Journal of Alloys and Compounds 535 (2012) 70–77

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Journal of Alloys and Compounds

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A calorimetric study of thermodynamic properties for binary Cu–Ge alloys

W. Zhai, D.L. Geng, W.L. Wang, B. Wei ⇑Department of Applied Physics, Northwestern Polytechnical University, Xi’an 710072, PR China

a r t i c l e i n f o a b s t r a c t

Article history:Received 24 February 2012Received in revised form 20 April 2012Accepted 23 April 2012Available online 1 May 2012

Keywords:Cu–GeDifferential scanning calorimetry (DSC)Enthalpy of fusionUndercoolabilitySolidification

0925-8388/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.jallcom.2012.04.091

⇑ Corresponding author. Tel.: +86 29 88431666; faxE-mail address: bbwei@nwpu.edu.cn (B. Wei).

The phase transformation temperatures and enthalpy of fusion for Cu–Ge alloys in the whole composi-tion range are systematically measured by differential scanning calorimetry (DSC). It is found that theundercoolability of liquid Cu–Ge alloys depends mainly on the nucleation ability of primary solid phases.Those liquid alloys solidifying with the preferential nucleation of intermetallic compounds exhibit smal-ler undercoolings than the others with the primary a(Cu) and (Ge) solid solution phases. Microstructuralobservation indicates that the n, e and e1 intermetallic compounds display non-faceted growth mode. InCu–Ge eutectic alloys, the n and e phases grow into lamellar structures, whereas the e2 and (Ge) phasesform irregular eutectics. The peritectic reactions can rarely be completed, and the peritectic microstruc-tures are usually composed of both the primary and peritectic phases.

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1. Introduction

Binary Cu–Ge alloys have attracted considerable research atten-tion because of their excellent physical and chemical properties,such as low room-temperature resistance and high thermal stabil-ity, which are potentially useful in the optical and electronicdevices [1–6]. The thermodynamic investigations of liquidCu-based alloys and their solidification characteristics are of signif-icance for understanding their physical and chemical properties[7–12]. Therefore, many efforts have been made to explore thesesubjects in recent years [13–16].

Up to now, Castanet has determined the enthalpy of mixing ofliquid Cu–Ge alloys at different temperatures by means of high-temperature calorimeter [17]. The formation enthalpy of a(Cu)solid solution phase at 1000 K was measured by Predel andSchallner [18] using solution calorimetry. Moreover, Wallbrecht[19] determined the heat capacity of the intermetallic compounde1(Cu3Ge) in the temperature range from 230 to 1000 K by differen-tial scanning calorimetry. The density and surface tension of liquidCu–Ge alloys in the temperature range between liquidus line and1373 K were studied by Gruner et al. [14]. Recently, Wang et al.[20] have assessed the excess Gibbs energies of Cu–Ge binarysystem by adopting the CALPHAD approach [21]. However, theenthalpy of fusion, which is one of the fundamental thermody-namic parameters and plays an important role in computing the

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Gibbs free energy and determining the crystal nucleation andgrowth process [22], has not yet been available in the publishedliterature. Although the enthalpy of fusion for binary alloys canbe roughly estimated by Neumann–Kopp’s rule [23] from the valuesof the two pure components, this method usually brings in largediscrepancy especially if one of the two elements is a semiconduc-tor such as Si, Ge or Sb. This is because the enthalpy of fusion ofsemiconducting elements is much higher than those of metallic ele-ments. In this point of view, the enthalpy of fusion for Cu–Ge alloysshould be measured experimentally.

On the other hand, some work has been done on the directionaland rapid solidification of Cu–Ge peritectic alloys [24–26]. Forexample, the structural morphologies of hyperperitectic Cu–Gealloys during unidirectional solidification were reported [24], andthe microstructural evolution of peritectic Cu–Ge alloys duringrapid solidification was investigated versus undercooling [25,26].Nevertheless, binary Cu–Ge system is characterized by numeroustypes of phase transformations, such as eutectic, peritectic, eutec-toid and peritectoid transitions. A comprehensive study on thesolidification mechanism involved in different types of Cu–Gealloys under near-equilibrium conditions is still expected.

The differential scanning calorimetry (DSC) is an efficient tech-nique for quantitative thermal analysis [27,28]. Meanwhile, theDSC heating–cooling curves provide the essential information onphase transformation characteristics [3,29–32]. The objective ofthis work is to determine the phase transformation temperaturesand enthalpy of fusion for Cu–Ge alloys by DSC method. Further-more, the liquid undercoolability and solidification microstruc-tures for various types of Cu–Ge alloys are also investigated inthe light of DSC calorimetric analyses.

Fig. 1. Selection of alloy compositions and measured phase transformationtemperatures illustrated in binary Cu–Ge phase diagram.

Fig. 2. Measured enthalpy of fusion of Cu–Ge alloys versus Ge content.

W. Zhai et al. / Journal of Alloys and Compounds 535 (2012) 70–77 71

2. Experimental procedures

Eighteen Cu–Ge alloys with different compositions were investigated, which arelisted in Table 1 and marked in the binary Cu–Ge phase diagram [33] shown inFig. 1. Each sample had a mass of about 100 mg and was prepared from high purityelements of Cu (99.999%) and Ge (99.999%) by rapid laser melting under the protec-tion of argon gas.

The DSC experiments were carried out with a Netzsch DSC 404 F3 differentialscanning calorimeter. The calorimeter was calibrated with the melting tempera-tures and the enthalpy of fusion for high purity In, Sn, Zn, Al, Ag, Au and Fe ele-ments. The measuring accuracies of temperature and enthalpy of fusion are ±1 Kand ±3% respectively, as verified by the measurements with pure Cu and Ge ele-ments. Before each DSC experiment, the alloy specimen was placed in an Al2O3 cru-cible. The chamber was evacuated and then backfilled with pure argon gas. The DSCthermal analyses were performed at a scan rate of 10 K/min, and the maximumheating temperatures were about 150 K higher than the liquidus temperatures.

After the DSC experiments, the alloy specimens were polished and etched witha solution of 5 g FeCl3 + 1 mL HCl + 99 mL H2O. The solidification microstructureswere analyzed with an optical microscope and an FEI Sirion scanning electronmicroscope.

3. Results and discussion

3.1. Enthalpy of fusion

The enthalpy of fusion for Cu–Ge alloys, covering all the heatevolution from solidus temperature to liquidus temperature, inthe whole composition range is determined by the solid–liquidtransformation peaks during melting process, as summarized inTable 1 and shown in Fig. 2. A polynomial relation is derived fromfitting the enthalpy of fusion DHf with respect to the mole fractionof Ge element C:

DHf ¼ 14:44� 0:96Cþ 0:04C2 � 6:20� 10�3C3 þ 3:14� 10�6 C4

ð1Þ

As seen from Fig. 2, the enthalpy of fusion versus Ge contentfirst decreases to a minimum value at 25% Ge, and then experi-ences a rise. By comparison, the enthalpy of fusion for Cu–Ge alloysis lower than those of pure Cu and Ge elements in the Ge contentrange of 0–45%, and lies between them if Ge content exceeds 45%.Meanwhile, the linearly approximated values H0 estimated byNeumann–Kopp’s rule are also plotted by the dashed line in Fig. 2:

DHo ¼ x1DH1f þ x2DH2

f ð2Þ

where xi and DHif are the molar fraction and enthalpy of fusion of

the pure component i, respectively. It is apparent that all the mea-sured data are lower than the linear fitting values.

Table 1Thermodynamic properties of Cu–Ge alloys measured by DSC method.

Alloycomposition

Liquidus temperature TL

(K)Enthalpy of fusion DHf

(kJ mol�1)

Cu97.8Ge2.2 1354 12.729Cu95.6Ge4.4 1334 10.774Cu93.4Ge6.6 1312 9.890Cu91.1Ge8.9 1293 9.735Cu89.3Ge10.7 1252 9.418Cu87.2Ge12.8 1220 8.074Cu84.8Ge15.2 1172 8.068Cu82.5Ge17.5 1103 8.062Cu78.05Ge21.95 1015 7.156Cu73.9Ge26.1 1009 7.050Cu68.0Ge32.0 957 9.175Cu63.5Ge36.5 915 11.022Cu53.3Ge46.7 988 13.282Cu43.2Ge56.8 1046 14.347Cu32.9Ge67.1 1093 15.698Cu21.2Ge77.8 1134 16.833Cu11.3Ge88.7 1186 20.691Cu5.1Ge94.9 1209 24.761

3.2. DSC curves and microstructure characteristics

In order to present a comprehensive survey on the phase tran-sition characteristics, the DSC curves and solidified structures fordifferent types of Cu–Ge alloys are analyzed.

3.2.1. Single (Cu) phase alloysFig. 3 presents the DSC melting curves of five single a(Cu) phase

alloys, in which the solidus and liquidus temperatures are marked.Clearly, the melting thermographs of these alloys are characterizedby only one endothermic peak, and both the solidus and liquidustemperatures decrease with increasing Ge content. However, theshapes of melting peaks for these single-phase alloys differ fromeach other. When Ge content is low, for example Cu97.8Ge2.2 alloy,the endothermic peak is very sharp and smooth with a narrowsolid–liquid temperature interval. As Ge content rises, the inflec-tion points appear obviously in the rising stages of the meltingpeaks, and the peaks become broader and broader. This indicatesthat the solid–liquid phase interval extends with the increase ofGe content in a(Cu) single-phase alloys. Fig. 4a shows a typicalDSC cooling curve of these single-phase alloys. It is evident thatthere is only one sharp exothermic peak at 1269 K in the solidifica-tion process of Cu95.6Ge4.4 alloy, and the a(Cu) phase is found toform coarse and well-developed dendrites in the solidified speci-men, as illustrated in Fig. 4b.

72 W. Zhai et al. / Journal of Alloys and Compounds 535 (2012) 70–77

3.2.2. Peritectic type alloysFig. 5a and b shows the DSC curves and solidified microstruc-

ture of peritectic Cu87.2Ge12.8 alloy. There are two endothermicevents during its melting process. The first endothermic peak cor-responds to the decomposition of solid peritectic n phase into theliquid and a(Cu) phases, while the second one relates to the melt-ing of a(Cu) phase. The solidus and liquidus temperatures of thisalloy are 1096 and 1220 K, respectively. During the cooling pro-cess, the primary a(Cu) phase nucleates at 1145 K with a verysharp crystallization peak, and the following peritectic transitionL + a ? n at 1091 K yields another small exothermal peak. Asshown in Fig. 5b, the solidified microstructure consists of boththe primary a(Cu) dendrites and the peritectic n phase. In fact, un-der equilibrium condition, 100% n phase is expected to be obtainedat the end of solidification. However, since the peritectic transfor-mation is mainly controlled by atomic interdiffusion and it is veryslow, the peritectic reaction can rarely be completed even underslow cooling condition during the DSC experiments. Consequently,the microstructure is composed of peritectic n phase and primarilyprecipitated a(Cu) phase.

The DSC profiles of peritectic Cu73.9Ge26.1 alloy are presented inFig. 5c. The four endothermic and four exothermic peaks are nearly

Fig. 3. DSC melting curves of single-phase Cu–Ge alloys.

symmetrical, suggesting that the same reaction sequence takesplace in reverse order during melting and solidification. In thecooling process, the first sharp exothermal peak at 991 K relatesto the phase transition L ? e, and its neighboring peak at 963 Kindicates the peritectic transition L + e ? e2. Once temperaturedrops down to 876 K, another small exothermic peak appears,which probably corresponds to the peritectoid transitione + e2 ? e1. This is quite different from the solidification route indi-cated by the Cu–Ge equilibrium phase diagram [33], in which thisreaction should not take place in Cu73.9Ge26.1 alloy. In the presentcase, the incomplete peritectic reaction results in the coexistenceof the primary and peritectic phases. This may lead to the peritec-toid reaction between the primary e and peritectic e2 phases. Thefinal exothermal peak at 866 K coincides with the eutectoid trans-formation e2 ? e1 + (Ge) shown in the Cu–Ge phase diagram [33].

As mentioned above, the solidification process of Cu73.9Ge26.1 al-loy involves the nucleation and growth of e and e1 intermetalliccompounds. The Jackson factor a is applied to predict the growthmodes of these intermetallic compounds [34]:

a ¼ DSf =R ¼ DHf =RTL ð3Þ

Here, R is the gas constant. The a values deduced by the experimen-tal enthalpy data are 0.84 and 0.85 for e and e1 phases, respectively.They are both smaller than the critical value of 2, indicating a non-faceted growth mode. In contrast, the calculated values derivedfrom Neumann–Kopp’s rule are found to be 2.2 and 2.1 > 2, which

Fig. 4. Typical cooling curve and structural morphology of single phase alloy: (a)cooling curve of Cu95.6Ge4.4 alloy and (b) a(Cu) phase microstructure.

Fig. 5. Thermal and structural analyses of two peritectic Cu–Ge alloys: (a) DSC curves of Cu87.2Ge12.8 alloy, (b) microstructure of Cu87.2Ge12.8 alloy, (c) DSC curves ofCu73.9Ge26.1 alloy and (d) microstructure of Cu73.9Ge26.1 alloy, and the inset shows enlarged eutectoid structure.

W. Zhai et al. / Journal of Alloys and Compounds 535 (2012) 70–77 73

predict faceted growth. In order to confirm the crystallizationbehavior of these two intermetallic compounds, the structural mor-phology of Cu73.9Ge26.1 alloy is presented in Fig. 5d, which provesthat the primary e phase grow just as normal non-faceted solutionphases. The inset SEM image of Fig. 5d illustrates the eutectoidstructure decomposed by peritectic e2 phase, in which the bright(Ge) phase and dark e1 phase grow as granular eutectoid structureand locate at the boundaries of e grains. Apparently, e1 phase exhib-its the same growth mode as e phase. Hence, it can be concludedthat the growth modes of these intermetallic compounds can bebetter predicted by the a values calculated from the measured val-ues of enthalpy of fusion rather than by the values calculated fromNeumann–Kopp’s rule. This further highlights the importance ofexperimental measurement of the enthalpy of fusion for binaryalloys including Ge element.

3.2.3. Eutectic type alloysFig. 6a depicts the DSC curves of eutectic Cu78.05Ge21.95 alloy.

The first exothermic peak at 1012 K during solidification is dueto the eutectic reaction L ? n + e, during which e and n phasesgrow cooperatively into lamellar eutectic structure with an interla-mellar spacing of 35 lm, as presented in Fig. 6b. As compared withthe first exothermic peak, the second one resulting from the eutec-toid transformation e ? n + e1 at 805 K is very small, and unfortu-nately, the eutectoid structure cannot be distinguished in the

solidified specimen even at large magnification. The DSC curvesof eutectic Cu63.5Ge36.5 alloy are shown in Fig. 6c. The two meltingpeaks at 885 and 915 K connect with each other, corresponding tothe solid transformation e2 ? (Ge) + e1 and the melting of e2 + (Ge)eutectic structure, respectively. The relevant exothermic peaksduring cooling are overlapped owing to the narrow temperatureinterval between these two transformations. The growth morphol-ogy of e2 + (Ge) eutectics is illustrated in Fig. 6d. Different fromregular (n + e) eutectics, the (e2 + Ge) eutectics tend to grow in anirregular mode, and the microstructure is characterized by strip(Ge) phase distributing in e2 phase with an average interphasespacing of about 12 lm.

In addition to eutectic Cu63.5Ge36.5 alloy, the DSC cooling curvesof six different hypereutectic Cu–Ge alloys are presented in Fig. 7a,whose common features are as follows: the (Ge) phase precipitatespreferentially from the alloy melts at different temperatures. Sub-sequently, eutectic transition L ? e2 + (Ge) takes place at about895 K. On further cooling, eutectoid reaction e2 ? (Ge) + e1 occursaround 870 K. Fig. 7b shows typical structural morphology of thesehypereutectic Cu–Ge alloys, in which the primary (Ge) phasegrows in faceted way to form very coarse polygonal blocks, ande2 + (Ge) eutectic structure keeps almost the same morphology asthat of eutectic Cu63.5Ge36.5 alloy.

The measured formation enthalpy of primary (Ge) phase,e2 + (Ge) eutectic and e1 + (Ge) eutectoid structures in these hyper-

74 W. Zhai et al. / Journal of Alloys and Compounds 535 (2012) 70–77

eutectic alloys is plotted in Fig. 8 and listed in Table 2. Evidently, asGe content rises, the formation enthalpy of primary (Ge) phase in-creases, whereas the formation enthalpy of eutectic and eutectoidstructures decreases monotonically. The linear relationships be-tween formation enthalpy and alloy composition are expressed as:

DHs�ðGeÞ ¼ 0:38C � 13:54 ð4Þ

DHs�ðGeÞþe2 ¼ 15:34� 0:16C ð5Þ

DHs�ðGeÞþe1 ¼ 2:68� 0:026C ð6Þ

On the basis of all the DSC melting curves, the transformationtemperatures are marked by solid circles in the Cu–Ge phase dia-gram [33] shown in Fig. 1, and the temperatures of typical reac-tions indentified by this work are also summarized in Table 3. Itneeds to be mentioned that the measured temperature of eutectoidreaction e ? e1 + n is 835 K, which is about 12 K higher than thosevalues reported in Refs. [20,33]. Besides, the peritectoid transfor-mation e2 + e ? e1in this work is determined to occur at 908 K,which is close to the value of 909 K in Ref. [33] and is about 40 Klower than that reported in Ref. [20]. Other typical reaction tem-peratures agree well with the published data.

Fig. 6. DSC thermographs and microstructures of two eutectic Cu–Ge alloys: (a) DSC curvcurves of Cu63.5Ge36.5 alloy and (d) e2 + (Ge) eutectic structure of Cu63.5Ge36.5 alloy.

3.3. Undercoolability and nucleation of Cu–Ge alloys

The undercoolings (DT = TL � Ts) of different liquid Cu–Ge alloysare measured by DSC method using a scan rate of 10 K/min in thecalorimeter to investigate their undercoolability versus composi-tion. Here, TL is the measured liquidus temperature of a specificCu–Ge alloy during heating, and Ts is the initial solidification tem-perature upon cooling. As shown in Fig. 9, the undercooling DT canbe divided into three regions as marked in Fig. 1, named region A(0–17.5 at.% Ge), B (17.5–36.5 at.% Ge) and C (36.5–100 at.% Ge).In region A, the a(Cu) phase always solidifies primarily in all thealloys, and the undercooling experiences an increase from 33 to73 K with the rise of Ge content. Then, undercooling drops dramat-ically to about 20 K in the alloys of region B. As for these alloys,their solidification processes initiate with the nucleation of inter-metallic compounds. By contrast, in region C, where the primary(Ge) phase nucleates preferentially from all the liquid alloys,the undercooling rises again from 46 to 73 K in the Ge contentrange of 36.5–77.8 at.%, and then falls again to a low value of28 K in pure Ge. These results suggest that the undercoolingsachieved in the DSC experiments are strongly dependent on theprimarily nucleating solid phases and follow the relation:

DTcomp < DT ðGeÞ < DTaðCuÞ ð7Þ

es of Cu78.95Ge21.95 alloy, (b) (n + e) eutectic structure of Cu78.95Ge21.95 alloy, (c) DSC

Fig. 7. DSC cooling curves and solidification microstructure of hypereutectic Cu–Gealloys: (a) cooling curves and (b) morphology of primary (Ge) phase in Cu5.1Ge94.9

alloy.

Fig. 8. Formation enthalpy of different structures versus Ge content in hypereu-tectic Cu–Ge alloys: (a) primary (Ge) phase, (b) (Ge) + e2 eutectic and (c) (Ge) + e1

eutectoid.

Table 2Measured enthalpy of liquid–solid and solid–solid transformations for hypereutecticCu–Ge alloys.

Alloy composition Enthalpy of transformation (kJ mol�1)

Primary (Ge) (Ge) + e2 eutectic (Ge) + e1 eutectoid

Cu63.5Ge36.5 0 11.343 1.898Cu53.3Ge46.7 4.337 6.419 1.193Cu43.2Ge56.8 8.221 5.814 1.183Cu32.9Ge67.1 13.808 4.674 0.949Cu21.2Ge77.8 15.337 3.412 0.760Cu11.3Ge88.7 19.897 1.553 0.335Cu5.1Ge94.9 22.901 0.780 0.160

Table 3Measured transformation temperatures of binary Cu–Ge system in comparison withliterature data.

Reaction Type Transformation temperature (K)

This work Ref. [33] Ref. [20]

L + (Cu) ? n Peritectic 1096 1097 1097L ? e + n Eutectic 1015 1016.5 1021L + e ? e2 Peritectic 969 971 971L ? e2 + Ge Eutectic 915 917 911e2 ? e1 + Ge Eutectoid 885 887 887e ? e1 + n Eutectoid 835 823 822e2 + e ? e1 Peritectoid 908 909 948

W. Zhai et al. / Journal of Alloys and Compounds 535 (2012) 70–77 75

In fact, the undercoolability of liquid alloys is closely related tothe nucleation processes of various solid phases within them.According to the classical nucleation theory [35], the activationenergy DGc for homogeneous nucleation is given by:

DGc ¼ 16pr3SL=3DG2

v ð8Þ

in which SL is the liquid/solid interfacial energy, and Gv is the differ-ence of Gibbs free energies of liquid and solid phases. Gv is approx-imated by:

DGv ¼ Hm � DT=ðVm � TLÞ ð9Þ

where Vm is the molar volume. From Eq. (10), it can be seen that theliquid/solid interfacial energy plays an important role in determin-ing the nucleation process. In the model developed by Spaepen [36],the liquid/solid interfacial energy of a crystalline phase is expressedas:

rSL ¼ amDSf TL=ðNAV2mÞ

1=3 ð10Þ

where am is a structure-dependent factor and NA is the Avogadro’snumber. According to Eq. (10), the liquid/solid interfacial energyof various phases are calculated and listed in Table 4. Due to therather small composition differences among the three intermetallic

compounds, only e phase is considered here. Apparently, the liquid/solid interfacial energy of e phase is significantly lower than that ofa(Cu) and (Ge) phases.

On the basis of calculated liquid/solid interfacial energy, theactivation energy for nucleation of the three phases versus und-ercooling is calculated, and the results are illustrated in Fig. 10.Clearly, if the nucleation takes place at the same undercooling,

Fig. 9. The measured undercoolings of Cu–Ge alloys versus composition.

Table 4Liquid/solid interfacial energy of various phases in binary Cu–Ge system.

Phase Composition (at.% Ge) am Interfacial energy (Jm�2)

a 4.4 0.71 0.347e 26.1 0.71 0.084(Ge) 100 0.86 0.283

Fig. 10. Activation energy for nucleation of different phases versus undercooling.

76 W. Zhai et al. / Journal of Alloys and Compounds 535 (2012) 70–77

the activation energy for homogeneous nucleation of the three so-lid phases follows the relation:

DGe < DGðGeÞ < DGaðCuÞ ð11Þ

It is reasonable to assume that inequality (11) is also valid in theheterogeneous nucleation processes of Cu–Ge alloys in the DSC cal-orimeter. The activation energy for heterogeneous nucleation ofintermetallic compounds is lower than that of a(Cu) and (Ge)phases, suggesting that the intermetallic compounds are easier tonucleate. This accounts for the weak undercoolability of thoseliquid alloys in which intermetallic compounds nucleate as theprimary phases, and reveals the fact that the activation energyfor primary phase nucleation determines the undercoolability ofliquid Cu–Ge alloys.

4. Conclusions

In summary, the phase transformation temperatures and en-thalpy of fusion for Cu–Ge alloys in the whole composition rangeare determined by DSC method. The temperatures of eutectoidreaction e ? e1 + n and peritectoid reaction e2 + e ? e1 are deter-mined to be 835 and 908 K, which are different from the publisheddata. The enthalpy of fusion first decreases in the compositionrange of 0–25%Ge, and then rises continuously with the increaseof Ge content. The measured enthalpy of fusion for Cu–Ge alloysis lower than those calculated by Neumann–kopp’s rule.

The maximum undercoolings of liquid Cu–Ge alloys in whichthe a(Cu) and (Ge) phases nucleate preferentially are 73 and71 K respectively in the DSC experiments. By contrast, the under-coolings of those liquid alloys in which intermetallic compoundsnucleate as the primary phases are only around 20 K. Their rela-tively weak undercoolability is due to the low activation energyfor nucleation of intermetallic compounds as compared with thatof a(Cu) and (Ge) phases.

Microstructural observation reveals that a(Cu) phase formswell-developed dendrites, whereas the (Ge) phase exhibits facetedgrowth in the form of polygonal blocks. The n, e and e1 intermetal-lic compounds are also found to display non-faceted growthmanner. Furthermore, in eutectic Cu–Ge alloys, the e phase growscooperatively with the n phase into lamellar structure, whereas thee2 and (Ge) phases tend to form irregular eutectic structure. Theperitectic reactions can rarely be completed, and the solidificationmicrostructures of peritectic Cu–Ge alloys consist of both theprimary and peritectic phases.

Acknowledgements

This work was supported by the National Natural ScienceFoundation of China (Nos. 50971105 and 51101123) andFundamental Research Fund of Northwestern PolytechnicalUniversity (Nos. JC201050 and JC20110280).

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