VOLUME 76, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 22 APRIL 1996

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L12-DO22 Competition in the Pseudobinary (Pt, Rh)3V, Pt3(V, Ti), and (Pd, Rh)3V Alloys:Phase Stability and Electronic Structure

E. Cabet,1 A. Pasturel,2 F. Ducastelle,1 and A. Loiseau11Laboratoire de Physique du Solide, Direction des Matériaux, Office National d’Etudes et de Recherches Aérospatia

(ONERAyOM), BP 72, 92322 Châtillon Cedex, France2Laboratoire de Thermodynamique et Physico-Chimie Métallurgique, ENSEEG, BP 75, 38402 St. Martin d’Hères Cedex,

(Received 15 January 1996)

It is shown that the progressive substitution of a small amount of Pd and Pt by Rh in Pd3V and Pt3Vwhose ground state is theDO22 structure, or the substitution of V by Ti in Pt3V, stabilizes a few simplelong period structures and finally theL12 structure. This occurs for an electron per atom ratio about8.6, in full agreement with accurate electronic structure calculations. [S0031-9007(96)00002-6]

PACS numbers: 61.66.Dk, 64.70.Kb, 71.15.Nc, 81.30.Bx

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The Pd3V and Pt3V alloys have a disordered fcc structure at high temperature and are ordered on this latticlow temperature. They display the particular featureexhibiting different local orders in the disordered anddered states. In the disordered state, the local, or shrange order, which is characterized by maxima of diffuintensity at positionsk100l in reciprocal space [1–3] is thaof the cubicL12 structure, built withk100l concentrationwaves. The ordered ground state has theDO22 structureof quadratic symmetry and can be obtained by introduceachL12 cube an antiphase boundary (APB) in the (00planes. This structure is built withk10 1

2 l andk001l wavesbut usual mean field theories predict that it should oconly when the high temperature diffuse intensity peaksk1 1

2 0l positions, which is the case, for example, of Ni3V[4,5]. The peculiar behavior of Pd3V and Pt3V has beenshown to be related to the quasidegeneracy of theL12 andDO22 structures or equivalently to the weakness ofAPB energy in these systems [1,3,6]. This has given risseveral theoretical studies which differ in details but whbasically agree with this quasidegeneracy effect, for Pd3Vat least [7,8].

Such a situation is propitious to the existence of intermdiate structures which can be stabilized through effecinteractions between APB. These structures are built frthe L12 structure by the introduction of a variable desity of (001) APB in a periodic manner and are frequencalled long-period structures (LPS) [5,9]. They are chacterized by the mean distanceM (in L12 cube units) be-tween APB,1yM being therefore the APB density. In thscheme,M is maximum inL12sM ­ `d, and minimumin DO22sM ­ 1d. Between these two limits, an infinitnumber of structures can occur and they all give risesuperstructure spots located on thek10z l line. In Pt3V,indeed, the LPSM ­ 4y3 as well asM ­ 3y2 in somecases have been found to be stable at high temperain a narrow temperature range close to the order-disotransition [10,11].

It is now well established, on the other hand, thatrelative stability of DO22 and L12 transition alloys is

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governed by the value of the number of valence eletrons per atomeya [12]. eya is equal to 10 for plati-num and palladium (T10 elements) and to 5 for vanadium(T 5 elements) and practically all compounds of typT10

3T5 (eya ­ 8.75) order according toDO22 or relatedstructures whereas theT 9

3T5 (eya ­ 8.00) and T103T4

compounds (eya ­ 8.50) display theL12 structure. Thistendency is well reproduced by electronic structure calclations which predict a change of stability foreya valuesabout 8.6 [13–15].

In this Letter, we show experimentally that theL12

structure and a series of LPS are stabilized in the Pand Pd-V systems when the mean electron concentratioslightly decreased through the addition of a third elemein substitution of Pt (Pd) or of V: Pd and Pt were substituted by Rh, which is aT 9 element, and V by Ti whichis a T4 element. Whatever the nature of the additioelement,L12 is found to be stabilized when the electronconcentration is below 8.6 [16]. These results are in fagreement with accurate electronic structure calculatioperformed within the local density approximation (LDAand prove definitely that Pd3V and still more Pt3V arenearly degenerate systems.

Different alloys have been prepared so thateya variesbetween 8.75 and 8.5:sPt12xRhxd3V and sPd12xRhxd3Vwith x between 0 and 0.3, and Pt3sV12xTixd with xbetween 0 and 0.9. The alloys were first homogenizedthe disordered state at 1200±C for Pt alloys and at 1100±Cfor Pd alloys and water quenched in order to retaa supersaturation of vacancies [17]. The homogeneitythe different alloys has been checked using local chemianalysis. Aging treatments were then performed at dferent temperatures below the order-disorder transitioParticular attention has been paid to the aging timnecessary to achieve an ordered state at equilibrium sithe kinetics is very sluggish in these systems, especiain Pt-V [11]: Typical aging times were one month a900±C for (Pt, Rh)-V alloys and one month and a half a600±C for (Pd, Rh)-V alloys. The microstructure of thalloys and the nature of the phases were investigated us

© 1996 The American Physical Society

VOLUME 76, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 22 APRIL 1996

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transmission electron microscopy (diffraction and hiresolution imaging). The samples were prepared accoing to the experimental procedure described in Ref. [10

The observations allow us to draw the schematiphase diagrams shown in Fig. 1. Although the differephase limits are not precisely determined, the similaritbetween the different systems are striking. The sasequence of phases has indeed been observed in all cwhen varying the Rh or Ti content. BesidesDO22 (M ­ 1or k1l) it consists of a series of LPS, the LPSM ­ 4y3 ork211l, M ­ 3y2 or k21l, andM ­ 2 or k2l, and finally theL12 structure itself. The notationk l is due to Fisher and

FIG. 1. Schematic phase diagrams of (a)sPt12xRhxd3V,(b) sPd12xRhxd3V, and (c) Pt3sV12xTixd. Measurement pointsare denoted by black dots.k1l and k`l are theDO22 and L12structures, respectively.

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Selke and describes the sequence of APB spacing inL12cube units [5]. For example, in theM ­ 3y2 structure,the spacing is alternatively two and one cubes, henthe notationk21l. Experimentally, the APB distributionis very simply determined from high resolution image[9]. Images of the different observed structures are shoin Fig. 2.

These structures are observed in wide areas withany defect and present fairly broad ranges of stabias a function of temperature and of the concentratof the substituting element. Special attention has bedevoted to the research of intermediate LPS obtainedcombining the local arrangements of the simple structumentioned previously, and which might be stablenarrow ranges of temperature. For example, the simpintermediate structure betweenM ­ 4y3 and M ­ 3y2is the structureM ­ 7y5 corresponding to the sequenck21211l [18]. If no intermediate structure is stablephase coexistence between the basic structures shouobserved. To solve that point, the 4y3-1, 3y2-4y3, 2-3y2,and L12-2 transitions have been studied as a functiontemperature.

FIG. 2. High resolution image of the long period structur(a) DO22 or k1l, (b) k211l, (c) k21l, (d) k2l, and (e) L12.The LPS are projected along a cube axis perpendicular tomodulation axis so that the APB are seen edge on. Alongmodulation axis, the structure consists of an alternate stackof Pt (Pd) planes and mixed Pt (Pd)-V planes. In the imagthe white dots represent the vanadium atomic columns whcan occupy two different positions in the mixed planes, labe1 and 2. Each shift1 to 2 is due to an APB, hence thedetermination of the APB distribution.

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VOLUME 76, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 22 APRIL 1996

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The transformation 4y3-1 has been first examined bmeasuring the variation as a function of temperaturethe resistivity of Pt3V samples initially ordered in the4y3 LPS state [11]. The resistivity curve shows a jumbetween 940 and 960±C which can be attributed to thetransformation between 4y3 and 1 (i.e.,DO22) but itsmagnitude is very large and could consist of a serof small jumps, corresponding to transitions involvinintermediate LPS. In fact, the kinetics is very slow, witime constants exceeding 100 h, so that the equilibricurve could not be determined exactly. After agintreatments at 940±C of initially disordered samples, highresolution observations reveal a chaotic mixture of varioAPB sequences interpolating betweenM ­ 1 and 4y3,but the only periodic sequences, i.e., those repeatingleast three times, are the sequencesk1l andk211l [9,11].

The same phenomenon has been observed at they2-4y3 transition studied in (Pt98Rh2)3V; an example of achaotic mixture in this alloy is shown in Fig. 3(a). Aftelong aging times, the microstructure consists of a fipatchwork of small domains of sequencesk21l andk211l ina proportion depending on the temperature. This defia complex two-phase microstructure for the 4y3 and 3y2LPS [16]. From this careful analysis we can conclude tthere is reasonably no intermediate structure betweeny2,4y3, and 1. Concerning the transition 2-3y2 studied in(Pt92Rh8)3V and in (Pd84Rh16)3V, the conclusion is notso clear, since in that case we have observed in additiothe periodic sequencesk21l andk2l some regions where thesequencek221l is repeating more than three times. Thisan indication that the structureM ­ 5y3 could exist in anarrow domain betweenk2l andk21l.

The L12-2 transition leads to completely differentwo-phase microstructures. In the different systems,observe an extended two-phase field and the microsttures show large (micronic size) domains of each phaAs shown in Fig. 3(b) the APB sequences are perfect,interfaces between the domains are perfectly coherent,their sharpness precludes the existence of any intermate LPS. However, the intermediateM ­ 3 LPS has beenobserved in the Pt3(V, Ti) alloys at low temperature as thinplatelets, with sequencesk3l repeating at least seven time

FIG. 3. (a) High resolution image in (Pt98Rh2)3V showinga chaotic mixture of sequencesk211l and k21l. (b) Highresolution image showing in the (Pt84Rh16)3V alloy an interfacebetween theL12 andk2l phases.

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embedded in a matrix either of LPS 2 or ofL12. This indi-cates that at least in the Pt3(V, Ti) system, LPS structureswith M values larger than 2 are stable at low temperatu

The similarities observed between the different systeprove that the type of order is mainly determined bthe mean electron concentrationeya of the alloy. Thephases are true electronic phases. In particular,L12 isstabilized for very similar values ofeya, about 8.6 at lowtemperature (see Fig. 1).

In view of these results, we have performed accrate electronic structure calculations of the variation weya of the energy difference betweenL12 and DO22,DEstab ­ EsL12d 2 EsDO22d for the threeT10

3T 5 com-pounds, Ni3V, Pd3V, and Pt3V, using the full potentiallinear-muffin-tin-orbital approach. Although some resuwere already available, we have found it necessary to trall systems in a single scheme. The energy differenDEstab are found equal to 102, 69, and 65 meVyatom forNi 3V, Pd3V, and Pt3V, respectively, in good agreemenwith previous results [8,14,15,19]. In order to have mophysical insight in the relative stability of theL12 andDO22 phases, we have also used a frozen-potentialproach in its simplest form, the atomic sphere approximtion. DEstab is then simply obtained from the differencof the band energies calculated using the same “frozpotential within the atomic spheres of the two latticeThe so-obtained energy differences are equal to 100, 6and 65 meVyatom for Ni3V, Pd3V, and Pt3V, respec-tively, which compares well with the fully self-consistenresults presented above. We can now interpret the sttural trends as a function ofeya within the rigid band ap-proximation. Using the frozen potential of theL12 phase,we have calculatedDEstab as a function ofeya. Figure 4shows that it vanishes close toeya ­ 8.6 in very goodagreement with the experimental results.

Since theL12 phase is known to display a ferromagnetic instability for eya . 8.6 [8,19,20], we have alsoperformed spin-polarized calculations for the three copounds. As found by previous authors, we see in Fig

FIG. 4. Structural energy difference betweenL12 and DO22as a function ofeya for Ni 3V (diamonds), Pd3V (circles),and Pt3V (triangles). Spin-polarized calculations for the binacompounds are also shown (black symbols).

VOLUME 76, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 22 APRIL 1996

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that this decreasesDEstab significantly (for a detailed dis-cussion see Ref. [20]). In such a situation where the fromagnetic state certainly depends oneya it is of coursedifficult to use the rigid band approximation, but we dnot expect the structural trends to be qualitatively modifiAnyway all calculations agree in predicting thatDEstab de-creases from Ni3V to Pt3V in full agreement with experi-mental data. A simultaneous tendency to ferromagnetiprincipally in theL12 phase is also predicted. Actualleven theDO22 phase of Pt3V has been found to be ferromagnetic [21] whereas both Ni3V and Pd3V are paramag-netic. We intend to investigate the magnetic propertiesour pseudobinaryL12 compounds.

All is still not completely understood in these systemFor example, the calculatedDEstab for the binary com-pounds is too large compared to the estimates dedufrom diffuse scattering data [4,8]. Another problem isunderstand the stability of the intermediate long peristructures. One may think of entropy driven effects, bthe ANNNI model which is generally called forth in thicontext is not relevant here: It can describe LPS betwk2l andL12, or betweenk2l and DO22, not betweenL12

and DO22 [5]. It might be that the LPS are true grounstates for definite values ofeya stabilized by interactionsof fairly long range [3]. Electronic structure calculationare under progress.

Many fruitful discussions with R. Caudron and A. Finare gratefully acknowledged.

[1] F. Solal, R. Caudron, F. Ducastelle, A. Finel, anA. Loiseau, Phys. Rev. Lett.58, 2245 (1987).

[2] D. Schryvers, G. Van Tendeloo, and S. Amelinckx, MateRes. Bull.20, 361 (1985).

[3] D. Le Bolloc’h, R. Caudron, E. Cabet, M. Barrachin, anA. Finel, J. Phys. IV (France) (to be published).

[4] M. Barrachin, A. Finel, R. Caudron, A. Pasturel, anA. Francois, Phys. Rev. B50, 12 980 (1994).

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[5] F. Ducastelle,Order and Phase Stability in Alloys(North-Holland, Amsterdam, 1991).

[6] R. Caudron, M. Sarfati, M. Barrachin, A. Finel, F. Ducastelle, and F. Solal, J. Phys. I (France)2, 1145 (1992).

[7] D. D. Johnson, J. B. Staunton, and F. J. Pinski, Phys. RB 50, 1473 (1994).

[8] C. Wolverton and A. Zunger, Phys. Rev. B52, 8813(1995).

[9] For a recent review, see A. Loiseau, in Proceedings of tInternational Centre of Electron Microscopy at the MPHalleySaale, edited by J. Heydenreich and W. Neuma(to be published), p. 159.

[10] D. Schryvers and S. Amelinckx, Acta Metall.34, 43(1986).

[11] J. Planès, A. Loiseau, F. Ducastelle, and G. Van TendelInst. Phys. Conf. Ser.90, 261 (1987).

[12] A. Bieber and F. Gautier, Solid State Commun.38, 1219(1981); Acta Metall.35, 1889 (1986).

[13] A. Bieber, F. Ducastelle, F. Gautier, G. Tréglia, anP. Turchi, Solid State Commun.45, 585 (1983).

[14] S. Pei, T. B. Massalski, W. M. Temmerman, P. A. Sternand G. M. Stocks, Phys. Rev. B39, 5767 (1989).

[15] W. Lin, Jian-hua Xu, and A. J. Freeman, Phys. Rev. B45,10 863 (1992).

[16] Preliminary observations have been presentedA. Loiseau and E. Cabet, J. Phys. IV (France)3, C7-2051(1994).

[17] The order-disorder transition occurs at 1030±C in Pt3V[11] and at 825±C in Pd3V [1].

[18] These so-called branching mechanisms are describeddetail in A. Loiseau, G. Van Tendeloo, R. Portier, anF. Ducastelle, J. Phys. (Paris)46, 595 (1985); see alsoD. De Fontaine and J. Kulik, Acta Metall.33, 145 (1985)and [5].

[19] N. M. Rosengaard and H. L. Skriver, Phys. Rev.50, 4848(1994).

[20] Z. W. Lu, B. M. Klein, and A. Zunger, Phys. Rev. Lett75, 1320 (1995).

[21] R. Jesser, A. Bieber, and R. Kuentzler, J. Phys. (Paris)42,1157 (1981);44, 631 (1983). These authors argue ththey are able to stabilize theL12 structure in Pt3V. Thereare indications that they were actually dealing with a LP

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