EnthalpiesofformationofbinaryLavesphases J.H.Zhu a ,C.T.Liu b, *,L.M.Pike c ,P.K.Liaw d a Department of Mechanical Engineering, Tennessee Technological University, TTU Box 5014, Cookeville, TN 38505, USA b Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6115, USA c Haynes International, Kokomo, IN 46904, USA d Department of Materials Science and Engineering, University of Tennessee, Knoxville TN 37996, USA Received 25 February 2002; accepted 5 March 2002 Abstract Enthalpies of formation of binary Laves phases have been critically surveyed and reviewed in this paper. The enthalpy-of-for- mationdataindicatethatbothgeometricandelectronicfactorsareimportantinstabilizingLavesphases.Analysisofenthalpydata revealsthattherearemetallic,covalent,andionicbonds,oramixedmetallic-covalent-ionicbond,inLavesphases.Theenthalpies of formation for binary transition-metal lanthanide Laves phases including ReCo 2 , ReNi 2 , ReFe 2 , ReRu 2 , ReRh 2 , ReOs 2 , ReIr 2 , and RePt 2 (Re—lanthanide element), as calculated by the semiempirical Miedema model, are found to be in good agreement with the available experimental data. This indicates that Miedema’s theory is capable of predicting the enthalpy of formation of transi- tion-metal lanthanide Laves-phase systems. # 2002PublishedbyElsevierScienceLtd. Keywords: A.Lavesphases;B.Thermodynamicandthermochemicalproperties;B.Crystalchemistryofintermetallics 1. Introduction On the formation of an intermetallic phase from its components,asarule,changesofstructureandofbond type and bond strength occur. An understanding of the nature of the intermetallic phase can be deduced from its thermodynamic properties. The free energy of for- mation gives an indication of the stability, and the enthalpy of formation is closely related to the type of bonding. The entropy of formation reflects changes in the vibrational behavior and configurational arrange- mentoftheatomsontheformationofthecompounds. Adecreaseinfreeenergyaccompaniestheformationof an intermetallic compound. A compound is stable with respect to competing neighboring phases in a multi- component system, if its free energy is lower than that ofamixtureofthesephases.Theenthalpyofformation of an intermetallic compound is usually also negative, because the free energy change must be negative, and the entropy-temperature product is small. For this reason,themagnitudeoftheenthalpyofformationofa compoundcanbeusedasameasureofitsstability. The enthalpy of formation is related to the bond energiesinthecompound.Ionic,covalent,metallic,and van der Waals bonds and the transitions between these pure types must be considered in discussing the enthal- piesofformationofintermetalliccompounds.Also,ina single compound, more than one type of bond may occur. For example, in compounds with layer struc- tures, the bonding within the layers differs from that betweenthelayers. An intermetallic compound has a large exothermic enthalpyofformation,whenthenatureofitsbondingis different from that in the component elements, e.g., when metallic elements form a compound in which the bonding is ionic or covalent. Robinson and Bever have analyzed the range of the enthalpy of formation of intermetallic compounds with different bonding nature [1]. The enthalpies of formation of intermetallic com- pounds with ionic bonding range from approximately 125 to 500 kJ/mol; the numerical values of the negativeenthalpyofformation(i.e.,theexothermicheat offormation)increasewiththedegreeofionicityofthe bond. The exothermic enthalpies of formation of cova- lent compounds are generally smaller than those of 0966-9795/02/$ - see front matter # 2002 Published by Elsevier Science Ltd. PII:S0966-9795(02)00030-4 Intermetallics 10 (2002) 579–595 www.elsevier.com/locate/intermet * Corresponding author. Tel.: +1-865-574-4459; fax: +1-865-574- 7221. E-mail address: liuct@ornl.gov (C.T. Liu).