Lambda Transitions in Minerals

Thompson, Alan Bruce; Perkins, E.H.

doi:10.1007/978-1-4612-5871-1_3

Cited by 14 publications

(13 citation statements)

References 42 publications

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“…The shape of this curve is compatible with that of a 1-transition (Carpenter, 1985). This type of behaviour occurs when there is a mixture of order-disorder and displacive transitions (Thompson and Perkins, 1981). At a critical point, a long-range order parameter, which is associated with Fig.…”

Section: Nature Of the Monoclinic-orthorhombic Transitionmentioning

confidence: 68%

“…As a result, the two techniques may report different values for the transition conditions. Although Landau theory (Thompson and Perkins, 1981;Ghose, 1985;Carpenter, 1985) does not apply for λ-transition, it can be used to describe the behavior of the long-range order parameter in the vicinity of the critical point. In this formalism, η oc (P c -Ρ) β , where P c is the critical pressure and β is the Landau exponent, which should be the inverse of an integer.…”

Section: Nature Of the Monoclinic-orthorhombic Transitionmentioning

confidence: 99%

“…It is necessary, therefore, to employ the secondorder equation, dP/dT = Δα/Δ β (Thompson and Perkins, 1981), where α and β are the coefficients of isobaric thermal expansion and isothermal compression, respectively. The precision of the present study is not sufficient to quantify a change of slope in the volume versus pressure (Fig.…”

Section: Clapeyron Slopementioning

confidence: 99%

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Crystal structure of monoclinic ilvaite and the nature of the monoclinic-orthorhombic transition at high pressure

Finger¹,

Hazen²

1987

Zeitschrift Für Kristallographie - Crystalline Materials

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Crystal structures of monoclinic ilvaites from Elba, Italy, and Seriphos, Greece, have been refined and an Fe 2+ -Fe 3+ order parameter has been related to the monoclinic angle β. Lattice constants have been determined as a function of pressure in a diamond-anvil cell. At high pressure the 0-angle decreases and the structure becomes orthorhombic. This transition, which is not first order, may be described as a λ-point, which has both order-disorder and displacive character. The electron disorders at the λ-point; however, there is residual short-range order above this point. One consequence is that the transition conditions observed by calorimetry are not necessarily the same as those of crystallography.

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Section: Nature Of the Monoclinic-orthorhombic Transitionmentioning

confidence: 68%

Section: Nature Of the Monoclinic-orthorhombic Transitionmentioning

confidence: 99%

Section: Clapeyron Slopementioning

confidence: 99%

See 1 more Smart Citation

Crystal structure of monoclinic ilvaite and the nature of the monoclinic-orthorhombic transition at high pressure

Finger¹,

Hazen²

1987

Zeitschrift Für Kristallographie - Crystalline Materials

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“…This kind of transition is usually considered to be of the mixed or )• transition type. Reviews of )• transitions in minerals, their classification, and an introduction to their thermodynamics are given by Helgeson et al [1978] and Thompson and Perkins [ 1981 ].…”

Section: Introductionmentioning

confidence: 99%

Equation of state for lambda transition in quartz

Dorogokupets¹

1995

J. Geophys. Res.

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An equation of state has been developed for quartz, a substance with a lambdatype phase transition. It has the properties of the Murnaghan equation of state in the normal region and reflects the fundamental behavior of thermodynamic functions in the anomalous region. The term j'T/(i-T) •a has been introduced in the temperature dependent equations of isobaric heat capacity and the volume coefficient of thermal expansion, where i and j' are fitting coefficients. The i coefficient is numerically close to the temperature of the phase transition To and is usually in the 0.1< l i-To 1<20 K interval. The range of applicability of the Murnaghan equation is delineated in the PT stability field of quartz. In the lambda range, the derivative of thermal expansion with respect to temperature is pressure dependent according to rules that allow integration of the thermal expansion and molar volume for calculation of the change in thermodynamic functions from room pressure to any given pressure. Available phase equilibria and thermochemical data have been used with the proposed equation of state to calculate the standard thermodynamic properties for coesite and the SiO: phase diagram including alpha quartz, beta quartz, and coesite. Renard and Garland, 1966]. Quartz has a )•-type transition [Mayer, 1960; Hughes and Lawson, 1962; Klernent, 1968; Klernent and Cohen, 1968; Hemingway, 1987], but Drebeshchak and Dement'ev [1993] suppose that the 0•-[3 transition in quartz is first order with an enthalpy of 300-400 J/mol. The correlations between thermodynamic functions for quartz achieved with the help of Pippard [1956] equations were also extensively investigated in these works but with moderate success, as noted by Hosieni et al. [1985]. 8489 Hosieni, K.R., R.A. Howald, and M.W. Scanlon, Thermodynamics of the lambda transition and the equation of state of quartz, Am. Miner., 70, 782-793, 1985. Hughes, A.J., and A.W. Lawson, Cylindrical approximation and the quartz transition, d. A determination of the elastic constants for [3-quartz, J. Appl. Phys., 19, 265-270, 1948. Karpov, I.K., A.I. Kiselev, and F.A. Letnikov, Chemical Thermodynamics in Petrology and Geochemistry (in Russian), 385 pp., Institute of Geochemistry and Institute of the Earth's Crust, Irkutsk, Russia, 1971. Kelley, K.K., Contributions to the data on theoretical metallurgy, XIII, High-temperature heat-content, heat capacity and entropy data for the elements, and inorganic compounds, U.S. Bur. Mines Bull., 584, 232 pp., 1960. Khodakovsky, I.L., International geothermodymanics tables, CODATA Bull., 7, 1990. Klement, W., High-low quartz inversion: Approximate relations for volume and compressibility versus temperature at high pressure, d. Geophys. Res., 73, 4711-4716, 1968. Klement, W., and L.H. Cohen, High-low quartz inversion: Thermodynamics of the lambda transition, d. Geophys. Res., 73, 2249-2259, 1968. Kuskov, O.L., and O.B. Fabrichnaya, The SiO2 polymorphs: The equation of state and thermodynamic properties of phase transformation, Phys. Chem. Miner., 14, 58-66, 1...

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“…The main discussion has concerned the α-β transition in quartz, not merely because this is a λ-transition, i.e., with discontinuities in the first and second derivatives of the internal energy and volume, but also because the thermal and elastic characteristics for (α-quartz are not known for T > T λ . General information on λ-transitions in minerals is available [25,41], and the physical and mathe matical techniques may be found, for example, in Stanley [13]. A detailed study has been made of the λ-transition in quartz [31], but Hosieni et al [27] pointed out that this was not notably successful.…”

Section: P I Dorogokupets I K Karpov and V V Lashkevichmentioning

confidence: 99%