2.2 Knudsen Effusion Studies. Knudsen effusion studies on liquid AI-Sr alloys (Xsr ~ 0.17) at 1323 K were conducted using cells made of steel. The alloys ...
Bd. 82 (1991) H. 9
Thermodynamics of Aluminium - Strontium Alloys
675
Thermodynamics of Aluminium - Strontium Alloys Srinivasan Srikanth and K. Thomas Jacob (Department of Metallurgy, Indian Institute of Science, Bangalore - 560012, India) The activity of strontium in liquid AI-Sr alloys (Xsr:::S 0.17) at 1323 K has been determined using the Knudsen effusion mass loss technique. At higher concentrations (XSr~ 0.28), the activity of strontium has been determined by the pseudo isopiestic technique. Activity of aluminium has been derived by Gibbs-Duhem integration. The concentration - concen tration structure factor of Bhatia and Thornton at zero wave vector has been computed from the thermodynamic data. The behaviour of the mean square thermal fluctuation in composition and the thermodynamic mixing functions suggest association tendencies in the liquid state. The associated solution model with AI 2Sr as the predominant complex can account for the properties of the liquid alloy. Thermodynamic data for the intermetallic compounds in the AI-Sr system have been derived using the phase diagram and the Gibbs' energy and enthalpy of mixing of liquid alloys. The data indi cate the need for redetermination of the phase diagram near the strontium -rich corner.
Thermodynamik von Aluminium-Strontium-Legierungen Mit der Knudsen-Effusions-Methode wurde die Aktivitat von Strontium in Aluminium -Strontium-Schmelzen uber den Gewichtsverlust im Bereich xSr :::S0,17 gemessen. Bei htiheren Konzentrationen (XSr ~0,28) wurde die Strontiumaktivitat durch eine pseudo-isopiestische Methode gemessen. Die Aluminiumaktivitat wurde durch Gibbs-Duhem -Integration berechnet. Der Konzentrations-Konzentrations-Strukturfaktor nach Bhatia und Thornton be im Wellenvektor Null wurde aus den thermodynamischen Daten berechnet. Das Verhalten des quadratischen Mittelwertes der thermischen Kon zentrations-Fluktuationen und der thermodynamischen Mischungsfunktionen deuten auf Assoziationstendenzen im flussigen Zustand. Das Assoziat-Modell mit AI 2Sr als bevorzugtem Komplex erklart die Eigenschaften der Legierungs schmelzen. Thermodynamische Daten fUr die intermetallischen Phasen des Systems AI -Sr wurden aus dem Zustands diagramm, dem Gibbs'schen Potential und der Enthalpie der Schmelze abgeleitet. Die Daten zeigen, daB das Zustands diagramm auf der strontiumreichen Seite neu bestimmt werden solite.
1 Introduction A knowledge of activities in liquid AI-Sr alloys is useful for a physico-chemical analysis of the "aluminothermic" reduc· tion of strontium oxide in vacuum . During this process an AI-Sr alloy is formed which red uces the driving force for the reaction. Thermodynamic measurements on liquid AI-Sr alloys are few. Sommer et a1. 1) have measured the enthal pies of formation of liquid alloys between 1070 to 1175 Kin a high-temperature mixing calorimeter. Their measure ments covered two concentration ranges - from 1.3 to 10.3 at.% Sr and 39.1 to 94.7 at.% Sr. Extrapolation of their meas ured values indicates a minimum at XSr "" 0.35 correspond ing to l:1H = -22.2 kJ/mol. Their studies do not indicate any t emperature dependence of the enthalpy of mixing. More recently, Esin et a1. 2) have measured the enthalpies of for mation of liquid alloys up to 45 at.% Sr at 1773 K in a high temperature calorimeter under a helium atmosphere. The minimum value of the enthalpy of mixing obtained in their study is -21.3 ± 0.3 kJ/mol at 35 at.% Sr. The values obtained in both these calorimetric measurements agree well within experimental error. A small decrease in the absolute value of enthalpy of mixing with increase in tem perature is observed. Burylev et a1. 3) have measured the vapour pressure of strontium over liquid AI-Sr alloys by Knudsen effusion - mass loss method between 1123 to 1373 K for two compositions, XSr = 0.2 and 0.33. Vakhobov et a1. 4) report measurements at XSr = 0.2 and 0.5. Identical equations have been reported in bot h these papers despite the apparent difference in composition. The values of the activities of Sr at 1300 K were given as 0.002 at 20 at.% Sr and 0.03 at 33.3 or 50 at.% Sr. Activity data over the entire concentration range are not available. The phase diagram of the AI-Sr system 5) shows the pres ence of three intermetallic compounds - AI 4 Sr melting congruently at 1313 K and the compounds AI 2 Sr and AI 2Sr3
melting incongruently at 1209 and 939 K, respectively. There exists considerable discrepancy over the existence of the compound "AI 2 Sr3'" This compound was first report ed by Bruzzone and Mer106) based on thermal analysis, X ray diffraction and metallographic res ults. Subsequent in vestigati on by Fornasini and Mer107) did not confirm the presence of the phase "AI 2Sr3'" Instead, they identified a new phase corresponding to the formula "AISr". Closset et a1. 8) have also indicated the presence of the compound "AISr" rather than "AI2 Sr3" in their experimental investiga tion of the AI-Sr phase diagram. However,a reexamination by Fornasin i9) of a single crystal sample used in the previ ous study7) using a more advanced experimental tech nique revealed that the form ula "AI7 Srs" better describes the phase close to the equiatomic composition. Experi mental information on the enthalpy an d free energy of for mation of these solid alloys is not avail able in the literature. However, estimations on the enthalpy and entropy of for mation of the intermetallic compounds based on the phase diagram have been reported 10)11). Kharif et a1. 10) have estimated the Gibbs' energies of formation as a func tion of temperature for the intermetallic compounds AI 4 Sr, AI 2Sr and AISr from the phase diagram assuming an ideally associated liquid solution. They observed that the calcu lated T-X diagram is in agreement with the experimental one only on the assumption that AISr is the stable com pound in the system and not A1 2 Sr3. These estimates have large uncertainties because the information used in their study is incomplete. Recently, Alcock and Itkinll) have made an evaluation of the phase diagram and thermo dynamic properties of the AI-Sr system. They have esti mated Gibbs' energies of formation of solid and liquid phases and have calculated the phase diagram. The calcu lated diagram agrees well with the experimental results except near the strontium corner. In the assessed phase diagram, the compound AI 7Sr8 is shown instead of the pre viously reported AI 2Sr35). Preference was given to the for
Srinivasan Srikanth and K. Thomas Jacob
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mula uAl 7 Srs" on the basis of the experimental results by Fornasini 9). Accurate information on activities in liquid AI Sr alloys over the complete composition range will permit a more rigorous assessment of the AI-Sr system. In this study, activity of strontium in liquid AI-Sr alloys has been measured at 1323 K over the entire range of composition using a combination of Knudsen effusion - mass loss anal ysis and pseudo-isopiestic measurements.
2
Experimental
2.1 Materials Strontium metal of 99.4 % purity was supplied by Dominion Magnesium Ltd. and aluminium of 99.99 % purity was obtained from Johnson Matthey Chemicals. The alumina crucibles for containing the alloy for Knudsen effusion measurements were obtained from Leico Industries Ltd. The strontium oxide crucibles for containing the alloy in the pseudo-isopiestic measurements were prepared by isostatic pressing, followed by sintering at 1973 K in a fur nace employing lanthanum chromite heating elements. The strontium oxide was prepared by thermal decomposi tion of SrC0 3 in vacuum at 900 K. Complete decomposi tion was confirmed by X-ray diffraction. Strontium carbon ate of 99.8 % purity was obtained from Aldrich Chemicals.
2.2 Knudsen Effusion Studies Knudsen effusion studies on liquid AI-Sr alloys (Xsr ~ 0.17) at 1323 K were conducted using cells made of steel. The alloys, prepared by in-situ melting, were held in alumina crucibles. The alumina crucible, 1.5 cm in diameter, was placed inside the Knudsen cell. A schematic diagram of the Knudsen cell is shown in Fig. 1. A thin foil of iron, 0.05 mm in thickness, was clamped between the lid and barrel sections of the Knudsen cell. Knudsen orifices ranging in diameter from 0.01 to 0.1 mm were made by laser drilling. The iron foil near the orifice was thinned to give a knife edge. The diameters were measured under an optical microscope provided with a sensitive internal scale that could be superimposed on the orifice image. The orifice diameter at the experimental temperature was calculated from that at room temperature using the thermal expan sion coefficient for iron.
Z. Metallkde.
tungsten resistance heater and molybdenum shields. The temperature of the furnace was controlled to ± 1 K and measured by a Pt/Pt-13%Rh thermocouple, calibrated against the melting point of gold. The vacuum was generat ed by a diffusion pump backed by a mechanical rotary pump. A typical pressure inside the furnace during most of the measurements was 10- 3 Pa. Effusion measurements were carried out on two AI-Sr alloys at 1323 K. There was sorne superficial reaction between the alloy and the alu mina crucible. Once the equilibrium ternary oxide forms at the interface, further reaction is sluggish. The strontium content of the alloy decreases by = 1 at.% during the first hour and then becomes approximately invariant. The true composition of the alloy corresponding to the measured vapour pressure was determined by chemical analysis after each experiment.
2.3 Pseudo-isopiestic Studies The apparatus for pseudo-isopiestic experiments was made of steel and consisted of upper and lower chambers connected by a long tube as shown in Fig. 2. The lower chamber contained pure strontium in iron crucibles. Liquid strontium was found to wet iron and exhibited a tendency to creep out of the crucible and along the walls of the chamber. The creep was minimized by sharpening the edge of the crucibles. The lower chamber was also provid ed with a thin steel baffle to prevent the creep of strontium into the connecting tube by capillary action. A thermo couple well was provided in the lower chamber for accu rate measurement of temperature of pure strontium. The upper chamber contained either pure Ai or AI-Sr alloy in a crucible made of SrO.The upper end of the connecting ~ ____ . P t / Pt -13"10 Rh
!I
Thermocouple
r
~
T
~
/",,1 ~
.r--ll ~~5rO
~
oppec 'homb" Crucible
'~AI-5r olloy ~"""-Co ns t r i ct ion
The experimental arrangement was similar to that used earlier12)13). The Knudsen cell was suspended from a Cahn microbalance inside a vacuum furnace provided with
Steel connecting tube
Steel lid
'---~4--
Iron foil wi th orifice
Iron Crucible
5r
Alumina crucible Sr-Al alloy Steel Knudsen cell
Fig. 1.
Schematic diagram of the Knudsen cell.
Fig. 2.
Schematic section of the pseudo-isopiestic apparatus.
Bd. 82 (1991) H. 9
Thermodynamics of Aluminium - Strontium Alloys
tube had a constriction, = 0.25 mm in diameter. The upper and lower chambers were provided with openings forfeed ing the metal and the alloy into the crucibles and subse quent evacuation. The iron crucible in the lower chamber was half filled with pure strontium and the opening was closed by crimping and flame-sealing. Pure AI or AI-Sr alloy was then charged into the upper crucible. The entire assembly was evacuated by a diffusion pump backed by a mechanical rotary pump to a pressure of 10- 2 Pa. After eva cuating for 3 h, the opening on the upper chamber was sealed. The evacuated steel assembly was placed in a two-zone split furnace. Pure Sr was held in the lower temperature zone and AI or AI-Sr alloy was held in the higher tempera ture zone as indicated in Fig. 2. The temperature of each zone was controlled independently to ± 0.5 K using thyris tor power controllers. The temperatures were measured by Pt/Pt-13%Rh thermocouples calibrated against the melting point of gold. The pressure of strontium in the steel apparatus is determined by the temperature of the lower chamber. After rising through the steel tube, the vapour enters the upper chamber and gets absorbed by liquid AI or AI-Sr alloy. This process proceeds till the alloy is saturat ed with respect to the vapour. At the end of a specified period, the furnace was opened and the pseudo-isopiestic apparatus was removed. High-pressure jets of air were directed on the apparatus for rapid cooling. The upper and lower chambers were cut open. The crucibles and the inte rior surface of the steel apparatus were examined. The alloy was analysed chemically. Preliminary experiments indicated that, depending on the temperature of the lower chamber, periods varying from 8 to 26 h were required for the alloy composition to reach a steady-state value. During quenching the steel container cools faster than the alloy. This leads to distillation of some strontium from the alloy and its condensation on the inside walls of the steel container. To obtain the correct composition of the alloy at temperature, it was necessary to dissolve the strontium condensed on the inner surface of the upper chamber and add this to the solution of the alloy solidified in the stron tium oxide crucible. The function of the constriction at the end of the connecting steel tube was to restrict the outflow of vapour from the upper chamber during quenching. The correction for composition of the alloy varied from 0.8 at.% for low concentration of Sr to 2.7 at.% for Sr-rich alloys. There was no evidence of reaction between the alloy and oxide crucible for alloys rich in Sr. There was some reaction between AI-rich melts and SrO crucible. However, since the alloy composition becomes invariant after a certain period, the equilibrium oxides are assumed to be found at the melt/crucible interface. Although attempts were made to identify the strontium aluminates present at the melt! crucible interface as a function of alloy composition by ray diffraction, reproducible results consistent with Gibbs' phase rule for the ternary AI-Sr-O system were not obtained.
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Results
3.1 Knudsen Effusion Measurements The vapour pressure of strontium was calculated from the rate of mass loss of the Knudsen cell using the equation,
m-/E
P = 2286 - - -f .t .A
. M
(1)
where P is the pressure in Pa, m is the weight loss in g, tis the time in s, A is the area of the Knudsen orifice in cm 2 , Tis the temperature in K, M is the molecular weight of the effusing species in g and f is the Clausing factor for non ideal orifice. The equilibrium vapour pressure of strontium for XSr = 0.091 calculated from the observed mass loss using Eq. (1) is 3.16 Pa. The vapour pressure for XSr = 0.17 is 28.8 Pa. Clausing factors used in this study were taken from Iczkowski et aI. 14). The measured vapour pressure was found to be independent of orifice diameter for both alloys. This suggests the absence of surface depletion of alloys due to preferential vapourisation of Sr. Alloys con taining XSr > 0.17 were not used because the partial pres sure of strontium over these alloys would lie in a range where the Knudsen results would be unreliable. To com pute activities of Sr in the alloy, the vapour pressure of pure Sr at 1323 K was taken from the recent studies of Jacob and Waseda 15). The calculated activities from Knudsen effusion measurements for XSr = 0.091 and 0.17 are 0.00045 and 0.0041, respectively, with respect to liquid strontium as the standard state.
3.2 Peudo-Isopiestic Measurements The results of pseudo-isopiestic measurements are sum marized in Table 1. Strictly, the pressure inside a non-iso thermal enclosure is not uniform 16). Since in the present study the correction for pressure differential is negligible in Table 1.
Results of pseudo-isopiestic experiments
Temperature of alloy, K (±O.5)
Temperature of pure Sr, K (±O.5)
Equilibration time, h
Sr in alloy,
1323.4 1323.1
1055.1 1055.1
38 47
28.4 } 28 0 27.6 .
245.7
0.035
1323.2 1322.9
1128.7 1128.6
33 44
35.2}350 34.7 .
723.0
0.103
1323.3 1322.8
1191 .6 1191.7
22 28
~~:~ }42.0
1636.0
0.233
1323.0 1323.2
1260.0 1259.0
17 24
56.8 } 571 57.4 .
3629.0
0.517
1323.1 1322.7
1288.2 1288.3
14 22
68.1 }67 9 67.7 .
4913.0
0.700
1322.8 1323.3
1300.4 1300.3
11
14
76.2 } 76 C
5573.0
0.794
1322.7 1323.1
1312.6 1312.8
8 14
~~:~ }88. 9
6331.0
0.902
1323.5 1322.8
1317.4 1317.2
6 11
93.9 } 941 94.3 .
6633.0
0.945
P Sr ,
aS r
Pa at % (±O.6)
75.7
.
Table 2. Activities of Sr and AI in liquid AI-Sr alloys at 1323 K relative to pure liquid AI and Sr as standard states. XSr
In YSr
aSr
In YAI
aAI
0.091 0.17 0.28 0.35 0.44 0.57 0.68 0.76 0.89 0.94 ·
-5.309 -3.725 -2.080 -1.223 -0.6357 -0.0976 0.0290 0.0438 0.Q134 0.0053
0.00045 0.0041 0.035 0.103 0.233 0.517 0.700 0.794 0.902 0.945
-0.122 -0.364 -0.821 -1.221 -1.611 -2.151 -2.352 -2.386 -2.209 -2.116
0.805 0.577 0.317 0.192 0.112 0.050 0.0305 0.0221 0.0121 0.00723
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Srinivasan Srikanth and K. Thomas Jacob
678
+2.5.---------------------------- Al - Sr System
1323 K
Al-Sr System, 1323 K
o
O. 0f----+-~c+_--___1~-_+_----I Sr 0.2 0.6 0.8 AI
0,75
-X AI
I
OJ 0.50
o
I
-5.0
0.25
- 7 .5'--______________-..:.1
o. 00 ~o--'=-_---1 At
0.2
_ _----L-_---L-=~
0.4 0.6 --- XSr-
Fig. 3. Variation of the a-function for Sr with the mole fraction of aluminium for liquid AI-Sr alloys at 1323 K.
0.8
Sr
Fig. 4. Composition dependence of activities in liquid AI-Sr alloys at 1323 K.
0.0.-----------------.
I
-
,
AI-Sr System
\
1323 K
-10.0-
o E
c.::>
