7/28/2019 Influence of Be addition on orderdisorder transformations in b CuAl

1/5

Influence of Be addition on orderdisorder transformations in b CuAl

Fernando Lanzini a,b,*, Ricardo Romero a,c, Mara Lujan Castro a,b

a IFIMAT Instituto de Fsica de Materiales Tandil, Universidad Nacional del Centro de la Provincia de Buenos Aires, Pinto 399, 7000 Tandil, Buenos Aires, Argentinab Consejo Nacional de Investigaciones Cientficas y Tecnicas, Argentinac Comision de Investigaciones Cientficas de la Provincia de Buenos Aires, Argentina

a r t i c l e i n f o

Article history:

Received 13 March 2008

Received in revised form 18 June 2008

Accepted 22 June 2008

Available online 5 August 2008

Keywords:

A. Intermetallics, miscellaneous

B. Electrical resistance and other electrical

properties

B. Orderdisorder transformations

a b s t r a c t

The dependence of resistivity with temperature around the orderdisorder transitions is measured for

bcc shape memory alloys CuAl (Be). The experimental curves are discussed in terms of the Rossiter

theory, and the parameters involved in this approach are determined. The model allows calculating the

variation with temperature of the long-range order degree. Whereas for the binary CuAl the kinetics of

the orderdisorder transformation is first order, the addition of Be leads to a gradual smoothing in the

variation of the order parameter below the transition temperature.

2008 Elsevier Ltd. All rights reserved.

1. Introduction

Cu-based shape memory alloys (SMA) belong to a group of

modern materials, which have undergone an extensive study due

to their interest in advanced technologies. These alloys exhibit the

so-called shape memory effect which is linked to a martensitic

transformation that takes place from a bcc derived intermetallic

b phase (the parent phase) to one between several types of close

packed structures (the martensitic phase) [1,2]. These alloys can be

used as both sensor and actuators. These interesting properties

joined with the relatively low production costs, made this family of

alloys candidate for several technological applications [3]. Such as

in other alloys based on noble metals, the phase stability is mainly

controlled by the concentration of valence electrons, e/a.

In the binary CuAl system, Cu and Al atoms contribute to the

electronic concentrationwith 1 and 3 electrons, respectively. In this

alloy, a disordered bcc phase is stable at high temperature in the

range 1.40 e/a 1.55. As the temperature decreases, this stabilityrange becomes smaller and a eutectoid point is reached for

e/a 1.48 at 840 K. Below this temperature, the equilibrium phases

are the complex cubic g phase, with stoichiometry Cu9Al4, and the

disordered fcc a phase [46]. When cooling from high temperatures

with relatively high cooling rates, it is possible to suppress almost

entirely the precipitation of stable phases. Under such conditions,

the metastable b phase experiences some type of atomic ordering.

For compositions close to the stoichiometric Cu3Al, two possible

ordering mechanisms have been proposed. Soltys [7] reported the

existence of two ordering reactions: the first one from the disor-

dered bcc A2 to a B2 (ClCs type) configuration at TA24B2z973 K,

and a B2/DO3 ordering at TB24DO3z843 K. However, subsequent

investigations [811] have not been able to confirm these results. In

fact, XRD measurements [8] indicate the occurrence of a single

transition at Tz800 K. Calorimetric and resistometric measure-

ments [9,10] also failed to find evidence of an additional ordering

transition. Indeed, both XRD [8,11] and neutron diffraction mea-

surements [12] indicate that the low temperature phase has DO3character. Thus, it seems to be well established now that there is

a single ordering transition from the disordered A2 to a DO 3 state;

as will be shown below, the results of the present work support this

conclusion.

Addition of small quantities of beryllium as third element sta-

bilizes the b phase: Belkhala et al. [13] reported that, for CuAl0.47 wt.% Be, the temperature of the eutectoid point is around 50 K

lower than for the binary CuAl system. On the other hand, Jurado

and co-workers [8] have studied the orderdisorder transitions in

ternary alloys with low beryllium content and compositions near

the eutectoid. They reported a single ordering reaction A2/DO3 at

around 800 K; besides, the ordering temperature does not vary

significantly with the beryllium content.

Since the type and degree of long-range order, lro, present in the

b phase influence several properties of this kind of alloys and, in

particular, the characteristics of the martensitic transformation

[1,2], a deep understanding of all the aspects related to the atomic

ordering is necessary.

* Corresponding author. IFIMAT Instituto de Fsica de Materiales Tandil, Uni-

versidad Nacional del Centro de la Provincia de Buenos Aires, Pinto 399, 7000

Tandil, Buenos Aires, Argentina. Tel.: 54 2293 439670; fax: 54 2293 439679.

E-mail address: flanzini@exa.unicen.edu.ar (F. Lanzini).

Contents lists available at ScienceDirect

Intermetallics

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i n t e r m e t

0966-9795/$ see front matter 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.intermet.2008.06.009

Intermetallics 16 (2008) 10901094

mailto:flanzini@exa.unicen.edu.arhttp://www.sciencedirect.com/science/journal/09669795http://www.elsevier.com/locate/intermethttp://www.elsevier.com/locate/intermethttp://www.sciencedirect.com/science/journal/09669795mailto:flanzini@exa.unicen.edu.ar

7/28/2019 Influence of Be addition on orderdisorder transformations in b CuAl

2/5

In order to quantify the type and degree of lro, it is convenient to

split the general bcc lattice into four interpenetrating fcc sublattices

as shown in Fig. 1, and then to define the occupation probabilities

pLX for a given atomic species X (Cu, Al or Be) to be placed in the

sublattice L (IIV) [1,14,15]. Whereas in the A2 configuration the

atomic distribution is at random,

pI

X

pII

X

pIII

X

pIV

Xthe DO3 ordered state is characterized by the relationship:

pIX pIIX p

IIIXsp

IVX

Between the various experimental techniques used to study

ordering reactions in alloys, the electrical resistometry has the

advantage of its relatively simple implementation and high sensi-

bility to changes in the degree of lro. Notwithstanding, there is not

a direct way to relate quantitatively the changes in resistivity to the

changes in lro; it is necessary to appeal to some theoretical ap-

proach, being the best known the one due to Rossiter [16]. In this

model, a simple relation between the resistivity r, the degree of lro

S, and the temperature T is proposed:

rS; T r001 S2

1 AS2 B

n0

11 AS2

T (1)

In this expression, the parameter Squantifies the degree of lro. It is

defined in terms of the sublattice occupationspLX and their defini-

tion varies according to the particular type of ordered structure

under consideration, in such a way that S 0 for the state com-

pletely disordered, and S 1 for the state completely ordered in

a stoichiometric alloy. The constant A (Rossiter-constant) takes

values between 1 and 1, and depends on the electronic structure

of the material. The remaining constants, r0 (0) and B/n0, refer to

the residual electrical resistivity and the thermal coefficient of re-

sistivity in the completely disordered state, respectively [16].

This model has been successfully applied to various binary [17

22] and ternary alloys [23]. In the present work, we apply theRossiter formalism to the orderdisorder transitions in CuAlBe;

the main parameters of the model are determined from the ex-

perimental results, and the evolution with temperature of the lro

degree is calculated.

2. Experimental details

The study has been performed on samples obtained from ele-

ments of 99.99% purity. Their compositions are Cu24.7 at.% Al, Cu

22.72 at.% Al5.5 at.% Be and Cu22.19 at.% Al8.04 at.% Be. The

polycrystalline samples used for the resistivity measurements were

parallelepiped-shaped between 8 and 13 mm long and (0.2

0.4) (11.8) mm2 in cross-section. Precise dimensional measure-

ments were performed using a micrometer and amplified images of

the samples. The electrical resistance was monitored using a stan-

dard four-point probe technique. The leads and a chromelalumel

thermocouple were spot welded to the sample. A constant current

generator was used to drive a current of 100 mA through the

sample. A Keithley 186 Nanovoltimeter measured the potential

drop across the sample. The specimens were cooled to room tem-

perature from 1000 K, within the b phase field, at different rates

just to avoid precipitation of stable phases. Typical cooling rates

were in the order of 120600 K/min. Previousresults on continuous

cooling experiments with this family of alloys show that, for this

range of cooling rates, the fraction of stable phase precipitated is, if

any, completely negligible [24,25].

In order to transform the measured resistance data, R, into re-

sistivity r, the former has to be divided by a shape factor, f:

r R

f

For the samples used in this work, f [

=s, being[

the distancebetween the points where the voltage drop is measured, and Sthe

(uniform) cross-section area. Even when fcan be easily determined

at room temperature, special care has to be paid to the possible

dependence of fon the order state. From data reported by Ochoa-

Lara and co-workers [11] for Cu23.77 at.% Al2.6 at.% Be and Cu

23.18 at.% Al2.62 at.% Be, we can estimate that the relative change

in lattice parameter for the A2/DO3 transition is near 0.2%. Jurado

et al. [8] report Da=az0:04% for Cu22.73 at.% Al5.5 at.% Be,Da=az0:03% for Cu22.72 at.% Al3.55 at.% Be, and Da=az0:035%

for Cu23.13 at.% Al2.7 at.% Be, being Da=a aA2 aDO3 =aA2 the

relative change in lattice parameter between the A2 and the DO3structures at the transition temperature. In all cases, the de-

pendence of the lattice parameter (and hence of the reciprocal of

the geometrical factor f) on the lro degree is within the experi-

mental uncertainty and can then be neglected. Thus, the trans-

formation of the resistance data to resistivity values was performed

dividing by a constant ffr as measured at room temperature.

Before the measurements on CuAl (Be), we performed resis-

tometric measurements on a binary CuZn alloy. As will be

discussed below, the aim of this measurement was to test our ex-

perimental method and the Rossiter approach on a well-known

orderdisorder transition, as is the case of the continuous A24B2

transition in this system. Measurements were made on a single

crystalline sample with composition Cu48 at.% Zn. As long as the

ordering reaction does not involve a significant change in lattice

a

II

I

I I

II

II

II

II

III

IIIIV

IV

I

II

I

II

II

II

II

II

III

III

IV

IV

I I

I

I I

II

II

II

II

II

I

I I

II

II

II

II

III

IIIIV

IV

I

II

I

II

II

II

II

II

III

III

IV

IV

I I

I

I I

II

II

II

II

b

Fig. 1. Disordered bcc phase (A2) and structure DO3 with order in nearest and next nearest neighbors.

F. Lanzini et al. / Intermetallics 16 (2008) 10901094 1091

7/28/2019 Influence of Be addition on orderdisorder transformations in b CuAl

3/5

parameter [26], the resistance data was transformed into resistivity

values dividing by a constant geometrical factor as determined at

room temperature.

3. Results and discussion

Fig. 2 shows the variation of resistivity for CuAl and CuAlBe,

and Fig. 3a the corresponding to Cu48 at.% Zn. Orderdisorderreactions involve a change in the slope of the curve; the critical

temperatures are indicated with arrows.

The resistivitytemperature curves were analyzed in the

framework of the Rossiter theory by means of Eq. (1), which pre-

dicts a linear behavior of resistivity with temperature either in the

high-temperature disordered state or in the low-temperature

completely ordered one:

r0; T r00

B

n0

T (2)

and

r1; T Bn0 1

1 AT (3)

Performing a linear fit to the resistivity data well above the or-

derdisorder temperature, it is possible to determine both con-

stants r0 (0) and B/n0 through Eq. (2). A similar fit in the range of

temperatures sufficiently below the ordering one allows de-

termining the value of parameter A, using Eq. (3) for stoichiometric

alloys, or Eq. (1) with S Smax for off-stoichiometry. Once the

former constants are determined, it is possible to invert Eq. (1), and

then an expression for the variation of the order degree with

temperature is obtained:

ST

r00 rT B=n0T

r00 ArT

1=2(4)

In order to test the quality of this approach, we applied it to the

transition A2/B2 in Cu48 at.% Zn. This transition is a paradig-

matic, widely studied, case of continuous transition, i.e., charac-

terized by a continuous variation of the order parameter below

the critical temperature. Fig. 3b shows the evolution of the order

parameter against temperature as calculated from resistivity data

by means of Eq. (4), with parameters A 0.36 and

B/n0 2.28 108 U cm/K. In Fig. 3b are also included, for com-

parison, values of S as a function of temperature obtained from

neutron scattering experiments [27]. As can be seen, Rossiter for-malism correctly accounts for the continuous character of the

transition and satisfactorily reproduces the evolution of lro below

the transition temperature.

Fig. 2 shows the resistivity curve for binary Cu24.7 at.% Al and

two similar ternary alloys with low beryllium content. The mea-

surements show evidence of a unique ordering transition at

Tz800 K. For Cu24.7 at.% Al, the starting of the martensitic

transformation at a temperature Msz620 K is also detected (inset

in Fig. 2a). Linear fits of the resistivity curves at temperatures well

above and below the ordering temperature lead to the values for

the Rossiter parameters indicated in Table 1. In our analysis, we

have assumed that the ordering reaction canbe described by means

of a unique lro parameter, S. This assumption is generally not true in

ternary alloys, where the occupation probabilities for two of thethree atomic species are independent. However, as long as

a

b

c

Fig. 2. Resistivity against temperature for (a) Cu24.7 at.% Al (the inset shows the

variation of resistivity over a wider interval of temperatures, where it is appreciable

the start of the martensitic transformation); (b) Cu22.72 at.% Al5.5 at.% Be; (c) Cu22.09 at.% Al8.04 at.% Be.

Fig. 3. (a) Resistivity against temperature for Cu48 at.% Zn; (b) evolution of the order

parameter Sas calculated from resistivity data (black dots) and from neutron scattering

[20] (open circles).

F. Lanzini et al. / Intermetallics 16 (2008) 109010941092

7/28/2019 Influence of Be addition on orderdisorder transformations in b CuAl

4/5

beryllium content is low, our ternary system can be treated as

a quasi-binary one; this hypothesis is additionally justified since Be

atoms distribute uniformly among the different sublattices [8].

Consequently, the order parameter S is defined in terms of the

occupation probabilities for Al or Cu atoms. Furthermore, we will

assume that Sis defined in such a way that takes a maximum value

of 1, independently of composition. The detailed way in which Sis

defined is not crucial in the analysis performed here, but affects the

numerical value of the Rossiter-constant, A.

In Fig. 4a the evolution ofSwith temperature for Cu24.7 at.% Al

is shown. As can be seen, at the transition temperature, the order

parameter experiences an almost sudden change from the value

0 in the disordered state to its maximum value. This discontinuity is

characteristic of the first order kinetics of the ordering reaction. Onthe other hand, the variation of the order parameter for Cu

22.19 at.% Al8.04 at.% Be (Fig. 4c) shows a continuous increment

below the orderdisorder temperature. This behavior resembles

that observed in CuZn (Fig. 3b), and is distinctive of a continuous

transition. Finally, for Cu22.72 at.% Al5.5 at.% Be (Fig. 4b) an in-

termediate situation occurs: there is a discrete jump in the order

parameter at the transition temperature followed by a smooth in-

crease as the temperature is reduced. This is an outstanding result if

we take into consideration that previous works with this family of

alloys [8] seem to indicate that the transition is first order in the

whole range of compositions studied here. This conclusion has

been partially supported by arguments based on the Landau theory

of phase transitions: according to some analysis based on this

theory, the A2/DO3 transition is necessarily first order [10,28].

However, this assertion has been questioned by other authors

[29,30]. In fact, calculations made within the BraggWilliams

Gorsky approximation [14], and in the tetrahedron approximation

of the cluster variation method [29], show that, for certain values of

the interaction parameters, the A2/DO3 transition could be sec-

ond order. These calculations seem to be in accordance with the

present results.

4. Conclusions

Electrical resistivity is a very sensitive indicator of the degree

of long-range order present in a given alloy system. We haveshown that, when resistivity data is analyzed in the framework of

the Rossiter formalism, it is possible to calculate the evolution of

the lro degree in a very simple way. Results obtained by applying

this method to the well-known A24B2 transition in CuZn

agree quite well with those obtained with more elaborated

techniques. The remarkable advantage of this method is the

comparatively easier implementation of resistometric techniques

as compared to other methods (for example, X-ray or neutron

diffraction). Also, it is worth noting that the rate of data acqui-

sition is higher for an electrical resistometry measurement than

for an X-ray or neutron diffraction measurement: this is a very

important advantage when working with metastable phases,

where it is generally necessary to use high cooling rates in order

to avoid phase decomposition.In this work, the temperature dependence of resistivity for a set

of CuAl and CuAlBe alloys has been measured. Orderdisorder

temperatures were determined from these measurements: order-

ing temperatures are around 800 K and do not show a significant

dependence on composition. The changes in resistivity were re-

lated to changes in the degree of long-range order by means of the

Rossiter formalism; the main parameters involved in this theory

were determined (Table 1), and the resistivity variation was

transformed into changes in the order parameter S. The A2/DO3transition in Cu24.7 at.% Al has first-order character: the lro pa-

rameter S suffers a finite jump, reaching its maximum value in

a small interval of temperatures below the transition (Fig. 4a). The

magnitude of this discontinuity becomes smaller as small quanti-

ties of beryllium are incorporated (Fig. 4b), and the maximum de-gree of order is attained after a subsequent cooling of about 300 K.

With further increase in the beryllium content (Fig. 4c), traces of

a discrete step in the order parameter do not remain, and the

transition is seemingly a continuous one. This last result is in

contradiction with previously published ones; complementary in-

vestigation will be necessary in order to clarify this point.

Acknowledgements

The authors acknowledge the financial support of the Agencia

Nacional de Promocion Cientfica y Tecnologica, Conicet, Secretara

de Ciencia y Tecnica (UNCentro), Argentina and Comision de

Investigaciones Cientficas de la Provincia de Buenos Aires. We arethankful to Dr. A. Planes for providing the alloys used in this work.

Table 1

Composition of the alloys, ordering temperatures and values obtained for the

Rossiter parameters

CCu (at.%) CAl (at.%) CBe (at.%) TA2/DO3 (K) A B/n0 (U cm/K)

75.3 24.7 0 z810 z0 1.96 (3) 108

71.78 22.72 5.5 z815 z0.53 2.04 (2) 108

69.77 22.19 8.04 z820 z0.75 2.47 (3) 108

a

b

c

Fig. 4. Evolution with temperature of the order parameter as determined from re-

sistivity measurements for: (a) Cu24.7 at.% Al; (b) Cu22.72 at.% Al5.5 at.% Be; (c)

Cu22.19 at.% Al8.04 at.% Be. Insets: comparison with the XRD data extracted fromRef. [8] (open symbols).

F. Lanzini et al. / Intermetallics 16 (2008) 10901094 1093

7/28/2019 Influence of Be addition on orderdisorder transformations in b CuAl

5/5

References

[1] Ahlers M. Prog Mater Sci 1986;30:135.[2] Planes A, Romero R, Ahlers M. Acta Metall Mater 1990;38(5):757.[3] Delaey L. In: Haasen P, editor. Materials science and technology: a compre-

hensive treatment, vol. 5. Weinheim: VCH; 1991.[4] Chen SW, Chuang YY, Chang YA, Chu MG. Metall Trans A 1991;22A:

283748.[5] Miettinen J. Metall Mater Trans A 2002;33A:163948.[6] Barret CS, Massalsky TB. Structure of metals. 3rd ed. McGraw-Hill; 1966.[7] Soltys J. Phys Status Solidi A 1981;63:401.[8] Jurado M, Castan T, Manosa Ll, Planes A, Bassas J, Alcobe X, et al. Philos Mag A

1997;75:1237.[9] Lanzini F, Romero R, Stipcich M, Castro ML. Phys Rev B 2008;77:134207.

[10] Obrado E, Frontera C, Manosa Ll, Planes A. Phys Rev B 1998;58(1):14245.[11] Ochoa-Lara MT, Flores-Zuniga H, Ros-Jara D, Lara-Rodrguez G. J Mater Sci

2006;41:47558.[12] Manosa Ll, Jurado M, Gonzalez-Comas A, Obrado E, Planes A, Zaretsky J, et al.

Acta Mater 1998;46:1045.[13] Belkhala S, Flores Zuniga H, Guenin G. Mater Sci Eng A 1993;169:119.[14] Inden G. Acta Metall 1974;22(2):945.[15] Wu H, Wayman CM. Scr Metall Mater 1991;25:1635.

[16] Rossiter PL. The electrical resistivity of metals and alloys. Cambridge Univer-sity Press; 1987.

[17] Lang H, Mohri T, Pfeiler W. Intermetallics 1999;7:137381.[18] Sprusil B, Chalupa B. Intermetallics 2000;8:8313.[19] Lang H, Uzawa H, Mohri T, Pfeiler W. Intermetallics 2001;9:924.[20] Dimitrov C, Tarfa T, Dimitrov O. Equilibrium and kinetics of thermal ordering

or disordering in Ni3Al. In: Yavari AR, editor. Ordering and disordering in al-loys. London: Elsevier Applied Science; 1992. p. 1307.

[21] Lang H, Rohrhofer R, Rosencranz P, Kozubski R, Puschl W, Pfeiler W. In-termetallics 2002;10:28392.

[22] Pfeiler W, Sprusil B. Mater Sci Eng A 2002;324:3442.[23] Frely E. Etude des interactions entre effets dirradiation et effets dordre

chimique dans les alliages ternaries NiCrFe. These, Universite Paris XI,Orsay; 1997.

[24] Castro ML, Romero R. Scr Mater 2000;42:15761.[25] Moon JR, Garwood RD. J Inst Metals 1968;96:17.[26] Bhatia ML, Cahn RW. Intermetallics 2005;13:47483.[27] Norvell JC, Als-Nielsen J. Phys Rev B 1970;2(2):27782.[28] Dunweg B, Binder K. Phys Rev B 1987;36(13):6935.[29] Rubin G. J Phys Chem Solids 1997;58(12):201722.[30] Ducastelle F. In: De Boer FR, Pettifor DG, editors. Order and phase stability in

alloys, vol. 3. North-Holland; 1991.

F. Lanzini et al. / Intermetallics 16 (2008) 109010941094