Thermochemistry of ytterbium silicides

Intermetallics 11 (2003) 1153–1159 www.elsevier.com/locate/intermet

Thermochemistry of ytterbium silicides S. Bruttia,*, G. Balduccia, A. Cicciolia, G. Giglia, P. Manfrinettib, A. Palenzonab a Dipartimento di Chimica, Universita` di Roma La Sapienza, Piazzale A. Moro 5, I-00185 Rome, Italy INFM, Dipartimento di Chimica e Chimica Industriale, Universita` di Genova,Via Dodecaneso 31, I-16146 Genoa, Italy

b

Abstract The results of the investigation of the high temperature decomposition reactions in vacuum under equilibrium conditions of ytterbium silicides in the whole composition range are reported. By means of the Knudsen Effusion–Mass Spectrometry (KE–MS) and the Knudsen Effusion–Weight Loss (KE–WL) techniques, the Yb(g) vapour pressures in equilibrium over the various high temperature and low temperature biphasic regions were measured in the temperature range 781–1395 K and the reaction enthalpies for the respective decompositions were derived. From this set of experimental data we derived for the first time the heats of formation of all the six known Si–Yb intermediate phases. The following values
fH
298 are recommended: Si3Yb5=48.3  3.6, Si4Yb5=53.2 4.6, SiYb=51.1  5.1, Si4Yb3=48.0  3.1, Si5Yb3=41.3 2.6, Si1.74Yb=37.4  0.9, all in kJ/mol atoms. # 2003 Elsevier Ltd. All rights reserved. Keywords: A. Silicides, various; Rare-earth intermetallics; B. Thermodynamic and thermochemical properties

1. Introduction Transition metals and Rare-Earth (RE) metal silicides have attracted interest for their outstanding physical and chemical properties, that make some of them candidates for technological applications e.g. as high temperature structural materials and contact materials in microelectronics. This interest is even higher for the Si– Yb intermediate phases where Yb mixed valence fluctuations can be observed between bulk silicides and their surfaces [1–4]. The modelling of solid-state siliconmetal interaction, interface formation, etc. would be aided by the knowledge of phase transformations and thermodynamic properties of the intermediate phases. The enthalpies of formation of several binary transition and rare-earth metal silicides have been measured calorimetrically (see refs. [5,6]) but in general both the phase diagram and the thermodynamic information for RE-Si binary systems are still far from satisfactory. Regarding the Si–Yb system in particular, until recently several doubts on the number and identity of the intermediate phases still remained. Moreover experimental or computed phase diagram and thermodynamic prop-

* Corresponding author. Fax: +39-064-991-3951. E-mail address: [email protected] (S. Brutti). 0966-9795/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0966-9795(03)00152-3

erties were completely missing. Very recently some works were devoted to the investigation of the phase diagram and the temperatures of the invariant equilibria in the whole composition range [7,8]. Two new phases (Si4Yb5 and Si4Yb3) have been identified and their magnetic and thermal low-temperature properties have been investigated [9]. As reported in Ref. [8] the existence of a further compound SiYb2 could not be definitely proven. The present paper reports for the first time the hitherto missing thermochemical data for the formation of the hitherto known phases in the Si-Yb system, namely Si3Yb5, Si4Yb5, SiYb, Si4Yb3, Si5Yb3 and Si1.74Yb. The thermodynamic properties of these phases were investigated by means of an equilibrium method based on vapour pressure measurements. Both Knudsen Effusion–Mass Spectrometry (KE–MS) and Knudsen Effusion–Weight Loss (KE–WL) techniques were used in order to measure the equilibrium vapour pressure of the effusing species in equilibrium over the various high temperature and low temperature biphasic regions in a wide temperature range. Only monatomic Yb is formed in the gas phase during the various decomposition reactions. From the temperature dependence of the measured pYb the reaction enthalpies at room temperature for the various processes were derived. From this set of experimental data we derived, for the first time,

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the heats of formation of all the intermediate Si–Yb phases.

2. Sample preparation Bulk alloys were prepared in two steps. Elemental silicon ‘‘electronic grade’’ (99.999 wt.% purity) and commercial available ytterbium (99.9 wt.% purity) in the form of small pieces were first pressed into Ta crucibles, sealed by arc-welding under pure argon and then melted in a high-frequency induction furnace and cooled down to room temperature. In this way possible losses of volatile Yb were practically avoided. The reaction products were examined in the as cast state by LOM and SEM-EPMA techniques. Specimens were then submitted to the annealing procedure again in Ta crucibles arc-welded under argon and closed under vacuum in quartz ampoules. No contamination of the alloys by container materials was observed even after treatment at high temperatures up to 1600
C. Alloy samples characterization was performed by metallographic examination with standard techniques and by XRD on sample powders using a Guinier–Stoe camera or a diffractometer (Phillips X’Pert Pro) with Cu Ka radiation; pure silicon was used as internal standard (a=5.4308 A˚). The X-ray intensities were compared with those calculated by means of the LAZY-PULVERIX program [10].

3. Experimental details 3.1. Vapour pressure experiments For all the decomposition reactions investigated the vapour pressures were measured by the Knudsen effusion–Mass spectrometry (KE–MS) and, to a lesser extent, the Knudsen effusion–Weight loss (KE–WL) techniques. In the Knudsen effusion–Mass spectrometry experiments a Nuclide-Patco mod. 12-60 HT single focusing magnetic sector mass spectrometer coupled with a Knudsen cell assembly was utilized [11,12]. The effusion cells consisted of tantalum or molybdenum cells with cylindrical effusion orifices of 1.0 mm in diameters that were inserted into an outer tungsten crucible. The effusion cell was heated with a tantalum coil resistance and temperatures were measured with a disappearingfilament optical pyrometer by sighting into a blackbody cavity in the bottom of the outer crucible. As mentioned previously the only vapour species effusing from the Knudsen cell at the temperature of the measurements (1055–1395 K) was monatomic Yb(g). Gaseous Yb was ionised using an emission current of 1 mA and an electron energy of about 25 eV, in the range of the maximum of the Yb+ ionisation efficiency curve, which

showed a plateau between 24 and 30 eV. At this operating electron energies the double ionisation contribution (Yb++) to the whole Yb intensity was less than 5%. In the data analysis we corrected the measured Yb+ intensities for the double ionisation contribution. In a KC–MS experiment the partial pressure of the species i, in this case Yb(g), is related to the measured ion current Iiþ by the relation: pi ¼ kstr fi Iiþ T; where kstr is the instrumental constant and fi=1/(sigiai) is a factor which includes the electron impact cross section (si), the multiplier gain (gi), and the isotopic abundance (ai) of the specific ion. The evaluation of the calibration constant, kstr, was performed by vaporization of a standard such as high purity elemental silver, and comparing its intensity versus temperature (including the melting temperature) to the reference vapor pressure data for silver [13]. Further checks of the calibration constant were made by studying the dissociation
equilibrium Ag2(g)=2Ag(g) for which DH0 is well established. Some vaporization experiments were also performed using a vacuum microbalance coupled with the same Mo effusion cell used in the KC–MS experiments. The cell was suspended at the arm of the balance using a tungsten chain. In the KE–WL experiments the total vapor pressure of the effusing species is given by the relation: sffiffiffiffiffiffiffiffiffiffiffiffi dmtot 2RT ptot ¼ ; Mav A0 dt where A0 is the area of the effusion orifice, Mav is the average molecular weight of the effusing species, in this case only Yb(g), and dmtot/dt is the measured weightloss rate. Vapour pressures were measured over the various biphasic regions in the temperature range 781– 1395 K; initial samples were biphasic or single phase alloys. Vaporization experiments details are summarized in Table 1.The occurrence of each high temperature equilibrium was checked by submitting in all cases the initial samples and the vaporization residues to XRD analysis. 3.2. Data analysis For all the decomposition reactions studied, by assuming that all the intermediate phases are treated as line compounds, the equilibrium constant is given by: K ¼ pYb =bar; where pYb is expressed in bar. Equilibrium data were analysed by the usual second-law method, which gives

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S. Brutti et al. / Intermetallics 11 (2003) 1153–1159 Table 1 Decomposition reactions studied and results of the XRD characterizations of the samples

(1) (2) (3) (4) (5) (6) (7)

Reactions

Measurement technique

Alloy composition %at. Si

Phase(s) before vaporization (XRD)

Phase(s) after vaporization (XRD)

4/5 Si3Yb5(s)=3/5 Si4Yb5(s)+Yb(g) Si4Yb5(s)=4 SiYb(s)+Yb(g) 4 SiYb(s)=Si4Yb3(s)+Yb(g) 2.35 SiYb(s)=1.35 Si1.74Yb(s)+Yb(g) 5/3 Si4Yb3(s)=4/3 Si5Yb3(s)+Yb(g) 7.91 Si5Yb3(s)=22.73 Si1.74Yb(s)+Yb(g) Si1.74Yb(s)=1.74Si+Yb(g)

KE–WL KE–WL KE–MS KE–MS KE–MS KE–MS KE–MS

40 44 50 55 57 62.5 65

Si3Yb5, Si4Yb5 Si4Yb5 SiYb SiYb, Si5Yb3 Si4Yb3 Si5Yb3 Si1.74Yb

Si3Yb5, Si4Yb5 Si4Yb5, SiYb SiYb, Si4Yb5 Si1.74Yb Si4Yb3, Si5Yb3 Si5Yb3, Si1.74Yb Si1.74Yb, Si

the standard enthalpy of reaction at the average temperature < T > =1/( < T1 > ), as slope of the leastsquares fitting of ln Keq vs 1/T: Dr H
hTi ¼ R

dðlnKÞ : dð1=TÞ

third-law analysis of the equilibrium data using Gibbs energy function changes estimated here again by the K– N rule. A more detailed description of the data analysis methods is reported elsewhere [16].

4. Results and discussion


The enthalpy change at room temperature (Dr H298 ) can be calculated if the heat capacities for all the species involved are known. Because of the lack of high temperature experimental heat capacities for all the ytterbium silicides, we estimated the Cpo for all phases from 298 K to the high temperature range by means of the well-known Kopp–Neumann rule (K–N), which derives the heat capacity of a compound as the weighted-sum of the heat capacities of the constituent elements. Relevant data for the elements were taken from Hultgren’s reference compilation [13]. In a recent paper Dhar et al. [9] reported the heat capacities for the new phases Si4Yb5 and Si4Yb3 in the low-temperature range 1–30 K. A tentative extrapolation of these data to 300 K using both the Nernst–Lindemann [14] and the Tarasov  [15] o equations yielded an estimate of the H298  H0o and o values. For Si4Yb5 we found a fairly good agreeS298 ment between our (5811 J mol atoms1  calculated values o o o 1 for H298  H0 and 42.9 J K mol atoms1 for S298 ) and the K–N estimates (respectively 5158 J mol at1 and 41.6 J K1 mol atoms1) while for Si4Yb3 the cono vergence was unsatisfactory [ðH298  H0o Þ (K–N)=4715 o o o and ðH298  H0 Þ(Tarasov)=6489 J mol at1; S298 o 1 (K–N)=36.4 and S298 (Tarasov)=54.7 J K mol atoms1]. Due to the limited temperature range for which experimental data are available no reliable extrapolation above 300 K could be performed. Moreover, as no further experimental heat capacities are available for the Yb silicides phases, for all the compounds studied here, estimates by the K–N rule were preferred in order to allow for a partial compensation of the inaccuracies. Further work is under way in order to measure high temperature Cpo for all the Si-Yb intermediate phases. Standard enthalpy changes at 298 K were also tentatively derived for reactions (1)–(7) by means of the

4.1. Yb-rich compositions and ytterbium monosilicide Decomposition reactions which occur for alloy samples in the Yb-rich two-phase regions Si3Yb5/Si4Yb5 and Si4Yb5/SiYb [reactions (1) and (2) in Tables 1–3] have been studied using the KE–WL technique. The first decomposition equilibrium was investigated starting from a biphasic sample of about 40% at.Si, composed of both Si3Yb5 and Si4Yb5, while in the study of equilibrium (2) an initial sample of a Si4Yb5 single phase alloy of 44% at. Si was used (see Table 1). A summary of the vaporization results is given in Table 2 where the temperature range, the number of data points collected and the linear-fit regression coefficients are shown. The vapor pressure data points as a function of temperature are also represented in Fig. 1 in a ln pYb vs 1/T plot. As can be appreciated in the recently determined experimental phase diagram [8], Yb monosilicide decomposes to Si4Yb3 below 1253 K [reaction (3)] and to the silicon defective high temperature phase Si1.74Yb above this temperature [reaction (4)]. From the partial pressure equations representative of the experimental data taken below and above 1253 K it was possible to check the temperature of the invariant equilibrium Si4Yb3(s)=1.649 SiYb(s)+1.351 Si1.74Yb(s). Indeed the two linear pressure-temperature equations for reactions (3) and (4) cross each other at 1261 K. This temperature, which is representative of the peritectoid decomposition reported above, is in good agreement with the DTA value of 1253 K (see ref. [8]). The decomposition enthalpy changes derived by the second- and the third-law methods for all the four equilibria here analysed are reported again in Table 2.

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283.52.0

265.25.3

252.80.9

254.72.1

431.77.2

271.52.2

250.91.8 240.412.0

250.30.7 248.64.7

208.82.3 221.79.0

4.0470.090 51 (7)

Si1.74Yb(s)=1.74Si+Yb(g)

1109–1395

12.857 0.111

12.8460.328 15 1088–1207 (6)

7.91 Si5Yb3(s)=22.73 Si1.74Yb(s)+Yb(g)

22.149 0.377

6.0720.103 13.680 0.117 1055–1230 (5)

5/3 Si4Yb3(s)=4/3 Si5Yb3(s)+Yb(g)

20

4.8050.468 (4)

21 1265–1426 2.35 SiYb(s)=1.35 Si1,74Yb(s)+Yb(g)

12.060 0.624

5.2150.213 12.578 0.246 1091–1229 (3)

4 SiYb(s)=Si4Yb3(s)+Yb(g)

20

6.0970.496 (2)

17 841–1046 Si4Yb5(s)=4 SiYb(s)+Yb(g)

11.276 0.471

4.7240.327 8.8330.280 17 781–921 (1)

4/5 Si3Yb5(s)=3/5 Si4Yb5(s)+Yb(g)

A.103

B

Dr HohTi II law A þB logpðYbÞ =bar ¼  T=K

Data points T range (K) Reactions

Table 2 Vapour pressures and standard enthalpy changes (kJ mol1) of the decomposition reactions studied

In all cases a fairly good agreement between secondand third-law data is found. However in view of the reproducibility and the large number of data points,
second-law Dr H298 values are to be preferred. 4.2. Si-rich compositions

169.15.4 at 857 K 215.89.0 at 949 K 240.74.7 at 1154 K 230.812.0 at 1335 K 261.82.2 at 1169 K 423.97.2 at 1151 K 246.12.1 at 1238 K

o Dr H298 II law

174.15.4

o Dr H298 III law

185.91.1

S. Brutti et al. / Intermetallics 11 (2003) 1153–1159

The decomposition reactions involving the Si-rich compounds Si4Yb3, Si5Yb3, Si1.74Yb [reactions (5)–(7)] have been studied starting from single-phase samples. In all cases the appearance of the former phase in the vaporization residues was verified by XRD (see Table 1). The experimental results are represented in Fig. 2 and Table 2 in the usual form ln pYb vs 1/T. The reaction enthalpy changes derived by the second- and the thirdlaw methods are listed in Table 2. It is worth noting that the second law-reaction enthalpy change for the decomposition of Si5Yb3 into Si1.74Yb [reaction (6)] is remarkably higher than the mean value of all the other reactions (see Table 2). This fact can be explained considering that reaction (6) involves a low-temperature phase (Si5Yb3) and a high-temperature phase (Si1.74Yb) of similar stoichiometries (Si/Yb ratio 1.67 and 1.74, respectively). Indeed the Si1.74Yb compound, being a high-temperature phase, is expected to have a lessnegative formation enthalpy compared to Si5Yb3. This difference reflects on the value of the reaction enthalpy for the decomposition reaction (6) in an amplified manner owing to the high values of the stoichiometric coefficients (in turn related to the similar composition of
Si5Yb3 and Si1.74Yb). The second-law Dr H298 is consistent with these observations, while the third-law value is significantly lower. This could be due to the assumption of simple additivity (KN rule) in the calculation of the Cpo for Si1.74Yb. This high-temperature phase is indeed expected to have a larger absolute entropy, which makes it a stable phase at high temperature. This effect is not accounted for when using the additivity rule, that merely includes the composition dependence. Due again to the high values of the stoichiometric coefficients of reaction (6) a small inaccuracy in the estio mated S298 of Si1.74Yb strongly reflects on the third-law
Dr H298 . Table 3 Comparison between the standard heats of formation (kJ/mol atoms, T=298 K) of the Si–Yb intermediate phases calculated from Miedema’s model and measured in the present work Phase

This study (experimental)

Miedema model (predicted)

Si3Yb5 Si4Yb5 SiYb Si4Yb3 Si5Yb3 Si1.74Yb

48.3 3.6 53.2 4.6 51.1 5.1 48.0 3.1 41.3 2.6 37.4 0.9

30.1 46.1 43.7 42.5

S. Brutti et al. / Intermetallics 11 (2003) 1153–1159

Fig. 1. Measured vapour pressures for the decomposition of the Yb-rich phases.

Fig. 2. Measured vapour pressures for the decomposition of the Si-rich phases.

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For equilibria (5) and (7) a significant disagreement was found between second- and third-law results. As mentioned before this was probably due to further inaccuracies in the estimation of the Cpo ’s in the whole temperature range. In view of this, and considering the excellent reproducibility of the vapour pressure data in different experiments, second-law reaction enthalpy changes are to be considered more reliable. As described in the previous section for the peritectoid reaction Si4Yb3(s)=1.649 SiYb(s)+1.351 Si1.74Yb(s), the two crossings between the partial pressure equations for the three neighbouring two-phase regions Si4Yb3/ Si5Yb3, Si5Yb3/Si1.74Yb and Si1.74Yb/Si occur at the invariant temperature for reactions: Si5Yb3(s)=2.459 Si1.74Yb(s)+0.180 Si4Yb3(s) and Si1.74Yb(s)=0.073 Si(s)+0.333 Si5Yb3(s). The invariant temperatures so derived are respectively, 1252 K and 1056 K to be compared with the two DTA values of 1238 K and 1043 K. 4.3. Heats of formation


The second-law decomposition enthalpies Dr H298 presented in Table 2 enable us to derive the standard enthalpies of formation of all the Si–Yb intermediate phases. Starting from the decomposition of Si1.74Yb and considering the sublimation enthalpy of pure ytterbium
(Dsub H298 (Yb)=152.1 kJ/mol [13]) a complete set of
Df H298 for all the Yb silicides can be derived by means of simple thermochemical cycles. Two different reactions [reactions (3) and (4)] allow for the determination
of Df H298 of SiYb: the two values are comparable within the standard deviations (respectively 54.0  5.6 and 48.3  4.5 kJ/mol atoms) so confirming the selfconsistency of the data. For this reason we propose for the heat of formation of SiYb the average of the two
results [Df H298 (SiYb)=51.1  5.1]. This value has been
used to calculate subsequently the Df H298 for the two latter ytterbium-rich silicides Si4Yb5 and Si3Yb5. Our
recommended Df H298 values are presented in Table 3. All these heats of formation are first determination and no comparison with previous experimental or calculated data is possible. The heats of formation for four of the intermediate phases (Si3Yb5, SiYb, Si5Yb3 and Si1.74Yb) were also estimated by Miedema’s model [17]. As pointed out by Miedema [18] attention should be paid in applying this model to Yb alloys, because of the fluctuant valence state of this element. Several researches have been devoted to the study of the fluctuations of the Yb valence in four out of six Si–Yb phases (Si3Yb5, SiYb, Si5Yb3 and Si1.74Yb) [1–4]: in these compounds both divalent and trivalent Yb atoms are present, depending on the crystal site. The average valence states of Yb were taken from the literature as follows: 3 (Si3Yb5) [4],

2.72 (SiYb) [2], 2.52 (Si5Yb3) [2] and 2.35 (Si1.74Yb) [1].
The Df H298 predicted by Miedema’s model are reported in Table 3: these formation enthalpies have been derived as the weighted average between those calculated using divalent and trivalent Yb parameters [17]. No estimates were made for the other ytterbium silicides owing to the absence of any determination of the Yb valence in these compounds. The heats of formation so calculated compare fairly well with our experimental values, except for Si3Yb5. For this phase a further comparison can be made considering two general trends for the Si3RE5 compounds proposed respectively by Gschneidner [19] and Meschel et al. [5,6]. Gschneidner suggested that the cohesion in RE compounds is directly related to the atomic radius contraction that occurs under alloy formation. Meschel et al. [5] pointed out that RE relative molar volumes (r.m.V.) in Si3RE5 compounds are approximatively constant when plotted against the
atomic number, while calorimetric Df H298 for many of these phases showed a small increasing trend in contrast to Gschneidner’s predictions. The relative molar volume for Yb in Si3Yb5 (r.m.V. ratio=0.95), recalculated using the molar volume of trivalent ytterbium [17], agrees with the trend observed by Meschel et al. [5]. However, the formation enthalpy measured for this phase is somewhat lower than for the other Si3RE5 compounds, so deviating from the trends proposed by both Gschneidner and Meschel.

Acknowledgements This research was supported by the Ministero dell’Istruzione, dell’Universita` e della Ricerca (MIUR), under the National Research Project, ‘Alloys and intermetallic compounds: thermodynamics, physical properties, reactivity’.

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