ALBERT

Description: The 1 bar Curie temperature, T C , at which cementite (anthropogenic form of the mineral cohenite, nominally Fe 3 C) abruptly loses ferromagnetism, is found to be sensitive to small deviations from the stoichiometric cementite composition. Stoichiometric Fe 3 C begins to lose magnetic susceptibility at 187 °C. The T C of ferromagnetic loss in cementite falls by about 13–14 °C, in either compositional direction, to the limits at either Fe-saturation or graphite-saturation. Formation of C vacancies in, or C stuffings into, Fe 3 C produces non-stoichiometry, disrupts and weakens the Fe magnetic ordering, and produces excess configurational entropy that is proportional to the disruption magnitude. C-excess (~0.6 at% C) at graphite-saturation is less than the C-deficiency at Fe-saturation (~2.6 at% C), so the rate at which Curie T C drops with cementite C% variation is asymmetric about the stoichiometric composition, being steeper on the C-excess side. This asymmetry reflects the higher excess configurational entropy (and consequently greater weakening of Fe magnetic ordering) generated by C excesses than by C vacancies. The application of ~6 GPa pressure to stoichiometric Fe 3 C leads to a drop in T C , of more than 160 °C, to below room T . This large drop in T C with pressure is shown by loss of ferromagnetism in a specimen compressed in a multi-anvil device at room T . Densely sampled synchrotron XRD cell volumes through the transition pressure interval at room T show that there is also a small drop in compressibility near 6 GPa for non-stoichiometric cementites. C-rich cementite retains its magnetism to ~1 GPa higher P than C-poor cementite. The drop in T C with pressure for stoichiometric cementite was tracked in an externally heated diamond-anvil cell by the jump in thermal expansion experienced when cementite loses its magnetostriction above T C ( Wood et al. 2004 ; Litasov et al. 2013 ). T C drops parabolically with pressure, as do the Invar alloys ( Leger et al. 1972 ; Winterrose et al. 2009 ). Both high T and P favor the magnetically disordered (Curie) paramagnetic over the ferromagnetic form of cementite. The observed large positive change in thermal expansion and small negative change in compressibility at the T C transition give a good quantitative account of the negative d T C /d P slope mapped by the ferro-paramagnetic phase stability boundary through Ehrenfest’s (1933) second relation. Our observations of cementite demagnetization at P ~6 GPa, room T confirm the synchrotron Mössbauer work of Gao et al. (2008) . The demagnetization pressures based upon experiment are lower than those estimated from existing theoretical treatments by about an order of magnitude. Stability calculations for carbide in the mantle and core are influenced by the choice among ferromagnetic, paramagnetic, and non-magnetic equations of state. Because the ferromagnetic phase is more compressible, the calculated P-T range for cementite stability would be too large under the assumption of ferromagnetism persisting to higher pressures than shown here experimentally. Our results diminish the theoretical P-T range of cementite stability.

Description: Synchrotron X-ray diffraction (XRD) was used to measure the unit-cell parameters of synthetic pyrope (Mg 3 Al 2 Si 3 O 12 ), grossular (Ca 3 Al 2 Si 3 O 12 ), and four intermediate garnet solid solutions. Garnets synthesized dry in multi-anvil (MA) apparatus at 6 GPa show irregular asymmetric positive quenchable excess volumes, with binary Margules parameters W V grossular = 2.04 ± 0.14 cm 3 /mol, and W V pyrope = 4.47 ± 0.15 cm 3 /mol. The two-parameter Margules equation is only an approximate description of the excess volumes in the pyrope-grossular garnets from this study and from the literature. The values for intermediate garnets in this report are roughly a factor of ~3 larger than previous literature reports of excess volumes of garnets grown at piston-cylinder (PC) pressures (2–4 GPa) with hydrothermal assistance. The discrepancy between our large dry excess volumes and the smaller hydrothermally assisted syntheses previously reported in the literature may be due in part to the hydrothermal assistance. When we do damp syntheses, we too get small excess volume. Although dampness produces smaller excess volumes, the mechanism by which this is achieved remains to be discovered. Does dampness relieve microstrains to relax excess volumes? Analysis of synchrotron X-ray diffraction profiles by using Williamson-Hall plots to test for microstrain shows that peak width does change with dampness and with garnet composition. Microstrain in the garnet structure, rather than grain size variation, is the principal reason for the observed XRD peak broadening. Damp garnets at Py 60 Gr 40 have less microstrain and lower excess volume than dry Py 60 Gr 40 , in accord with the working hypothesis that dampness is responsible for diminished excess volume through strain relief. However garnets with compositions Py 80 Gr 20 and Py 20 Gr 80 , close to the negligibly strained end-members pyrope (Py 100 ) and grossular (Gr 100 ), have large microstrains but relatively small excess volume. This is in contrast to Py 40 Gr 60 , which has the largest excess volume but almost no microstrain. (The end-members have no excess volume, by definition, and little microstrain.) This uncorrelated behavior demonstrates that microstrain in general is not directly related to the excess volumes, whatever else dampness may do to a specific composition, for instance introduce a small amount of clinopyroxene into the mode that partitions Ca preferentially away from garnet. Thus the mechanism responsible for the difference between our large excess volumes and the smaller ones in the literature may not be as complete or as simple as dampness relieves microstrain and relaxes excess volume. Our dry intermediate garnets have already been relieved of their microstrain by some other mechanism than dampness and still have large excess volume. The state of Ca-Mg ordering may also change, and we show that this may have a small effect on the excess volume through experiments using variable synthesis time and temperature. A potential test for whether our large, complex excess volumes, of whatever origin, are real (or not) is whether the rise of the solvus with pressure is better described by our large excess volumes or those smaller ones in the literature. We observe garnet phase exsolution at 8 GPa and show it to be reversible, at a temperature consistent with theoretical calculation using the large mixing volume presented in the current study.

Description: Unit-cell volume and microstrain of Py 40 Gr 60 garnets vary with synthesis temperature and annealing time, showing a strong negative correlation, as is also seen in another garnet solid solution, Py 20 Gr 80 . This anti-correlation is explained by local Ca-Mg cation arrangement in which Ca-Ca and Mg-Mg third-nearest-neighbor (Same 3NN = S3NN) pairs form at rates other than those expected from random Ca-Mg distribution. S3NN pairs cause microstrain ( Bosenick et al. 2000 ) but allow more efficient packing than random Ca-Mg pairings that contribute to excess volume, hence smaller cell volumes correlate with more microstrain. Both longer annealing time and higher heating temperature cause more S3NN formation, larger microscopic strain, and smaller unit-cell volume. The anti-correlation of microstrain and excess volume is weaker in our previous study of pyrope-rich solutions (i.e., Py 80 Gr 20 , Du et al. 2016 ) because excess volume varies little from Ca-Ca S3NN pairings in pyrope-rich solutions, whereas Mg-Mg S3NN pairings in grossular-rich solutions studied here are effective at reducing excess volume. Heating to 600 °C under room pressure or cold hydrostatic compression to 10 GPa does not reset microstrain. Margules’ formulations for microstrain and volume as a function of Ca/Mg ratio captures these features, especially the two-peaked distribution of microstrain with composition discovered by Du et al. (2016) . The similar two-peaked distributions of microstrain and excess energies derived from ab initio calculation with short-range ordering of Mg and Ca cations ( Vinograd and Sluiter 2006 ) indicate that the macroscopic thermodynamic mixing properties of solid solutions are directly related to arrangement of cations with large size misfit. The observed changes of microstrain with annealing temperature suggest that mixing properties measured from our pyrope-grossular garnet solid solutions synthesized at same temperature can serve as better experimental constrains for computational work.