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Cite this: Dalton Trans., 2012, 41, 14225

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Challenges in intermetallics: synthesis, structural characterization, andtransitions

Robin T. Macaluso* and Benjamin K. Greve

Received 20th June 2012, Accepted 2nd September 2012DOI: 10.1039/c2dt31328f

Intermetallics that contain rare-earth elements are particularly interesting because of their temperature-andpressure-dependent structural and physical transitions that make them potential candidates for magneticapplications. This article highlights synthetic routes and structural characterization advancements used toinvestigate intermetallic materials. Experimental and theoretical examples of three intermetallic structuretypes – ThCr2Si2, Heusler and Laves – are discussed to present a historical review and to illustrate thegrand challenges in unravelling structure–property relationships of intermetallic compounds.

Introduction

Intermetallic compounds are extended solids that can be broadlydefined as the combination of two or more elements that borderor lie to the left of the metalloid line on the periodic table.Unlike ionic solids, the limited electronegativity differencesamongst constituent elements within an intermetallic compoundconsequently present a challenge in predicting structures basedon a priori knowledge of oxidation states. Even more difficult isto predict how stoichiometric composition or external stimulisuch as temperature, pressure and magnetic field induce struc-tural transitions.

Transitions in solids are ubiquitous. For example, diamonds –the cubic form of carbon – are stable at high temperatures(900–1300 °C) and high pressures (45–60 kbar) and convert tographite upon reaching the Earth’s surface. (The graphite is thenoxidized by oxygen in the atmosphere.) In fact, diamond onlyreaches the Earth’s surface during rapid volcanic eruptions wherefast kinetics prevents thermodynamic pressure and temperature-dependent phase transitions. The Iron Age (ca. 1300 BC–200AD) evolved from the Bronze Age because of the technology toproduce steel tools using martensitic transitions between marten-site Fe and austenite Fe.1 Martensitic transitions were firstreported by Adolf Martens in the 1890s when he obtainedmicroscopy images that beautifully displayed martensite needlesin a matrix of austenite.2

Martensitic transitions are one example of many temperatureand pressure-dependent transitions that are important in numer-ous modern-day applications, e.g., shape-memory alloys, super-conductivity and magnetic resonance imaging, thermoelectricmaterials for refrigeration, magnetism in hard drives, etc. In thisPerspective, we discuss synthetic conditions and structure–prop-erty relationships that yield intriguing composition, temperature

and pressure-dependent transitions in intermetallic materials.This discussion is limited to three structure types well known inintermetallic literature: ThCr2Si2, Heusler, and Laves.

Synthesis

In the synthesis of organic compounds, coordination spheres offour about carbon and six around transition metal centres arecommon. Bonding in intermetallics, on the other hand, can becomplex and extensive. Local coordination spheres beyond sixare common, making the prediction of structure and behaviourof intermetallics a challenge. Therefore, the choice of startingmaterials, relative molar ratios, and thermodynamically relatedvariables such as temperature and pressure must be considered inlight of phase diagrams. Binary and ternary phase diagramsbecome immensely useful tools for predicting and avoidingundesirable transitions and to encourage growth of the desiredphase.

Some general considerations for the synthesis of intermetallicsare described below:

• Melting points of most metals are typically greater than∼1000 °C; however, a combination of metals may lower themelting point of an elemental metal. For example, melting Sialone requires 1600 °C, but mixing Au with Si lowers themelting point down to 363 °C.3

• Metals can react with the reaction vessels. Attention must bepaid to the reactivity between constituent metals and the reactionvessel at the desired temperature and pressure of the synthesisprocedure. Typical container materials include Al2O3, Pt, andY-stabilized ZrO2.

• Metals will readily form oxides in air at high temperatures.Special care must be taken to prepare the reactions in an inertenvironment. Because glass melts at ∼400 °C, intermetallics arecommonly synthesized in sealed ampoules made of quartz, mo-lybdenum or tungsten. However, very oxophilic metals such asscandium are known to vitrify quartz.

University of Northern Colorado, Department of Chemistry andBiochemistry, Greeley, CO 80639, USA. E-mail: robin.macaluso@unco.edu;Fax: +1 970 351 2559; Tel: +1 970 351 1282

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Polycrystalline materials

Arc melting is a common method for the synthesis of poly-crystalline intermetallic materials. A typical arc-melting set-up,pictured in Fig. 1, includes a water-chilled sample chamber, athorium-impregnated tungsten stinger, and a high voltage powersupply.

Stoichiometric amounts of metals are placed on a copperhearth inside the sample chamber. In the presence of an inert gas(usually argon), the tungsten stinger is used to create a plasma,which is, in turn, manually placed in the vicinity of the initialmetal mixture. The plasma melts the metal almost instantly, andthe resulting product is commonly referred to as a “button”. Thebutton is usually turned over and melted multiple times to ensurehomogeneity. Because the button is situated on a water-cooledcopper hearth, the button cools within a matter of minutes.

Arc melting can be an attractive synthesis method. Samplescan be produced within just a few hours, and the procedure issimple. One simply needs to weigh out the materials accurately.Gram-size samples can be produced easily as long as the hearthwill contain the desired mass.

Because there is no control over the cooling rate of the melt,arc melting is essentially limited to congruently melting com-pounds with eutectic points in the phase diagram. In addition,some metallic elements with a low sublimation or vaporizationpoint solidify on relatively cool chamber surfaces before reactingwith other starting materials. If the initial materials were weighedstoichiometrically, structural defects may result from sublimationor vaporization. This can be overcome by placing an excess ofthe metal in the furnace before the initial melt; however, theappropriate amount of excess metal can only be determined bytrial-and-error.

Single crystals

Flux growth. Flux growth has been commonly used to syn-thesize single crystals of intermetallics, including heavy fermionmaterials discussed later in this Perspective. A brief overview isgiven here, and the reader is referred to ref. 3 for a morethorough review of flux growth.3

A schematic of typical ampoule for flux growth is pictured inFig. 2.

Molar ratios of the starting materials are placed in a crucibletogether with an excess of metal flux. The crucible and its

contents are then sealed into an evacuated secondary container,which is usually made of quartz. The high softening point ofquartz (∼1200 °C) and lack of reactivity with most metals makeit an attractive choice of material for use as secondary containers.The flux serves as a solvent that lowers the melting points of theother metals by solubilising them. The flux can be a metal thatwill be incorporated into the final product, which is also knownas a ‘reactive flux’. Typical fluxes include: Al, In, Ga, Pb, Bi,and Sn. Many crystals produced in this manner are on the milli-metre or centimetre scale, which are appropriate dimensions forelectrical transport and magnetic property measurements.

Because the flux has the lowest melting point of all constituentelements, the ampoule is removed at some temperature above themelting point of the flux, immediately inverted and spun in acentrifuge to separate excess liquid flux from the solid crystals.Residual flux on crystal surfaces can be removed by etching.Some images of crystals grown from this technique are includedin Fig. 3.

In a single flux growth attempt, one has control over severalvariables: choice of flux, molar ratios of starting materials, con-tainer material, temperature profile, and heating and coolingrates.

In addition to thermodynamically stable compounds (rep-resented as “line compounds” in a phase diagram), flux growthcan enable access to kinetically stable phases by controlling thecooling rate from a peritectic point.

We refer to a recent example, CePd3Ga8 – a potential magneticspin glass and whose image is shown in Fig. 3 – to illustratehow a kinetically stable product can be isolated. For CePd3Ga8,the cooling rate had a significant impact on the resulting struc-ture. Fast cooling of the melt produced large crystals of therhombohedral polymorph, whereas slow cooling yielded the

Fig. 1 Interior of a sample chamber of induction-melting apparatus.Melt occurs on the water-cooled copper hearth.

Fig. 2 Photograph of typical flux growth ampoule.

Fig. 3 Scanning electron microscope images of (a) Ce1.33Pt4Ga10 and(b) CePd3Ga8 crystals grown in the author’s laboratory (reproduced withpermission).

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orthorhombic polymorph. In fact, high-resolution in situ syn-chrotron studies clearly showed that the two polymorphs couldtransition back and forth by cooling and/or heating.4

Other methods. The concept of enhancing the solubility ofmetals can be combined with well-known single-crystal syn-thesis methods such as the Bridgman method, Czochralskigrowth and float-zone refining, which are particularly useful inproducing single crystals that are several centimetres long – anadvantage for neutron scattering studies. Czochralski andBridgman growth methods rely on an initial seed crystal, whichgrows with slow extraction from a liquid melt. In float-zonerefining, a polycrystalline rod of the product is slowly passedthrough an induction coil and crystallizes as it cools on the otherside of the coil. An additional advantage of float zone refining isthat impurities in the polycrystalline rod can be separated fromthe single crystal of the desired intermetallic product. This tech-nique is commonly used in the industrial production of high-purity Si wafers.

Some combinations of elements provide significant challengesand can contribute to sample-dependent physical properties.Take YbRh2Si2, for example. The high vapour pressure of Yb,which has a lower melting point than Rh or Si, results insamples of varying stoichiometry. Although the chemical com-position of the crystals most likely average to 1Yb : 2Rh : 2 Si(in excess In flux), small deviations in stoichiometry can resultin observable differences in physical behaviour. To control thestoichiometry, YbRh2Si2 was grown from combining the conceptof excess In flux and the Bridgman method; an optimal 3Yb : 2.1-Rh : 1.8Si melt (in excess In) remained at liquidus temperaturesfor an hour in the liquid state before slow-cooling.5

Structural characterization

In situ diffraction technologies

Both X-ray and neutron diffraction techniques are widely usedfor the structural characterization of intermetallic compounds. Asmentioned above, intermetallic compounds are frequently pre-pared as polycrystalline materials; therefore, powder X-ray dif-fraction (PXRD) is perhaps one of the most widely usedtechniques for the initial characterization of intermetallic com-pounds. This technique is rapid and easily implemented in labo-ratory settings for routine analysis of intermetallic compounds.

Advancements in X-ray and neutron diffraction have readilyenabled in situ studies of materials under non-ambient con-ditions, such as variable temperature and pressure. Furthermore,advancements in synchrotron X-ray sources, which providehigh-energy, high-flux X-rays, combined with advancements indetector technology allow one to record high quality diffractionpatterns in a fraction of a second; a diffraction pattern of compar-able quality may potentially require hours to collect on alaboratory X-ray diffractometer. The development of new spalla-tion neutron sources, such as the Spallation NeutronSource (SNS) at Oak Ridge National Lab, Oak Ridge, TN, pro-vides a high flux source of neutrons; and permits studies on con-siderably smaller sample sizes of materials and of a muchsmaller time scale.

Studying materials under non-ambient conditions is importantbecause such conditions can often induce phase transitions.Studying the phase transition of a material is of criticalimportance not only for scientific interest but also for potentialapplications. Two phases can exhibit vastly differentphysical properties although they possess the same chemicalcomposition.

The effects of temperature and pressure are readily studiedusing X-ray and neutron scattering. A variety of variable temp-erature sample environments, such as cryostats, cryostreams,resistance heaters, refrigerators, etc., enable detailed studies oftemperature induced phase transitions in materials. These sampleenvironments can permit detailed examinations of the structuresat temperatures as low as a few K to greater than 1600 K.

Pressure-dependent transitions can be observed in situ becauseof recent advances in sample environments. Pressures as high asseveral hundred GPa can be achieved using diamond anvil cells(DACs), which compress the sample between two diamondfaces. A schematic depicting a DAC is provided in Fig. 4.A number of specialized DACs are capable of heating or coolinga sample while simultaneously applying pressure, which permitsin situ studies to examine the effects of both pressure and temp-erature. In general, pressure in a DAC is manually controlled bytightening screws that bring the diamond faces into closercontact. While the DAC design readily permits achieving veryhigh pressures, on the order of hundreds of GPa, there is verylittle fine control over the pressure, especially in the low-pressureregion.

Gas pressure cells, on the other hand, can be used to preciselycontrol pressure ranges up to ∼0.5 GPa, and they are routinelyincorporated with refrigerators to examine the combined effectsof temperature and pressure on a material. These pressure cellsare most often used with neutron diffraction techniques becausethe thickness of the sample environment requires highly pene-trating radiation sources.

Furthermore, diffraction techniques can be combined withother physical property measurements in situ. For instance, it ispossible to simultaneously measure the resistivity change of amaterial as a function of temperature while collecting diffractiondata. Such an experiment permits direct correlations of structure–property relationships while eliminating errors that may poten-tially arise from performing the measurements separately, e.g.,

Fig. 4 Schematic diagram of a diamond anvil cell used in pressure-dependent scattering experiments.

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temperature calibration, slight deviations in the sample stoichio-metry from different synthetic batches, etc.

Total scattering techniques

As mentioned above, local structure is important to the complexnature of bonding in intermetallic compounds. Total scatteringtechniques, which involve the analysis of both the Bragg diffrac-tion and the diffuse scattering from a material, enables the under-standing of structure on the order of a few nanometers. Fromtotal scattering experiments, the atomic pair distribution function(PDF) provides the probability of finding two atoms separated bysome distance, r, and can be modelled to represent the localstructure of a material.

Although total scattering techniques have been instrumental incharacterizing nanoscale samples of intermetallics and have beenapplied extensively to solid materials in general, there remainsmuch to be learned from applying total scattering to bulk inter-metallics. When designing a total scattering experiment, oneneeds to consider sample absorption, which becomes a signifi-cant problem with heavier elements such as those inintermetallics.

In an ideal X-ray scattering experiment in transmission geo-metry, such as that used for total scattering experiments, the totalabsorption, μR, should be less than one. If a polycrystallinesample of PrInAg2 is packed in a capillary of radius = 0.4 mmwith a 60% sample packing fraction and one assumes an X-ray λof 0.71 Å (which is equal to wavelength of Mo Kα radiation),then μR ∼ 15.2, an order of magnitude larger than the desired μR< 1. Diluting the sample with quartz is commonly used to over-come absorption problems in diffraction experiments because itdoes not possess long-range structural order; however, quartzdoes contribute significantly to diffuse scattering. The combi-nation of higher energy X-rays and a smaller capillary diametercould potentially be used to overcome absorption problemsinstead. For the same PrInAg2 sample packed in a capillary witha radius = 0.20 mm with 60% sample packing fraction, μR is∼0.51 with X-ray λ of 0.1378 Å. Hence, local structure of inter-metallics can be experimentally characterized by slight modifi-cations to the capillary radius and more importantly, conductingtotal scattering experiments at a synchrotron.

Spectroscopic techniques

In addition to diffraction techniques, spectroscopic techniquessuch as XAS, Mössbauer spectroscopy, and solid-state NMRhave been employed for studying the structures of intermetalliccompounds. XAS includes both the extended X-ray absorptionfine structure (EXAFS) and X-ray absorption near edge structure(XANES) and can provide information regarding the oxidationstate and coordination environment of the elements. XASmeasurements have been employed in studies of the local struc-ture of a variety of intermetallic compounds. A combinedEXAFS and neutron diffraction study was used to examine theHeusler compound Co2MnSi, which revealed the presence ofconsiderable chemical disorder that had a negative influence onthe spin polarization in this material.

Mössbauer spectroscopy relies on a gamma source of thesame isotope as the element of interest to examine the chemicalenvironment of a material. The use of this technique is limitedby the choice of gamma emitters. Mössbauer spectroscopy is fre-quently used for characterizing Fe containing intermetallicsbecause the gamma source, 57Co, is relatively stable for a longtime. Cu2GdIn has been studied with 155Gd Mössbauer spec-troscopy, and the presence of magnetic dipole hyperfine inter-actions in the electronic structure of this material wasdetermined.6

Solid-state NMR techniques have also been employed for thestructural characterization of intermetallic compounds. However,similar to Mössbauer spectroscopy, these measurements arelimited to compounds containing certain elements because of theuse of specialized probes for the element of interest. Whenappropriate NMR probes are available, a considerable amount ofinformation about the structure of the material can be obtained.For example, the half-Heusler compound YbPtSb was examinedusing a combination of 121Sb and 198Pt solid-state NMRmeasurements, and similar to the Mössbauer studies ofCu2GdIn, allowed the authors to present information about thehyperfine structure of this material.6

Common intermetallic structure types

ThCr2Si2 and CaBe2Ge2 structure types

Rare-earth intermetallics of the composition, RT2X2 (R = rare-earth, T = transition metal, X = main-group metal) and classifiedwith the ThCr2Si2 (space group I4/mmm, No. 139) type havebeen studied intensely, in part because of the unconventionalsuperconductivity exhibited in some of these materials. Inaddition, the ability of this structure type to host an extensivearray of elements results in a diverse set of materials, rangingfrom oxypnictides and borocarbides to intermetallics. Structure–property relationships of the ThCr2Si2 type are important in twomajor research areas – heavy-fermion superconductivity andquantum phase transitions. Because the ThCr2Si2 structure typeis very closely related to the CaBe2Ge2-type, transitions betweenthem will be discussed. Readers who are interested in the richchemistries of rare-earth borocarbides and rare-earth pnictideoxides should refer to ref. 7 and 8, respectively.

Crystal structure. The ThCr2Si2 type is commonly referred toas a variant of the BaAl4 type and is shown in Fig. 5. The unit

Fig. 5 BaAl4 structure showing the Ba and Al sites as black and grayspheres, respectively. Dashed lines represent the unit cell.

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cell is composed of layers of interconnected tetragonal SiCr4pyramids stacked along the (001) direction where Th liesbetween the pyramid layers.

The space group of ThCr2Si2 is I4/mmm and there are twomolecules per unit cell (Z = 2). Atomic coordinates are listed inTable 1.

Lanthanides, actinides, or alkaline earths typically occupy the2a site. Main group metals are usually located on either the 4dor 4e sites, although the 4d site can also accommodate transitionmetals.

In a comprehensive review article, Just and Paufler comparedthe c/a and z-parameters for ∼600 compounds characterized withthe ThCr2Si2 type.10 The c/a and z-parameters can be used incombination to understand the range of structural features andstability of this vast family of compounds. Fig. 6 is a plot of theatomic coordinate, z, versus c/a. Most materials are clusteredbetween two points, A and B, where Point A represents a16-coordinate Th with all Cr–Th and Si–Th bond distancesequal and Point B represents a 12-coordinate Th with four Si–Thdistances shorter than the next nearest 12 Cr–Th bonds. Sincethe Th-site is equivalent to the 2a Wyckoff position, which hostspotentially magnetic ions, the variation in Th-coordinationimplies that changes in local structure about the magnetic ioncan have a profound impact on magnetic behaviour.

ThCr2Si2 and CaBe2Ge2 type materials crystallize with tetra-gonal unit cells, with lattice parameters a ∼ 4 Å and c ∼ 10 Å.However, the T and X-sites are swapped in every other squarepyramid layer. This seemingly minor interchange between the Tand X metals can imply different magnetic and transport

properties. Hoffmann and Zheng demonstrated elegantly withMonte Carlo simulations that the presence of the more electro-negative X metal on the tetrahedral site in the CaBe2Ge2 struc-ture increases the dispersion of the valence band, thereforematerials with the CaBe2Ge2 structure type should be character-ized with a smaller band gap and higher Fermi energy comparedto similar compounds with the ThCr2Si2 structure.11 Examplesof this structural importance will be discussed in this section.

Structural challenges. The reflection condition for body-centred lattices is that only reflections with h + k + l = 2n areobserved; therefore, one may expect that differentiating betweenthe ThCr2Si2 and CaBe2Ge2 structure types would be straight-forward. In practice, reflections due to h + k + l = 2n + 1 can beweak in intensity, and the coexistence of the two closely relatedphases can present characterization challenges as strong reflec-tions in the body-centered tetragonal phase (ThCr2Si2) may bemasked by reflections from the primitive phase (CaBe2Ge2).High-resolution capabilities of synchrotron and neutron scatter-ing under various conditions, e.g., pressure, temperature, etc.,have advanced structural understanding of relationships betweenthese two structure types.

Structural transitions. For some compounds, both α(ThCr2Si2) and β (CaBe2Ge2) structure types have beenobserved. For example, α-REIr2Si2 (RE = La, Ce, Pr, and Nd)can be obtained by slow-cooling or annealing powdered samplesat 870 K and β-LaIr2Si2 can be obtained by quenching or rapidcooling from a melt, growing single crystals with theCzochralski techniques, or from flux growth.12 Mihalik et al.studied the temperature-dependent structural transitions withdifferential thermal analysis, neutron diffraction, and in situpowder X-ray diffraction.3,13 The c/a ratio changes appear to befirst-order and change dramatically at critical transition temp-eratures. In addition, DTA experiments revealed hysteresis up to300 °C, which provides further support for the nature of the firstorder transition. Their crystal structures verified from neutrondiffraction experiments agree with the calculations performed byHoffmann and Zheng, which predicted that both structure typescould be described with an energy minimum. The structuralphase transition has been correlated to physical behaviour; the αphase is characterized with a Ce valence of 3.56 and becamesuperconducting at Tc ≤ 1.6 K while the β phase is characterizedwith a Ce valence of 3.32 and did not exhibit any signs of super-conductivity down to 1 K. Ab initio electronic structure calcu-lations suggest that the structural transition is accompanied by achange in the valence state of cerium.14

YbIr2Si2 also crystallizes in both body-centered and primitiveunit cells. By including a 10% excess of Yb in the crystalgrowth procedures, the CaBe2Ge2 type was favored. The primi-tive cell exhibited a magnetic ordering state at T ≤ 0.7 K. On theother hand, stoichiometric ratios of the elements led to theThCr2Si2 type with a non-magnetic ground state. LaIr2Si2 andYIr2Si2 have also been observed to crystallize in both structuretypes.15

Superconductivity in AFe2As2 (A = Ca, Ba, Sr, or Eu),16,17

sometimes referred to as the “122 iron arsenide superconductors”have generated a great deal of interest in the science community.Hole-doping the Ba-site with K yielded Ba0.6K0.4 Fe2As2 with a

Table 1 Atomic coordinates of ThCr2Si2 structure type

Atom Wyckoff site Atomic coordinate

R 2a 0, 0, 0T 4d 0, 12,

14

X 4e 0, 0, zRef. 9

Fig. 6 Free-parameter space of ThCr2Si2 considering two parameters,the atomic coordinate, z (on the z-axis) and lattice parameters, c/a, onthe x-axis. Reproduced with permission. Modified from ref. 9.

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superconducting transition temperature Tc = 38 K. Cs-dopedSrFe2As2 also yielded materials with Tc = 37 K. Evidenceobtained from Mössbauer spectroscopy and powder X-ray dif-fraction on SrFe2As2 and EuFe2As2 point towards interestingsecond-order phase transitions from the tetragonal ThCr2Si2 typeto the orthorhombic β-SrRh2As2 type occur at 203 and 190 Kfor A = Sr and Eu, respectively. This suggests that structural tran-sitions play an important role in superconductivity; however,temperature-dependent trends in the c-axis are yet to bedetermined.17

Heavy fermion intermetallics. Heavy fermion materials arepartially characterized by large Sommerfeld coefficients of elec-tronic specific heat.18 The Sommerfeld coefficient, γ, is relatedto heat capacity, Cp in eqn (1):

Cp ¼ γT þ αT 3 ð1Þwhere the αT3 term describes the classic phonon contributionand the γT term describes the electronic contribution, whichbecomes dominant at low temperatures. In a typical metal,γ ∼ 10 mJ mol−1 K2. For a heavy fermion, however, γ is largerby at least two orders of magnitude. This anomalously large γreflects the large degree of hybridization of the valence f-elec-trons associated with the Ln3+ (lanthanide) or An3+ (actinide)ion. Table 2 lists some heavy fermion superconductors with theThCr2Si2 structure type.

Distances between the rare-earth ions are typically greaterthan 4 Å, which are too long to be considered bonding. Thus, anunderstanding the cooperativity of distant ions to yield magnet-ism and superconductivity requires investigations into the localstructure of the magnetic ion.

Rare-earth intermetallics, namely Ce- and Yb-intermetallics,with the ThCr2Si2 structure type have played an important rolein our understanding of unconventional superconductivity andmore recently, these materials have come to be important inlaying the foundation of research in quantum criticality.

Superconductivity and quantum criticality. Quantum phasetransitions (QPT) result in a separation of magnetic and nonmag-netic ground states where the transition between the two statescan be controlled by non-thermal parameters such as chemicalcomposition, external pressure, or magnetic field. Although theground states are inherently defined by low temperatures, under-standing the structure–property relationships at or around thevicinity of the quantum critical point would lead to a profoundability to control material properties. With hundreds of ThCr2Si2structure types already reported and continuously being discov-ered, this Perspective will highlight two compounds that havepioneered this area of work.

Heavy-fermion superconductivity was first observed inCeCu2Si2 with a Tc = 600 mK which has been reported topossess the ThCr2Si2 structure type.19 Contrary to the seminalwork on phonon-mediated superconductivity,24 heavy-fermionsuperconductivity in CeCu2Si2 is due to localized magnetic Ce3+

ions. The presence of nonmagnetic La3+ ions suppressessuperconductivity.

Approximately thirty years after the initial report of heavy-fermion superconductivity, thermodynamic and transportmeasurements revealed antiferromagnetic order below TN =800 mK.25 By applying hydrostatic pressure, magnetic order wassuppressed while the superconducting phase was revealed. ThisQCP is further supported by resistivity and thermodynamicmeasurements that obey non Fermi-liquid behaviour in the vici-nity of the QCP. Powder neutron diffraction showed an incom-mensurate AF magnetic order for x ≥ 0.6 in a solid solution,CeCu2(Si1−xGex)2. The spin propagation vectors lie along the(hhl) planes at 50 mK, but slow down (as the diffraction intensi-ties decrease) as temperature approaches 0 K.26 Single-crystalneutron scattering experiments support findings from powderneutron diffraction data.27

The pioneering finding of heavy-fermion superconductivity inCeCu2Si2 led to observations of pressure-induced superconduc-tivity in CePd2Si2,

28 CeRh2Si2,22 and CeCu2Ge2.

21

Work on Yb heavy fermions is emerging as an exciting area inwhich to discover new compounds and explore quantum critical-ity more deeply. The rationale behind exploring Yb is that the4f13 Yb3+ electron configuration provides a hole–electronanalogy when compared to 4f1 electronic configuration of Ce3+.The first Yb heavy-fermion compound, YbRh2Si2, becomesmagnetic under pressure. Two anomalies in the temperature-dependent electrical resistivity appear under the application of1.5 GPa of pressure; these anomalies indicate that magneticordering can be induced out of a quantum critical point.29

YbIr2Si2, on the other hand, with a γ = 370 mJ mol−1 K2, pos-sesses a nonmagnetic ground state, and heat capacity and resis-tivity studies suggest that external parameters may be used toinduce a quantum critical transition to a magnetic or supercon-ducting state.30

Spin glasses. Magnetic spin glass materials are of interest tochemists and physicists because they represent a body ofmaterials that are on the verge of magnetic order. Severalthorough reviews of spin glasses are available. (See ref. 31.)Long-range magnetic order cannot be achieved in spin glassesbecause of impurities or geometric features such as tetrahedra,triangular nets, kagomé lattices, etc. The inability of spins toalign at low temperatures is characterized by a freezing tempera-ture, Tf, which can be observed with dc and ac susceptibilitymeasurements.

URh2Ge2 is the first CaBe2Ge2-type material where spin glassbehaviour was reported. The observation of a freezing temp-erature, Tf = 9 K, was attributed to structural disorder. Withneutron powder diffraction measurements alone, Süllow et al.were only able to conclude that there existed a superstructure,but structural details of structural disorder could not beelucidated confidently.32 XAFS measurements were later used tocharacterize the structural disorder as site mixing betweenRh and Ge.33

Table 2 Heavy fermion superconductors with the ThCr2Si2 type

Compound Tc (K) Reference

CeCu2Si2 0.6 19CePd2Si2 0.5 20CeCu2Ge2 ∼0.6 at 9.4 GPa 21CeRh2Si2 0.25 22SrPd2Ge2 2.7 23

14230 | Dalton Trans., 2012, 41, 14225–14235 This journal is © The Royal Society of Chemistry 2012

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The observation of spin glass behaviour in PrAu2Si2 with afreezing temperature Tf = 3 K was quite surprising: powder dif-fraction experiments did not reveal sufficient impurities toexplain the observation of spin glass behaviour nor does therare-earth ion occupy an atomic position with triangular or tetra-hedral coordination. Alloying with Ge, however, to yieldPrAu2(Si1−xGex)2, revealed a critical composition, x = 0.3, wherelong-range antiferromagnetism was observed for x > 0.3 andspin freezing was observed for x < 0.3. Inelastic neutron scatter-ing revealed that spin glass behaviour was observed because ofthe small crystal-field splitting (Δ = 0.7 meV) between theground and the singlet states and the fast dynamics of the spintransitions between these two states.34

Heusler compounds

Fritz Heusler first discovered Heusler compounds in 1903 whenhe observed ferromagnetism in Cu2MnAl although none of theconstituent elements exhibit magnetic moments as individualelements. There are currently over 1500 known Heusler-typematerials, and these materials have been of considerable researchinterest because of their magnetic behaviour, potential use inspintronics applications, heavy fermion behaviour, superconduct-ing behaviour, and excellent thermoelectric properties. Thesecompounds are typically characterized by a 1 : 1 : 1 (half-Heusler) or 1 : 1 : 2 (Heusler) stoichiometry, and they are knownto form with over fifty different elements from the periodic tableincluding 13 different rare earth elements.35 Heusler compoundsare interesting for several reasons, including superconductivity,half-metallic ferromagnetism, and as potential topologicalinsulators.

Topological insulators. One of the most interesting researchapplications of Heusler compounds is in the quest to identifytopological insulators. Topological insulators exhibit electricalconductivity on the surface of the material while remaining insu-lating in the bulk.36 These materials were only realized experi-mentally in 2007, and have since been the focus of considerableresearch because of their potential for applications in spintronicsand quantum computing.36 Approximately 50 Heusler materialsshow electronic band properties that hint at topological insulatingbehaviour.37 Many of these promising Heusler compoundscontain rare-earth elements, e.g., LnAuPb, LnPdBi, LnPtSb, andLnPtBi.37

Superconductivity and magnetism. Rare-earth containingHeusler compounds can also exhibit exotic superconductivity,magnetism, and heavy fermion behaviour. There are currently 28known Heusler superconductors, including the series REPd2Sn(RE = Er, Tm, Yb, Lu, Y, and Sc) and REPd2Pb (RE = Tm, Yb,Lu, Y, and Sc). The availability of numerous superconductors inone class of materials has enabled researchers to search forcharacteristics that are essential for superconducting behaviour.In a recent paper, Klimczuk et al. compared the physical proper-ties in the (Sc, Y, Lu)Pd2Sn and (Hf, Zr)Pd2(Al, In) supercon-ductors and compared all known Heusler superconductors on thebasis of valence electron count.38 The authors observed that forthe (Sc, Y, Lu)Pd2Sn series, the superconducting transitiontemperature increased with increasing unit cell size, which is

consistent with previous high pressure studies on REPd2Z (RE =Sc, Y, Tm, Yb, Lu; Z = Sn, Pb), where the superconducting tran-sition temperature was suppressed with increasing pressure and acorresponding decrease of the unit cell size. However, an oppo-site trend was observed in the (Hf, Zr)Pd2(Al, In) series, inwhich the superconducting transition was increased withdecreasing unit cell size. The authors stated that this unusualbehaviour may be a result of electronic reasons, but still warrantsfurther investigation.

Interestingly, Kilmczuk et al. found that the majority of super-conducting Heusler compounds contained 27 valence electrons.Though there are certainly not concrete rules for predicting theproperties of intermetallic compounds, this correlation raisesnew questions about predicting the stability of superconductivityin Heusler compounds.

The majority of Heusler compounds are ferromagneticmaterials, however, the introduction of a rare-earth element gen-erally results in antiferromagnetic behaviour.6 Gofryk et al.examined the magnetic and charge transport properties of a wideseries of Heusler phases comprised of REPdZ and REPd2Z(RE = Y, Ho, Er, Nd, Dy, Gd, and Tb, Z = Sb, Bi).39 The moststriking observation was that the half-Heusler variants of thesecompounds exhibited high Seebeck coefficients at room temp-erature (as high as 200 μV K−1), which is promising for thermo-electric applications.

As previously mentioned, heavy fermion behaviour is an inter-esting phenomenon that has implications for other propertiessuch as superconductivity and quantum critical phase transitions.While some of the most intensely studied heavy fermion com-pounds contain cerium, the first Pr-containing heavy fermioncompound in the literature was the Heusler compoundPrInAg2.

40

Half-metallic ferromagnetism. In 1983, de Groot et al. exam-ined the half-Heusler material, NiMnSb, using first-principleselectronic structure calculations and discovered half-metallic fer-romagnetism.41 A schematic of a generalized band diagram for ahalf-metallic ferromagnet is shown in Fig. 7. In a half-metallicferromagnet, an energy gap between the valence and conductionbands for one spin polarization results in semiconducting behav-iour. However, for the opposite spin polarization, the absence of

Fig. 7 Schematic of the band diagram for a half-metallic ferromagnet.For one spin polarization, a gap exists at the Fermi-level, EF. For theopposite spin polarization EF intersects the conduction band.

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an energy gap between the valence and conduction bands resultsin metallic behaviour.

This unusual phenomenon has attracted immense interest inhalf-Heusler compounds as promising candidates for spintronicsapplications.42 Following the theoretical discovery of half-metallic ferromagnetism, considerable efforts have been devotedto realizing materials that exhibit this behaviour. For example, acomprehensive electronic structure study of 810 potentialHeusler compounds revealed that approximately 60% of thesecompounds are thermodynamically stable. Of these, about 230compounds with potentially interesting magnetic behaviour,including half-metallicity, are yet to be experimentally realized.43

Co2FeSi is particularly interesting because it exhibits bothhalf-metallic ferromagnetism and a very large magnetic moment(∼6 μB) with a high Curie temperature (∼1100 K).44

Crystal structure. Half-Heusler compounds have the generalformula XYZ and crystallize in the cubic F4̄3m space group(C1b, no. 216), which contains three interpenetrating fcc sub-lattices (Fig. 8a, Table 3).35 The half-Heusler structure is alsoviewed as a ZnS sublattice.

Heusler compounds have the general formula X2YZ and crys-tallize in the cubic Fm3̄m space group (L21, no. 225), whichconsists of four interpenetrating fcc sublattices (Fig. 8b).35,45

Atomic coordinates for the Heusler structure type are provided inTable 4. In this structure, the most electronegative (Y) and themost electropositive (Z) elements are octahedrally coordinatedand form a NaCl type lattice.

Structural challenges

One of the primary challenges with characterizing Heusler com-pounds arises from the considerable amount of structural dis-order that can occur in these materials. Disorder among the

available atomic positions in Heusler compounds is quitecommon, as their structures and composition afford a variety ofacceptable atomic arrangements.

Understanding structural disorder in these materials is impor-tant because it can directly impact physical behaviour.46 Forhalf-Heusler compounds, there are five types of structural dis-order that describe the distribution of atomic positions; these dis-orders are classified as: CaF2-type, BiF3-type, Cu2MnAl-type,CsCl-type, and W-type.35 Similarly, for the full Heusler com-pounds, four primary types of structural disorder exist: CsCl-type, BiF3-type, W-type, and NaTl-type.35 Several extensivereports thoroughly discuss the different types of disorder and theexperimental difficulties associated with characterizing the dis-order in these materials.35,45

Fig. 9 compares simulated X-ray powder diffraction patternsof fully ordered Heusler, BiF3 and W-type disordered Heuslercompounds. The intensity ratio between the (111) and (200)Bragg reflections is unique to each of these structural variantsand can therefore, be used to distinguish structural disorder inHeusler compounds; however, the relatively weak intensities ofthese Bragg reflections makes structural characterization usingconventional laboratory XRD techniques difficult.

Synchrotron diffraction techniques can be used to overcomethese challenges. For example, the atomic disorder between Coand Mn in the Heusler compound Co2MnGe could not be distin-guished with conventional lab X-ray sources because of thesimilar scattering factors of Co and Mn47 employing anomalous.

X-ray diffraction at a synchrotron source enabled the charac-terization of antisite disorder because: (1) of the increased

Table 3 Atomic coordinates for ideal half-heusler

Atom Wyckoff site Atomic coordinate

X 4a 0, 0, 0Y 4b 1

2,12,

12

Z 4c 14,

14,

14

Ref. 35

Fig. 8 Crystal structures of (a) an ideal half-Heusler and (b) an idealHeusler phases. Gray, red, and black represent X, Y, and Z, respectively.Cubic unit cells are outlined as dashes.

Table 4 Atomic coordinates for ideal heusler

Wyckoff site Atomic coordinate

X 8c 14,

14,

14

Y 4a 0, 0, 0Z 4b 1

2,12,

12

Ref. 35

Fig. 9 Simulated X-ray diffraction patterns of Cu2MnAl with fullatomic order (black line), partial disorder (BiF3-type, blue line), and fullatomic disorder (W-type, red line). Simulations based on Cu Kα radi-ation. The (111) and (200) reflections are identified.

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resolution of a synchrotron source and (2) of the ability to pre-cisely tune the X-ray wavelength† to the Co K-edge (∼7709 eV)to measure the (111) Bragg reflection.

Structural transitions. One of the most important and well-known structural transitions exhibited by Heusler compounds isthe martensitic transition where the cubic Heusler structure ischaracterized by a cooperative motion of the constituent atoms.This transition was fundamental in the first discovery of mag-netic shape memory properties in 1996, where in Ni2MnGa, itwas discovered that a martensitic transition can be triggered bythe application of an external magnetic field.

Ni2MnAl is isovalent to Ni2MnGa under ambient conditions;therefore, this material has also been of interest to researchers forpotential shape memory effects. However, various experimentalstudies have reported conflicting magnetic behaviour in thismaterial, including the presence of a mixture of both ferro- andantiferromagnetic ordering. It has been reported that the discre-pancies arise from the synthesis conditions, which can result inthe presence of either the ordered L21 phase or the disorderedB2 phase of Ni2MnAl, or a mixture of both phases. Based onab initio calculations, the ordered L21 and B2 phases areexpected to exhibit ferromagnetic and antiferromagnetic order-ing, respectively.

Laves phases

Laves phases have the general composition AB2 where A is gen-erally an electropositive metal and B is a less electropositivemetal. These compounds, which comprise one of the largestclasses of intermetallic materials, typically crystallize in one ofthree structure types: MgCu2, MgZn2, or MgNi2.

Rare-earth Laves phases are especially interesting for studyingmagnetic phenomena because the relatively simple cubic struc-tures theoretically allow for straightforward correlations betweenstructure and properties. In rare-earth Laves structures, thelanthanide or actinide typically occupies the A site. These threeclosely related structure types are shown in Fig. 10, and their keystructural information is presented in Table 5.

As seen in Fig. 10, the MgCu2 structure can be viewed as aface-centred cubic structure, and there are 8 formula units perunit cell. In this structure, the A-sublattice forms a cubicdiamond net and the B-sublattice can be visualized as a series ofB4 corner sharing tetrahedra in a staggered conformation. TheMgZn2 structure is hexagonal, and accordingly, the A-sublatticeforms a hexagonal diamond net. The B-sublattice can also bevisualized as a series of B4 tetrahedra, but in this structure, thetetrahedra share both corners and faces. Finally, the MgNi2 struc-ture is also hexagonal and can be considered to be a mixture ofthe MgCu2 and MgZn2 structure types.

In addition to the three aforementioned structures, there havealso been reports of rhombohedrally distorted Laves structures.TbFe2 has been reported to crystallize in the rhombohedral R3̄mspace group, with a primitive angle, α, equal to 59.62°.49 An αvalue equal to 60° is equivalent to a cubic unit cell, therefore the

reported angle for TbFe2 suggests a very subtle rhombohedraldistortion in TbFe2.

There are also a considerable number of ternary derivativeswith the general composition A2B3C. It has been reported thatthere is a considerable structural disorder in these ternary deriva-tives, similar to the case of the Heusler compounds mentionedearlier in this Perspective, which results in these compoundsmaintaining an average cubic symmetry. However, rhombohedraldistortions have also been observed in ternary Laves phases.

Synthesis and structural characterization. This section willfocus on RENi2 and RECo2 Laves phases to illustrate the uniquesynthesis and structural characterization challenges associatedwith rare-earth Laves phases.

A major area of research on the Laves phases is devoted toestablishing a set of ‘rules’ for predicting the structure type for agiven composition. Thus, authors have attempted to establishcorrelations between the ratios of the A and B ions (rA/rB) andvalence electron configurations.48,50 While some simple modelsexist for predicting whether a Laves phase will form from aspecific combination of certain metals, a complete model forsuch a prediction currently not available.49

With respect to rare-earth Laves phases, it has been reportedby several authors that the preparation of a single-phase REM2

(RE = rare-earth, M = Mn, Fe, Co, Ni) compound requires an

Fig. 10 (a) Cubic MgCu2 Laves structure, (b) hexagonal MgNi2 Lavesstructure, and (c) hexagonal MgZn2 Laves structure. The black and greyatoms represent the A and B metal atoms, respectively.

Table 5 Structural information for laves phases

Structure type Atom Wyckoff site Coordinates

MgCu2 (C15, Fd3m)A (Mg) 8a 0, 0, 0B (Cu) 16d 5/8, 5/8, 5/8

MgZn2 (C14, P63/mmc)A (Mg) 4f 1/3, 2/3, 1/16B1 (Zn) 2a 0, 0, 0B2 (Zn) 6h 5/6, 5/3, 1/4

MgNi2 (C36, P63/mmc)A1 (Mg) 4e 0, 0, 3/32A2 (Mg) 4f 1/3, 2/3, 27/32B1 (Ni) 6g 1/2, 0, 0B2 (Ni) 6h 1/6, 1/3, 14B3 (Ni) 4f 1/3, 2/3, 1/8

Ref. 48.

†Such X-ray wavelengths are only available at synchrotron sources.

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off-stoichiometric composition. In the case of RECo2, an excessof the rare-earth metal is required to produce a single-phase com-pound; when synthesized in stoichiometric compositions, theferromagnetic RECo3 phase accompanies the RECo2 phase,thereby making magnetic measurements challenging.51

For the RENi2 series an excess of nickel is required toproduce a single-phase compound. In the case of the RENi2series, the excess of nickel results in the appearance of regularrare-earth vacancies in the structure.

A detailed study of the RENi2 (RE = Y, Sm, Gd, and Tb)series reported that the room temperature structure of thesematerials was in fact a supercell of the cubic Laves structure(F4̄3m with the lattice parameter of the cubic Laves structuredoubled).52 This supercell consists of a regular, highly orderedarrangement of RE vacancies. Through a series of variable temp-erature and high-pressure diffraction measurements, the authorsreported that the room temperature supercell structure underwenta transition at high temperature (T > ∼800 K) or high pressure(P > ∼25 GPa) to a regular cubic Laves phase (Fd3̄m). The low-T, low-pressure structure was characterized with disordered REvacancies. The stability of the superstructure was explainedspace-filling arguments. The tightest packing arrangement ofspheres in a cubic Laves structure can be obtained with a ratio,rA/rB ∼ 1.25. In RENi2, the rA/rB ratios deviate considerablyfrom 1.25, hence, the authors concluded that ordered REvacancies stabilized the superstructure.

The RECo2 family of Laves phases has been of considerableinterest for several decades because of the diversity of magneticbehaviour.51 For example, in RECo2 compounds, the magneticmoment of Co is aligned parallel to the 4f magnetic momentwhen RE = light rare-earth elements, e.g., Tb, Gd, Nb, but themoments are aligned antiparallel to the 4f magnetic momentwhen RE = heavy rare-earth elements, e.g., Er, Ho, Dy.

One interesting example is NdCo2, whose magnetic and struc-tural properties have been studied extensively.53 Under ambientconditions, this material adopts the cubic MgCu2 structure type,and orders ferromagnetically at 100 K. This ferromagnetic order-ing is accompanied by magnetovolume and magnetostrictioneffects that tetragonally distort the cubic structure. Upon furthercooling to 42 K, a second magnetic transition occurs (spin re-orientation) that further distorts the tetragonal structure into anorthorhombic structure. These magnetic effects on the structuraltransitions can be visualized in the diffraction patterns presentedin Fig. 11.

Conclusions

Research on the synthesis and structural and physical characteriz-ation of ThCr2Si2, Heusler and Laves phases have demonstratedto the scientific community the importance of composition,temperature, and pressure-dependent transitions. There are hun-dreds of intermetallic compounds that also exhibit interestingstructure–property relationships, and these materials are challen-ging, yet fascinating to characterize. These transitions lead us tonew and exciting insights into quantum phase transitions, super-conductivity, and magnetic behaviour. Whether the structuralchanges are subtle or dramatic, local distortions can lead todramatic transitions in magnetic behaviour.

Current theoretical models for the prediction of intermetallicphases rely on radius ratios, valence electron counts, and detaileddensity of state diagrams, and while these models have beenuseful, they are limited. As Ibers wrote in a Perspective on solid-state actinides, “sorting through the diverse variables is an artform”.54 Discovery of intermetallic materials remains a combi-nation of science, art, and serendipity. Continued advancementsin synchrotron and neutron facility technologies and collabor-ations that combine synthesis, structural characterization andphysical property measurements will hopefully lead to therational prediction and design of intermetallic materials.

Acknowledgements

We gratefully acknowledge the National Science FoundationCAREER Award No. 105615 for support.

Notes and references

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Fig. 11 Neutron diffraction patterns simulated using the reported struc-tural parameters from ref. 43 that illustrate the cubic, NdCo2 structure(black line), tetragonal structure at (100 K, blue line), and orthorhombicstructure (∼42 K, red line). Inset shows splitting of the cubic (911) peak.

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