Calorimetric investigation of the excess entropy of mixing in analbite-sanidine solid solutions: lack of evidence for Na,K short-range order and implications for two-fbldspar thermometry

Heat capacities (5-380 K) have been measured by adiabatic calorimetry for five highly disordered alkali feldspars (AbeeOr1, Ab65Or15, Ab55Ora5, Ab25Ory5, and AblOree). Positive heat capacity deviations from a linear combination of the end-member heat capacities, which are present mostly at very low temperatures, result in an excess entropy for intermediate compositions. The excess entropy at 298.15 K is well described by the symmetric expression Sids : Xebxo,(10.3-+0.3 J/mol.K). For practical calculations, the entropy and enthalpy of mixing can be regarded as temperature-independent above room temperature. The excess entropy and volume of mixing have been combined with solvus determinations to obtain a calculated enthalpy of mixing. Because the measured enthalpies of mixing are essentially coincident with those calculated from the solvus determinations, no shortrange order for the alkali site could be inferred. The new data for the alkali feldspars have been combined with recent data for plagioclase feldspars to derive an expression for the two-feldspar thermometer that is consistent with present knowledge of the thermodynamics of these solid solutions. ,* _ (xdff(lssto + tzoro xA[ + 0.364p -_(x:h2e8230 3ssz0 x1b) 10.3 (x6FF + 8.31431n {rxftl'qxltl i t xf,'b ) where the mole fractions refer to the ternary system and P is in bars. Temperatures calculated from this expression tend to be higher than those calculated from previous formulations. Introduction necessity for such terms has been demonstrated conclusively, through calculations based on phase-equilibrium, Inmostdiscussionsof themixingpropertiesof mineradata for pyrope-grossular garnets (Hensen et al., 195\ logic solid solutions, the heat capacity is implicitly asand for alkali feldspar (e.g., Thompson and Waldbaum, sumed to vary linearly with composition. As a result, the 1968; Thompson and Hovis, 1979). mixing properties at constant pressure are defined entireHaselton and Westrum (1979) showed that the heat Iy by entropy and enthalpy terms that are temperature capacities of pyrope-grossular garnets are nonlinear with independent. For many solutions ofgeologic interest, the respect to composition at temperatures below about 120 inclusion of temperature-dependent terms is not required K. These heat-capacity deviations from a linear combinafor the representation of available data; however, the tion of the end-member heat capacities result in an excess 0003-004v83/0304-0398$02.00 39E entropy of mixing. For this garnetjoin, the excess entropy and enthalpy of mixing can be assumed to be constant at higher temperatures, because there the heat-capacity deviations are most probably negligible. When volume terms were added to the temperature-dependent activity expressions derived from calorimetry, the results of Hensen et al. (1975) were easily reproduced in calculations. Recently, Thompson and Hovis (1979) refined the earlier calculations (Thompson and Waldbaum, 1968) of excess entropy parameters for high structural state alkali feldspars by combining measured enthalpies (Hovis and Waldbaum, 1977) and volumes of mixing (Hovis, 1977) with phase-equilibrium data (Orville, 1963; Iiyama, 1965, 1966; Delbove, l97l; and Traetteberg and Flood, 1972). Their calculations indicate that an excess entropy of mixing, which is greatest for potassic compositions, is necessary to make the available thermodynamic data selfconsistent. The maximum magnitude of the predicted excess entropy is approximately half of the expected configurational entropy of mixing; clearly, it cannot be neglected in phase-equilibrium calculations. Thompson and Waldbaum (1969a) noted that, although short-range order (SRO) could be an important source of deviations from the ideal configurational entropy of mixing, the principal source ofan excess entropy is probably vibrational. If the vibrational contributions are significant, as they appear to be in the alkali feldspars, they can be measured quite readily and precisely by modern lowtemperature adiabatic calorimetry. The contributions can be positive or negative; they are expected, if present, only at low temperatures, because the effects of structure on the heat capacities generally diminish as temperature increases. With regard to SRO in the alkali distribution, Thompson and Hovis (1979) noted that this effect could only decrease the entropy of mixing because of the nonrandom configuration. They suggested that short-range ordering might be identified through phase-equilibrium calculations once the excess entropy attributable to vibrational contributions had been quantified. In practice, however, because of the slope of the function relating configurational entropy to order, the energy efect associated with small amounts of ordering from a disordered configuration will be very difrcult to detect unambiguously. The environment of the Na ion in highly disordered alkali feldspars has features that affect interpretations relating heat capacities to structure. In analbite, the AVSi feldspar framework collapses about the alkali site, producing triclinic symmetry, because the Na ion is apparently too small to maintain a more symmetric site. At 35 to 40 mole percent KAlSi3O8, the structure becomes monoclinic (Hovis, 1980; Kroll et al.,1980).In a rigorous thermodynamic description of high structural state alkali feldspar solid solutions, terms describing the symmetry change should be included. At present, however, phase equilibrium data are not sufficiently precise to permit a meaningful quantitative formulation. At very high tem399 peratures, topochemically monoclinic albite becomes symmetrically monoclinic (Okamura and Ghose, 1975; Kroll et a/., 1980), but most applications to geological problems and the most useful phase-equilibrium data are for triclinic albite. The mode of residence of Na on the alkali site may also affect the entropy. The results of several X-ray diffraction studies (Ribbe et al., 1969; Prewitt et al., 1976) indicate that the Na ion in analbite may vibrate about two or more nodes, which are probably determined by the occupancy ofthe adjacent tetrahedral sites (Brown and Fenn, 1979). Alternatively, the X-ray data could result from an unexpectedly large vibrational amplitude about a single node. From structural refinements at a variety of temperatures, Prewitt et al. (1976) have provided good evidence for the space average, but whether the number of nodes present is 2 or 4 is still unknown (Brown and Fenn, 1979; Prewitt et al., 1976). An X-ray structure refinement of AbazOrss (Fenn and Brown, 1977) provides some evidence for the existence of multiple nodes for the Na ion in Or-rich (Ab = NaAlSi:Or, Or : KAlSi3Os) solid solutions. Unlike the Na ion, the K ion apparently is centrally located in the alkali site; no indication of multiple nodes has been found. Both the change of symmetry and the probable existence of multiple nodes suggest that the vibrations related to the Na ion may result in unexpectedly large contributions to the heat capacity at temperatures less than 298 K. A prodigious amount of work has been published on the solvus relations of high-structural-state alkali feldspar solid solutions since the initial study by Tuttle and Bowen (195E). Luth (1974) and Parsons (1978) have discussed the attempts by Orville (1963), Luth and Tuttle (1966), Seck (1972), Goldsmith and Newton (1974), Smith and Parsons (1974), and others to locate the binodal solvus directly at a variety of pressures up to 15 kbar. Many determinations of the distribution coefficients of Na and K between alkali feldspars and aqueous alkali halide solutions or fused alkali chlorides are available (Orville, 1963;Iiyama, 1965, 1966; Delbove, l97l; Traetteberg and Flood, 1972; Lagache and Weisbrod, 1977; and Merkel and Blencoe, 1980). Volumes of mixing for high alkali feldspar, prepared by alkali ion exchange from natural starting materials and from glasses and gels, have been measured by Donnay and Donnay (1952), Orville (1967), Luth and Querol-Sufl€ (1970), and Hovis (1977). Hovis and Waldbaum (1977) measured enthalpies of mixing for an alkali exchange series prepared from AVSi disordered Amelia albite. Low-temperature (15-375 K) heat capacities for analbite and sanidine prepared from Amelia albite have been measured (Openshaw et al., 1976). Heat capacities from 320 to 1000 K have been measured by diferential scanning calorimetry on the same samples (Hemingway et al., l98l). The heat capacities ofanalbite and sanidine are the same within analytical error (0.2 percent to 380 K, I percent from 380 to 1000 K) at temperatures above -220K. X-ray evidence of AVSi ordering is cited in some of the HASELTON ET AL,: CALORIMETRIC INVESTIGATION OF ANALBITE_SANIDINE HASELTON ET AL.: CALORIMETRIC INVESTIGATION OF ANALBITE-SANIDINE phase equilibrium studies mentioned above. Knowledge of the mixing properties of low structural state alkali feldspars is necessary for assessing this additional variable. The low feldspar solvus has been located independently by Bachinski and Miiller (1971) and Delbove (1975) using ion exchange in fused alkali halides and homogenization-unmixing techniques. Enthalpies of mixing were measured for a low alkali feldspar series by Waldbaum and Robie (1971). Volumes of mixing have been given by Orville (1967), Waldbaum and Robie (1971), and Hovis and Peckins (1978). In the present work, low-temperature heat capacities (5-380 K) have been measured for a series of five high structural state alkali feldspars. The excess entropy arising from excess heat capacities has been quantified and has been combined with phase-equilibrium data to examine the possibility of short-range order in the alkali site. The evaluation leads to mixing expressions for high alkali feldspars that, together with recent measurements for plagioclase feldspars (Newton et al., 1980), permit a reformulation of the two-feldspar thermometer.