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Birch-Murnaghan equation

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Residuals of the  PVT  <span class="search-highlight">Birch</span>-<span class="search-highlight">Murnaghan</span> <span class="search-highlight">equation</span> of state as a function of (...
Published: 01 May 2011
F igure 2. Residuals of the PVT Birch-Murnaghan equation of state as a function of ( a ) pressure and ( b ) temperature.
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<span class="search-highlight">Birch</span>-<span class="search-highlight">Murnaghan</span> <span class="search-highlight">equation</span> of state of Al-bearing stishovite (dashed line). S...
Published: 01 October 2002
F igure 3. Birch-Murnaghan equation of state of Al-bearing stishovite (dashed line). Solid circles = experiment in Ar; Solid squares = experiment in NaCl.
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The comparison of <span class="search-highlight">Birch</span>-<span class="search-highlight">Murnaghan</span> <span class="search-highlight">equations</span> of state among 17TiPv (red), 25...
Published: 01 November 2024
Figure 4. The comparison of Birch-Murnaghan equations of state among 17TiPv (red), 25TiPv (blue), pure CaSiO 3 ( Chen et al. 2018 ; Mao et al. 1989 ; Shim et al. 2000b ; Sun et al. 2022 ; Yagi et al. 1989 ), and pure CaTiO 3 ( Guennou et al. 2010 ). Opening squares of 17TiPv
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Pressure-volume data and the fitted third-order <span class="search-highlight">Birch</span>-<span class="search-highlight">Murnaghan</span> <span class="search-highlight">equations</span> o...
Published: 01 January 2017
Figure 4 Pressure-volume data and the fitted third-order Birch-Murnaghan equations of state for candidate dolomite phases. Experimental pressure-volume data for CaMg 0.6 Fe 0.4 (CO 3 ) 2 are shown in gray plus (+) symbols, with a second-order phase transition to dolomite II at 17 GPa and a first
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<span class="search-highlight">Birch</span>-<span class="search-highlight">Murnaghan</span> <span class="search-highlight">equations</span> of state for zircon and reidite (dashed lines). S...
Published: 01 January 2004
F igure 5. Birch-Murnaghan equations of state for zircon and reidite (dashed lines). Symbols are as follows: solid squares, zircon; solid circles, reidite.
Journal Article
Published: 01 November 2009
American Mineralogist (2009) 94 (11-12): 1596–1602.
.... The room-temperature cell-volume data, from 0.001 to 33 GPa, were fitted to a third-order Birch-Murnaghan equation-of-state, and a bulk modulus K 0 = 86(7) GPa with K ′ = 2.5(3) was obtained. The axial compressibility values are β a = 3.7(2), β b = 3.6(1), and β c = 2.8(1) GPa −1 (×10 −3 ) showing...
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Journal Article
Published: 01 June 2019
American Mineralogist (2019) 104 (6): 897–904.
... data combined with the five data points between 5.34 and 7.93 GPa from Angel and Hugh-Jones (1994) yields a second-order Birch-Murnaghan equation with K T0 = 121(2) GPa and V 0 = 403.9(5) Å 3 (with K T0 ′ = 4 implied). Further reduction of misfit upon fitting a third-order Birch-Murnaghan equation...
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Journal Article
Published: 01 June 2009
European Journal of Mineralogy (2009) 21 (3): 561–570.
... up to 9.75(3) GPa. A second-order BirchMurnaghan equation-of-state fit to the isothermal P - V data below 8.7 GPa yields values of K 0T = 109.29(18) GPa and K 0 ′ = 4. A third-order Birch-Murnaghan equation fit to the P - V data results in K ′ values equal to four, within an estimated standard...
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Journal Article
Published: 01 October 2007
American Mineralogist (2007) 92 (10): 1573–1585.
... ′ 0 ) of 3.9 ± 0.3 in a third-order Birch-Murnaghan equation of state. Revised values for the enthalpy and entropy of fusion of high albite at one bar and 1100 °C [Δ H T f = 64.5 ± 2.1 kJ/mol and Δ S T f = 47.0 J/(mol·K)] are recommended on the basis of improved heat capacity equations for NaAlSi 3 O...
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Journal Article
Published: 01 February 2006
American Mineralogist (2006) 91 (2-3): 319–326.
...Jason B. Burt; Nancy L. Ross; Ross J. Angel; Mario Koch Abstract The equations of state and structures of andalusite and sillimanite have been determined using high-pressure single-crystal X-ray diffraction. A third-order Birch-Murnaghan equation-of-state fit to 14 P - V data points measured...
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Journal Article
Published: 01 July 2005
American Mineralogist (2005) 90 (7): 1115–1120.
... pressure range and no phase transitions were observed although the evolution of the unit-cell parameters and volume exhibit some unusual features at pressures above 4 GPa. A third-order Birch-Murnaghan equation of state fit to 6 P - V data points up to 3.4 GPa has K 0 = 54.2(7) GPa and K ′ = 5.3(6...
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Journal Article
Published: 01 May 2002
European Journal of Mineralogy (2002) 14 (3): 561–565.
... a fit of sixteen measurements to a second-order Birch-Murnaghan equation of state ( K 0 ’ = 4) is K 0 = 81.0 ± 0.5 GPa. Fitting to a third-order Birch-Murnaghan equation of state gives K 0 = 83.1 ± 1.7 GPa and K 0 ’ = 3.3 ± 0.6 and, within error, the two fits are indistinguishable over this pressure...
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Journal Article
Published: 01 May 2014
American Mineralogist (2014) 99 (5-6): 908–913.
... ) measured by single-crystal X-ray diffraction as a function of pressure up to 7 GPa. The P - V data are adequately described to a fourth-order Birch-Murnaghan equation of state with the following coefficients: V 0 = 947.86(6) Å 3 , K T0 = 88(1), and K ′ = 6.3(9), K ″ = −1.1(4). This is the first time...
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Journal Article
Published: 01 August 2007
American Mineralogist (2007) 92 (8-9): 1446–1455.
... in compression mechanism arising from the changes in the O1 position is associated with changes in the compression of the unit-cell axes and the unit-cell volume. The volume can be described by fourth-order Birch-Murnaghan equation-of-state with parameters V 0 = 723.57(4) Å 3 , K T0 = 47.32(26) GPa, K ′ = 2.77...
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Journal Article
Published: 01 July 2005
American Mineralogist (2005) 90 (7): 1139–1145.
... for the I a polytype to 5.9 GPa was determined by fitting pressure-volume data to a second-order Birch-Murnaghan equation of state: K 0 = 78.7 ± 1.4 GPa. This value is close to that of clinochlore-II b ( K 0 = 81 GPa). Elastic moduli for a , b , and d 001 obtained from second-order fits to a Birch-Murnaghan...
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Journal Article
Published: 01 May 2001
European Journal of Mineralogy (2001) 13 (3): 497–506.
... with a third-order Birch-Murnaghan equation are: V 0 = 2121(2) Å 3 , K 0 = 26.4(1.0) GPa, K 0 ' = 4.9(8). If fitted with second-order Birch-Murnaghan equation of state, fixing K 0 ' = 4, K 0 becomes 27.5(2) GPa. The bulk heulandite structure compression was the result of the “soft” behaviour of the channels...
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Journal Article
Published: 01 January 2000
American Mineralogist (2000) 85 (1): 206–216.
... pressure transmitting conditions, NaCl served as an internal standard for pressure calibration. The pressure data at room temperature were fitted to a Birch-Murnaghan equation of state ( K ′ T 0 assumed to be 4), yielding isothermal bulk moduli K T 0 = 106.7 ± 1.3 GPa for lawsonite and 125.1 ± 2.1 GPa...
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Journal Article
Published: 01 May 2018
European Journal of Mineralogy (2018) 30 (3): 491–505.
... under neon in a diamond anvil cell. The volume-pressure data, collected up to 10.7 GPa, were fitted to a third-order Birch-Murnaghan Equation-of-State, yielding V 0 = 332.4(4) Å 3 , K 0 = 49(3) GPa, and K ′ = 6.9 (9). The compressibilities of the lattice parameters, up to 10.7 GPa, were calculated...
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The pressure-volume data and <span class="search-highlight">equations</span> of state of albite ( Benusa et al. 2...
Published: 01 February 2011
F igure 1. The pressure-volume data and equations of state of albite ( Benusa et al. 2005 ; open circles and dashed lines), high albite ( Tenner et al. 2007 ; filled squares), and analbite (this work; filled circles and solid lines). Lines are fourth-order Birch-Murnaghan equations of state
Journal Article
Published: 01 February 2014
American Mineralogist (2014) 99 (2-3): 511–518.
..., collected up to 11.2 GPa, were fitted by a second- and a third-order Birch-Murnaghan equation of state (EOS), yielding V 0 = 495.6(7) Å 3 with K 0 = 39.9(6) GPa, and V 0 = 496.9(7) Å 3 , with K 0 = 36(1) GPa and K ′ = 5.1 (4) GPa −1 , respectively. The axial moduli were calculated using a Birch-Murnaghan...
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