William Klement

Investigation of phase transformations at elevated temperatures and pressures by differential thermal analysis in piston-cylinder apparatus☆

Abstract Differential thermal analysis (DTA) has proven to be among the more reliable and convenient of the several methods devised for the determination of phase boundaries at high pressures and temperatures. This paper discusses in detail the techniques, with the problems of material, design, and operation set forth and an assessment made of the quality of data obtainable by DTA using piston-cylinder apparatus.

Melting and freezing of selenium and tellurium at high pressures

Abstract The melting curve of selenium, as determined by differential thermal analysis, rises with pressure from 217°C at one atmosphere to about 636°C at 40 kbar; the slope decreases rapidly from 22° kbar to approximately 5° kbar at 40 kbar. Selenium crystallized readily from the melt only at temperatures above 400° and this is believed to be due to the decrease in viscosity of the liquid along the melting curve with increasing pressure and temperature. The melting of tellurium was studied under a wide variety of experimental conditions but the data obtained were not sufficiently reproducible to be definitive. The present experiments lend support to the results of Chaney and Babb and of Kennedy and Newton, but not to those of Tikhomirova and Stishov or of others. Extensive undercooling, with some dependence upon thermal history, was observed for the freezing of tellurium at pressure.

Determination of High-Temperature Transition in Calcite to 5 Kbar by Differential Thermal Analysis in Hydrostatic Apparatus

The high-temperature transition in calcite, located by extrapolation near 985° at 1 bar, has been determined to 5 kbar by differential thermal analysis in hydrostatic apparatus. The transition temperature increases with pressure at the rate of 3.0 ± 0.3°C/kbar, in contrast to the recent hypotheses which project a decrease.

High-low cristobalite transitions in SiO2, A1P04 and GaPO4Investigations by differential thermal analysis under hydrostatic pressures ≲ 6 kbar

Abstract High-low cristobalite transition temperatures in SiO2 and A1P04 were deter mined by differential thermal analysis (DTA) under hydrostatic pressures of Ar and of CO2 to 6 kbar, using ‘well-crystallized’ materials with known (at 1 bar) enthalpies and volumes. The high-low GaPO4 cristobalite transitions were also investigated at pressures ∼ 3 kbar, conversion to quartz being unavoidable; these low → high and high → low transition temperatures increase with pressure at ∼34° kbar−1. For the low → high and high → low transitions in SiO2 and A1P04, there are regions of anomalous curvature (- d2T/dp2<0) up to ∼ 1-2 kbar, the pressure-induced variations of transition temperatures then being linear and the hystereses decreasing with increasing pressures. Slopes for the phase transitions are compatible with the thermodynamic data at 1 bar. Since the high-pressure data on the cristobalite transition do not seem to be explained fully by current theories, further theoretical attention is needed. ACKNOWLEDGMENTS

Determination of the β ↔ αL′ transition in Ca2SiO4 to 7 KBAR

Abstract Differential thermal analysis in hydrostatic apparatus to 7 kbar shows that the β → α L ′ transition temperature in Ca 2 SiO 4 linearly increases from 701° ± 2°C at 1 bar at the rate of 10.5 ± 0.5 deg kbar −1 . The α L ′ → β transition temperature is observed some 20°–30° lower in temperature than the β → α L ′ transition and no variation in this hysteresis with pressure is indicated.

Melting of Iodine at High Pressures

The melting curve of iodine, which has been determined by differential thermal analysis, monotonically increases from about 114°C at zero pressure to about 590°C near 30 kbar. The extrapolated zero‐pressure slope for the melting curve is consistent with the value of 27.2 deg/kbar, as calculated from zero‐pressure data for the volume and entropy changes, and with the 27.8‐deg/kbar value from the unpublished data of Babb; near 30 kbar, the slope is about 11 deg/kbar. To a good approximation, the melting characteristics of the isostructural elements—iodine, bromine, and chlorine— should be quite similar, and the data for these other halogens are examined in an effort to anticipate their behavior at high pressure.

Tridymite: Effect of hydrostatic pressure to 6 kbar on temperatures of two rapidly reversible transitions

Trajectories of two reversible phase transitions in a low-Na synthetic tridymite have been determined to 6 kbar by differential thermal analysis (DTA) in hydrostatic apparatus using Ar or CO2. The temperature of the lower transition increases from ≈111 ° C at 1 bar linearly with pressure with slope ∼15 deg kbar−1. Pressure raises the temperature of the upper transition from 157 ±2 ° or 159 ° C (independently determined) at 1 bar witħ a slope of ≈53 deg kbar−1, up to ∼0.7 kbar; for the data above that pressure, the initial slope is ≈64 deg kbar−1. Above 2−1/2 kbar, the variation is linear with slope ≈70 deg kbar−1. No evidence for other transitions was found at any of the apparent changes of slope. Hystereses for both transitions decreased at high pressures compared to 1-bar. Preferred values for the transition enthalpies, together with these slopes and the Clausius-Clapeyron equation, yield estimates for the volume changes at the transitions of ≈0.01 (lower) and 0.15 to 0.25 (upper) cm3 gfw−1. These calculated volume changes are not consonant with many of the high temperature volumetric data on tridymites of varying origins.

Melting of Tin Teliuride at High Pressures

The melting curve of tintelluride (Sn0.496Te0.504 was determined by differential thermal analysis at pressures between 5 and 40 kilobars. Near 844��4�C and 12.0�1.0 kb, the liquid and two solid polymorphscoexist.

Phase relations of HgI2 at pressures < 0.7 GPa studied by differential thermal analysis especially the red ⇌ yellow transition

Differential thermal analyses of high-purity HgI2, under Ar pressure of ≲ 0.7 GPa, narrowly constrain the location of the phase boundary between the high-temperature yellow and low-temperature red polymorphs. This transition is unique among solid–solid transitions because of its maximum in transition temperature, with the initially less dense yellow phase becoming, with pressure, as dense and then denser than the red phase. The red → yellow and yellow → red transition temperatures, obtained mostly at heating and cooling rates of 30–60 K min–1, were from four runs on one sample plus a single run on another. The data suggest an initial slope dTt/dp= 0.237 ± 0.021 µK Pa–1 and initial curvature –d2Tt/dp2= 5.2–5.8 mK Pa–2. From the areas of the differential temperature peaks transition enthalpies and then transition entropies were estimated; ΔSt/R decreases rapidly with pressure from 0.81 ± 0.06 at 0.1 MPa to ca. 0.25 near the maximum at ca. 0.43 GPa. That the hysteresis in the transition varies little, despite the considerable variation in transition volume, is ascribed to the negligible role of strain energy, because of plastic deformation. A single run corroborated the Bardoll–Todheide results for the high-temperature, high-pressure transitions between yellow solid, liquid and the S3 polymorph; the triple point is located near 0.32 ± 0.01 GPa and 335 ± 3 °C and changes in entropy and volume are estimated there.

Temperatures of solid-to-solid transitions in (NH4)SO4, Rb2SO4, Cs2SO4, Cs2SeO4, and Cs2CrO4 under hydrostatic pressures to 0.6 GPa

Abstract Differential thermal analyses (d.t.a.) in hydrostatic apparatus to 0.6 GPa using Ar or CO2 have yielded the following linear variations with pressure, d T tr dp , of the temperatures of rapidly reversible solid-to-solid transitions: [substance, 0.1 MPa transition temperature T tr K , ( d T tr dp ) Pa μ K −1 ] Cs2CrO4, ≈ 1017 to ≈ 1024, ≈ 0.22; Cs2SeO4, (848 ± 4) or (886 ± 4), ≈ 0.24; Cs2SO4, (973 ± 4), (0.173 ± 0.013); Rb2SO4, (915 ± 3), (0.20 ± 0.01); (NH4)2SO4, (629 ± 3), (0.24 ± 0.02). The transition in (NH4)2SO4 apparently has not been encountered previously. Inconsistencies in and lack of measurements on entropy and volume changes thwart attempts to achieve self-consistent thermodynamic quantities for these transitions by using the Clausius-Clapeyron equation.