Abstract

This research proposal seeks support for a program of research on the structure of crystals of complex intermetallic compounds and other alloy phases by x-ray diffraction methods. This research is to be carried out in the Division of Chemistry and Chemical Engineering of the California Institute of Technology with Professor Linus Pauling as principal investigator and Dr. Sten Samson as co-investigator.

A detailed description of the research plans is given below preceded by a brief historical review.

Development of Research on the Structure of Intermetallic Compounds and Other Alloys at the California Institute of Technology

Research on the structural chemistry of metals and alloys has been carried out in the Division of Chemistry and Chemical Engineering of the California Institute of Technology for 40 years. The crystal structure of the compound Mg₂Sn was determined by x-ray diffraction and described by Linus Pauling, J. Am. Chem. Soc., 45, 2777 (1923); this was the first publication reporting the determination of the crystal structure of an intermetallic compound. In the same paper mention was made of a study of NaCd₂, which was found to be extremely complicated.

An x-ray study of the alloys of lead and thallium was carried out by Edwin McMillan, as a first-year student, in collaboration with Pauling, and published in J. Am. Chem. Soc, 49, 666 (1927). During the following years further experimental studies of metals and intermetallic compounds were carried out; in particular a continued attack was made on the structure of NaCd₂, but without success until this problem was solved by Sten Samson in 1962.

The first of a series of theoretical papers on the nature of the bonds in metals and intermetallic compounds was published by Pauling in Phys. Rev., 54, 899 (1938). The theory of resonating chemical bonds in metals and alloys developed in this paper was then extended and refined in later years. The second paper in this field, on atomic radii and interatomic distances in metals, was published in J. Am. Chem. Soc, 69, 542 (1947).

Experimental work on the structure of intermetallic compounds was intensified during the five years subsequent to 1946, when a grant was given to the California Institute of Technology by the Union Carbon and Carbide Company for support of research in this field. At the time of expiration of this grant support of the work was assumed by the Office of Naval Research.

During the last fifteen years special attention has been paid to the determination of the crystal structures of intermetallic compounds with large unit cells and many parameters. The reason for interest in these structures will be discussed later.

Among the interesting structures discovered in the course of these investigations is the structure of the sigma phase, an important phase found in ferrous alloys. This work was carried out by Gunnar Bergman and David Shoemaker and published in Acta Cryst., 7, 857 (1954). A significant step in the direction of determination of structures of greater complexity was the successful attack on the intermetallic compound Mg₃₂(Al, Zn)₄₉ by Linus Pauling, Gunnar Bergman, and John Waugh, Acta Cryst., 7, 857 (1954). This structure, with a large unit containing 162 atoms, provided the basis for the formulation of a series of other very complex structures by Sten Samson. Among these are the structures of Mg₃Cr₂Al₁₈, Acta Cryst., 11, 851 (1958), and ZrZn₂₂, Acta Cryst., 14, 1229 (1961), both containing 184 atoms per unit cell.

The results of the latter three investigations led to the recognition of certain atomic configurations, especially the icosahedron and the Friauf polyhedron, as significant for the stability of complex intermetallic compounds; and it became apparent that these two coordination polyhedra should dominate in several of the most complex intermetallic compounds known. Samson successfully applied this principle in the derivation of the atomic arrangement for the crystal of NaCd₂. The unit of structure is a cube containing 1192 atoms; there are 280 Friauf polyhedra, 528 icosahedra, and 384 irregular polyhedra. This is the most complicated inorganic structure yet determined, but still more complex structures of intermetallic compounds remain to be solved. The structure of NaCd₂ is published in Nature, 195, 259 (1962).

During his work on complex structures of intermetallic compounds, Samson developed also a general method which greatly facilitates the synthesis of cubic structures of extreme complexity. This work has recently been submitted for publication.

Current Investigations

The experimental x-ray data used in the work on NaCd₂ sufficed to verify the correctness of the proposed atomic arrangement. We now desire to refine the structural parameters to a high degree of accuracy. Absorption errors, for example, need to be reduced by the use of spherically ground crystals. Since, however, the crystals decompose with time; refinement of the experimental procedure requires first of all that the x-ray data be obtainable more efficiently than our present photographic instrumentation permits. The detailed refinement of NaCd₂ has therefore been postponed to await adequate instrumentation.

In the meantime structure investigations of the intermetallic compounds Cu₄Cd₃ and Mg₂Al₃ are being carried out. Crystals of Cu₄Cd₃ are cubic, the edge of the unit cell being a₀ = 25.83 A. The unit of structure contains about 1116 atoms. At the present stage of our investigation this compound seems to be considerably more complicated than NaCd₂. The structure of Mg₂Al₃, the ß(MgAl) phase, seems on the basis of our present diffraction data to be very similar to that of NaCd₂. The unit cell is a cube of edge 28.2 A and contains about 1200 atoms. Samson deduced two reasonable trial structures for this compound, but he is still trying to obtain diffraction data of adequate quality to test the correctness of a trial structure. The crystals so far have always been twinned, but special techniques are now being tried to resolve this difficulty.

Binary magnesium-aluminium compounds and ternary Mg-Al-X compounds (X = transition metal) have been under investigation and reexamination here for some time. Magnesium and aluminium are very similar to one another in electronegativity. Electron transfer is therefore unlikely to occur in compounds formed between these two elements. In ternary compounds Mg-Al-X (X as above) electron transfer is more likely. Previous investigations have shown that structures of such ternary compounds exhibit the same kind of coordination polyhedra (icosahedra, Friauf polyhedra) as those of binary Mg-Al compounds. Detailed analysis of these polyhedra will enable us to study the influence of electron transfer on the interatomic distances between magnesium and aluminium.

The intermetallic compounds VAl₁₀ and Mg₃Cr₂Al₁₈ have very similar crystal structures, each of which incorporates eight Friauf polyhedra per unit cell. In VAl₁₀ each such polyhedron consists of 16 (4 + 12) aluminium atoms, but in Mg₃Cr₂Al₁₈ it consists of 4 magnesium atoms, 12-aluminium atoms and one additional magnesium atom which is at the center of the polyhedron. Accordingly, the Friauf polyhedron of VAl₁₀ is empty, while the one of Mg₃Cr₂Al₁₈ is filled. It seems very likely that if in VAl₁₀ some of the aluminium atoms (3-valent) were replaced by magnesium (2-valent), the polyhedron would fill up, so as to keep the sum of the valencies of the magnesium atoms and the aluminium atoms constant. It seems therefore possible that there exists a homogeneity range that extends from V₂Al₂₀ to Mg₃V₂Al₁₈. An investigation of this part of the ternary system will soon be started.

A detailed study of the γ(MgAl) phase by single-crystal x-ray diffraction has progressed very favorably during the last few months. The phase is body-centered cubic and has a composition range which extends at least from 45 atomic per cent Mg to 59 atomic per cent Mg with a corresponding variation of the cube edge from 10.44 A to 10.60 A. We have succeeded in obtaining single crystals of the two extreme compositions Mg₁₃Al₁₆ and Mg_{17Al12 and have collected complete sets of intensity data from both crystals. The structural parameters for the first crystal have been refined to the point that R = 0.056. The intensity data obtained from the second crystal are being processed. The crystal of composition Mg13Al16 is highly disordered; it transforms on annealing at about 350°C into a very complicated phase, the β phase. Crystals of the β phase have been obtained and will be studied later. The crystal of composition Mg17Al12, which is supposedly ordered, is stable down to room temperature.}

The magnesium atoms have a metallic radius about 15 per cent greater than that of the aluminium atoms. The considerable difference in composition between the two γ(MgAl)-phase crystals, therefore, will have to be associated with differences in size and regularity of those coordination polyhedra in which the disorder takes place. Hence the distribution of the two kinds of atoms over the crystallographically different positions can be traced through detailed metrical analysis of these polyhedra. We have thus obtained strong evidence that in Mg₁₃Al₁₆ the disorder is localized in one of the two crystallographically different Friauf polyhedra in the structure. The calculated metallic valencies are in very good agreement with this result. The "ordered" Friauf polyhedron is almost identical in size and shape with that observed in the Mg₃Cr₂Al₁₈ structure, while the disordered polyhedron is distorted and larger in size. A similar analysis will soon be made of Mg₁₇Al₁₂.

The crystal of Mg₂Al₃, the β(MgAl) phase, referred to earlier in this proposal, presumably incorporates five crystallographically different Friauf polyhedra.

The intermetallic compounds Fe₃Zn₁₀ , Ni₃Zn₁₀, and Mn3Zn10 commonly referred to as the T-phases, are reported in the literature to as the Γ-phases, are reported in literature to be cubic with a cell edge of approximately a₀ = 8.8 A and space group. The structure proposed by Osawa and Ogawa, Z. Krist., 68, 177 (1928), has been generally accepted and is described in handbooks such as Pearson, Handbook of Lattice Spacings and Structures of Metals, Pergamon Press (1958); it has been assigned the type number D8₁. This structure is not in accord with the fundamental structural principles that we would expect to apply in these three compounds. A re-examination was therefore initiated. We have so far explored single crystals of Ni₃Zn₁₀ only. A complete three-dimensional set of diffraction data has disproved the assigned type number D8₁. The actual atomic arrangement in the crystal of Ni₃Zn₁₀ is based on icosahedral configurations, as we expected, and not, as was claimed, on "body-centered" cubes. It seems to us that structures of type number D8₂ do not exist. We shall soon re-examine crystals of Fe₃Zn₁₀ and Mn₃Zn₁₀.

Investigations of a series of intermetallic compounds referred to in the literature as γ-brass-type compounds with doubled and tripled unit-cell edges, i.e., with cube edges of the order of 18 A and 27 A respectively have recently been started, with the object of studying the mechanism of this doubling or tripling. So far two such phases have been attacked, the NiCd₄ phase and the Cu₄Sn phase. The studies are based on complete three-dimensional sets of intensity data obtained with the use of single crystals.

We have noted that Cu₄Sn has a cube edge of 18 A and not of 27 A as is sometimes stated in the literature.

We have found that Ni-Cd alloys on slow cooling form crystals of one and the same habit regardless of composition over a range between about 12 atomic per cent nickel and 55 atomic per cent nickel. The x-ray diffraction patterns of these crystals are very similar to one another, except that some patterns indicate primitive cubic cells of edge a₀ ~ 9 A and others face-centered cubic cells of edge a₀ = 19 A. A fairly detailed study has been made of a crystal of approximate composition NiCd₄, which is face-centered cubic with cell edge a₀ = 19.5 A. This crystal exhibits disorder between slightly different atomic arrangements. It seems likely that this phase has a very wide range of homogeneity, and that the degree of disorder varies with composition. In order to obtain a detailed picture about the nature of this phase it will be necessary to obtain a complete three-dimensional set of intensity data from each of a number of single crystals of different compositions and then to compute three-dimensional Fourier maps. Such a procedure may very likely be necessary to clarify the nature of several presumably related phases in a number of other alloy systems. Of particular interest are the systems cadmium-palladium and cadmium-platinum, in each of which there seem to be three phases that differ only very slightly in structure.

It is very easy to obtain single crystals of the various nickel-cadmium phases. The use of our present conventional photographic methods for the collection of the x-ray data would require a formidable investment of labor. With an automatized x-ray diffractometer and a powerful x-ray source the investigation could be carried out with moderate effort. At present we shall conduct detailed studies on only one crystal of each phase and shall carry out supplementary studies of preliminary nature with powder methods, using crystal-monochromatized radiation.

The intermetallic compounds Mg₆Pd and Mg₆Pt seem to have structures very similar to those of the aforementioned compounds. The crystals are cubic, the edge of the unit cell being a₀ = 20 A. These compounds will be investigated later.

We know of many more alloy phases that are likely to provide valuable information about the nature of bonding in metals, but it is very likely that the work outlined above will lead us to even more important structure problems that we might prefer to pursue. We anticipate that the prosecution of the research so far described will require several years.

Theoretical studies on the nature of intermetallic compounds and other alloy phases will be carried out in parallel with the experimental investigations.

A summary of our present and future research is given below:

1. Accurate refinement of the atomic positional parameters of NaCd₂.
2. Detailed crystal structure investigations of Cu₄Cd₃, Mg₂Al₃, γ(MgAl), jS'(MgAl), Fe₃Zn₁₀ , Ni₃Zn₁₀, Mn₃Zn₁₀ (“T” phases), Cu₄Sn, all existing phases in the system Ni-Cd, several phases in the systems Pd-Cd and Pt-Cd, and Mg₆Pd and Mg₆Pt.
3. Phase-diagram studies of (a) the system Mg-Al-X (X = transition element), with special attention to be given to Mg-Al-V. (b) the entire system Ni-Cd.
4. Theoretical studies on the nature of intermetallic compounds and other alloy phases.

General Objectives of the Program

The reason for our particular interest in crystal structures of extreme complexity is that in general the diversity of environment enables the atoms to assume positions relative to one another characteristic of their sizes and bond-forming powers, whereas a simple structure involves adjustment of one atom to another in such a way that only an average value of atomic properties finds expression. In the complex structures, dependent on many parameters, there are many independent interatomic contacts, and many different values of interatomic distances can be determined.

At the present time the resonating-valence-bond theory of metals and alloys, developed in association with the experimental work in the California Institute of Technology, provides a moderately satisfactory explanation for many of the observed features of the complex structures determined for intermetallic compounds. The theory of these compounds is, however, far from complete, and it is probable that further experimental and theoretical work can lead to great progress in the understanding of the nature of intermetallic compounds and other alloys (crystalline solutions) and in the correlation of the physical properties of alloys with their composition and structure.

In many instances, interpretation or even detection of important structural details is, unfortunately, inhibited due to lack of accuracy of the experimental work and lack of completeness of the refinement of the structural parameters. The scope of our present plans requires that the experimental work as well as refinement calculations be carried on to a high degree of accuracy.

Experiments and Instrumentation

For the collection of intensity data for x-ray reflections from single crystals we have been using conventional photographic methods, especially the Weissenberg technique. The intensities are estimated from photographs by visual comparison with a calibrated scale. This is the most time-consuming and cumbersome phase of many of our present experiments, especially when crystals of very complex intermetallic compounds are to be studied. Such crystals produce between one thousand and two thousand symmetrically independent reflections. These have to be measured in sets; and in order to obtain correlation factors between the sets, many reflections have to be measured repeatedly on different photographs. The quality of these data determine the meaningful degree of accuracy to which refinement can be carried out. The considerable investment of labor required to obtain by the visual method complete sets of data of adequate accuracy is at present the obstacle most urgently to be alleviated.

A second difficulty sometimes arises from the fact that certain intermetallic compounds form only crystals of extremely small size. The intensity data for Cu₄Cd₃ and Ni₃Zn₁₀, for instance, had to be obtained with the use of crystals about 10 microns in diameter; exposure times of about 250 hours were required for each photograph and the x-ray camera had to be modified to allow a reasonable signal-to-noise ratio.

An automatized x-ray diffractometer operated with a powerful x-ray source (rotating-tar get tube) and reliable counter equipment would considerably facilitate our research on complex intermetallic compounds. Such an instrument would also stimulate more detailed investigations of alloy phases of varying composition, for which complete sets of intensity data will have to be obtained from several single crystals as was mentioned earlier in this report.

A General Electric x-ray diffractometer and single-crystal orienter has been made available to us through a grant from ARPA; a locally assembled stabilized constant-potential power supply and counter equipment are on hand. It is our plan to accumulate experience with this instrument through manual operation and then to develop an instrument that is rigid and accurate enough to be automatized and that can be used with a rotating-target tube. A separate equipment proposal is being prepared for submission to NSF.

In parallel with our single-crystal studies, supplementary metallographic investigations will be carried out to establish composition ranges of alloy phases and also to explore and re-examine a number of phase diagrams. A fairly complete metallographic laboratory has been set up during the last two years, including levitation-melt furnace, electric-arc button furnace, polishing equipment, and a Zeiss Ultraphot II Pol microscope. A few pieces of equipment such as cut-off machine, ultrasonic cleaner, and re-circulator are still lacking.

Requested Financial Support

Our research on the structure of intermetallic compounds and other alloy phases has been carried on through contracts from the Office of Naval Research. At present this work is supported under Contract Nonr-220(33) at a rate not to exceed 20, 000 dollars per year. The support will very likely continue through August 31, 1964, but presumably with reduced funds. It is very likely that the present contract will be discontinued after August 31, 1964. The Office of Naval Research has recommended us to seek support from the NSF.

Our research on complex intermetallic compounds has been ever more intensified during the last years and has now reached a level that can be maintained only with additional financial support. This is due to the fact that our investigations have led us to ever-more important and complex structure problems that we liked to pursue, but also to gradual solution of the problem of obtaining qualified technical assistants.

Mrs. B. Christiansson and Mr. K. Christiansson joined our research group in December last year. Mrs. Christiansson has many years' experience in metallurgy and x-ray diffraction, and Mr. Christiansson has unusual qualifications of temperament and broad technical experience. He is an excellent experimentalist. Mr. K. Lautsch has been trained here. So far, he has carried out most of the x-ray photography and the collection of data.

Our ONR funds to pay these practically irreplaceable assistants will be expended by June 31, 1963.

Graduate and undergraduate students show increasing interest and desire to participate in the research as the results become known and the program develops. At present, these students have to be paid from other than ONR funds.

The salaries given in the attached budget are the ones at present paid plus an anticipated increase. Only one graduate student is at present participating in this program.

The amounts estimated for computer charges and expendable items also correspond to our present expenditures. During the current fiscal year a considerable fraction of our computer charges has been covered by other than ONR funds. Such funds will not be available to us during the coming year.

We respectfully request support of $367,035 for a period of five years; that is, $73,407 per year according to the attached budget. The desired starting date is July 1, 1963, since we anticipate that our present funds will be depleted by June 31, 1963.

Proposed Budget

Salaries
Senior Research Fellow, S. Samson	$6,700
Research Assistant, K. Lautsch	5,700
Research Assistant, B. Christiansson	5,700
Technical Assistant, K. Christiansson	5,700
3 Graduate Students for summer research (no staff benefits)	2,160
3 Graduate Students, 12 months (no staff benefits)	11,640
Manuscript typing and clerical assistance	750
Instrument shop assistance for repairs, minor alterations, adapters, structure models, including glass blowing, etc.	3,000
Total Salaries	$41,350
Approved staff benefits
10.7% of faculty salaries	$717
7.0% of non-academic salaries	1,459
Total staff benefits	2,176
Publication charges	600
Computer charges	5,000
Expendable equipment and supplies
Film, glassware, crucibles, refractory materials, chemicals, etc.	3,000
X-ray tubes, rectifiers, electronic tubes, counter tubes, etc.	3,000
Total expendable items	6,000

Proposed Budget (Continued)

Minor permanent equipment per year
Cut-off machine and ultrasonic cleaner for metallographic samples, resistance furnaces, variacs, vacuum pumps and gauges, crystal grower, etc.	$3,000
Travel to scientific meetings	600
Total direct cost per year	$58,726
Indirect costs
25% of total direct costs	14,681
Total cost per year	$73,407
Amount requested for a period of five years	$367,035