Motivation
Laves phases have the general composition AB2 and form one of the largest groups of intermetallic compounds with more than 1400 known examples. They crystallize in three structure types: cubic MgCu2 (C15), hexagonal MgZn2 (C14) and hexagonal MgNi2 (C36). In the first half of the last century it was shown in the pioneering works of J. B. Friauf, F. Laves, G. E. R. Schulze, F. C. Frank and J. S. Kasper, that the Laves phases can be regarded as tetrahedrally close packed structures of components A and B with tetrahedral interstices only. The ideal ratio of the radii based on a hard-sphere model is rA/rB = √(3/2) with two kinds of coordination type polyhedra. The icosioctahedron surrounding the A atoms has 4 six-fold A vertices and 12 five-fold B vertices, whereas the icosahedron surrounding the B atoms has 6 five-fold A and 6 five-fold B vertices.
The structure types C15, C14 and C36 can be regarded as polytypes with c3, h2, and (ch)2 stacking sequences in Jagodzinski-Wyckoff notation of one common slab composed of tetrahedra and truncated tetrahedra. The A atoms form a four-connected network interpenetrated by a six-connected network of the B atoms. Approximately 25% of the binary Laves phases exhibit considerable homogeneity ranges.
Laves phases have been studied intensely to understand the fundamental aspects of phase stability. However, simple factors governing the crystal structure type of geometric (rA/rB) and electronic (valence electron concentration vec and electronegativity difference χA–χB) nature have proven to be helpful in predicting the occurrence and stability of the Laves phases only in strictly limited cases. In general, phase stability and properties of Laves phases are difficult to forecast, especially the origin of the homogeneity ranges and disorder phenomena.
In order to understand the nature of Laves phases, studies on a number of Nb-TM alloy systems with TM = Cr, Mn, Fe and Co are in progress by combining experimental and theoretical methods.
Inter-Institutional Research Initiative
The Nature of Laves Phases
Since January 2006 this work is part of an inter-institutional research initiative of the Max Planck Society 
The Nature of Laves Phases with the Max Planck Institutes Metallforschung and Festkörperforschung in Stuttgart, Eisenforschung in Düsseldorf and Chemischer Physik fester Stoffe in Dresden as members.
The group in Dresden is currently working on the following research topics:
— Site occupation reversal in the C14 Laves Phases
— Chemical bonding in Laves phases
— Mechanical behavior of the intermetallic phase Nb2Co7
— Defect softening of NbFe2 and NbCo2
— Phase stability, structure and disorder of Co-Nb Laves phases and
ternary Laves phases
— The magnetic phase diagram of the Laves phase Nb1-yFe2+y and quantum critical phenomena in NbFe2
Phase Diagram Studies
Today’s collection of phase diagrams is a constantly growing body, but coverage and precision of published phase diagrams—even for binary systems—is insufficient. Phase diagram studies with the major goal to obtain very precise information for the setup of crystal growth experiments and to understand phase stabilities have been performed on a number of binary and ternary systems. Here, the main achievement is the exceptional precision of the accumulated data which is mandatory for the development of tools for modelling and predicting of Laves Phases. As an example the redetermined Co-Nb phase diagram is shown below.
Disorder and Defects
For a large number of Laves phases phenomena like constitutional vacancies, substitutional disorder and local displacements have been studied in detail to give an answer to the question of the effect of entropic stabilization. These investigations are quite unique in their complexity and will help in the future to address fundamental questions concerning phase stabilities at higher temperatures.
Only one example is discussed here. In case of ternary Laves phases of C14 structure type with the general formula A(B'1-xB''x)2 usually smaller B atoms occupy the Wyckoff positions 2a (B2) and 6h (B1) of the space group P63/mmc. Experimental studies of ternary phase diagrams containing a C14 Laves phase along the section AB'2-AB''2 have shown considerable homogeneity ranges for many systems. Thus far, only a few studies on C14 A(B'1-xB''x)2 compounds dealt with the distribution of the B atoms among the two possible crystallographic positions.
The results of the single crystal structure refinements for C14 Nb(Cr1-xCox)2 at various compositions reveal substantial deviations from the idealized C14 crystal structure: (i) the networks of the smaller Cr or Co atoms and of the Nb atoms are distorted; (ii) there is Cr/Co substitutional disorder at 2a and 6h Wyckoff sites with preferential occupation of the respective minority component at the 2a site. The refinements clearly reveal a composition dependence of the site preference, including evidence for a site occupation reversal. In the case of the Cr-rich crystal (x = 0.33), Co atoms prefer the B2 (2a) site, whereas in the Co-rich crystals (x = 0.67 and 0.80), the B2 (2a) site is preferred by Cr atoms. In other words, the minority component prefers the B2 (2a) site. The crystal with x = 0.50 exhibits no preference of Cr/Co for either of the sites.
Modelling
Phases and phase diagrams of special interest have been modelled by means of first-principles calculations and the semi-empirical CALPHAD approach. Because modelling and simulation methods for condensed matter relies on approximations it is important to examine carefully the theoretical results and—if needed—to modify the theoretical ansatz to obtain finally a match of the experimental and theoretical data. This is an important progress towards the dream of a materials scientist, to predict structure and properties of materials.
The heat of formation at T = 0 K was computed by first-principles full-potential electronic structure calculations for selected compositions Nb4Cr8-NCoN with N = 0 - 8 to obtain information on the ordered state at low temperatures for the C14 phase Nb(Cr1-xCox)2. According to these calculations the C15 structure is stable for the binary phases and the C14 structure is stabilized by going ternary. Within the approximation of the calculations (selected compositions, translationengleiche subgroups, no relaxation of structural parameters or cell shape) two ordered phases are stable at T = 0 K, (Nb4Cr2(2a)(Cr3Co3)(6h)) and (Nb4Cr2(2a)Co6(6h)).
Physical Properties
Our focus lies on magnetic, electrical and mechanical properties of Laves and related phases. Only mechanical properties are discussed here.
At room temperatures, Laves phases show a brittle behavior. Above the brittle-to-ductile transition temperature
Laves phases can be deformed plastically. The mechanical behavior of Laves phases strongly dependents
on the composition. In the Co-Nb system all three polytypes of the Laves phase exist in dependence on composition
and temperature. Therefore it was possibile to study the effect of the different crystallographic structures on the hardness.
It was found that maxium hardness occurs for stoichiometric composition, thus the system shows defect softening.
Nb2Co7 forms at 22 at.% Nb and is structurally related to the Laves phases. However, the phase exhibits different mechanical properties. The material can be strongly deformed at room temperature by hammering without shattering or fracturing and it can be strained in compression to at least 5% without fracture. At
the same time, Nb2Co7 behaves like a brittle material when tested under bending or tensile load. The mechanical properties of this phase were systematically studied by microhardness, compression, tensile and bending tests and the microstructure was analysed by light-optical and scanning electron microscopy
before and after testing. A typical Vickers indent in Nb2Co7 as shown on the right side reveals anisotropic plastic deformation near the indent.
This work is done with the collaboration of