Thermodynamic behaviour of the high-temperature P\bar 1{\text{-}}I\bar 1 phase transition along the CaAl2Si2O8–SrAl2Si2O8 join     

M. Tribaudino  P. Benna  F. Nestola  C. Meneghini  E. Bruno 《Physics and Chemistry of Minerals》2005,32(4):314-321

In situ high-temperature synchrotron radiation powder diffraction patterns were taken from room temperature to T = 740°C from synthetic feldspars along the join CaAl₂Si₂O₈–SrAl₂Si₂O₈ (An–SrF). Three samples of composition An₉₅SrF₅, An₉₀SrF₁₀ and An₈₅SrF₁₅ were investigated, and the evolution of cell parameters with T was determined by Rietveld analysis of powder X-ray diffraction patterns. The high-temperature $P\bar 1{\text{-}}I\bar 1$ phase transition, previously observed with T _c = 241°C in anorthite, was found in An₉₅SrF₅, An₉₀SrF₁₀ and An₈₅SrF₁₅ feldspars at T _c = 233(5)°, 195(2)° and 174(2)°C respectively. The transition was revealed by the disappearance of critical reflections and variations in the rate of change of cell parameters with temperature. A significant, although small (between 0.0025 and 0.0012 at room temperature), spontaneous strain could be measured, allowing the thermodynamic behaviour of the transition to be modelled. A second-order trend for An₉₀SrF₁₀ and An₈₅SrF₁₅ [β = 0.504(7) and 0.505(7) respectively] or nearly second-order for An₉₅SrF₅[β = 0.458(4)] was observed in contrast with tricritical behaviour of end member anorthite. An extrapolation of the T _c versus composition to room temperature indicates that the critical composition for the $P\bar 1$ phase is An₆₀SrF₄₀.  相似文献   

The thermodynamics of the I \overline{1} –P \overline{1} phase transition in Ca-rich plagioclase from an assessment of the spontaneous strain     

Mario Tribaudino  Ross J. Angel 《Physics and Chemistry of Minerals》2012,39(9):699-712

In-situ powder diffraction measurements between 90 and 935?K on four anorthite-rich plagioclase samples (An₁₀₀, An₉₆Ab₄, An₈₉Ab₁₁ and An₇₈Ab₂₂) were used to determine the detailed evolution of these samples through the $I \overline{1} $ – $P \overline{1} $ phase transition. The c-type reflections indicative of $P \overline{1} $ symmetry were detected only in An₁₀₀, An₉₆Ab₄, whereas deviations in the evolution of the unit-cell parameters with temperature were observed in all samples, most prominently in the β unit-cell angle. The c-type reflections disappear at ~510 and ~425?K in An₁₀₀ and An₉₆Ab₄ respectively, and their intensity decreases according to a tricritical trend $ I^{2} \propto \left( {T - T_{\text{c}} } \right) $ . The cell parameter changes were used to determine the spontaneous strains arising from the transition which were modelled with Landau theory, allowing for low-temperature quantum saturation, in order to determine the thermodynamic behaviour. In An₁₀₀ tricritical behaviour was observed [T _c?=?512.7(4)?K; θ_s?=?394(4)] in good agreement with previous studies, and the c-type superlattice reflections indicative of $P \overline{1} $ symmetry persist up to the T _c determined from the spontaneous strain, and then disappear. The evolution of the spontaneous strain in An₉₆Ab₄ is tricritical at low temperatures [T _c?=?459(1) K, θ_s?=?396(5)] up to the temperature of disappearance of c-type reflections, but becomes second order beyond ~440?K. In An₈₉Ab₁₁ the strain displays second-order behaviour throughout [T _c?=?500(1) and θ_s?=?212(5)], and the c-type reflections are not detected in the powder diffraction patterns at any temperature. The apparent discrepancy between the absence of c-type reflections in temperature ranges where the cell parameters display significant spontaneous strain is resolved through consideration of the sizes of the anti-phase domains within the crystals. It is deduced that the tricritical phase transition occurs in well-ordered crystals with large domains in which the behavior of individual domains is dominant (i.e. in pure anorthite) or where the $P \overline{1} $ distortions within the domains are large enough to dominate the structural coherency strains between the domains. When both the magnitude of the $P \overline{1} $ pattern of displacements of the tetrahedral framework become smaller and the influence of the structural coherency between anti-phase domains becomes significant, the thermodynamic behavior becomes 2nd-order in character, the c-type reflections disappear, and the orientation of the spontaneous strain changes.  相似文献   

Thermodynamics of plagioclase III: Spontaneous strain at the I\overline 1 - P\overline 1 phase transition in Ca-rich plagioclase     

Simon A. T. Redfern  Ann Graeme-Barber  Ekhard Salje 《Physics and Chemistry of Minerals》1988,16(2):157-163

The lattice parameters of anorthites An₉₈Ab₂ and An₁₀₀ have been measured from 22 to 1100 K. The spontaneous strain arising from the \(I\overline 1 - P\overline 1\) displacive transition in An₉₈ follows second order Landau behaviour. The spontaneous strain (? _s) couples quadratically to the order parameter (Q ⁰) with ? _s∝Q ⁰²∝(T _c ^* ?T) and T _c ^* =530 K in An₉₈. This is in contrast to the tricritical behaviour observed in pure anorthite. These observations are consistent with a Landau model for the free energy of Ca-rich plagioclases in which Al/Si order and Na content renormalize the fourth order coefficient.  相似文献   

Iī-I2/c phase transition in alkaline-earth feldspars along the CaAl2Si2O8-SrAl2Si2O8 join: Thermodynamic behaviour     

M. Tribaudino  P. Benna  E. Bruno 《Physics and Chemistry of Minerals》1993,20(4):221-227

Feldspars crystallized in the range SrF₈₀An₂₀-SrF₆₀An₄₀ of the join CaAl₂Si₂O₈-SrAl-₂Si₂O₈ from gels at T = 1350–1500° C for short time show cell parameters significantly different from those obtained from longer heating. This difference has been interpreted as due to higher metastable Al/Si disorder in short heated samples and to more ordered configurations with longer heat treatments. HT powder spectra show that the T _c of the Iī-I2/c phase transition of feldspars changes with composition and with the degree of order at constant composition; the evolution of the spontaneous strain (～cosα^*) versus T for the samples examined shows a variation in the order of the transition from continuous (II order) in more ordered and Sr-rich samples to a discontinuous behaviour (presumably I order) for more disordered and Sr-poor samples. A biquadratic coupling between displacive and OD parameters is therefore suggested.  相似文献   

Atomic displacements in the normal-incommensurate phase transition in Co-åkermanite (Ca2CoSi2O7)     

N. E. Brown  C. R. Ross II  S. L. Webb 《Physics and Chemistry of Minerals》1994,21(7):469-480

New in-situ high-temperature X-ray powder diffraction data on the normal-incommensurate phase transition in Co-åkermanite (Ca₂CoSi₂O₇) are presented. Evidence for the phase transition is found in the abrupt change in the thermal expansivity of the c lattice parameter at 220° C. In addition, the c lattice parameter exhibits premonitory effects of the phase transition through the leveling out of the thermal expansivity at temperatures from 87 to 220° C. The c/a ratio for X₂ZSi₂O₇ incommensurate melilites is shown to be constant for a wide variety of compositions. Correlation of the trends in mean atomic positions with c/a ratio and the sigmoidal variation in the c/a ratio for Ca₂CoSi₂O₇ provide insight into the atomic displacements occurring in the melilite structure as a function of temperature. Three temperature regimes are discussed in detail (i.e. temperatures well above T _c, temperatures just above T _c, and temperatures below T _c). The atomic displacements occurring in each temperature regime are correlated with the changes in anisotropy and orientation of the atomic displacement ellipsoids for each site, as well as spectroscopic evidence for the increasing number of Z- and T-site environments.  相似文献   

The crystal and magnetic structure of Li-aegirine LiFe3+Si2O6: a temperature-dependent study     

G. J. Redhammer  G. Roth  W. Paulus  G. André  W. Lottermoser  G. Amthauer  W. Treutmann  B. Koppelhuber-Bitschnau 《Physics and Chemistry of Minerals》2001,28(5):337-346

Single crystals of Li-aegirine LiFe³⁺Si₂O₆ were synthesized at 1573?K and 3?GPa, and a polycrystalline sample suitable for neutron diffraction was produced by ceramic sintering at 1223?K. LiFe³⁺Si₂O₆ is monoclinic, space group C2/c, a=9.6641(2)?Å, b= 8.6612(3)?Å, c=5.2924(2)?Å, β=110.12(1)^° at 300?K as refined from powder neutron data. At 229?K Li-aegirine undergoes a phase transition from C2/c to P2₁ /c. This is indicated by strong discontinuities in the temperature variation of the lattice parameters, especially for the monoclinic angle β and by the appearance of Bragg reflections (hkl) with h+k≠2n. In the low-temperature form two non-equivalent Si-sites with 〈SiA–O〉=1.622?Å and 〈SiB–O〉=1.624?Å at 100?K are present. The bridging angles of the SiO₄ tetrahedra O3–O3–O3 are 192.55(8)° and 160.02(9)° at 100?K in the two independent tetrahedral chains in space group P2₁ /c, whereas it is 180.83(9)° at 300?K in the high-temperature C2/c phase, i.e. the chains are nearly fully expanded. Upon the phase transition the Li-coordination changes from six to five. At 100?K four Li–O bond lengths lie within 2.072(4)–2.172(3)?Å, the fifth Li–O bond length is 2.356(4)?Å, whereas the Li–O3?A bond lengths amount to 2.796(4)?Å. From ⁵⁷Fe Mössbauer spectroscopic measurements between 80 and 500?K the structural phase transition is characterized by a small discontinuity of the quadrupole splitting. Temperature-dependent neutron powder diffraction experiments show first occurrence of magnetic reflections at 16.5?K in good agreement with the point of inflection in the temperature-dependent magnetization of LiFe³⁺Si₂O₆. Distinct preordering phenomena can be observed up to 35?K. At the magnetic phase transition the unit cell parameters exhibit a pronounced magneto-striction of the lattice. Below T _N Li-aegirine shows a collinear antiferromagnetic structure. From our neutron powder diffraction experiments we extract a collinear antiferromagnetic spin arrangement within the a–c plane.  相似文献   

P-T-X data on P21/c-clinopyroxenes and their displacive phase transitions     

Thilo Arlt  Martin Kunz  Jano Stolz  Thomas Armbruster  Ross J. Angel 《Contributions to Mineralogy and Petrology》2000,138(1):35-45

The P2₁/c clinopyroxene kanoite (ideally MnMgSi₂O₆) was studied as a function of pressure and temperature using powder X-ray diffraction, differential scanning calorimetry (DSC) and optical methods. The temperature of the P2₁/c to high-temperature (HT) C2/c transition ranges from 425?°C in endmember MnMgSi₂O₆ to 125?°C in natural samples with an aegirine component. Compiling pigeonite and clinoenstatite–clinoferrosilite literature data, the temperature of the transformation was found to decrease linearly with M2 cation size. A synchrotron powder diffraction study in a heated diamond-anvil cell (DAC) yielded compression and thermal expansion data for low kanoite of composition Mn_1.2Mg_0.4Fe_0.4Si₂O₆. The high-pressure (HP) phase transition from P2₁/c to HPC2/c was reversed at 5.8 GPa at 417?°C. The high-temperature phase transition from P2₁/c to HTC2/c was rather indistinct and occurred at approximately 530?°C and 0.76 GPa. In a separate experiment, the HT transition was observed optically in a hydrothermal DAC between 0.0 and 0.4 GPa. The in-situP-T data of both experiments yielded an increase in transition temperature with increasing pressure (approx. 149?°C/GPa) and suggest a change in character of the transition from first order to continuous with increasing pressure. The data indicate that the HTC2/c and HPC2/c polymorphs are distinct phases with different stability fields. Since the high-temperature and the high-pressure polymorphs of kanoite were shown to be isotypic with other low-Ca clinopyroxenes such as the (Mg,Fe)SiO₃ series, the conclusions we draw from this study are valid for all clinopyroxenes with small (<0.88 Å) M1 and M2 cation sizes. The petrologic implications of these conclusions for the occurrence of “clinoenstatite” in the Alpe Arami peridotite are discussed.  相似文献   

Thermal expansion and high-temperature P21/c–C2/c phase transition in clinopyroxene-type LiFeGe2O6 and comparison to NaFe(Si,Ge)2O6     

Günther J. Redhammer  Fernando Cámara  Matteo Alvaro  Fabrizio Nestola  Gerold Tippelt  Sebastian Prinz  Jan Simons  Georg Roth  Georg Amthauer 《Physics and Chemistry of Minerals》2010,37(10):685-704

A synthetic clinopyroxene with composition LiFe³⁺Ge₂O₆, monoclinic s.g. P2₁/c, a = 9.8792(7), b = 8.8095(5), c = 5.3754(3) Å, β = 108.844(6)°, V = 442.75(16) ų, has been studied by in situ low- and high-temperature single-crystal X-ray diffraction. The variation of lattice parameters and the intensity of the b-type reflections (h + k = 2n + 1, only present in the P-symmetry) with increasing temperature showed a displacive phase transition from space group P2₁/c to C2/c at a transition temperature T _tr = 789 K, first order in character, with a sudden volume increase of 1.6% and a decrease of β by 1° at the transition. This spontaneous dilatation is reversible, shows a limited hysteresis of ±10°C, and corresponds to the vanishing of the b-type reflections, thus indicating a symmetry increase to space group C2/c. Below T _tr an expansion is observed for all the cell parameters, while the β angle remained almost constant; at T > T _tr the thermal volume expansion is due to dilatation of the structure in the $(\bar{1}\,0\,1) A synthetic clinopyroxene with composition LiFe³⁺Ge₂O₆, monoclinic s.g. P2₁/c, a = 9.8792(7), b = 8.8095(5), c = 5.3754(3) ?, β = 108.844(6)°, V = 442.75(16) ?³, has been studied by in situ low- and high-temperature single-crystal X-ray diffraction. The variation of lattice parameters and the intensity of the b-type reflections (h + k = 2n + 1, only present in the P-symmetry) with increasing temperature showed a displacive phase transition from space group P2₁/c to C2/c at a transition temperature T _tr = 789 K, first order in character, with a sudden volume increase of 1.6% and a decrease of β by 1° at the transition. This spontaneous dilatation is reversible, shows a limited hysteresis of ±10°C, and corresponds to the vanishing of the b-type reflections, thus indicating a symmetry increase to space group C2/c. Below T _tr an expansion is observed for all the cell parameters, while the β angle remained almost constant; at T > T _tr the thermal volume expansion is due to dilatation of the structure in the ([`1] 0 1)(\bar{1}\,0\,1) plane, mostly along [0 1 0], and pure shear in the (0 1 0) plane due to the decrease of β. From comparison with silicate analogues, the germanate clinopyroxenes are more expansible, while the P2₁/c expands more than the C2/c phase. The evolution of Q ² (calculated as the normalized intensity of b-type reflections) with T in the framework of the Landau theory has been done using a standard expression for a first order phase transition. We observe a jump of Q ₀² = 0.538(2) at T _tr, with T _c of 481(7) K, b/a = −2,290 K, and c/a = 3,192 K, and thus far from being tri-critical point. A closely related composition (LiFe³⁺Si₂O₆) shows an equivalent phase transition at 228 K, which is very close to the tri-critical point and 561 K cooler. This result indicates that a change in the composition of tetrahedral sites can have dramatic effects on the P2₁/c ↔ C2/c displacive phase transition in clinopyroxenes. The major changes observed in the evolution of the crystal structure with T are observed in the M2 polyhedron, with a volume decrease by ca. 13.3%, compared to ca. 1.3% observed in the M1 polyhedron. The tetrahedra behave as rigid units with neither a significant change of volume at T > T _tr (<1‰), nor a change of tilting of the basal plane. No change in coordination is observed at T > T _tr in the M2 polyhedron, which remains sixfold coordinated although a strong deformation of this polyhedron is observed. This deformation is related to a strong change by 51.4° at T _tr of the kinking angle (O3–O3–O3 angle) of the B-chain of tetrahedra, which switches from O-rotated to S-rotated [from 143.3(5)° to 194.7(6)°]. The A-chain is S-rotated at T < T _tr [206.8(5)° at 703 K] and extends by 12° at the transition.  相似文献   

Paraelectric-antiferroelectric phase transition in titanite,CaTiSiO5     

C. Van Heurck  G. Van Tendeloo  Subrata Ghose  S. Amelinckx 《Physics and Chemistry of Minerals》1991,17(7):591-603

The paraelectric to antiferroelectric phase transition in titanite at ～500 K involves a displacement of the titanium atom from the center of the [TiO₆] octahedron in the paraelectric phase (A2/a) to an off-center position in the antiferroelectric (P2 ₁/a) phase. We have carried out a detailed single crystal high temperature x-ray diffraction study of the phase transition including structure refinements at 294, 350, 400, 430, 440, 450, 500, 600, and 700 K. The unit cell dimensions show a pronounced hysteresis effect in the 450–500 K range on heating and cooling during the first cycle along with a reduction of the transition temperature, T _c from 495 ± 5 K on heating to 445 ± 5 K on cooling. The hysteresis effect disappears on further heating and the superstructure reflections show residual intensities above T _c (445 K). An order parameter treatment of the phase transition is presented in terms of Landau theory and induced representation theory. The Ti-displacements parallel and antiparallel to a are taken as the primary order parameter η, which transforms as the Y ₂ ⁺ representation. A coupling of Y ₂ ⁺ with T ₁ ⁺ results in the linear-quadratic coupling of the spontaneous strain components, ? _ij with η. The Ti-displacements are coupled linearly to the Cadisplacements. Both sets of displacements predicted from induced representation theory are observed experimentally. The phase transition is initially driven by the soft mode at the zone boundary point Y ₂ ⁺ ; near T _c critical fluctuations set in and an order-disorder mechanism finally drives the phase transition, whereby parallel and antiparallel Ti-displacements related by [0, 1/2, 1/2] in adjacent domains are dynamically interchanged. Immediately above T _c , the high temperature (A2/a) phase is a statistical average of small dynamic antiphase domains of the low temperature (P2 ₁/a) phase. Vacancies and defects pinning the domain boundaries may drastically alter the transition behavior and affect the domain mobility.  相似文献   

A dynamical model for the P1 — I1 phase transition in anorthite,CaAl2Si2O8     

G. Van Tendeloo  Subrata Ghose  S. Amelinckx 《Physics and Chemistry of Minerals》1989,16(4):311-319

Electron diffraction and electron microscopic evidence is presented for a dynamical and reversible phase transition in anorthite at T _c=516 K. Antiphase boundaries with a displacement vector, R=1/2[111] become unstable at T _c, while other antiphase boundary loops with the same displacement vector are formed. These interfaces are very mobile and vibrate with a frequency which increases strongly with temperature. At temperatures considerably above T _c, a shimmering effect is observed on imaging in dark field using diffuse c reflections. These observations are in agreement with the interpretation of the high temperature body-centered phase as a statistical dynamical average of very small c type antiphase domains of primitive anorthite. We propose that the c type antiphase domains in primitive anorthite originate from ordered and anti-ordered configurations around Ca²⁺ ions at (ooo) and (oio) [likewise (zoo) and (zio)] positions. The dynamical model for the transition involves a two-stage mechanism: a softmode mechanism causing the aluminosilicate framework to approach body-centered symmetry, followed by an orderdisorder of the Ca²⁺ ion configurations. Close to T _c, statistical fluctuations set in and breathing motion type lattice vibrations of the aluminosilicate framework cause the configurations around Ca (ooo) and Ca(oio) [likewise Ca(zoo) and Ca(zio)] in the configuration to dynamically interchange through an intermediate configuration. The dynamical nature of the phase transition in anorthite is comparable to the — phase transition in quartz.  相似文献   

High-pressure X-ray study of LiCrSi2O6 clinopyroxene and the general compressibility trends for Li-clinopyroxenes     

Benedetta Periotto  Ross J. Angel  Fabrizio Nestola  Tonci Balić-Žunić  Cinzia Fontana  Daria Pasqual  Matteo Alvaro  Günther J. Redhammer 《Physics and Chemistry of Minerals》2013,40(5):387-399

High-pressure single-crystal X-ray diffraction measurements of synthetic LiCrSi₂O₆ clinopyroxene (with space group P2₁/c) were performed in a diamond-anvil cell up to 7.970 GPa. No phase transition has been observed within the pressure range investigated, but the elastic behavior at lower pressures (up to ~2.5 GPa) is affected by an anomalous softening due to the proximity of the phase transition to the HT-C2/c phase at 330 K and at ambient pressure. A third-order Birch–Murnaghan equation of state fitted to the compression data above 2.5 GPa yields a bulk modulus K _T0 = 93(2) GPa and its first derivative K′ = 8.8(6). The structural data measured up to 7.970 GPa confirm that the space group P2₁/c is maintained throughout the whole pressure range investigated. The atomic parameters, obtained from the integrated diffraction intensities, suggest that the Li coordination polyhedron changes its coordination number from 5 to 6 at 6–7 GPa by means of the approach of the bridging O atom, related to the increased kinking of the B tetrahedral chain. Furthermore, at higher pressures, the structural evolution of LiCrSi₂O₆ provides evidence in the variation of kinking angles and bond lengths of a potential phase transition above 8 GPa to the HP-C2/c space group. A comparison of the Li-clinopyroxenes (M1 = Cr, Al, Sc, Ga, Mg + Fe) previously investigated and our sample shows that their elastic behavior and structural mechanisms of compression are analogous.  相似文献   

The R{\overline{3}} c \to R{\overline{3}} m transition in nitratine, NaNO3, and implications for calcite, CaCO3     

Sytle M. Antao  Ishmael Hassan  Willem H. Mulder  Peter L. Lee 《Physics and Chemistry of Minerals》2008,35(10):545-557

The temperature dependences of the crystal structure and superstructure intensities in sodium nitrate, mineral name nitratine, NaNO₃, were studied using Rietveld structure refinements based on synchrotron powder X-ray diffraction. Nitratine transforms from $R{\overline{3}} c\;\hbox{to}\;R{\overline{3}} m$ at T _c = 552(1) K. A NO₃ group occupies, statistically, two positions with equal frequency in the disordered $R{\overline{3}} m$ phase, but with unequal frequency in the partially ordered $R{\overline{3}} c$ phase. One position for the NO₃ group is rotated by 60° or 180° with respect to the other. The occupancy of the two orientations in the $R{\overline{3}} c$ phase is obtained from the occupancy factor, x, for the O1 site and gives rise to the order parameter, S = 2x ? 1, where S is 0 at T _c and 1 at 0 K. The NO₃ groups rotate in a rapid process from about 541 to T _c, where the a axis contracts. Using a modified Bragg–Williams model, a good fit was obtained for the normalized intensities (that is, normalized, NI^1/2) for the (113) and (211) reflections in $R{\overline{3}} c\hbox {\,NaNO}_{3},$ and indicates a second-order transition. Using the same model, a reasonable fit was obtained for the order parameter, S, and also supports a second-order transition.  相似文献   

A computational study of Al/Si ordering in cordierite     

S. Thayaparam  V. Heine  M. T. Dove  K. D. Hammonds 《Physics and Chemistry of Minerals》1996,23(2):127-139

The ordering of Al and Si in Mg cordierite Mg₂Al₄Si₅O₁₈ is considered using computer simulation. First the enthalpy of interaction J _ij between sites is derived by computer modelling 101 different Al/Si configurations and analysing their energies. They are compared with similar results for three other minerals and with ab initio calculations to assess the whole approach. Secondly the ordering process is studied using Monte Carlo simulation applied to the J _ij . The ordering phase transition temperature T _c is found as 1800°C in reasonable agreement with the experimental estimate of 1450° C. These are much lower than the estimate T _c(ABW)≈7600°C obtained from Bragg-Williams theory. Strong short-range order sets in below T _c(ABW), and the reasons for much lower temperature T _c of long-range ordering are discussed. Strong short-range also sets in very rapidly in a simulated anneal, in agreement with experiment. Thirdly an attempt is made to compare our calculated enthalpies directly with the results of NMR and calorimetry experiments, not completely successfully. A free energy ΔG≈4.6 eV for the activation barrier for ordering is suggested.  相似文献   

Non-convergent ordering and displacive phase transition in pigeonite: in situ HT XRD study     

F. Cámara  M. A. Carpenter  M. C. Domeneghetti  V. Tazzoli 《Physics and Chemistry of Minerals》2002,29(5):331-340

A natural Ca-rich pigeonite (En₄₇Fs₄₃Wo₁₀), free of augite exsolution products, was studied by in situ high-temperature single-crystal X-ray diffraction. The sample, monoclinic P2 ₁ /c (a=9.719(7) Å, b=8.947(9) Å, c=5.251(3) Å, β=108.49(5), V=433.0(6) ų), was annealed up to 1000 °C to induce a phase transition from P2 ₁ /c to C2/c symmetry. Complete single-crystal X-ray diffraction data collections were carried out in situ at 650, 750, 850 and 950 °C after the crystal had reached equilibrium for the Fe–Mg intracrystalline exchange reaction at each temperature. The variation, with increasing temperature, of lattice parameters, of intensity of hkl reflections with h + k=2n + 1 (which vanish at high temperature) and of some geometrical parameters from structure refinement, showed that the displacive phase transition P2 ₁ /c?C2/c was continuous in character. This contrasts with the first-order character for the HT phase transition in pigeonite containing significantly less calcium.  相似文献   

In situ observation of a phase transition in Fe2SiO4 at high pressure and high temperature     

Shigeaki Ono  Takumi Kikegawa  Yuji Higo 《Physics and Chemistry of Minerals》2013,40(10):811-816

We used an in situ measurement method to investigate the phase transition of Fe₂SiO₄ polymorphs under high pressures and temperatures. A multi-anvil high-pressure apparatus combined with synchrotron X-ray radiation was used. The stability of each polymorph was identified by observing the X-ray diffraction data from the sample. In most experiments, the diffraction patterns were collected 10–30 min after reaching the desired pressure and temperature conditions. The transition boundary between the olivine and spinel phase at T = 1,000–1,500 K and P = 2–8 GPa was determined to occur at P (GPa) = 0.5 + 0.0034 × T (K). The transition pressure determined in this study was in general agreement with that observed in previous high-pressure experiments. However, the slope of the transition, dP/dT, determined in our study was significantly higher than that estimated by the previous study combined with the in situ X-ray method.  相似文献   

Ferroelastic phase transition in cryolite,Na3AlF6, a mixed fluoride perovskite: High temperature single crystal X-ray diffraction study and symmetry analysis of the transition mechanism     

Hexiong Yang  Subrata Ghose  Dorian M. Hatch 《Physics and Chemistry of Minerals》1993,19(8):528-544

Cryolite, Na₃AlF₆[ = 2Na⁺(Na_0.5 ⁺Al_0.5 ³⁺)F₃] is a mixed fluoride perovskite, in which the corner-sharing octahedral framework is formed by alternating [NaF₆] and [AlF₆] octahedra and the cavities are occupied by Na⁺ ions. At 295 K, it is monoclinic (α phase), space group P2 ₁/n with a = 5.4139 (7), b = 5.6012 (5) and c = 7.7769 (8) Å and β = 90.183 (3)°, Z = 2. A high temperature single crystal X-ray diffraction study in the range 295–900 K indicates a fluctuation-induced first-order phase transition from monoclinic to orthorhombic symmetry at T ₀ ～ 885 K, in contrast to a previous report that it becomes cubic at ～823 K. The space group of the high temperature β phase is Immm with a = 5.632 (4), b = 5.627 (3) and c = 7.958 (4) Å, Z = 2 at 890 K. Above T ₀, the coordination number of the Na⁺ ion in the cavity increases from eight to twelve and the zigzag Na1 — Al octahedral chains parallel to c become straight with the Na1-F-Al angle = 180 °. The phase transition is driven by two coupled primary order parameters. The first corresponds to the rotation of the nearly rigid [AlF₆] group and transforms according to the Γ ₄ ⁺ irreducible representation of Immm. Coupled to the [AlF₆] rotation is a second primary order parameter corresponding to the displacement of the Na2⁺ ion in the cavity from its equilibrium position. This order parameter transforms according to the X ₃ ⁺ irreducible representation of Immm. Following Immm → P2 ₁ /n phase transition, four equivalent domains of P2 ₁/n are determined relative to Immm, which are in an antiphase and/or twin relationship. The abrupt shortening of the octahedral Al-F and Na-F bonds and a sudden change in orientations of the atomic thermal vibration ellipsoids above T ₀ indicate a crossover from displacive to an order-disorder mechanism near the transition temperature. The β phase is interpreted as a dynamic average of four micro-twin and -antiphase domains of the a phase. This view is consistent with the entropy of phase transition, ΔS_trans (11.43 JK^?1 mol^?1) calculated from heat capacity measurements (Anovitz et al. 1987), which corresponds closely to R ln4 (11.53 JK^?1 mol^?1), where 4 is the number of domains formed during the phase transition. The dynamic nature of the β phase is independently confirmed from a considerable narrowing of the ²⁷Al nuclear magnetic resonance (NMR) line-shape above T ₀ (Stebbins et al. 1992).  相似文献   

Magnetization,mössbauer spectroscopy and structural studies of a ferrimagnetic Fe-Oxide formed by heating nontronite in air     

N. Petersen  N. Schembera  E. Schmidbauer  H. Vali 《Physics and Chemistry of Minerals》1987,14(2):118-121

On heating the paramagnetic clay mineral nontronite for ≈ 30 h at 970 °C in air, a new ferrimagnetic phase forms which was studied by magnetic techniques, microprobe analysis, x-ray diffraction and Mössbauer spectroscopy. The new phase has a Curie temperature T _c ≈ 240°C and high magnetic anisotropy at room temperature with a spontaneous magnetization >12 Am²/kg. Semiquantitative microprobe analyses show Fe to be the dominating consistuent. X-ray analysis points to a lattice which may be similar to that of ?-Fe₂O₃ but differs from it in detail. ⁵⁷Fe Mössbauer spectra, taken between 78 K and 295 °C, can be deconvoluted into three sextet subpatterns in the ferrimagnetic region which are well resolved at room temperature and exhibit a rather small line width. Above T _c, a doublet is visible which is typical for Fe³⁺ ions.  相似文献   

Microsommite: crystal chemistry, phase transitions, Ising model and Monte Carlo simulations     

E. Bonaccorsi  S. Merlino  M. Pasero  G. Macedonio 《Physics and Chemistry of Minerals》2001,28(8):509-522

Microsommite, ideal formula [Na₄K₂(SO₄)] [Ca₂Cl₂][Si₆Al₆O₂₄], is a rare feldspathoid that occurs in volcanic products of Vesuvius. It belongs to the cancrinite–davyne group of minerals, presenting an ABAB… stacking sequence of layers that contain six-membered rings of tetrahedra, with Si and Al cations regularly alternating in the tetrahedral sites. The structure was refined in space group P6₃ to R=0.053 by means of single-crystal X-ray diffraction data. The cell parameters are a=22.161?Å=√3a _dav, c=5.358?Å=c _dav; Z=3. The superstructure arises due to the long-range ordering of extra-framework ions within the channels of the structure. This ordering progressively decreases with rising temperature until it is completely lost and microsommite transforms into davyne. The order–disorder transformation has been monitored in several crystals by means of X-ray superstructure reflections and the critical parameters T _c?≈?750?°C and β?≈?0.12 were obtained. The kinetics of the ordering process were followed at different temperatures and the activation energy was determined to be about 125?kJ?mol^?1. The continuous order–disorder phase transition in microsommite has been discussed on the basis of a two-dimensional Ising model in a triangular lattice with nn (nearest neighbours) and nnn (next-nearest neighbours) interactions. Such a model was simulated using a Monte Carlo technique. The theoretical model well matches the experimental data; two phase transitions were indicated by the simulated runs: at low temperature only one of the three sublattices begins to disorder, whereas the second transition involves all three sublattices.  相似文献   

Optical absorption spectroscopy of the P213-P212121 transformation in K2Co2(SO4)3 langbeinite     

M. J. L. Percival  E. Salje 《Physics and Chemistry of Minerals》1989,16(6):563-568

Crystal field spectra have been obtained from K₂Co₂(SO₄)₃ at a number of temperatures from 20 K to room temperature. The transition to the ⁴ T _1g(P) excited state is found to be split at all temperatures owing to the trigonal distortion of the Co site. Below the P2₁3-P2₁2₁2₁ phase transition temperature an excess splitting is observed owing to the additional distortion of the site in the orthorhombic phase. This excess distortion is found to be a linear function of temperature with no first order step at T _c. Thus on a local scale the transition appears to be second order. The trigonal splitting increases with increasing temperature above T_c; this is not expected from the Speer-Salje model of the transition mechanism, which predicted decreasing distortion of the oxygen octahedra with increasing temperature. We propose that the apparent increase of asymmetry is due to the off centring of the Co atom in the high temperature phase in a more regular environment.  相似文献   

Equilibrium thermodynamics of Al/Si ordering in anorthite     

M. A. Carpenter 《Physics and Chemistry of Minerals》1992,19(1):1-24

Variations in the equilibrium degree of Al/Si order in anorthite have been investigated experimentally over the temperature range 800-1535° C. Spontaneous strain measurements give the temperature dependence of the macroscopic order parameter, Q, defined with respect to the \(C\bar 1 \rightleftharpoons I\bar 1\) phase transition, while high temperature solution calorimetric data allow the relationship between Q and excess enthalpy, H, to be determined. The thermodynamic behaviour can be described by a Landau expansion in one order parameter if the transition is first order in character, with an equilibrium transition temperature, T _tr, of ～2595 K and a jump in Q from 0 to ～0.65 at T_tr. The coefficients in this Landau expansion have been allowed to vary with composition, using Q=1 at 0 K for pure anorthite as a reference point for the order parameter. Published data for H and Q at different compositions allow the calibration of the additional parameters such that the free energy due to the \(C\bar 1 \rightleftharpoons I\bar 1\) transition in anorthite-rich plagioclase feldspars may be expressed (in cal. mole^-1) as: \(\begin{gathered}G = \tfrac{1}{2} \cdot 9(T - 2283 + 2525X_{Ab} )Q^2 \\ {\text{ + }}\tfrac{1}{4}( - 26642 + 121100X_{Ab} )Q^4 \\ {\text{ + }}\tfrac{1}{6}(47395 - 98663X_{Ab} )Q^6 \\ \end{gathered}\) where X _Ab is the mole fraction of albite component. The nature of the transition changes from first order in pure anorthite through tricritical at ～An₇₈ to second order, with increasing albite content. The magnitude of the free energy of \()\) ordering reduces markedly as X _Ab increases. At ～700° C incommensurate ordering in crystals with compositions ～An₅₀–An₇₀ needs to have an associated free energy reduction of only a few hundred calories to provide a more stable structure. These results, together with a simple mixing model for the disordered ( \()\) ) solid solution, an assumed tricritical model for the incommensurate ordering and published data for ordering in albite have been used to calculate a set of possible free energy relations for the plagioclase system. The incommensurate structure should appear on the equilibrium phase diagram, but its apparent stability with respect to the assemblage albite plus anorthite at low temperatures depends on the values assigned to the mixing parameters of the $$$$ solid solution.  相似文献