- Email: [email protected]
TmSe: A system with valence fluctuations
Journal
of the Less-Common
Tm-Se:
110
(1985)
A SYSTEM WITH VALENCE
H. SPYCHIGER, Laboratotium (Received
Metals,
E. KALDIS
61
- 73
FLUCTUATIONS*
and B. FRITZLER**
fiir Festkb’rperphysik,
March
61
ETH
Hiinggerberg,
CH-8093
Zurich
(Switzerland)
28, 1985)
Summary In this paper new results are given concerning the influence of valence fluctuation on the thermodynamic stability of the Tm-Se system. Initial measurements of the determination, by fluorine combustion calorimetry, of the enthalpy of formation of Tm,Se as a function of the nonstoichiometry are presented. A discussion of the apparatus is given. It is shown that a miscibility gap exists between the normal metallic TmSe phase and the valence fluctuating phase. The repulsive forces are probably due to the very different valence states of the two phases. Two additional intermediate phases are indicated by fluorine combustion calorimetry. Samples quenched from high temperatures reveal the co-existence of two phases: Tm a. &3e (normal metallic) and Tm i. &Se (valence fluctuating). These phases react during cooling to give the corresponding solid solutions with lattice constants following Vegard’s law. These results can be explained by the existence of a wide miscibility gap (0.94
1. Valence fluctuations Valence fluctuation is a phenomenon which appears in lanthanide compounds having the 4f level very near to the Fermi energy (proximity effect). In SmS a semiconductor band gap (AE = 0.1 - 0.01 eV) exists between the 4f and the 5d levels which can be closed by external physical pressure (6 kbar) or internal chemical pressure (solid solutions). In TmSe the gap is almost closed. The compound has metallic character, therefore, but with only a small decrease in the internal pressure due to nonstoichiometry *Paper presented at the International Rare Earth Conference, land, March 4 - 8,1985. **Present address: Siemens AG, Oscar V. Miiller Ring, Munich, 0022-5088/85/$3.30
@ Elsevier
ETH Zurich,
Switzer-
F.R.G.
Sequoia/Printed
in The Netherlands
62
(slight lattice expansion via filling of vacancies) it can arrive at the valence fluctuating state, The mechanism of closing or opening the gap involves change of the crystal-field splitting which can be controlled by the ionic radii of the cation or anion. Decrease of the interatomic distance increases the overlap of the tzs orbitals of the cations and leads to a widening of the 5d band and therefore closing of the 5d-4f gap (increase of the internal, chemical pressure). This is well exemplified in the case of TmS, which is metallic due to the small ionic radius of sulfur. Due to the occupation of the 5d band the cation becomes trivalent (Tm3’S) with the electronic configuration [Xe]4f1*5d’6sZ. TmTe is the opposite case. The larger separation of the Tm cations due to the larger Te anions leads to a small overlap of the t,, orbit& of Tm. The crystal-field splitting of the 5d band is small and therefore a band gap remains open between 4f and 5d. The electronic configuration of the cation is [ Xe]4f135d06s2, therefore Tm*+ 1s . divalent and semiconducting. The question arises whether TmSe with the intermediate anionic radius is still metallic or semiconducting, i.e., trivalent or divalent. One of the important breakthroughs of solid-state research in recent years has been the discovery of the existence of the non-integer valence due to valence fluctuations. Although a quantitative theoretical description, as yet, does not exist, there is now ample experimental support for the following model: Under the influence of physical or chemical pressure the proximity of 4f to the Fermi level increases and the two possible valence states, e.g., for thulium 4f135d0 (Tm*+) and 4fi25d’ (Tm3’), reach comparable energies. The fluctuation appears because not only are 4f electrons from some atoms promoted to the 5d band, but some 5d’ electrons are also transferred back to the 4f shells of neighbouring atoms. Depending upon the extent to which these two effects take place, various intermediate valence values arise. The frequency of these fluctuations is of the order of lo9 - 10” Hz. Valence fluctuation is the result of partial hybridization between two quite different electronic states: the strongly localized, heavy (high effective mass), atomlike 4f electrons and the strongly delocalized, light, itinerant 5d electrons. Therefore, under certain conditions the same compound may show quite different conduction properties (metallic, semiconducting). In that sense the new family of compounds with valence fluctuations takes an intermediate position between the classical metals and semiconductors. Softening of the lattice (high compressibility, low microhardness) are characteristic of the valence transition. The question, arises therefore, whether valence instability influences the thermodynamic stability of the compound. A few years ago, we published a first review of our thermodynamic and structural investigations into the Tm-Se system [ 11. In this paper we report on recent developments, with particular reference to the thermodynamic instabilities: (a) At room temperature: enthalpy of formation as a function of nonstoichiometry, quantitatively measured by fluorine combustion calorimetry. (b) At high temperatures: evaluation of the lattice constants of samples quenched from between 1900 and 2000 “C. For a gen-
63
eral introduction to the solid-state chemistry of materials with valence instabilities the reader should consult ref. 2. References 3 and 4 are recommended as excellent sources of many other aspects of valence instabilities. 2. Control
of properties
via nonstoichiometry
Using the nonstoichiometry variation it was possible to change by up to 25% the valence of Tm from 3+ (at the selenium-rich phase boundary Tm/Se = 0.87) to 2.75+ (at the Tm-rich phase boundary Tm/Se = 1.05). This variation is reflected in a very large change (Au/a = 1.7%) of the lattice constant as a function of nonstoichiometry. Physical measurements show that the onset of valence fluctuation is at Tm/Se N 1.00. Figure 1 gives a fascinating example of the influence of valence fluctuation on the electrical resistivity uersus temperature, using the nonstoichiometry as a parameter to control the valence. It can be seen that for Tm/Se < 0.97 the resistivity behaves as a “normal metal” (Tm3’), decreasing with temperature. However at Tm/Se > 1.00 an unexpected increase in resistivity takes place, indicating the onset of valence fluctuation. The effect appears particularly at temperatures lower than the NQel point and it can be extinguished by applying a magnetic field. Therefore the same crystal may, at low temperatures, show either the resistivity of a semiconductor (H = 0) or a metal (H > 0). This is a typical example of the unexpected properties of materials with intermediate valence. 3. Phase diagram Tm-Se:
old version
In order to investigate systematically the thermodynamic stability of TmSe, we have started on the phase diagram of the Tm-Se system. This has
15 --\
\
-14 1
\
\
5
k- T \
cE 5La z .?4---
I \
. .
2
‘..
: = 3z .u L ; 2-
I , ..-. p :0.97
I I
’ ‘. !
y:0.99
---~:I.03
;
--
y:1.05
‘I J
Y Y
‘1
l0
-.-
--r:l.00
(
, 0.1
,\, 1
1.:
\
\
.-_~.~::.::.~ 10 100 Temperature (K)
Fig. 1. Anomaly of the electrical resistivity of nonstoichiometry after refs. 5 and 6.
of Tm,Se
at low temperature
as a function
64 mol Tm qcCf
0.6
0,7
Tm$,
0.8
!,9<
mof 1,2,1,3
IX
/
0.83 0.44 &I 0,57 0,98
Ii 0.40
I,O,I,!
II
I
Td’
0.50 ,&a-
‘Trn
c
0
Fig. 2. The T-x phase diagram of the Tn-Se system. The shadowed part indicates a metastable region. The lower composition scale is in mole fraction (XT&. Composition numbers at the top are in mole ratio x = Tm/Se.
been measured by high-temperature DTA f T < 2400 “C) under conditions of vapor-liquid or vapor--solid equilibrium in sealed tungsten capsules. Figure 2 shows the phase diagram we have published in the past [l] with two minor revisions: (a) a wider miscibility gap range, (b) the field of stability of Tm,Se6 (the boundaries of this field are still tentative, therefore the change is only due to formal reasons). Most important from the point of view of the thermodynamic stability of materials with valence fluctuations, is the homogeneity range of TmSe. Two of its features will be discussed: the existence of a wider miscibility gap at higher temperatures, which has a direct consequence for the thermodynamic stability, and the form of the solidus and liquidus curves. 4. Low-temperature miscibility gap In our previous work [ 21, the evidence concerning the miscibility gap was incomplete. X-ray investigations did not reveal the coexistence of two phases. DTA curves indicated a c, shift of the base line rather than peaks. Therefore, additional measurements were necessary. Initially, we determined the enthalpy of reaction of Tm,Se with 4N HCl as a function of nonstoichiometry [ 11. The results showed at least one miscibility gap and an
65
astonishingly large change of enthalpy for the Tm3+Se phase. In order to obtain quantitative data of the enthalpy of formation as a function of nonstoichiometry we have developed fluorine combustion calorimetry in our laboratory. 4.1. Fluorine combustion calorimetry Apparatus Based on the work of Hubbard and coworkers at Argonne National Laboratory [ 71 we developed a fluorine combustion calorimetry system consisting of: (a) a manifold for handling and analyzing pure and commercial fluorine, (b) a distillation column, (c) a fluorine combustion bomb, and (d) an isoperibol calorimeter. Manifold. Figure 3 shows, schematically, the manifold for handling the fluorine, the purification, analysis and storage. The system is constructed totally from stainless steel and includes storage tanks for the purified fluorine and many large filters of activated alumina to avoid atmospheric contamination by the fluorine purification and handling waste. To increase security, the whole apparatus is installed within an hermetically closed hood-glovebox made from stainless steel.
Fig. 3. Manifold. 1, Commercial fluorine; 2, purified fluorine container; 3, 4, reservoirs; 5, combustion bomb; 6, furnace for reactions with fluorine; 7, alumina filter; 8, rotary pump; 9, distillation vessel; 9a, distillation column; 11 - 13, manometer; 14, mercury titration; 15, precision manometer; 16, QMS; 17, LN,-cool trap; 18, mercury diffusion pump; 19, rupture disc; 20, sodium fluoride filter; 21, expansion vessel.
66
Distillation column. Commercial fluorine has a purity of approx. 98.5%. The accuracy of the enthalpy determination is therefore greatly decreased if fluorine of a purity greater than 99.5% is not used. Figure 3, nos. 9, 10, shows the distillation column schematically. The distillation vessel has a volume of 800 cm3 (no. 9). The column (no. 9a) has an internal diameter of 1.75 cm and is packed with 4 mm nickel helices for a height of 134 cm. The vessel is in a liquid N2 dewar and another dewar at the top allows refluxing of the liquid fluorine. By inducing a slight ~mperatur~ gradient between the dewars, a part of the refluxing fluorine can be distilled over the reservoirs (nos. 3 and 4). The purity of the distillate can be monitored by a quadrupole mass spectrometer with a special inlet system (Balzers AG) and/or by mereury titration [ 71. With the above distillation system, fluorine of a purity > 99.99% is obtained in one throughput. Combustiorz bomb. The following partly contradictory boundary conditions had to be taken into consideration for the design of the combustion bomb and the isoperibol calorimeter. (a) The po~ib~ity of investigating substances reacting spontaneously with fluorine. Highly reactive compounds such as the lanthanides are expected to fulfill this condition except when passivation in F,-atmosphere takes place. For this reason a two chamber bomb (Fig. 4) was constructed from one single piece of nickel. The internal combustion chamber has a volume of 600 cm3. The sample is charged in an argon glovebox. The outer
i - ,-_ -_ .. _.-. -\ -.
_ -
_. -_ -_ ,\ __ --_ -
*. c
-._
A
_--
-. r..
-
I-.
Fig. 4. Two-chamber fluorine combustion bomb, immersed in the isoperibol calorimeter.
61
fluorine storage chamber has a volume of 800 cm3. Both chambers can be filled and evacuated separately. (b) High pressure fluorination. This condition has been proven quite necessary, e.g., in the case of TmTe, where PF2 > 1 .l MPa was found to be the lowest limit for quantitative combustion [8]. Our construction allows a final pressure of 1.6 MPa to be reached, when the initial fluorine pressure in the storage chamber is 2.8 MPa. Clearly, an increase in the working pressure creates a problem: larger mass (thicker walls), higher energy equivalent, and therefore a decrease in the final accuracy, particularly when (c) also is required. (c) Samples with large composition gradients over relatively small volumes. In this case, bomb charges of small volume (mass) are necessary. To attain high accuracy, a small energy equivalent of the bomb and a high precision calorimeter are required. It is clear from this discussion, that either compromises must be made for an all-purpose bomb or special designs for particular problems should be constructed. The bomb used for this work had an all-purpose design. Isoperibol calorimeter. To attain high accuracy and to comply particularly with condition (c) above, the best possible superinsulation has been used. A multilayer insulation consisting of 70 mylar foils, each gold-coated on each side, was used for the calorimeter walls. The water bath was kept at 25 “C via a PTC 40 temperature controller (Tronac Inc). As a result of the above the calorimeter shows a temperature drift of only 3 X lop4 “C/week. The temperature is monitored by an Hewlett Packard quartz thermometer (resolution 0.0001 “C by one reading in ten seconds), tape recorded and transmitted to a computer. The combustion bomb is placed in the inner copper vessel (Fig. 4) surrounded by 2800.00 * 0.02 g of water. For reasons of mechanical stability the outer vessel is stainless steel. To minimize heat transfer via radiation the surfaces of the vessels are gold plated. Experimental
procedure
To avoid any humidity in the combustion bomb all the manipulations such as weighing the charge, opening, filling, and closing the bomb were undertaken in our train of glove boxes. These are made from stainless steel and glass, and the recirculating argon is gettered by hot cerium turnings. The residual impurities are 0, + H,O < 3 at. ppm. Selenium and tungsten were burned directly on a nickel crucible (Fig. 4), whereas TmSe was sited on a hard, polycrystalline layer of TmF,. Single crystals do not react with fluorine because of a very stable TmF3 layer which forms on the surface of the crystals. Pulverized TmSe reacts spontaneously with fluorine, but not completely, even at elevated final pressures. Complete combustion is obtained by adding selenium. The ignition of tungsten was also achieved using selenium. The impurities in the selenium and tungsten were determined by spark source mass spectroscopy. The mean values of the impurities were in at. ppm
68
in selenium: C, 4000; 0, 2000; K, 11000; Na, 1700; Ca, 4300; and in tungsten: C, 2000; 0, 2000; Na, 1000. The initial pressures were equal in every experiment, with 0.9 MPa fluorine in the storage chamber and 0.1 MPa argon in the combustion chamber. Calibration
Calibration with benzoic acid would raise the temperature of our calorimeter approx. 4.5 “C. However, the typical rise in a TmSe combustion experiment was approx. 0.5 “C. This is the result of using small samples (x500 mg TmSe, x200 mg Se) in order to increase the mapping resolution of the enthalpies of the various phases in a TmSe batch. To avoid a large temperature increase we used fluorine combustion of selenium to calibrate our calorimeter and not the usual oxygen combustion of benzoic acid. The results of the calibration are listed in Table 1. The corrected value of the heat of reaction of selenium, taking the impurities into account, is 14 211 J “C-l. The energy equivalent was measured to be E = 20 912 J “C’ (mean value of six determinations). To confirm this value we remeasured the heat of reaction of tungsten (Table 2). The value we obtained for the heat of reaction of Ma = 1723 f 6 kJ compares very well with the value of 1721 + 1.6 kJ mol-’ reported in the literature [ 71. TABLE
1
Determination of the energy equivalent, E, of the two chamber fluorine combustion of selenium The value of 1116.934 kJ mol-’ has been used for the enthalpy
based
of formation
on the of SeF6
[ 71. For improved
statistics
%elenium
(9)
E selenium
[ii
1.01100 14367.3 80.0 14447.3 0.68974
1.23567 17560.1 80.0 17640.1 0.84521
1.44209 20493.5 80.0 20573.5 0.98243
1.46610 20834.7 80.0 20914.7 0.99236
1.41667 20132.3 80.0 20212.3 0.97324
0.99632 14158.7 80.0 14238.7 0.68213
20946
20870
20941
21075
20768
20874
Ebhk
EtOt AT E
(J) (“C) (J “C-l)
Mean value E = 20912 TABLE
six measurements
bombs
have been made.
+ 42 J “C-l.
2
Determination
of the enthalpy
mtunssten
(9)
0.28773
%elenium
(9)
0.26963
AT --E x AT
(“C) (J)
E selenium &rank
E tungsten
of formation
of WF6 using the E value of Table
1
(J) (J)
0.31717 -6632.7 3830.3 80.0
0.26473 0.30883 0.26473 -6925.5 4388.8 80.0
0.23597 0.32723 0.23597 -6929.5 4650.9 80.0
0.26423 0.37794 0.26423 -7923.1 5370.9 80.0
0.25493 0.35394 0.25493 -7515.5 5029.8 80.0
0.27573 0.36489 0.27573 -7851.7 5185.5 80.0
(Jg-‘)
-9461.0
-9280.2
-9320.0
-9356.0
-9436.4
-9379.8
Mean value AH,
= 9372
+ 33 J g-l
= 1723
+ 6 kJ mol-‘.
69
4.2. Enthalpy of formation of Tm,Se as a function of nonstoichiometry Figure 5 shows the results of our combustion experiments on Tm,Se with various nonstoichiometric compositions of x. Although the results at x <0.94 roughly represent homogeneous samples, we have doubts for those with 3c> 0.94 due to the complicated phase transitions taking place (compare Sect. 4.3.). For this reason we concentrate here mainly on the samples with x < 0.94. The enormous increase (43%) in the enthalpy for 0.92 < x < 0.935 shows clearly the existence of a miscibility gap. Confirmation of the miscibility gap supports the previously presented argument [l] that the nature of the repulsive forces results from the change in the chemical bonding between metallic trivalent TmSe [ Xe]4f1’5d’6s2 and the valence fluctuating state [Xe] ((u4f l3 + /34f12)5d16s2. This is the result of the decreasing 4f-6d overlap following the increase of the lattice constant (decrease of the crystal-field splitting of the 5d band) as the Tm/Se ratio increases and the selenium vacancies are slowly filled [ 11. The calorimetric results confirm that in the TmSe homogeneity range several phases appear to exist. Although the miscibility gap between the Tm o.935Se and Tm o.,,,Se is clearly seen due to the strong enthalpy decrease of the Tm-rich boundary of the Tm 0.9,+Se phase, the other three phases are not yet well established. Of course, only after measuring the entropies, and calculation of the free-energy curves, can the exact composition range of the miscibility gaps be determined. Based on the few data existing at present, it seems that two other miscibility gaps may exist at approximately x = 0.96 and x = 0.99, respectively. Examination of Fig. 1 shows that the change in the resistivity behaviour takes place just in this composition range. This would
-1001’
’
’
’
0.90
’
o
’
’
’ 0.95
’
’
’
’
’ ’ 1.oo
’
x . mol
’
’
Tm/mol
’
1.05 Se
Fig. 5. Enthalpies of formation of Tm,Se as a function of nonstoichiometry. Q = sample quenched from the melt (2100 “C). The black corners of the error crosses indicate the number of experiments performed.
70
indicate that in addition to the normal metallic Tm3%e (x < 0.94) and the valence fluctuating phase (x > 0.99), two additional, narrow intermediate phases may exist in the quenched samples. The results of DTA at T < 800 “C include these phases in the miscibility gap.
5. High-temperature
miscibility
gap
In order to investigate the high-temperature phase transitions in the TmSe homogeneity range (Fig. 2) we have carried out high-temperature susceptibility measurements* in Tm o.g,Se (Fig. 6). The magnetic moment scale is arbitrary due to the lack of calibration. Although no abrupt valence transition takes place up to 1700 ‘C!, it is clear at T > 1100 ‘C, which is the temperature of the first phase transition (compare phase diagram, Fig. 2) that a distinct change (slope increase = 12%) towards higher moments (increasing Tm3+ contribution) takes place. To investigate the phase relationships above the phase transition at T = 1700 “C, several samples were quenched from between 1900 and 2100 “C. Quenching was not extremely rapid due to the rather large mass of the tungsten crucibles. X-ray investigations showed clearly that no structures other than NaCl appear at high temperature. This is in agreement with over 70 X-ray investigations of slowly cooled samples and the electron diffraction investigations reported in the past [ 11. This can also be understood from the I/X
4.0+02
5.0'02
Fig. 6. Susceptibility
1.8'83
of Tm,-,$3e
1.5+e3
us. temperature.
Arbitrary
T LK)
units.
*Work performed in the Inst. of Physics, University of Basle in collaboration R. Meier and Prof. H. Giintherodt, to whom the authors are indebted.
with
71
T >
-5.85
1900%
-5. _
- 5.64
-5.83 _
--t---t 5.02 II 0.80
I
I
I 0.90
I
I
I
I,,, 1.00
fm/Se
tx
Fig. 7. Lattice constants of slowly cooled and quenched l&Se samples as a function of nonstoichiometry. The fully drawn line shows the situation near room temperature with a miscibility gap 0.94 < Tm/Se < 0.98. The shadowed bands indicate the situation at high temperatures where the miscibility gap expands at 0.94 < Tm/Se < 1.05.
homogeneously mixed valence (valence fluctuation) of TmSe which is best accommodated to the NaCl structure 123. Figure 7 shows the lattice constants of quenched and slowly cooled samples of TmSe as a function of nonstoichiometry. As with the measurements of the enthalpy of formation, the selenium-rich part (X < 0.94) has clearly defined values. Independently of quenching or slow cooling, the lattice constants lie neatly on the Vdgard’s law line. The situation at x > 0.94 is quite different. Here, it is only possible to reach the Vegard’s-law line by slow cooling. In fact, all physical measurements in our laboratory have been performed on such crystals. The quenched samples, however, indicate the coexistence of only two phases at high temperatures: the Tm-rich phase boundary, Tm,,$e, of the homogeneity range, and the Se-rich boundary of the miscibility gap, Tm,.&e. This means that at high temperatures no solid-solution range exists, but only one v~ence-~uctuat~g (Tm r&3e) and one normal metallic phase (Tm,.&e). We may therefore conclude that the repulsive forces between normal and valence-fluctuating phases are increasing (i.e., the width of the miscibility gap increases). For the a uersus Tm/Se diagram this would mean that at high
72
temperatures the miscibility gap expands to 0.94
new version
The results of Section 5 show that samples quenched from the melt (2100 “C) also contain the two phases Tm,_,,Se and Tm0&3e. In this case it could be expected that the liquidus curve of the phase diagram (Fig. 2) has eutectic or peritectic form. In fact, in an earlier publication [9] when we had only a few DTA measurements, we suggested that the compound melts with a very narrow eutectic. With the much improved statistics of Fig. 2 it becomes clear that the flat maximum m.p. diagram fits the data better. Therefore, the appearance of the two phases in the quenched samples indicates the existence of a high temperature miscibility gap. As the quenching is not perfect, we probably freeze, even from the molten samples, the states just under the solidus. In Fig. 2 we therefore draw the upper boundary of this miscibility gap very close to the solidus line. At present we have little knowledge of the lower boundary of this miscibility gap. At T < 800 “C we have the miscibility gap shown by the DTA. As a working hypothesis we assume that a narrow, metastable region links the two miscibility gaps at high and low temperatures. Samples quenched from 1400 “C at compositions outside this narrow, metastable region did not show deviations from Vegard’s law. We must therefore conclude that outside this metastable region, solid solutions exist, and ‘that the miscibility gap is much wider at higher temperatures.
73
7. Acknowledgments One of us (E.K.) is greatly indebted to Dr W. Hubbard and Dr J. Johnson of the Argonne National Laboratory, U.S.A., for an introduction to the difficult technology of fluorine combustion calorimetry during a summer visit to ANL. The authors gratefully acknowledge exceptional funding by the Schulleitung of the ETH which made the fluorine combustion project possible.
References E. Kaldis and B. Fritzler, in G. M. Rosenblatt and W. L. Worrel (eds.), Prog. Solid State Chem., 14 (1982) 95. E. Kaldis, B. Fritzler and H. Spychiger, in R. Metselaar, H. J. M. Heifligers and J. Schoonman (eds.), Solid State Chemistry 1982, Elsevier, Amsterdam, 1983, p. 89. J. M. Lawrence, P. S. Riseborough and R. D. Parks, Rep. Prog. Phys., 44 (1981) 1. P. Wachter and H. Boppart (eds.), Valence Instabilities, North-Holland, Amsterdam, 1982. B. Batlogg, H. R. Ott, E. Kaldis, W. Thoni and P. Wachter, Phys. Rev. B, 19 (1979) 247. P. Haen, F. Holtzberg, F. Lapierre, J. Mignot and R. Tournier, Phys. Rev. Lett., 43 (1979) 304. W. Hubbard, G. K. Johnson and V. Ya. Leonidov, in S. Sunner and M. Mansson (eds.), Combustion Calorimetry, Pergamon, Oxford, 1979, Chap. 12. H. Spychiger, Dissertation, ETH, Zurich; H. Spychiger and E. Kaldis, to be published. E. Kaldis, B. Fritzler and W. Peteler, 2. Naturforsch., Ted A:, 34 (1974) 55.
of the Less-Common
Tm-Se:
110
(1985)
A SYSTEM WITH VALENCE
H. SPYCHIGER, Laboratotium (Received
Metals,
E. KALDIS
61
- 73
FLUCTUATIONS*
and B. FRITZLER**
fiir Festkb’rperphysik,
March
61
ETH
Hiinggerberg,
CH-8093
Zurich
(Switzerland)
28, 1985)
Summary In this paper new results are given concerning the influence of valence fluctuation on the thermodynamic stability of the Tm-Se system. Initial measurements of the determination, by fluorine combustion calorimetry, of the enthalpy of formation of Tm,Se as a function of the nonstoichiometry are presented. A discussion of the apparatus is given. It is shown that a miscibility gap exists between the normal metallic TmSe phase and the valence fluctuating phase. The repulsive forces are probably due to the very different valence states of the two phases. Two additional intermediate phases are indicated by fluorine combustion calorimetry. Samples quenched from high temperatures reveal the co-existence of two phases: Tm a. &3e (normal metallic) and Tm i. &Se (valence fluctuating). These phases react during cooling to give the corresponding solid solutions with lattice constants following Vegard’s law. These results can be explained by the existence of a wide miscibility gap (0.94
1. Valence fluctuations Valence fluctuation is a phenomenon which appears in lanthanide compounds having the 4f level very near to the Fermi energy (proximity effect). In SmS a semiconductor band gap (AE = 0.1 - 0.01 eV) exists between the 4f and the 5d levels which can be closed by external physical pressure (6 kbar) or internal chemical pressure (solid solutions). In TmSe the gap is almost closed. The compound has metallic character, therefore, but with only a small decrease in the internal pressure due to nonstoichiometry *Paper presented at the International Rare Earth Conference, land, March 4 - 8,1985. **Present address: Siemens AG, Oscar V. Miiller Ring, Munich, 0022-5088/85/$3.30
@ Elsevier
ETH Zurich,
Switzer-
F.R.G.
Sequoia/Printed
in The Netherlands
62
(slight lattice expansion via filling of vacancies) it can arrive at the valence fluctuating state, The mechanism of closing or opening the gap involves change of the crystal-field splitting which can be controlled by the ionic radii of the cation or anion. Decrease of the interatomic distance increases the overlap of the tzs orbitals of the cations and leads to a widening of the 5d band and therefore closing of the 5d-4f gap (increase of the internal, chemical pressure). This is well exemplified in the case of TmS, which is metallic due to the small ionic radius of sulfur. Due to the occupation of the 5d band the cation becomes trivalent (Tm3’S) with the electronic configuration [Xe]4f1*5d’6sZ. TmTe is the opposite case. The larger separation of the Tm cations due to the larger Te anions leads to a small overlap of the t,, orbit& of Tm. The crystal-field splitting of the 5d band is small and therefore a band gap remains open between 4f and 5d. The electronic configuration of the cation is [ Xe]4f135d06s2, therefore Tm*+ 1s . divalent and semiconducting. The question arises whether TmSe with the intermediate anionic radius is still metallic or semiconducting, i.e., trivalent or divalent. One of the important breakthroughs of solid-state research in recent years has been the discovery of the existence of the non-integer valence due to valence fluctuations. Although a quantitative theoretical description, as yet, does not exist, there is now ample experimental support for the following model: Under the influence of physical or chemical pressure the proximity of 4f to the Fermi level increases and the two possible valence states, e.g., for thulium 4f135d0 (Tm*+) and 4fi25d’ (Tm3’), reach comparable energies. The fluctuation appears because not only are 4f electrons from some atoms promoted to the 5d band, but some 5d’ electrons are also transferred back to the 4f shells of neighbouring atoms. Depending upon the extent to which these two effects take place, various intermediate valence values arise. The frequency of these fluctuations is of the order of lo9 - 10” Hz. Valence fluctuation is the result of partial hybridization between two quite different electronic states: the strongly localized, heavy (high effective mass), atomlike 4f electrons and the strongly delocalized, light, itinerant 5d electrons. Therefore, under certain conditions the same compound may show quite different conduction properties (metallic, semiconducting). In that sense the new family of compounds with valence fluctuations takes an intermediate position between the classical metals and semiconductors. Softening of the lattice (high compressibility, low microhardness) are characteristic of the valence transition. The question, arises therefore, whether valence instability influences the thermodynamic stability of the compound. A few years ago, we published a first review of our thermodynamic and structural investigations into the Tm-Se system [ 11. In this paper we report on recent developments, with particular reference to the thermodynamic instabilities: (a) At room temperature: enthalpy of formation as a function of nonstoichiometry, quantitatively measured by fluorine combustion calorimetry. (b) At high temperatures: evaluation of the lattice constants of samples quenched from between 1900 and 2000 “C. For a gen-
63
eral introduction to the solid-state chemistry of materials with valence instabilities the reader should consult ref. 2. References 3 and 4 are recommended as excellent sources of many other aspects of valence instabilities. 2. Control
of properties
via nonstoichiometry
Using the nonstoichiometry variation it was possible to change by up to 25% the valence of Tm from 3+ (at the selenium-rich phase boundary Tm/Se = 0.87) to 2.75+ (at the Tm-rich phase boundary Tm/Se = 1.05). This variation is reflected in a very large change (Au/a = 1.7%) of the lattice constant as a function of nonstoichiometry. Physical measurements show that the onset of valence fluctuation is at Tm/Se N 1.00. Figure 1 gives a fascinating example of the influence of valence fluctuation on the electrical resistivity uersus temperature, using the nonstoichiometry as a parameter to control the valence. It can be seen that for Tm/Se < 0.97 the resistivity behaves as a “normal metal” (Tm3’), decreasing with temperature. However at Tm/Se > 1.00 an unexpected increase in resistivity takes place, indicating the onset of valence fluctuation. The effect appears particularly at temperatures lower than the NQel point and it can be extinguished by applying a magnetic field. Therefore the same crystal may, at low temperatures, show either the resistivity of a semiconductor (H = 0) or a metal (H > 0). This is a typical example of the unexpected properties of materials with intermediate valence. 3. Phase diagram Tm-Se:
old version
In order to investigate systematically the thermodynamic stability of TmSe, we have started on the phase diagram of the Tm-Se system. This has
15 --\
\
-14 1
\
\
5
k- T \
cE 5La z .?4---
I \
. .
2
‘..
: = 3z .u L ; 2-
I , ..-. p :0.97
I I
’ ‘. !
y:0.99
---~:I.03
;
--
y:1.05
‘I J
Y Y
‘1
l0
-.-
--r:l.00
(
, 0.1
,\, 1
1.:
\
\
.-_~.~::.::.~ 10 100 Temperature (K)
Fig. 1. Anomaly of the electrical resistivity of nonstoichiometry after refs. 5 and 6.
of Tm,Se
at low temperature
as a function
64 mol Tm qcCf
0.6
0,7
Tm$,
0.8
!,9<
mof 1,2,1,3
IX
/
0.83 0.44 &I 0,57 0,98
Ii 0.40
I,O,I,!
II
I
Td’
0.50 ,&a-
‘Trn
c
0
Fig. 2. The T-x phase diagram of the Tn-Se system. The shadowed part indicates a metastable region. The lower composition scale is in mole fraction (XT&. Composition numbers at the top are in mole ratio x = Tm/Se.
been measured by high-temperature DTA f T < 2400 “C) under conditions of vapor-liquid or vapor--solid equilibrium in sealed tungsten capsules. Figure 2 shows the phase diagram we have published in the past [l] with two minor revisions: (a) a wider miscibility gap range, (b) the field of stability of Tm,Se6 (the boundaries of this field are still tentative, therefore the change is only due to formal reasons). Most important from the point of view of the thermodynamic stability of materials with valence fluctuations, is the homogeneity range of TmSe. Two of its features will be discussed: the existence of a wider miscibility gap at higher temperatures, which has a direct consequence for the thermodynamic stability, and the form of the solidus and liquidus curves. 4. Low-temperature miscibility gap In our previous work [ 21, the evidence concerning the miscibility gap was incomplete. X-ray investigations did not reveal the coexistence of two phases. DTA curves indicated a c, shift of the base line rather than peaks. Therefore, additional measurements were necessary. Initially, we determined the enthalpy of reaction of Tm,Se with 4N HCl as a function of nonstoichiometry [ 11. The results showed at least one miscibility gap and an
65
astonishingly large change of enthalpy for the Tm3+Se phase. In order to obtain quantitative data of the enthalpy of formation as a function of nonstoichiometry we have developed fluorine combustion calorimetry in our laboratory. 4.1. Fluorine combustion calorimetry Apparatus Based on the work of Hubbard and coworkers at Argonne National Laboratory [ 71 we developed a fluorine combustion calorimetry system consisting of: (a) a manifold for handling and analyzing pure and commercial fluorine, (b) a distillation column, (c) a fluorine combustion bomb, and (d) an isoperibol calorimeter. Manifold. Figure 3 shows, schematically, the manifold for handling the fluorine, the purification, analysis and storage. The system is constructed totally from stainless steel and includes storage tanks for the purified fluorine and many large filters of activated alumina to avoid atmospheric contamination by the fluorine purification and handling waste. To increase security, the whole apparatus is installed within an hermetically closed hood-glovebox made from stainless steel.
Fig. 3. Manifold. 1, Commercial fluorine; 2, purified fluorine container; 3, 4, reservoirs; 5, combustion bomb; 6, furnace for reactions with fluorine; 7, alumina filter; 8, rotary pump; 9, distillation vessel; 9a, distillation column; 11 - 13, manometer; 14, mercury titration; 15, precision manometer; 16, QMS; 17, LN,-cool trap; 18, mercury diffusion pump; 19, rupture disc; 20, sodium fluoride filter; 21, expansion vessel.
66
Distillation column. Commercial fluorine has a purity of approx. 98.5%. The accuracy of the enthalpy determination is therefore greatly decreased if fluorine of a purity greater than 99.5% is not used. Figure 3, nos. 9, 10, shows the distillation column schematically. The distillation vessel has a volume of 800 cm3 (no. 9). The column (no. 9a) has an internal diameter of 1.75 cm and is packed with 4 mm nickel helices for a height of 134 cm. The vessel is in a liquid N2 dewar and another dewar at the top allows refluxing of the liquid fluorine. By inducing a slight ~mperatur~ gradient between the dewars, a part of the refluxing fluorine can be distilled over the reservoirs (nos. 3 and 4). The purity of the distillate can be monitored by a quadrupole mass spectrometer with a special inlet system (Balzers AG) and/or by mereury titration [ 71. With the above distillation system, fluorine of a purity > 99.99% is obtained in one throughput. Combustiorz bomb. The following partly contradictory boundary conditions had to be taken into consideration for the design of the combustion bomb and the isoperibol calorimeter. (a) The po~ib~ity of investigating substances reacting spontaneously with fluorine. Highly reactive compounds such as the lanthanides are expected to fulfill this condition except when passivation in F,-atmosphere takes place. For this reason a two chamber bomb (Fig. 4) was constructed from one single piece of nickel. The internal combustion chamber has a volume of 600 cm3. The sample is charged in an argon glovebox. The outer
i - ,-_ -_ .. _.-. -\ -.
_ -
_. -_ -_ ,\ __ --_ -
*. c
-._
A
_--
-. r..
-
I-.
Fig. 4. Two-chamber fluorine combustion bomb, immersed in the isoperibol calorimeter.
61
fluorine storage chamber has a volume of 800 cm3. Both chambers can be filled and evacuated separately. (b) High pressure fluorination. This condition has been proven quite necessary, e.g., in the case of TmTe, where PF2 > 1 .l MPa was found to be the lowest limit for quantitative combustion [8]. Our construction allows a final pressure of 1.6 MPa to be reached, when the initial fluorine pressure in the storage chamber is 2.8 MPa. Clearly, an increase in the working pressure creates a problem: larger mass (thicker walls), higher energy equivalent, and therefore a decrease in the final accuracy, particularly when (c) also is required. (c) Samples with large composition gradients over relatively small volumes. In this case, bomb charges of small volume (mass) are necessary. To attain high accuracy, a small energy equivalent of the bomb and a high precision calorimeter are required. It is clear from this discussion, that either compromises must be made for an all-purpose bomb or special designs for particular problems should be constructed. The bomb used for this work had an all-purpose design. Isoperibol calorimeter. To attain high accuracy and to comply particularly with condition (c) above, the best possible superinsulation has been used. A multilayer insulation consisting of 70 mylar foils, each gold-coated on each side, was used for the calorimeter walls. The water bath was kept at 25 “C via a PTC 40 temperature controller (Tronac Inc). As a result of the above the calorimeter shows a temperature drift of only 3 X lop4 “C/week. The temperature is monitored by an Hewlett Packard quartz thermometer (resolution 0.0001 “C by one reading in ten seconds), tape recorded and transmitted to a computer. The combustion bomb is placed in the inner copper vessel (Fig. 4) surrounded by 2800.00 * 0.02 g of water. For reasons of mechanical stability the outer vessel is stainless steel. To minimize heat transfer via radiation the surfaces of the vessels are gold plated. Experimental
procedure
To avoid any humidity in the combustion bomb all the manipulations such as weighing the charge, opening, filling, and closing the bomb were undertaken in our train of glove boxes. These are made from stainless steel and glass, and the recirculating argon is gettered by hot cerium turnings. The residual impurities are 0, + H,O < 3 at. ppm. Selenium and tungsten were burned directly on a nickel crucible (Fig. 4), whereas TmSe was sited on a hard, polycrystalline layer of TmF,. Single crystals do not react with fluorine because of a very stable TmF3 layer which forms on the surface of the crystals. Pulverized TmSe reacts spontaneously with fluorine, but not completely, even at elevated final pressures. Complete combustion is obtained by adding selenium. The ignition of tungsten was also achieved using selenium. The impurities in the selenium and tungsten were determined by spark source mass spectroscopy. The mean values of the impurities were in at. ppm
68
in selenium: C, 4000; 0, 2000; K, 11000; Na, 1700; Ca, 4300; and in tungsten: C, 2000; 0, 2000; Na, 1000. The initial pressures were equal in every experiment, with 0.9 MPa fluorine in the storage chamber and 0.1 MPa argon in the combustion chamber. Calibration
Calibration with benzoic acid would raise the temperature of our calorimeter approx. 4.5 “C. However, the typical rise in a TmSe combustion experiment was approx. 0.5 “C. This is the result of using small samples (x500 mg TmSe, x200 mg Se) in order to increase the mapping resolution of the enthalpies of the various phases in a TmSe batch. To avoid a large temperature increase we used fluorine combustion of selenium to calibrate our calorimeter and not the usual oxygen combustion of benzoic acid. The results of the calibration are listed in Table 1. The corrected value of the heat of reaction of selenium, taking the impurities into account, is 14 211 J “C-l. The energy equivalent was measured to be E = 20 912 J “C’ (mean value of six determinations). To confirm this value we remeasured the heat of reaction of tungsten (Table 2). The value we obtained for the heat of reaction of Ma = 1723 f 6 kJ compares very well with the value of 1721 + 1.6 kJ mol-’ reported in the literature [ 71. TABLE
1
Determination of the energy equivalent, E, of the two chamber fluorine combustion of selenium The value of 1116.934 kJ mol-’ has been used for the enthalpy
based
of formation
on the of SeF6
[ 71. For improved
statistics
%elenium
(9)
E selenium
[ii
1.01100 14367.3 80.0 14447.3 0.68974
1.23567 17560.1 80.0 17640.1 0.84521
1.44209 20493.5 80.0 20573.5 0.98243
1.46610 20834.7 80.0 20914.7 0.99236
1.41667 20132.3 80.0 20212.3 0.97324
0.99632 14158.7 80.0 14238.7 0.68213
20946
20870
20941
21075
20768
20874
Ebhk
EtOt AT E
(J) (“C) (J “C-l)
Mean value E = 20912 TABLE
six measurements
bombs
have been made.
+ 42 J “C-l.
2
Determination
of the enthalpy
mtunssten
(9)
0.28773
%elenium
(9)
0.26963
AT --E x AT
(“C) (J)
E selenium &rank
E tungsten
of formation
of WF6 using the E value of Table
1
(J) (J)
0.31717 -6632.7 3830.3 80.0
0.26473 0.30883 0.26473 -6925.5 4388.8 80.0
0.23597 0.32723 0.23597 -6929.5 4650.9 80.0
0.26423 0.37794 0.26423 -7923.1 5370.9 80.0
0.25493 0.35394 0.25493 -7515.5 5029.8 80.0
0.27573 0.36489 0.27573 -7851.7 5185.5 80.0
(Jg-‘)
-9461.0
-9280.2
-9320.0
-9356.0
-9436.4
-9379.8
Mean value AH,
= 9372
+ 33 J g-l
= 1723
+ 6 kJ mol-‘.
69
4.2. Enthalpy of formation of Tm,Se as a function of nonstoichiometry Figure 5 shows the results of our combustion experiments on Tm,Se with various nonstoichiometric compositions of x. Although the results at x <0.94 roughly represent homogeneous samples, we have doubts for those with 3c> 0.94 due to the complicated phase transitions taking place (compare Sect. 4.3.). For this reason we concentrate here mainly on the samples with x < 0.94. The enormous increase (43%) in the enthalpy for 0.92 < x < 0.935 shows clearly the existence of a miscibility gap. Confirmation of the miscibility gap supports the previously presented argument [l] that the nature of the repulsive forces results from the change in the chemical bonding between metallic trivalent TmSe [ Xe]4f1’5d’6s2 and the valence fluctuating state [Xe] ((u4f l3 + /34f12)5d16s2. This is the result of the decreasing 4f-6d overlap following the increase of the lattice constant (decrease of the crystal-field splitting of the 5d band) as the Tm/Se ratio increases and the selenium vacancies are slowly filled [ 11. The calorimetric results confirm that in the TmSe homogeneity range several phases appear to exist. Although the miscibility gap between the Tm o.935Se and Tm o.,,,Se is clearly seen due to the strong enthalpy decrease of the Tm-rich boundary of the Tm 0.9,+Se phase, the other three phases are not yet well established. Of course, only after measuring the entropies, and calculation of the free-energy curves, can the exact composition range of the miscibility gaps be determined. Based on the few data existing at present, it seems that two other miscibility gaps may exist at approximately x = 0.96 and x = 0.99, respectively. Examination of Fig. 1 shows that the change in the resistivity behaviour takes place just in this composition range. This would
-1001’
’
’
’
0.90
’
o
’
’
’ 0.95
’
’
’
’
’ ’ 1.oo
’
x . mol
’
’
Tm/mol
’
1.05 Se
Fig. 5. Enthalpies of formation of Tm,Se as a function of nonstoichiometry. Q = sample quenched from the melt (2100 “C). The black corners of the error crosses indicate the number of experiments performed.
70
indicate that in addition to the normal metallic Tm3%e (x < 0.94) and the valence fluctuating phase (x > 0.99), two additional, narrow intermediate phases may exist in the quenched samples. The results of DTA at T < 800 “C include these phases in the miscibility gap.
5. High-temperature
miscibility
gap
In order to investigate the high-temperature phase transitions in the TmSe homogeneity range (Fig. 2) we have carried out high-temperature susceptibility measurements* in Tm o.g,Se (Fig. 6). The magnetic moment scale is arbitrary due to the lack of calibration. Although no abrupt valence transition takes place up to 1700 ‘C!, it is clear at T > 1100 ‘C, which is the temperature of the first phase transition (compare phase diagram, Fig. 2) that a distinct change (slope increase = 12%) towards higher moments (increasing Tm3+ contribution) takes place. To investigate the phase relationships above the phase transition at T = 1700 “C, several samples were quenched from between 1900 and 2100 “C. Quenching was not extremely rapid due to the rather large mass of the tungsten crucibles. X-ray investigations showed clearly that no structures other than NaCl appear at high temperature. This is in agreement with over 70 X-ray investigations of slowly cooled samples and the electron diffraction investigations reported in the past [ 11. This can also be understood from the I/X
4.0+02
5.0'02
Fig. 6. Susceptibility
1.8'83
of Tm,-,$3e
1.5+e3
us. temperature.
Arbitrary
T LK)
units.
*Work performed in the Inst. of Physics, University of Basle in collaboration R. Meier and Prof. H. Giintherodt, to whom the authors are indebted.
with
71
T >
-5.85
1900%
-5. _
- 5.64
-5.83 _
--t---t 5.02 II 0.80
I
I
I 0.90
I
I
I
I,,, 1.00
fm/Se
tx
Fig. 7. Lattice constants of slowly cooled and quenched l&Se samples as a function of nonstoichiometry. The fully drawn line shows the situation near room temperature with a miscibility gap 0.94 < Tm/Se < 0.98. The shadowed bands indicate the situation at high temperatures where the miscibility gap expands at 0.94 < Tm/Se < 1.05.
homogeneously mixed valence (valence fluctuation) of TmSe which is best accommodated to the NaCl structure 123. Figure 7 shows the lattice constants of quenched and slowly cooled samples of TmSe as a function of nonstoichiometry. As with the measurements of the enthalpy of formation, the selenium-rich part (X < 0.94) has clearly defined values. Independently of quenching or slow cooling, the lattice constants lie neatly on the Vdgard’s law line. The situation at x > 0.94 is quite different. Here, it is only possible to reach the Vegard’s-law line by slow cooling. In fact, all physical measurements in our laboratory have been performed on such crystals. The quenched samples, however, indicate the coexistence of only two phases at high temperatures: the Tm-rich phase boundary, Tm,,$e, of the homogeneity range, and the Se-rich boundary of the miscibility gap, Tm,.&e. This means that at high temperatures no solid-solution range exists, but only one v~ence-~uctuat~g (Tm r&3e) and one normal metallic phase (Tm,.&e). We may therefore conclude that the repulsive forces between normal and valence-fluctuating phases are increasing (i.e., the width of the miscibility gap increases). For the a uersus Tm/Se diagram this would mean that at high
72
temperatures the miscibility gap expands to 0.94
new version
The results of Section 5 show that samples quenched from the melt (2100 “C) also contain the two phases Tm,_,,Se and Tm0&3e. In this case it could be expected that the liquidus curve of the phase diagram (Fig. 2) has eutectic or peritectic form. In fact, in an earlier publication [9] when we had only a few DTA measurements, we suggested that the compound melts with a very narrow eutectic. With the much improved statistics of Fig. 2 it becomes clear that the flat maximum m.p. diagram fits the data better. Therefore, the appearance of the two phases in the quenched samples indicates the existence of a high temperature miscibility gap. As the quenching is not perfect, we probably freeze, even from the molten samples, the states just under the solidus. In Fig. 2 we therefore draw the upper boundary of this miscibility gap very close to the solidus line. At present we have little knowledge of the lower boundary of this miscibility gap. At T < 800 “C we have the miscibility gap shown by the DTA. As a working hypothesis we assume that a narrow, metastable region links the two miscibility gaps at high and low temperatures. Samples quenched from 1400 “C at compositions outside this narrow, metastable region did not show deviations from Vegard’s law. We must therefore conclude that outside this metastable region, solid solutions exist, and ‘that the miscibility gap is much wider at higher temperatures.
73
7. Acknowledgments One of us (E.K.) is greatly indebted to Dr W. Hubbard and Dr J. Johnson of the Argonne National Laboratory, U.S.A., for an introduction to the difficult technology of fluorine combustion calorimetry during a summer visit to ANL. The authors gratefully acknowledge exceptional funding by the Schulleitung of the ETH which made the fluorine combustion project possible.
References E. Kaldis and B. Fritzler, in G. M. Rosenblatt and W. L. Worrel (eds.), Prog. Solid State Chem., 14 (1982) 95. E. Kaldis, B. Fritzler and H. Spychiger, in R. Metselaar, H. J. M. Heifligers and J. Schoonman (eds.), Solid State Chemistry 1982, Elsevier, Amsterdam, 1983, p. 89. J. M. Lawrence, P. S. Riseborough and R. D. Parks, Rep. Prog. Phys., 44 (1981) 1. P. Wachter and H. Boppart (eds.), Valence Instabilities, North-Holland, Amsterdam, 1982. B. Batlogg, H. R. Ott, E. Kaldis, W. Thoni and P. Wachter, Phys. Rev. B, 19 (1979) 247. P. Haen, F. Holtzberg, F. Lapierre, J. Mignot and R. Tournier, Phys. Rev. Lett., 43 (1979) 304. W. Hubbard, G. K. Johnson and V. Ya. Leonidov, in S. Sunner and M. Mansson (eds.), Combustion Calorimetry, Pergamon, Oxford, 1979, Chap. 12. H. Spychiger, Dissertation, ETH, Zurich; H. Spychiger and E. Kaldis, to be published. E. Kaldis, B. Fritzler and W. Peteler, 2. Naturforsch., Ted A:, 34 (1974) 55.