical ordering of atoms on the A2 sites was proposed for both the y\ modification and for ys» a cubic structure with ayS - 2 • ay found at Higher solute contents than y% .* These models could not quantitatively predict the observed x-ray scattered data, however.

Matt and Stewart124 and Yakel125 showed that models involving regular displacements of half of the atoms from their A2 sites did yield adequate agreement with observations. Hatt and Stewart worked principally with U-8.5 at. % Ru alloy crystals, but also examined U-ll.l to 20 at. % Ho, and U-15.8 and 18.1 at. % Nb crystals; Yakel worked with U-16.6 at. % Nb-5.6 at. % Zr alloy crystals. Both investigations found atoms displaced in <100 >Y directions, the particular direction chosen becoming the tetragonal c axis. The atom arrangement following displacement is shown at the top of Fig. 7; with relaxation of c/a from its ideal value, the structure shown in the lower half of Fig. 7 is produced. Note that the latter structure is formally identical with that of 3-neptunium (Fig. 1), except for a smaller distortion of a/a and smaller atom shifts. The magnitude of the z shift in Y$ was given as 0.095 in the ruthenium phase12^ and as 123 0.047 in the niobium-zirconium tenary phase. The network of short contacts between an assembly of atoms takes the form of regularly kinked corrugated sheets that lie normal to [112]y or [012]yo directions (see Fig. 8),

Better agreement with diffraction data from the U-8.5 at. % Ru crystal was claimed if small x and y displacements were also given to the shifting atoms, and if the unshifted atoms were uranium only while the shifting atoms were a random (83% U, 17% Ru) mixture. The magnitudes of the additional shifts were ha • Ly « 0.015; their presence destroys the C-centering of the large tetragonal unit cell, the space group becoming PZ, with a Q d - 2 • V "

The argument for chemical order is a tentative one since such ordering effects on the observations are swamped by those due to the positional parameter changes. Diffraction results from some of the other alloy crystals examined by Hatt and Stewart suggested only partial order or disorder in the Y° or YJ states. Shifts in a: and y were determined only for the ruthenium phase, and it is not clear if they were required by data for the other

One should probably equate the YS notation with y°(a/a - 0.5). The problem of how best to treat the total diffraction pattern of this phase is discussed below. 30

ORNL-DWG 74-198

Fig. 7. Views of the y° (Top) and y% (Bottom) Structures Found in U-16.60 at. % Nb-5.64 at. % Zx Alloys. Eight unit cells of the original A2 y structure are outlined by thin bonds; heavier solid bonds indicate the primitive y% unit cell. Dotted atoms at the centers of the eight y cells in the top drawing shift to final positions shown at the ends of open stick bonds. Dashed lines connect strings of atoms shifted in a common (100)Y direction. In the y° phase, the (100)Y direction chosen for the shift is followed for only a small number of adjacent cells, and the average structure remains cubic. In the Y$ structure (bottom), the common shift direction extends over long distances and the tetragonality of this ordered structure produces a sensible difference in ola. Atom shifts and el a deviations have been deliberately exaggerated for display purposes. 31

OKNL-LR-DWG 74-374

GRMMfl O(D)

Fig. 8. An Assembly of Atoms in the YJ Structure Showing the Network of Nearest-Neighbor Interatomic Distances (Thick Bonds). Thin bonds indicate original y-cell-edge directions. Atoms drawn as spheres with perpendicular great circles were unshifted in the y "*" Y5 transition; unmarked atoms were shifted in directions parallel to the Y-cell edge direction extending to the upper right of the drawing. 32

alloys. Yakel125 found no diffraction results requiring either chemical order or x3 y shifts in studies of the U-Nb-Zr ternary phase.*

The magnitude of the atom shifts and the o/a values of the y% structure are functions of alloy composition and heat-treatment. Published results for both lattice and atom parameters are summarized in Table 4. Note that increases in As accompany increases in the deviation of a/a from an ideal ratio, and that this deviation in a/a decreases as solute content increases and as quenching rate increases. Jackson105 found reversible changes in o/a as a function of specimen temperature between -120 and 200°C for a y

The structural consequences of the y •*• Y° transition are easily described; they are the same as those for the y •* g transition in elemental neptunium. Thus each atom moves from an environment with eight near- neighbors (^3.0 A separation) arranged in a cubic coordination polyhedron to one with four nearest neighbors (^2.9 A separation) in a square pyramidal or distorted tetrahedral coordination. The picture is more com- plicated if Xj y displacements are allowed, but in either case interatomic distances and close-bonded sheet configurations approaching those in ct- uranium are established. It is of interest to note that the x3 y shifts suggested by Hatt and Stewart12tf do not correspond to the additional shifts marking the & •*• o phase change in neptunium. Other consequences of the y •*• y° transition as they affect the overall y •*• a decomposition scheme are discussed in the next section.

Both Hatt and Stewart12** and Yakel125 report that when a/a is 1/2 (or 1//2 for the primitive cell) x-ray diffraction maxima from y° alloy crystals may be classified as sharp (those corresponding to "fundamental" A2 structure reflections) and diffuse (corresponding to "superlattice" reflections caused by the atom shifts). The former authors state that in this condition their diffraction patterns could be interpreted simply as a super- position of patterns from three y° orientations, each with Cy0 lying in a different <100 > v direction. I have not found this to be so in data

Presence or absence of these structural features may be assessed qualitatively by a careful examination of the diffraction maxima in the hkO zone from a single y% orientation. If chemical order and/or x, y displacements are present, reflections other than those expected from an A2 structure will be observed. This test must be done with care since the multiple orientations of YJ usually encountered may lead to confusion. 33

Table 4. Lattice and Atom Position Parameters in y°-Type Phases

Parameters, A „ , _ Composition Conditions Refer- Solute /' _.. _ „ _. a/a Lz (at. Z) of Formation ence a Ru 8.5 End-quenched 7.00 3.40 0.49 0.095a 124 into Hg from 890°C Mo 10 Not stated 6.94 3.41 0.49 124 Ho 11.1 Slow cooled from 900°C 0.5 0.07 124 Mo 11.9 Quenched into H2O from 900°C 0.5 0.06 124 Mo 12.5 Air cooled b from 910°C 6.88 3.44 0.5 0.04 124

Mo 12.5 As above, 6.94 3.37 0.486 0.06 124 Aged 90 min at 300°C Mo 15 Slow cooled 0.5 0.04D 124 frns 900°C Mo 15 As above, 0.5 0.06 124 Aged 36 hr at 300°C Mo 20 Slow cooled 0.5 0.02 124 from 900°C Nb 15.8 Air cooled 0.5 0.06 124 from 9506C Nb 18.1 Quenched into 0.5 0.06 124 H20 from 940°C Nb, Zr 16.6, Quenched into 6.928 6.928C 1.0 0.03 125 5.6 HaO from 800°C

Nb, Zr 16.6, As above, 6.998 3.371 0.482 0.047 125 5.6 Aged 2 hr at 150°C Nb, Zr 16.6, As above, 7.06 3.30 0.467 0.08 125 5.6 Aged 1 hr at 350°C Nb 19 Quenched into 6.95 3.43 0.494 104 H20 from 850°C Nb 17 Quenched into 6.97 3.41 0.489 104 H20 from 850°C 34

Table 4 (continued)

o ™~~

_ , . Composition Conditions ' , A Refer- Solute (at. Z) of Formation ofa ** ence

Nb 16.8 Quenched into 6.968 3.383 0.486 107 H20 from 900°C Nb 18.15 Quenched into 6.943 3.387 0.488 107 H20 from 900°C Nb 16.25 Quenched into 7.014 3.369 0.480 101 H2O from 1000°C Nb 16.25 Quenched into 0.477 101 oil from 1000°C Nb 16.25 Quenched in an 0.477 101 Ar jet from 1000°C Nb 17.3 Quenched into 6.969 3.406 0.489 101 H20 from 1000°C Nb 17.3 Quenched into 0.479 101 oil from 1000°C Nb 17.3 Quenched in an 0.479 101 Ar jet from 1000°C Ru 7.74 Quenched into 6.962 3.384 0.486 111 H20 from 900°C Ru 9.51 Quenched into 6.948 3.385 0.487 111 H20 from 900°C Pu, Fs 20, 5d Quenched from 6.92 3.43 0.496 82 775 °C Pu, Fs 20, 5d Quenched from 6.92 3.40 0.491 82 625°C

a - bx - Ay » U.015 also indicated by data. Ordered structure. Partial ordering indicated by data. cCould also be considered y" with a/a • 0.5, but see discussion in text concerning interpretation of diffraction pattern. Composition given in wt. X Pu, Fs. 35

recorded from uranium-niobium-zirconium crystals using a well-aligned single-crystal diffractometer. Here the sharp reflections correspond to a strictly cubic lattice, but the diffuse reflections are displaced as they might be if produced by tetragonal YJ lattices (e/a less than ideal) whose C axes could lie in any of the three (100 >y directions. I interpret the Y° diffraction pattern, as I now know it, as the displacement analogue of short-range chemical order. If this is true, the composite diffraction pattern must be analyzed on a basis similar to that recently developed by Borie, Sass, and Andreassen126 to explain ( diffraction data from "diffuse" u phases in titanium and zirconium alloys. When a/a, as measured by the sharp reflections, departs sensibly from the ideal ratio, I believe the system changes from a short-range to a long-range ordering of atom displacements. Interpretation of the composite diffraction pattern in terms of superposed y% patterns is only then justified.

TRANSITIONS BETWEEN NONEQUILIBRIUM PHASES

In a previous section I described briefly the few statements regarding the B -*- a1 transitions that have appeared in the available literature. So little is known about the transition that, pending further experiments, no additional discussion of it will be fruitful.

The series of transitions from y •*• y° •*• YJ •* o" -•• a1 is perhaps better studied and hence somewhat better understood. Experimental evidence suggests a diffusionless character for at least the first two and perhaps the third; yV, •*• a'' and Y J "*" o' transitions may also involve solute diffusion out of the ot-like phase. Regardless of detailed kinetic features, x-ray diffraction data point to definite orientation relationships among these intermediate structures. Lattice correspondences for the direct Y "•" <*' transition were analyzed by Hatt.96 The a-like structure is derived from a mbnoclinic cell in the A2 structure with [100]a,11[lll]y, f010]a,11Ell3Jy, and [001)a,|J [110]^; the angle y between the nonorthogonal axes of this cell is 100°. A shear on a (112)y plane in a [lll]y direction decreases y to 90°, and a small displacement of atoms completes the transition. Its course is readily followed from the schematic drawings of Fig. 6. Note that 12 equivalent a-like orientations are predicted from one y orientation, corresponding to 12 possible choices of shear plane in the cubic y structure. Hatt9* showed that, in a slow-cooled U-50 at. % Zr alloy and in a water-quenched U-10 at. % Zr alloy, each of these orientations was observed with essentially equal probability.

Tangri and Williams110 and Stewart and Williams113 confirmed Hatt's guess that a monoclinic phase could intervene in the Y "*" <*' transition if the lattice shear did not proceed completely toy- 90°. Tangri and 36

Williams110 discussed a "stress/stiffness ratio" whose value would reflect the stress levels induced in the alloy by quenching and the resistance to shear produced in the y structure by solute additions. They proposed that if this ratio fell below a critical value the monoclinic a" modification would be found. The y -*- a'1 ->• a' lattice relationships are obvious in Fig. 6. Again 12 a" orientations should be produced in equal amounts from a given y orientation.

The y% phase structure has a lower crystal symmetry than y, and the 12 ot-like orientations, which would be equivalent if formed from y, should be distinguishable if formed from y%. It is easily shown that the four a-like cells with [001J , ,,||[100] Q constitute a set of orientations

(set 1) distinct from the eight with [001] , „ ,,||[112] 0, (set 2). a or a YJ The a-like cells in the former set are strictly monoclinic, but those in the latter are triclinic. Moreover, the y angle for orientations in the first set decreases linearly from 100° with decreasing o/a ratios of y% , but the same angle in the second set increases above 100° with decreasing a/a. A third difference between the sets is that the atom shifts (ignoring possible xy y components) characterizing the y •*• y° transition all lie in a plane normal to [001]o, of ,, for the first, but lie out of that plane for the second. As Figs. 6 and 7 show, the shifts also shorten distances between atoms that will become near neighbors in an a-like cell from set 1. The same is not true if an a-like cell from set 2 is chosen.

The net result of these differences — which were noted by Hatt and Stewart121* and independently in our laboratory — is that the four orientations in set 1 will be preferentially formed from a given yV, crystal. Since three equally probable YJ orientations will, in general, be produced from a single y crystal ([001] o I! < 100 )Y), the four a-like cells yd preferred by each of these will regenerate the condition of 12 equally probable a-like orientations. However if one or two of the y% orientations is preferred in the Y "*• Y J transition because of external factors

*-Direction- - s fo- r ,y%o here and in Fig. 6 are referred to the small y% cell

{i.e., a o - & • a. , [100] 0 II [HO] ). Conversion to directions in yd Y yd y the larger C-centered unit cell is straightforward. 37

(e.g., stress applied before or during the reaction), then a subsequent Y*l -»• o" or a* transition must yield preferred a-like cell orientations. This effect has been observed in my experiments. Crystals with a-single Y*j orientation (obtained by chance from rolled alloy sheet) aged at 350°C underwent ayj+u" transition; only the four a1' orientations of set 1 were observed. Similar crystals aged at 500°C underwent a y% •*•-,,-• a' + Y? (solute enriched) reaction; the four o' orientations of set 1 were about twice as prominent as those of set 2. Retention of preferred orientations through metastable phase transitions should play a major role in "memory effects" shown during heat treatment of some of these Y-quenched uranium alloys.

Tangri and Williams110 note that the Y •* Y!J lattice transformation

may be formally produced by shear on two {112>Y planes parallel to a <110 >y direction. They postulate that A2 structures with high solute concentrations may be so resistant to deformation that only a limited amount of shear on a system of two symmetry-related planes can occur.

Hewlett127 has estimated the enthalpies of y% •*• o1' transitions in uranium-molybdenum alloys using measurements of temperature differences between the transforming specimens and their surroundings.He found that Afl varies with molybdenum content and that, if Stewart and Williams' reported variations of Y with temperature113 are assumed, LH decreases linearly as y (computed at the transformation temperature) increases. The y value at zero enthalpy change is extrapolated to be near 100°, in agreement with the value of this angle in the undistorted A2 structure and close to its value in the YJ phase.

The y •*• Y° •*• YJ transformations may be induced by stress alone,128 and in this case might be expected to show extreme preferred orientation effects. Dean129 has examined the transformation kinetics of U-7.5 wt % Nb-2.5 wt % Zr alloys at temperatures from 200 to 800°C. His time- temperature-transformation diagrams show two aging reactions, the first occurring below 400°C (which I would identify as the YJ "*" <*" transition), the second occuring between 400 and 650°C [which I would identify as the Y'J •* a' + yS (solute enriched) transition]. It is my opinion, based principally on my own experiments but also supported by Howiett's results,127 that there is still a third transition curve that could be drawn on TTT diagrams if the as-quenched phase configuration is Y° (i.e., a short-range ordering of atom displacements). This would be identified as the y° •*• YJ transition, which I have observed to occur in as-quenched y° phases after aging times of a few hours at 150°C. 38

SUMMARY In this review I have attempted to present results of significant x-ray diffraction experiments dealing with equilibrium crystal structures of uranium and uranium-rich alloys, and, briefly, with transitions between these phases. By way of summary it is instructive to consider these results as they compare with data for other elements whose allotropies resemble that of uranium, and then to define areas for useful additional work.

COMPARISON WITH OTHER SYSTEMS There are several similarities between the allotropic behavior of the Group IVA metals (Ti, Zr, Hf) and the thermal sequence of elemental uranium structures. In both, a high-temperature body-centered cubic A2 structure eventually transforms to an arrangement based on the hexagonal close-packed A3 structure.130 The distortion of the A3 configuration in ot-uranium is ascribed to localized 5/ electron bonding effects not possible for the IVA metals.

The g-uranium allotrope intrudes into this simple picture, but Kitchingman53 has noted that a-like phases often occur in the passage from more open A2 structures to more closely packed A3 and Al structures.131 It seems significant, however, that o-like phases, except for f3-uranium, are always found as intermetallics in alloy systems containing at least one transition group element. The mechanism of the A2 -> 0 transition proposed by Kitchingman involves regular atom displacements from the unstable A2 structure — a feature common to most of the transitions I have described here.

If the Y "*• £ transition is suppressed by alloying additions to uranium, another similarity to the transitions of IVA metals appears. This is the production of metastable a-like phases by homogeneous shear of {112} planes in <111 > directions of the A2 structure, followed by small atom shifts.132 These shifts are different in the y -> a' uranium transition than, for example, in the g •+ a1 zirconium transition, as may be appreciated from Fig., 6. The special bonding features of a'-uranium are again responsible for this difference. A third similarity between structures of uranium and IVA metal alloys is the occurrence of metastable u> phases in the decomposition of solute- stabilized A2-type phases. The A2 •*• u> transition is produced by a "shuffle" of {112} planes in <111 > directions of the A2 structure. The sequence followed by the shuffle is easily seen in Fig. 4(2>). The u relaxation of the A2 arrangement may be described in terms of static displacement waves traveling in a <111 >.» direction.133 In this displacement-wave model, Cook133 also introduces an order parameter n. which is zero if atoms in A, B, and C planes normal to a <111 > .„ direction are unshifted, positive if atoms in two of these plajies shift toward each other and 39

away from the third (the omega structure), and negative if atoms in two of these planes shift away from each other and toward the third. Cook calls the latter configuration "anti-omega", but it is clear that it is equivalent to the first stage in Kitchingman's mechanism for the A2 •*• a transition. The influence of chemical order on the A2 •*• to transition, as it might occur in uranium-titanium or uranium-zirconium alloys, has not been studied in detail, though some theoretical models may be applicable.13 "+ ; '

The y° and YJ transitional structures found in uranium alloys represent another mode of relaxation for an unstable A2 structure. In this case, the resemblence to the allotropic behavior of neptunium is note- worthy. The essential identity of y\ and g-neptunium crystal structures has been demonstrated. The fact that ^-neptunium does not undergo a transformation with decreasing temperature to something like a hexagonal close-packed structure may be due to special bonding requirements or, following Tangri and Williams,110 to an inherent resistance of y-*iike neptunium phases to shearing deformations. If the latter explanation is valid, it would imply that small alloying additions could "stabilize1' the y-neptunium phase to a degree not realized in comparable uranium alloys.

The possible role of chemical order in the y •*• y% transition is at present unclear. If the YJ + «" transition is indeed diffusionless, the chemical order present in y*i should persist in a". However, Howlett127 has failed to find x-ray diffraction evidence of this in a" uranium-molybdenum alloys. It is perhaps significant in this respect that the y% phases, in which Hatt and Stewart121* reported some evidence of chemical order, occur in the uranium-molybdenum system, where a chemically ordered equilibrium phase clearly related to y exists at U2M0, and the uranium-ruthenium system, where a chemically ordered equilibrium phase exists at UgRu, though its structural relation to y is not obvious.135 The y° and y^ phases formed by uranium-niobium and uranium-niobium- zirconium alloys do not show any evidence of chemical order, and in the binary uranium-niobium system no equilibrium intermetallic phases are known.* The logical inference and experimental verification of preferred orientation effects persisting through the y •> y° •*• y^ •*• a" •*• a uranium

4t Peterson and Ogilvie136 reported microstructural evidence for the formation of an intermetallic phase in U-Nb diffusion couples at temperatures up to about 1000°C. They estimated compositions of 50 to 75 at. % Nb for this phase. 40

transition sequence could have an obvious counterpart in the y •*• 3 •*• »- neptunium phase changes. No experimental evidence bearing on such an effect in neptunium is available, other than the observation that shear components are involved in S •• <*» a ->• p and y -*• & transitions.137 There are, of course, many aspects of the structures of uranium and and its dilute alloys that are unique. The existence of the a1 transition. There is some possibility that the apparent uniqueness of these features is simply due to the absence of careful experimental observations on comparable elements and alloys.

AREAS FOR USEFUL ADDITIONAL WORK The remarks made in the preceding paragraphs lead to the conclusion that additional work is needed to clarify certain problems concerning the crystal structures and transitions of elemental uranium and uranium alloy phases. I list below what I feel to be some important problems that can be attacked by diffraction methods.

Alpha Phases The effects of alloying additions on the a •*•

The work of Stewart and Williams113 on determination of a" parameters in uranium-molybdenum alloys should be extended to other solute systems. Measurements of variations of these parameters with temperature could support or refine theories of critical stress-to-stiffness ratios. Diffraction studies of long-range or short-range chemical order in both a'' and a' should be made in a number of alloy systems.

Beta Phases There is a paramount need to obtain x-ray or neutron diffraction data of sufficient quality to permit determination of precise crystal structures for a ^-stabilized uranium alloy and for elemental g-uranium itself. The former structure should be more easily attacked. The latter would have to be deduced from high-temperature single-crystal diffraction data, col- lection of which would present some obvious difficulties. 41

Orientation relationships of g-uranium: y-uranium phases involved in the y •*• B transition should be experimentally determined. Difficulties may again be anticipated, but the validity of Kitchingman's model for this transition should be tested. The existence and crystal structures of metastable intermediate phases formed in g -> a reactions should be examined more fully.

Gamma Phases :, v :

Additional experiments are needed to ascertain precise y% structures in as many uranium alloy systems as possible. Results of tests for chemical order and/or x3 y atom displacements would be especially significant. X-ray diffraction measurements of short-range chemical order as a function of composition in the y equilibrium fields of several uranium alloys systems would be useful in comparison with the presence or absence of order in the Y-like transition phases. The few such measurements reported to date sug- gest unlike near-neighbor preferences at 50 at. % solute concentrations.*38

The diffuse x-ray scattering produced by models of possible short- range Y° displacement structures should be theoretically derived. Careful mappings of experimental diffuse intensity distributions in reciprocal space are a necessary prerequisite to fixing values of the variable parameters in such models;139 no maps of this kind have been published for Y° uranium alloy phases.

Transitions Between Phases

Areas for additional x-ray diffraction work on the several transitions between equilibrium and nonequilibrium phases discussed in this review have been indicated in a recent commentary by Rechtien and Nelson.140 I would add to their suggestions the study of the possible role of non-metallic impurities in some of the transitions, particularly y ->• Y° •* YJ •

An appreciation of the ordering of atom displacements as an important transformation process in many metallic systems seems to be growing,141 though its potential significance in the phase changes of body-centered cubic A2 metal structures was implied by Zener142 as long ago as 1948. Displacement instability is, of course, not restricted to uranium, zirconium, and titanium alloys. Discovery of the metastable phases in these alloy systems seems to have been directly related to the care with which they were sought; the same statement might well be made for other "well- known" metals. The refined x-ray, neutron, and electron diffraction techniques available to the modern metallurgist have most certainly not been applied in their full power to such problems. 42

ACKNOWLEDGMENTS

• I would like to «xpr«ss my thanks to B. S. Borie, S. Peterson, and R. A. Vanderueer of the Metals and Ceramics Division, Oak Ridge National Laboratory, for their help in reviewing the draft of this paper. 1 am also indebted to the staffs of the ORNL Central Research Library and the Graduate Chemistry Library at the State University of New York, Stonybrook, for their assistance in the literature survey, and to C. K. Johnson of the ORNL Chemistry Division for his useful suggestions regarding several structure drawings.

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