Thermodynamic stabilities of intermediate phases in the Ca-Si system

Article abstract of DOI:10.1016/S0925-8388(00)01381-5

Vaporization thermodynamics in the binary system calcium-silicon has been studied by Knudsen effusion-mass spectrometry and vacuum microbalance techniques. The equilibrium partial pressure of Ca(g) over the two-phase regions in the composition range 20-75

Full text of DOI:10.1016/S0925-8388(00)01381-5

Journal of Alloys and Compounds 317–318 (2001) 525–531
L
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Thermodynamic stabilities of intermediate phases in the Ca–Si system
a
b
b
S. Bruttia, A. Cicciolia, G. Balduccia , , G. Gigli , P. Manfrinetti , M. Napoletano
*
a
`
Dipartimento di Chimica, Universita di Roma La Sapienza, p.le A. Moro 5, I-00185, Roma, Italy
Dipartimento di Chimica e Chimica Industriale, Universita di Genova, via Dodecaneso 31, I-16146, Genova, Italy
b
`
Abstract
Vaporization thermodynamics in the binary system calcium–silicon has been studied by Knudsen effusion-mass spectrometry and
vacuum microbalance techniques. The equilibrium partial pressure of Ca(g) over the two-phase regions in the composition range
20–75at.% Si has been measured and the standard enthalpy changes for the appropriate vaporization reactions were determined from the
temperature dependence of the measured vapor pressures. The standard reaction enthalpy changes were also evaluated by the third-law
method using the pressure data in conjunction with estimated Gibbs energy functions. Standard enthalpies of formation of the calcium
silicides were derived from the standard reaction enthalpy values at room temperature. The results obtained for DfH8298 were the
following: Ca2Si5256.163.1, Ca5Si3 5255.363.5, CaSi5249.662.2, Ca3Si4 5240.661.5, Ca14Si19 5244.462.3, CaSi2 5
237.861.6 all in kJ/mol atoms. The results for Ca2Si, CaSi and CaSi2 may be compared with previous measurements, all other results
are first determinations.
2001 Elsevier Science B.V. All rights reserved.
Keywords: Calcium silicides; Intermetallics; Thermodynamic and thermochemical properties; Heats of formation; Vaporization behaviour; Knudsen
effusion-mass spectrometry
1. Introduction
phase diagram a correct attribution of vapor pressures to
well defined two-phase equilibria appears questionable. A
similar argument applies to the previous effusion data by
Muradov et al. [6]. Finally, emf measurements on the
CaSi2 phase were reported [7]. On the basis of phase
diagram and thermodynamic information at the time
available, Anglezio et al. assessed the whole system by
using the Calphad approach [8].
In view of the renewed interest in the calcium silicides,
due to the electronic and superconductive properties of
some of these compounds which make them potentially
attractive in materials applications, recently a great deal of
research has been carried out mainly on the physical
properties, but also in crystal chemistry and low-tempera-
ture thermodynamic properties.
Manfrinetti et al. [9] recently reinvestigated the Ca–Si
phase diagram in the composition range 0–75at.% Si (Fig.
1). They confirmed the existence of five intermediate
phases and characterized for the first time a new com-
pound, the Zintl-phase Ca3Si4. Affronte et al. [10] mea-
sured the low temperature heat capacities and resistivities
for CaSi and CaSi2. Canepa et al. [11] measured by
adiabatic calorimetry the heat capacities in the temperature
range 3–300 K for three silicon-rich Ca–Si compounds
(Ca3Si4, Ca14Si19, CaSi2). They calculated the thermo-
dynamic functions at 298 K and subsequently extended
Although the Ca–Si system has been in the past the
object of several investigations, mainly concerning the
phase diagram, many uncertainties remained until recently
in the liquidus curves and invariant temperatures as well as
in the number and identity of the intermediate phases.
Therefore the published phase diagram in current compila-
tion [1] of the whole system cannot be considered as
definitive. The available data of the thermodynamic prop-
erties of the intermediate phases are rather scarce and
controversial.
Kubaschewski and Villa [2] determined calorimetrically
in an early study the heats of formation of the three solid
silicides Ca2Si, CaSi and CaSi2. Apart from a subsequent
work from Shchukarev et al. [3] limited to the Ca2Si
compound, these data apparently remain the only
calorimetric results on Ca–Si alloys. Wynnyckyj et al. in
two papers [4,5] reported on the measurement of calcium
vapor pressure over a few calcium–silicon alloys mainly in
the silicon rich side of the phase diagram (50–76at.% Si)
and in the liquidus domain, and calculated the components
activity. However, due to the incomplete knowledge of the
*Corresponding author.
E-mail address: balducci@axcasp.caspur.it (G. Balducci).
0925-8388/01/$ – see front matter
PII: S0925-8388(00)01381-5
2001 Elsevier Science B.V. All rights reserved.

526
S. Brutti et al. / Journal of Alloys and Compounds 317–318 (2001) 525–531
welding. The samples were annealed in sealed quartz tubes
under vacuum and then characterized by X-ray diffraction.
The composition of some of them were also checked by
electron probe microanalysis (EPMA). In most cases the
vaporization residues (see subsequent section) were also
subjected to this analysis procedure.
2.2. Vapor pressure measurement
Vaporization experiments were mainly performed using
a Nuclide model 12-60 HT single focusing magnetic sector
mass spectrometer coupled with a Knudsen cell assembly.
The effusion cells consisted of tantalum or molybdenum
cells with cylindrical effusion orifices of 1.0 mm or 0.5
mm in diameter which were inserted in an outer
molybdenum crucible. The non-ideality of the effusion
orifice was accounted for in the subsequent calibration
procedure for converting ion intensities into pressures.
The cell was heated with a tungsten resistance heater.
Temperatures were measured with a disappearing-filament
optical pyrometer by sighting into a blackbody cavity in
the bottom of the crucible. In a few experiments tempera-
tures were also measured with a calibrated Pt–Pt(10% Rh)
thermocouple placed in tight contact with the bottom of the
crucible. In a preliminary experiment the vapors effusing
from the Knudsen cell were ionized using an electron
energy of 70 eV and a total emission current of 1 mA. Only
monoatomic Ca(g) was detected in the vapor at the
temperature of the measurement. This was confirmed in all
subsequent experiments. At 70 eV the positive ions formed
by electron impact were Ca1 and Ca21, the contribution of
the double ionized calcium being 10–15% of the Ca1
intensity. As the ionization efficiency curves showed a
maximum between 25 and 30 eV we choose to perform all
the subsequent intensity measurements at an operating
electron energy of 25 eV, practically below the threshold of
the second ionization potential of Ca.
Fig. 1. Ca–Si phase diagram after Manfrinetti et al. [9].
these measurement to the other compounds of the same
system [12].
On the whole, accurate thermodynamic data are rather
scarce or lacking, in particular high temperature free
energy data for the formation of the Ca–Si compounds. On
the other hand these data are required in phase diagram
optimization and in modeling deposition processes using a
free energy minimization approach.
In the present paper we report the results of high
temperature vaporization experiments carried out on sever-
al Ca–Si alloys in the composition range 20–75at.% Si.
From the temperature dependence of the vapor pressure
values measured over a single phase or two-phase mixtures
the enthalpy changes for the decomposition reactions were
determined and hence the standard enthalpies of formation
for the various calcium silicides present in the phase
diagram [9], were derived.
In a KC–MS experiment the partial pressure of the
species i, in this case Ca(g), is related to the measured ion
current I1i by the relation:
pi 5 kstr fiI1i T
(1a)
where kstr is the instrumental constant, the factor fi 5
1/(sig ai ) includes the electron impact cross section (si ),
i
2. Experimental
the multiplier gain (g ), and the isotopic abundance (ai ) of
i
the specific ion. The determination of kstr was performed
repeatedly by vaporization of a standard substance 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 52Ag for which the DH80
is well established.
2.1. Sample preparation and characterization
Calcium–silicon alloys were prepared by melting
elemental calcium (purity 99.5 wt%) and silicon (purity
99.999 wt%) in closed containers due to the much higher
vapor pressure of calcium compared to silicon. Weighted
amounts of the two elements in form of small Ca chips and
Si powder were pressed into pellets and then molten in an
induction furnace in tantalum crucibles closed by arc
Some vaporization runs, in particular for Ca-rich com-
positions, were also performed with a vacuum microbal-

S. Brutti et al. / Journal of Alloys and Compounds 317–318 (2001) 525–531
527
ance to the arm of which was suspended an effusion cell
identical in material and geometry to that used in the
KC–MS experiments. In the Knudsen effusion-weight loss
(KC–WL) experiments the partial vapor pressure of the
species i is given by the relation:
In the third-law method the DrH8298 is calculated at each
experimental temperature by the relation:
DrH8298 5 2 RT ln K 2 TDr(G.e.f.)8T
(6a)
where Dr(G.e.f.)8T is the Gibbs energy functions change of
the reaction. The G.e.f.s for each species can be calculated
if the heat capacities are known from 0 K to the ex-
perimental temperatures:
]
2pRT
Mi
dmi
]
]
pi 5
(2a)
A dt
œ
0
were A0 is the area of the effusion orifice, Mi is the
molecular weight of the effusion species and dmi /dt is the
weight-loss rate.
G8T 2 H8298
]
(G.e.f.)8T 5
T
T
T
C8p
1
]
T
]
5
E
C8pdT 2
E
dT 2 S8298
(7a)
3. Results and discussion
T
298
298
Therefore the derivation of DrH8298 by both the second-
and the third-law analyses of equilibrium data requires heat
capacities data, although at a different extent. While the
heat capacities were very recently [11,12] measured for all
the calcium silicides between 3 and 300 K, apparently no
data are available above room temperature. An approxi-
mation often employed is the Kopp–Neumann (KN) rule,
i.e. the heat capacity of a compound is equal to the sum of
the heat capacities of the constituent elements. However,
the heat capacities and the absolute entropies obtained by
applying this rule to calcium silicides at low temperatures
are substantially lower (10% on average for absolute
entropies) than the experimental ones for almost all the
intermediate phases. Therefore the heat capacity values
obtained with the additivity rule were scaled by a tem-
perature-independent constant in order to eliminate the
discontinuity with the experimental values at 298 K
[11,12]:
3.1. Thermodynamic calculations
In the composition range 20–75at.% Si, Ca(g) was the
only species detected in the vapor phase. The decomposi-
tion equilibrium can then be written (by mole of gas) in the
form:
z
y
]
]
CawSiz(s)
CaxSiy(s) 5 Ca(g) 1
(3a)
zx 2 wy
zx 2 wy
where CaxSiy and CazSiw are two intermediate phases
contiguous in the phase diagram. Apparently no accurate
solid solubility data for this system are available in the
literature. However, solubility in both the Ca-rich and
Si-rich terminal regions is likely to be very small. The
vaporization processes in these regions can then be de-
scribed with good approximation by Eq. (3a) with x51,
y5 0 (Ca-rich end: vaporization of pure calcium) and
x5z51, y52, w50 (Si-rich end: decomposition of CaSi2
to pure silicon), respectively. Therefore, by assuming
negligible solid solubility and considering that all the
intermediate phases are of fixed composition, the equilib-
rium constant for all the decomposition reactions is given
by:
C8p,T 5 C8p,T(KN) 1 [C8p,298(exp) 2 C8p,298(KN)]
(8a)
The H8T 2 H8298 and the high-temperature term of G.e.f.
were then calculated, while the S8298 values in Eq. (7a)
were those given in [11,12]. The G.e.f. values estimated for
the calcium silicide phases are reported in Table 3. For
sake of comparison, all the calculations were also per-
formed assuming the Kopp–Neumann rule valid over the
entire temperature range.
K 5 pCa /bar
(4a)
where pCa is expressed in bar. By measuring pCa over
equilibrated two-phases mixtures as a function of tempera-
ture is then possible to derive the enthalpy changes for the
relevant reactions applying the second-law and third-law
methods.
The second-law method is based on the Van’t Hoff
equation and gives the standard enthalpy of reaction at the
mid-range temperature kTl 5 1/kT 21l, as slope of the
least-squares fitting of ln K vs. 1/T:
3.2. Enthalpy changes of decomposition reactions
Vaporization runs were performed on various alloy
samples constituted of single phase stoichiometric com-
pounds or mostly of two phases mixtures.
The decomposition equilibria studied were the follow-
ing:
d(ln K)
DrH8kT l 5 2 R
(5a)
d(1/T)
The enthalpy change at room temperature (DrH8298) can
be calculated if heat capacities for all the species involved
are known.
1. Ca(s)5Ca(g)
2. 3Ca2Si5Ca5Si3 1Ca(g)

528
S. Brutti et al. / Journal of Alloys and Compounds 317–318 (2001) 525–531
3. 1/2Ca5Si3 53/2CaSi1Ca(g)
4. 4CaSi5Ca3Si4 1Ca(g)
5. 19/5CaSi51/5Ca14Si19 1Ca(g)
6. Ca3Si4 52CaSi2 1Ca(g)
7. 2/9Ca14Si19 519/9CaSi2 1Ca(g)
8. CaSi2 52Si(s)1Ca(g)
The occurrence of these reactions was confirmed by
XRD spectra performed on samples before and after
vaporization. In particular we confirmed the high tempera-
ture decomposition of Ca3Si4 to Ca14Si19 in a 63at.% Si
sample. This decomposition reaction occurs quickly, while
the Ca14Si19 tends to remain as a metastable phase below
the decomposition temperature.
A summary of the experimental features and the mea-
sured vapor pressure Eqs. log pCa /bar5 2 (A/T) 1 B is
reported in Table 1 and in Figs. 2 and 3 as log pCavs. 1/T
plots for the Ca-rich and the Si-rich samples, respectively.
In the same plots are also reported for comparison the few
sets of calcium pressures measured previously by
Wynnyckyj [4]. For easier comparison, these data were
labelled by full markers with the same shape as our data
points for samples of similar composition.
Fig. 2. Log ( pCa /bar) vs. 1/T plot for the decomposition reactions of the
Ca-rich phases in the Ca–Si system.
It has to be noted that in general our measurements, due
to higher sensitivity of the techniques employed, extend to
lower temperature and pressure ranges. In the case of
Ca-rich alloys, namely for the two-phase region Ca5Si3 /
CaSi (40.8at.% Si) the agreement is fairly satisfactory both
in slope and in calcium pressure between ours and
Wynnyckyj’s [4] data. For the Si-rich alloys the pressure
values we measured with two independent techniques
appear somewhat higher than those reported by Wynnyckyj
[4]. Furthermore the slope for the 51.4at.% Si alloy is
considerably steeper compared with our result for reaction
(5).
However, considering the high number of our data
points and their reproducibility in different runs our results
should be considered reliable and representative of equilib-
rium pressures over the two phase regions studied accord-
ing to the phase diagram recently determined by Man-
frinetti et al. [9].
Fig. 3. Log ( pCa /bar) vs. 1/T plot for the decomposition reactions of the
Si-rich phases in the Ca–Si system.
which were derived from the second-law and third-law
analysis of pressure–temperature data are presented in
Table 2. For sake of comparison (and to demonstrate the
The enthalpy changes for the vaporization reactions
Table 1
Experimental conditions and measured vapor pressures for the decomposition reactions investigated
Reaction
Data points
Temperature
range (K)
log pCa /bar52A/T 1B
A?1023 (K)
B
Ca(s)5Ca(g)
31
28
15
24
22
19
20
35
817–960
971–1160
990–1098
1075–1178
1200–1341
1030–1160
1186–1298
1118–1283
9.02660.215
9.59460.299
12.91760.615
13.42360.542
12.37760.476
11.83760.188
11.21960.676
14.25660.554
5.37560.244
4.36660.279
6.68860.588
5.69460.482
4.79360.373
4.01860.144
3.49260.547
5.51660.460
3Ca2Si5Ca5Si3 1Ca(g)
1/2Ca5Si3 53/2CaSi1Ca(g)
4CaSi5Ca3Si4 1Ca(g)
19/5CaSi51/5Ca14Si19 1Ca(g)
Ca3Si4 52CaSi2 1Ca(g)
2/9Ca14Si19 519/9CaSi2 1Ca(g)
CaSi2 52Si(s)1Ca(g)

S. Brutti et al. / Journal of Alloys and Compounds 317–318 (2001) 525–531
529
Table 2
Vaporization enthalpies for the intermediate phases of Ca–Si system
Reaction
DrH8kT l
II law
kJ/mol
DrH8298
II lawa
kJ/mol
DrH8298
II lawb
kJ/mol
DrH8298
DrH8298
III lawb
kJ/mol
III lawa
kJ/mol
(trend J/K)
(trend J/K)
Ca(s)5Ca(g)
172.861.8 at 880 K
183.665.7 at 1066 K
247.2611.8 at 1046 K
256.8610.4 at 1124 K
236.969.1 at 1275 K
226.563.0 at 1094 K
214.7612.9 at 1235 K
272.864.6 at 1205 K
178.361.8
240.665.7
250.5611.8
300.2610.4
253.169.1
235.163.0
264.1612.9
291.764.6
178.361.8
192.665.7
255.7611.8
267.0610.4
250.969.1
236.063.0
227.7612.9
285.164.6
180.661.3
(3.2)
111.767.4
(2123.2)
241.761.2
(29.7)
191.367.3
(2142.7)
265.462.4
(10.9)
261.361.0
(23.1)
178.861.2
(1.0)
211.061.7
(17.1)
227.461.4
(226.9)
256.261.5
(213.1)
255.462.5
(12.2)
275.461.3
(33.3)
260.360.7
(210.6)
267.062.5
(221.9)
3Ca2Si5Ca5Si3 1Ca(g)
1/2Ca5Si3 53/2CaSi1Ca(g)
4CaSi5Ca3Si4 1Ca(g)
19/5CaSi51/5Ca14Si19 1Ca(g)
Ca3Si4 52CaSi2 1Ca(g)
2/9Ca14Si19 519/9CaSi2 1Ca(g)
CaSi2 52Si(s)1Ca(g)
189.162.4
(282.3)
279.864.0
(20.1)
a Calculated by means of thermal functions estimated correcting additive heat capacities according to the low temperature C8ps of Canepa et al. [11,12]
(see Eq. (8a)).
b Calculated assuming additivity of the heat capacities (Neumann–Kopp rule).
influence of the uncertainties in the thermodynamic func-
tion estimates) we have reported DrH8298 values which
were derived using different sets of thermodynamic func-
tions (H8T 2 H8298 and G.e.f.s) calculated with different
options as described previously in the text and in footnotes
to Tables 2 and 3.
For some of the reactions studied the agreement between
second-law and third-law DrH8298 is unsatisfactory. The
difference in values is particularly striking in the case of
reactions (2), (4), and (7) when the third-law values are
calculated with the set of G.e.f. functions estimated from
the low temperature Cp8s and S8298 [11,12] (see Section
3.1). The agreement improves somewhat using the set of
thermodynamic functions estimated with the additivity of
the heat capacity in the entire temperature range. The
discrepancy in the second-law and third-law DrH8298
parallels the anomalously large trend in the third-law
DrH8298 values with temperature. For example in reaction
(2) the Ca2Si phase is involved for which the measured
S8298 is much higher (20%), than the value calculated
assuming additivity, compared to the other calcium
silicides. As a consequence, and for sake of argument, the
G.e.f. values calculated at 900 K for Ca5Si3 using either
complete additivity or the low-temperature C8ps differ by
2 J/K mol atoms (or 4%) while the difference for Ca2Si
amounts to 12 J/K mol atoms (or 19%). The uncertainty in
the calculated G.e.f. values is ultimately reflected in the
third-law values of DrH8298. Incidentally, we note that the
entropies of formation of calcium silicides calculated from
experimental heat capacities [11,12] are positive or slightly
negative while, in contrast, the few earlier data indicate
strikingly large negative values [6,7]. Measurements of
heat capacities at high temperature for the pure calcium
silicide phases would be necessary to improve the calcula-
tion of the thermodynamic functions, in primis of the
Gibbs energy functions. As we have no indication of gross
errors in temperature and vapor pressure measurements we
assume that a major role may be played in the observed
discrepancy between second-law and third-law results by
inaccuracies in the heat contents and Gibbs energy func-
tions used in the analysis.
Table 3
Estimated Gibbs energy functions (G8T 2 H8298)/T (J/K mol atoms) for
the intermediate phases of the Ca–Si systema
T/K
298b
400
500
600
700
800
900
1000
1100
Ca2Si
Ca5Si3
CaSi
Ca3Si4
Ca14Si19
CaSi2
240.8
242.8
245.4
248.4
251.5
254.5
257.5
260.3
262.6
233.5
234.0
236.1
238.5
241.0
243.5
245.9
248.2
250.1
234.1
235.8
238.1
240.8
243.5
246.2
248.8
251.3
253.4
228.1
230.7
232.7
234.9
237.2
239.4
241.6
243.8
245.5
234.5
235.9
238.2
240.9
243.7
246.4
249.0
251.5
253.6
228.0
229.4
231.3
233.6
235.9
238.1
240.3
242.4
244.1
The slopes of ln K vs. 1/T curves are not affected by
possible inaccuracies in the value of the instrumental
constant kstr while this is the case of the third-law results.
In view of this fact and the large number of pressure data
points and the reproducibility of data in the various
vaporization experiments, we believe that the second-law
values are more reliable for all the studied decomposition
reactions.
a G.e.f.s estimated by additive heat capacities corrected according to the
low temperature C8ps of Canepa et al. [11,12] (see Eq. (8a)).
b (G.e.f.)8298 52S8298
.

530
S. Brutti et al. / Journal of Alloys and Compounds 317–318 (2001) 525–531
3.3. Heats of formation of calcium silicides
The decomposition enthalpies DrH8298 presented in
column 3 of Table 2 enable us to calculate the standard
enthalpies of formation of the solid calcium silicides. The
heat of formation of CaSi2 was simply calculated by
subtracting the standard vaporization enthalpy of pure
calcium (DsubH8298(Ca)5178.2 kJ/mol [13]) from DrH8298
for reaction (8). Incidentally, in a vaporization experiment
of pure Ca(s) we found a DsubH8298(Ca) practically co-
incident with the assessed value [13]. Thereafter values for
all the intermediate phases were derived from reactions (7)
to (2). Due to the presence of two different vaporization
equilibria involving the CaSi decomposition (equilibria (4)
and (5)), our experimental DrH8298 data exceed the un-
knowns to be calculated. In other words, two different
DfH8298for CaSi may be derived from reactions (4) and
(5), respectively. However both values are in close agree-
ment: 250.761.8 and 248.462.6 kJ/mol atoms, indicat-
ing the self-consistency of the data. For this reason we
propose for the heat of formation of CaSi the average of
the two results. This value has also been used to calculate
the DfH8298 for Ca5Si3 and Ca2Si. The enthalpies of
formation are presented in the last column of Table 4 and
in Fig. 4.
Our values can be compared with literature data for
Ca2Si, CaSi and CaSi2; for the other phases Ca5Si3,
Ca3Si4 and Ca14Si19 they represent first determinations.
The results reported many years ago from Kubaschewski
and Villa [2] are practically the only published calorimetric
data of the formation enthalpies of calcium silicides. These
authors carried out adiabatic calorimetry measurements on
a number of Ca–Si alloys and then derived DfH8940 for the
three phases known at the time. Previous calorimetric
results from Schneider and Stobbe (private communication
in Ref. [2]) were therein criticized and the value sub-
sequently determined for the Ca2Si phase (DfH8298 52
161.8 kJ/mol atoms) seems unreasonably negative [3]. The
Kubaschewski and Villa’s results are reported in Table 4,
Fig. 4. Heats of formation at 298 K for the calcium silicides.
along with the only electrochemical data [7] and the values
derived by phase diagram optimization [8]. Table 4 and
Fig. 4 reveal that the DfH8298 we derived are quite lower
than the calorimetric data [2]. Wynnyckyj and Pidgeon [4]
came to a similar conclusion from their activity data.
Though they did not derive any numerical data for the
heats of formation of calcium silicides, they stated that ‘the
calorimetric values [of Kubaschewski and Villa] are
substantially higher than the present ones’. Indeed, the
heats of formation derived in Ref. [8] from the Wynnycky-
j’s data (DfH8298(CaSi)5246.0 kJ/mol atoms and
DfH8298(CaSi2)5236.7 kJ/mol atoms) are in excellent
agreement with our results. On the other hand, the electro-
chemical value for CaSi2 is very close to the calorimetric
value. Another feature of our DfH8298 is that the maximum
is obtained for the phase Ca2Si whose melting point is
508C lower than that of CaSi. This results apparently
confirm the findings from the phase diagram optimization
(Table .4).
The influence of the estimated heat contents of the
compounds on DfH8298 should be emphasized. For exam-
Table 4
Comparison between standard heats of formation (kJ/mol atoms, T5298 K) of Ca–Si intermediate phases from literature and present work
Phase
Kubaschewski and
Villa
(calorimetry)
[2]
Zviadadze
and Kereselidze
(emf)
Anglezio et al.
(phase diagram
assessment)
[8]
This worka
[7]
Ca2Si
271.464.2
269.7
256.163.1
(at T5940 K)
Ca5Si3
CaSi
255.363.5
249.662.2b
279.164.2
260.3
(at T5940 K)
Ca3Si4
Ca14Si19
CaSi2
240.661.5
244.462.3
237.861.6
252.762.5
251.5
250.1
(at T5940 K)
a Calculated assuming DrH8298 reported in the column 3 of the Table 2.
b Average value calculated from reactions (4) and (5) (see text).

S. Brutti et al. / Journal of Alloys and Compounds 317–318 (2001) 525–531
531
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ple, adopting the additivity of C8p would result in heat of
formation values fairly lower (by up to 15% for the phase
Ca2Si), with the phase Ca5Si3 having the most negative
DfH8298 (251.0 kJ/mol atoms). In order to display the
potential effects of the inaccuracies in heat content esti-
mates, we also calculated the heats of formation at T5
1100 K for all phases. This temperature is approximately
the mid-range temperature of our experiments. Therefore
these values are only weakly affected by the heat contents.
At this temperature the most stable phase is Ca5Si3
(DfH8298 5 2 53.0 kJ/mol atoms), followed by Ca2Si
Chimica alle Alte Temperature and Universita di Roma
‘La Sapienza’.
Thanks are also due to Mr. P. Trionfetti for carrying out
thermogravimetric experiments and to Mr. G. Minelli of
the CNR–SACSO for checking by XRD some vapor-
ization residues.
References
[1] T.B. Massalski, P.R. Subramanian, H. Okamoto, L. Kacprzak,
Binary Alloy Phase Diagrams, 2nd Edition, ASM International,
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[2] O. Kubaschewski, H. Villa, Z. Elektrochem. 53 (1949) 32.
[3] S.A. Shchukarev, M.P. Morozova, G.F. Pron, Zh. Obshch. Khim. 32
(1962) 2069.
[4] J.R. Wynnyckyj, High Temp. Sci. 4 (1972) 205.
[5] J.R. Wynnyckyj, L.M. Pidgeon, Met. Trans. 2 (1971) 975.
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(1967) 5.
(DfH8298 5 2 48.5 kJ/mol atoms) and CaSi (DfH8298
2 44.5 kJ/mol atoms).
5
To conclude, in order to definitely set the thermoch-
emistry of the calcium–silicon system, we would suggest
further accurate calorimetric determination of the heats of
formation of all the calcium silicides phases and the
measurement of the heat capacities at high temperature.
[7] G.N. Zviadadze, M.V. Kereselidze, Tr. Inst. Met. Akad. Nauk. Gruz.
SSR 15 (1966) 88.
Acknowledgements
[8] J.C. Anglezio, C. Servant, I. Ansara, CALPHAD 3 (1994) 273.
[9] P. Manfrinetti, M.L. Fornasini, A. Palenzona, Intermetallics 8 (2000)
223.
[10] M. Affronte, O. Laborde, G.L. Olcese, A. Palenzona, J. Alloys
Comp. 274 (1998) 68.
[11] F. Canepa, M. Napoletano, P. Manfrinetti, A. Palenzona, J. Alloys
Comp. 299 (2000) 20.
[12] F. Canepa et al., to be published.
The planning and development of the studies here
presented form a part of an Italian National Research
Project entitled ‘Leghe e Composti Intermetallici: stabilita
termodinamica, proprieta fisiche e reattivita’. The authors
would like to thank the Ministero per la Ricerca Scientifica
e Tecnologica (Programmi di rilevante interesse tec-
nologico) for their financial support. This work was also
partially supported by CNR–Centro di Termodinamica
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[13] R. Hultgren, P.J. Desai, D.T. Hawkins et al., Selected Values of
Thermodynamic Properties of the Elements, American Society of
Metals International, Metals Park, OH, 1973.