Order parameter coupling in leucite: a calorimetric study
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The thermal anomalies associated with the Ia3d → I41/acd → I41/a transition sequence of phase transitions in leucite have been studied by differential scanning calorimetry and interpreted with Landau theory. Both transitions are close to the tricritical point. The coupling between the two transitions is biquadratic, and reduces the stability of the I41/a phase.
KeywordsLeucite Calorimetry Phase transitions
Silicate frameworks of this type tend to be rather flexible (Dove 1997). These degrees of freedom mean that framework silicates frequently undergo displacive phase transitions. They also tend to have good tolerance for chemical substitution. Whilst natural leucites depart only slightly from the ideal composition KAlSi2O6 (Deer et al. 2004), leucite analogues with a wide range of compositions have been synthesised (Bayer 1973; Taylor and Henderson 1968; Galli et al. 1978).
The precise details of the transformation behaviour of leucite have proved difficult to pin down. The most important complication is that there are two phase transitions in leucite, separated by a rather small temperature interval. The first evidence for this was from thermal analysis (Faust 1963) indicating transitions at 938 and 918 K; subsequent measurements (Lange et al. 1986) indicated that the behaviour was more complex and sample-dependent; in particular, annealing a natural leucite reduced the transition temperatures by 24 K. Meanwhile, crystallographic experiments indicated that the space group of the high temperature phase was Ia3d (Peacor 1968) and that of the room temperature phase was I41/a (Mazzi et al. 1976). Later studies (Grögel et al. 1984; Boysen 1990) found the intermediate phase, indicated by the calorimetric data, to have space group I41/acd.
Palmer and co-workers studied leucite using a range of experimental techniques (Palmer et al. 1989, 1990, 1997). Combining these data, Palmer concluded that the Ia3d → I41/acd transition was due to an acoustic shear distortion (Palmer et al. 1990) and that the I41/acd → 41/a transition was associated with the freezing of the K+ substructure combined with an additional framework distortion (Palmer 1990).
Despite the progress in understanding the mechanisms of the transformations in leucite, a complete quantitative description of the transformations has proved more elusive. Approaches based on Landau theory have proved to be very effective in describing phase transitions in framework silicates (Salje et al. 2005), particularly in situations where several transitions interact. In this paper, we combine new calorimetric results for leucite with existing structural data to determine a complete Landau potential for the two phase transitions in leucite and the interaction between them.
A sample of natural leucite from the Roman volcanic province was obtained from the University of Cambridge collection. The lattice parameters and composition of the leucite sample studied here were checked for consistency with other experiments. Lattice parameters were determined using powder X-ray diffraction at room temperature, using a Bruker D8 diffractometer. The diffraction pattern refined as a tetragonal structure, with a = 13.0547(8) Å, c = 13.7555(11) Å. These values are similar to the natural leucite from near Rome, Italy studied by Palmer et al. (1997). They are also close to the values obtained for natural leucite L999 of Palmer et al. (1989, 1990), which were a = 13.059(3) Å, c = 13.756(2) Å.
The composition was determined with a Cameca SX100 electron microprobe. The analysed formula (K0.999Na0.012)(Al1.005Fe0.012Ca0.001)Si1.986O6, is close to the ideal formula of leucite, KAlSi2O6; this is common in natural leucites (Deer et al. 2004). The differences between this sample and natural leucite L999 (Palmer et al. 1989, 1990), which has been analysed as K0.97(Al0.99Fe0.01)Si2.01O6 do not seem significant.
A large euhedral single crystal was prepared for calorimetry by being cut into thin slices with a diamond saw. It was then polished into a thin disc, with 45 mg mass. This sample was heated in a Perkin-Elmer “Diamond” DSC from 325 to 973 K at a rate of 20 K min−1. Comparison of the heat flow data for this sample with results for an empty calorimeter and a sapphire standard were used to determine the temperature dependence of the specific heat.
Landau coefficients for phase transitions in leucite
Coefficients for Ia3d → I41/acd transition
J K−1 mol−1
Coefficients for I41/acd → I41/a transition
J K−1 mol−1
Data analysis and discussion
Using Eqs. 3 and 5, we may compare the (actual) coupled behaviour of Q1 with its uncoupled behaviour (Q1,0) for each coupling model. If we make the approximation that Q1,0 is nearly tricriticial, then
The problem of determining the parameters in Eq. 2 therefore needs to be tackled in several discrete steps. Experimental data for the I41/acd phase permits the fitting of the parameters A1, B1, C1 and TC1. These parameters then determine what the behaviour of Q1 in the I41/a phase would be in the absence of order parameter coupling. The deviation of Q1 from this behaviour constrains the form and magnitude of the coupling, which then allows the bare free energy parameters for Q2 (A2 etc.) to be determined.
Use of spontaneous strains to measure order parameters
Carpenter et al. (1998) review the use of spontaneous strains to measure order parameters associated with phase transitions in minerals. The lowest order coupling (for example e ∝ Q or e ∝ Q2) allowed is constrained by group theoretical principles. Higher order couplings not commonly significant, but are allowed.
The symmetry breaking strain esb vanished at the upper transition temperature. This suggests that it can be associated with Q1. From symmetry arguments, we expect esb ∝ Q. A volume strain, ensb is allowed in any structural phase transition, with ensb ∝ Q2.
Characterisation of the Ia3d → I41/acd transition
Coupling between Q1 and Q2
The sign of the coupling constant λ2 is positive (that is, the coupling increases the overall free energy of the system). This is manifest by the observation that the lower temperature peak in the dsc data occurs at 900 K, whereas the lower “bare” transition temperature is 907 K.
Bare behaviour of Q2
As noted above, the deviations seen in Q1 below the lower transition temperature, together with the form of the specific heat anomaly, imply that the behaviour of Q2 is essentially tricritical. No latent heat was observed around TC2. Whilst a small positive B2 is possible, none of the results of this study require it, or allow its numerical value to be determined. As a result of the coupling between Q1 and Q2, the lower temperature transition happens around 10 K below TC2; this is because the coupling reduces the stability of the I41/a phase.
Assuming that the lower temperature transition is exactly tricritical, there are then two independent parameters describing the thermodynamics of this transition. The value of A2 was found from the magnitude of the entropy anomaly at the lower transition, and TC2 from the observed transition temperature (taking account of the effect of the coupling with Q1). For a tricritical transition, B2 = 0, and C2 = A2 TC2, both by definition.
Our new measurements of the heat capacity of leucite demonstrate that the underlying thermodynamic character of both transitions is near-tricritical. Landau theory successfully describes the individual transitions, and the coupling between them. The data indicate that the dominant interaction between the two order parameters is biquadratic; whilst a linear-quadratic coupling is allowed by symmetry, in practice it is either undetectably weak or absent. The likely reason for this is that coupling via the spontaneous strain is a physically plausible mechanism for the interaction between the two order parameters (Salje and Devarajan 1986), and that coupling is biquadratic in the case of leucite.
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