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Thermophysical Properties of the Lanthanide Sesquisulfides. III

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Thermophysical Properties of the Lanthanide Sesquisulfides. III Thermophysical properties of the lanthanide sesquisulfides. Ill. Determlnatlon of Schgttky and lattice heat-capacity contributions of y-phase Sm,S, and evaluation of the thermophysical properties of the y-phase Ln,S, subset Roey Shaviv”) and Edgar F. Westrum, Jr. Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-105.5 John. B. Gruber Department of Physics,San JoseState University, San Jose, California 95192-0106 8. J. Beaudry and P. E. Palmer Ames Laboratory, Iowa State University, Ames, Iowa SOO1I-3020 (Received 18 October 1991;accepted 10 January 1992) We report the experimental heat capacity of y-phaseSm, S, and derived thermophysical properties at selectedtemperatures. The entropy, enthalpy increments, and Gibbs energy function are 21SOR, 3063R.K, and 11.23Rat 298.15K. The experimental heat capacity is made up of lattice and electronic (Schottky ) contributions. The lattice contribution is determined for all y-phaselanthanide sesquisulfides(Ln, S, ) using the Komada/Westrum model. The differencebetween the experimental heat capacity and the deducedlattice heat capacity is analyzed as the Schottky contribution. Comparisonsare made betweenthe calorimetric Schottky contributions and those determined basedon crystal-field electronic energy levels of Ln3 + ions in the lattice and betweenthe Schottky contributions obtained from the empirical volumetric priority approach and from the Komada/Westrum theoretical approach. Predictions for the thermophysical properties of y-phaseEu, S, and y-phasePm, S, (unavailable for experimental determination) are also presented. INTRODUCTION by the volumetric scheme’ for estimation of lattice heat ca- The first‘two papersin this series’**describe the experi- pacity was found to be useful-as it was for the bixbyite mental determination and the resolution of the heat capaci- sesquioxides.’ ties of La2S3,’ Ce,S,,’ Nd2S3,’ Gd,S,,’ Pr2S3,* Tb2S3,* The main task in the analysisof the heat-capacityvalues and Dy, S, (Ref. 2) all of which are isostructural, y-phase in this system is the resolution of the electronic heat capac- members of the lanthanide sesquisulfidesystem. Most of ity. As illustrated in the previous papers in this seriesrV2in these lanthanide (Ln, S, ) compounds exhibit-in addition solid lanthanide compounds the electronic heat capacity to their lattice heat-capacitycontribution-excess contribu- takes the form of a Schottky contribution which is the heat tions as a result of the electrons in the 4f” shell of the lanth- capacity of a system with a finite number of energy levels. anide ion.3” The study of thesephenomena by calorimetric, The lowest level is defined as the zero energy of the system. spectroscopic,and magnetic techniques-as previously not- Each level i has a degeneracygj and an energyEj abovethe edI,*-has led to the resolution of their energetic spectra. ground level. The heat capacity of this system is The electronic configuration of the 4forbitals and the crys- -$$- [i$2giEfe-E’kT tal-field splitting of theseorbitals, which causesthe removal C, ( TJW = of somedegeneracies, gives rise to Schottky contributions to n-l n the heat capacities. Analysis of the crystal-field splittings, +iz2j ~+l~(Ej-Ei)2e-“+E’kT , the infrared and Raman spectra, and the magnetic suscepti- I bilities of thesecompounds are consistentwith the resolution which is equivalent to of the observedheat capacities. Cryogenic heat-capacity measurementsprovide an im- C, (T,E&) =-$$ [$tg,giEfe-E’kT portant technique for the study of the Schottky and magnet- ic contributions of these materials. Resolving these excess -- contributions from the typically larger lattice contribution b (,z gjEjemEfkT)*] f J 1 where R is the universal gasconstant, Ei and g, are the ener- gy and degeneracyof the ith state, respectively,and q is the partition function for the system. Tis the temperatureand k *) Current address: Department of Chemistry, University of Illinois at Chi- is the Boltzmann constant. For a system in which n-+ 03, cago, Chicago, Illinois 60680. Ei = iE,, and gi = g, for all i values,the Schottky heat- J. Chem. Phys. 96 (8), 15 April 1992 0021-9606/92/086149-OS$OS.OO @ 1992 American Institute of Physics 6149 6150 Shaviv &al.: Lathanide sesquisulfides. III capacity function reducesrigorously to an Einstein heat-ca- ments in a manner similar to that described earlier.’ The pacity function. samarium metal usedwas preparedin the Ames Laboratory For the special casein which a large energy gap exists and has the chemical analysis typical of the highly purified betweena subsetof lower energy levels and any higher ener- materials produced in that laboratory.” Sublimed sulfur gy level the heat capacity, due to thermal excitation in the (99.999%) was obtained from ASARCO.” lower levels, will be unaffected by the higher levels and ex- In the preparation of Sm, S, , stoichiometric quantities hibit Schottky-type morphology. The lanthanide com- of samarium and sulfur were sealedin a quartz ampoule.The pounds are an example of such a system. In the Ln, S, sys- sealedampoule was then heatedslowly to 575 “C, and held tem the typical energy spacing in the lower set of electronic for two weeks at this temperature by which time all sulfur energy levels is about 100 to 400 cm-‘. The origin of this had reacted. The ampoule was then heated slowly to low-energy spacing is the removal of the degeneracyof 4f 1000‘ C, held there for three days, cooled to room tempera- orbitals by the crystalline electric field. ture, and opened.The sulfide was ground and sieved to 200 The Schottky contributions observedin this system are mesh powder. The powder was cold pressed into pellets 4 broad and may cover the entire experimental temperature mm thick by 15mm diameter. The pressedpellets were heat- range. Phenomenaof such breadth posea difficulty in their ed to 1350“ C under a dynamic H, S atmospherefor 9 h. A resolution becausethere is but little direct experimental in- small random portion was removed for x-ray and chemical formation about the lattice contributions. Excess contribu- analysis. tions can often be analyzed by graphical means since the Debye-Scherrer x-ray patterns contained only lines of lattice contribution, outside the affectedtemperature range, the y-phase structure. The lattice parameter cl0 is deter- is known. When broad contributions are present,the lattice mined in this study to be (8.4383 k 0.0001) A while the heat capacity must be evaluatedindependently-as is neces- literature value*’ is 8.448 A. The final S to Sm ratio deter- sary in the analysis of the heat-capacity data in the present mined by chemical analysis is 1.499f 0.003. system. The volume-weighted lattice approximation has beenused previously with successfor severalother groups of Automated adiabatic calorimetry lanthanidecompounds,7-14 as well as for someof the sesqui- The data were taken in the Mark X calorimetric cryos- sulfides. Its application to the lanthanide sesquisullldeswas tat, an improved version** of the Mark II cryostat previous- presentedin the first two papersof this series.‘**The use of ly described.23Data acquisition was computer assisted.In- the volume-weighted lattice-approximation technique is, formation on the initial, final, and mean temperatures, on however, presumed to be most appropriate where the rel- the energy input and the resistanceof the heater, together evant compounds are isostructural or is one where the ions with the apparentheat capacity of the system were recorded. have at least the same coordination numbers. A gold-plated, oxygen-free, high-conductivity ( OFHC ) The Komada/Westrum phonon distribution mode11s-‘8 copper calorimeter (laboratory designation W-61 > was em- provides the meansto overcome the limitations of the volu- ployed in the measurement.The calorimeter is especially metric method. The model calculates a lattice heat capacity equippedwith two pairs of perforated copper, spring-loaded based upon structural and physical properties. Moreover, sleeves,soldered to the heater-thermometerwell, to hold the similarities betweencompounds may be utilized to interpo- sample pellets. After loading, and soldering the cover in late between reference compounds. Thus the method al- place (with Cerrosealsolder-50 mass % of Sn and In) the lows-by meansof three related computer programs called calorimeter was evacuated and approximately 2 kPa (at “LEM” programs-evaluation of the lattice contribution of about 300 K) helium gaswere addedto facilitate rapid ther- compoundsin an isostructural seriesbased upon known lat- mal equilibration. The temperatureswere measuredwith a tice heat capacities of related-isostructural compounds. Leeds h Northrup platinum-encapsulated, platinum-resis- This paperalso reports on the measurementsand inter- tance thermometer which was calibrated by the National pretation of the thermophysical properties of yet another- Bureau of Standardsagainst the IPTS-48 temperaturescale. the last accessible-member of the y-phase lanthanide ses- All other quantities were referencedto standardsof the Na- quisulfide subset, Sm, S, . Two other members of this sub- tional Bureau of Standards. set-not available for measurement-are Pm,S, and Eu, S, . The former is not readily available becauseof the nuclear instability of promethium, the latter by reasonsof Optical spectroscopy the relative instability of the III oxidation state of europium. Samarium sesquisulfideused for the optical spectra ex- Their thermophysical properties have beenevaluated by ap- periments was prepared in powder form by
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