W-WO and WdW-WO OFitRltihitHihT t dPOxygen Fugacity ...W-WO 2 and WdW-WO 3 OFitRltihitHihT t...
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W WO dW WO O F it R l ti hi t Hi h T t dP W - WO and W - WO Oxygen Fugacity Relationship at High Temperature and Pressure W - WO 2 and W - WO 3 Oxygen Fugacity Relationship at High Temperature and Pressure W WO 2 and W WO 3 Oxygen Fugacity Relationship at High Temperature and Pressure 2 3 TJ D TJ Deane TJ Deane Advisor: Dr Andrew Campbell Advisor: Dr. Andrew Campbell Advisor: Dr. Andrew Campbell Introduction Experiment Conclusion Introduction Experiment Conclusion ff Understanding different thermodynamic (b) (a) Understanding different thermodynamic 2” (b) (a) WWO2 - WWO3 Buffer Curve Comparison properties of materials is important for a Thermocouple to WWO2 - WWO3 Buffer Curve Comparison properties of materials is important for a measure temperature 10 it f T t i d tl of sample 10 variety of reasons Tungsten is a moderately Wires connecting 2 5 variety of reasons. Tungsten is a moderately Wires connecting power supply to ” 5 siderophile element considered to be found in power supply to heater siderophile element considered to be found in heater 0 both the o e nd ili te po tion of the 2 WWO3 - 40 GPa both the core and silicate portions of the ” (c) -5 WWO3 40 GPa WWO2 40 GP both the core and silicate portions of the 2 (c) -5 WWO2 - 40 GPa Earth x-ray ” 10 2) WWO3 - 20 GPa Earth. x ray beam -10 O2 WWO2 - 20 GPa beam g(fO WWO2 - 20 GPa WWO3 0 GP H t ()i l ti bl k -15 og WWO3 - 0 GPa Ud t di h t t bh d Heater (a), insulating block lo WWO2 - 0 GPa Understanding how tungsten behaves under (b) and diamond anvil cell 20 Understanding how tungsten behaves under Detector (b), and diamond anvil cell -20 high temperature and pressure conditions can Detector (c) that were used to high temperature and pressure conditions can (c) that were used to generate temperature and -25 help to le d to bette nde t nding of ho generate temperature and help to lead to a better understanding of how pressure -30 help to lead to a better understanding of how f pressure 30 and under what conditions the core formed Sample along the x -ray beam line during trip to 35 and under what conditions the core formed. Sample along the x ray beam line during trip to NSLS i B kh N Y kJl 2009 -35 NSLS in Brookhaven New York, July 2009 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 1/T (1/K) F ll d t di th t t id b ff 1/T (1/K) Fully understanding the tungsten oxide buffer X ray diffraction experiments were conducted at the National Synchrotron Light Source Fully understanding the tungsten oxide buffer X -ray diffraction experiments were conducted at the National Synchrotron Light Source system is essential for scientists who would (NSLS) i B kh N Y k A hi h d di td t th l system is essential for scientists who would By calculating the difference in (NSLS) in Brookhaven New York. A high powered x -ray was directed at the sample e t ng ten o ide me n of ont olling By calculating the difference in (NSLS) in Brookhaven New York. A high powered x ray was directed at the sample use tungsten oxide as a means of controlling f it bt WO d which was held within a diamond anvil cell to generate high pressures and surrounded use tungsten oxide as a means of controlling f oxygen fugacity between WO 3 and which was held within a diamond anvil cell to generate high pressures and surrounded oxygen fugacity within their experiments oxygen fugacity between WO 3 and by individually constructed heaters to generate high temperatures Multiple diffraction oxygen fugacity within their experiments. WO we find that the ΔfO is always by individually constructed heaters to generate high temperatures. Multiple diffraction WO 2 we find that the ΔfO 2 is always by individually constructed heaters to generate high temperatures. Multiple diffraction k i P T di i d l d d i h l 2 2 positive indicating the fO of WO is patterns were taken at varying P- T conditions and analyzed to determine the molar C t h t th t t hi h positive, indicating the fO 2 of WO 3 is patterns were taken at varying P T conditions and analyzed to determine the molar Current research suggests that at high 2 3 ti ll hi h th th t f WO volumes of each of the phases present Current research suggests that at high continually higher than that of WO 2 volumes of each of the phases present. pressures W 4+ becomes more stable than W 6+ continually higher than that of WO 2 pressures W 4+ becomes more stable than W 6+ for this pressure temperature A t in ili te melt oe i ting ith for this pressure – temperature A computer program in silicate melts coexisting with i Thi i di t th t WO h A computer program in silicate melts coexisting with regime. This indicates that WO 2 has called Fit2D reads the metal [3] regime. This indicates that WO 2 has called Fit2D reads the metal. [3]. a lower Gibbs free energy in this diffraction patterns a lower Gibbs free energy in this diffraction patterns regime making it the more stable t tb th dt t Gibb f dG SdT VdP regime, making it the more stable output by the detector Gibbs free energy : dG = -SdT + VdP h Thi ΔfO ii i l output by the detector Gibbs free energy : dG SdT + VdP phase This ΔfO 2 is increasingly and turns them into - for fixed T : dG = VdP phase. This ΔfO 2 is increasingly and turns them into - for fixed T : dG = VdP more positive as the pressure is lt f2 th t l more positive as the pressure is plots of 2-theta angle i d i WO ib i plots of 2 theta angle f increased, meaning WO 2 is becoming vs peak intensity We Relating Gibbs free energy and oxygen increased, meaning WO 2 is becoming vs. peak intensity. We Relating Gibbs free energy and oxygen more and more stable at increasing assign each peak a fugacity: more and more stable at increasing assign each peak a fugacity: pressure supporting the results h d t f G RTl fO pressure, supporting the results phase and a set of G (O2) = RTlnfO 2 f d ith [3] hil di i phase and a set of G (O2) RTlnfO 2 found with [3] while disproving my Miller indices which found with [3], while disproving my Miller indices which hypothesis dt i th l Unde t nding th t fo the t ng ten hypothesis. determine the molar Understanding that for the tungsten – determine the molar Understanding that for the tungsten volume of a particular tungsten oxide system volume of a particular tungsten oxide system phase for that x/2G G G phase for that x/2G (O2) = G (WOx) - G (W) diff ti tt (O2) (WOx) (W) diffraction pattern diffraction pattern. Therefore along an isotherm Therefore, along an isotherm References RTlnfO RTlnfO + ∫∆VdP References RTlnfO 2(P T) = RTlnfO 2(1 bar T) + ∫∆VdP Results RTlnfO 2(P,T) RTlnfO 2(1 bar, T) + ∫∆VdP f Results [1] Bouvier P et al ; “X -ray diffraction study of WO 3 at high - where the oxygen fugacity at 1bar is Results [1] Bouvier , P. et al.; X ray diffraction study of WO 3 at high ” J l f Ph i C d d M tt 14 (2002) where the oxygen fugacity at 1bar is pressure.” Journal of Physics: Condensed Matter 14 (2002) known leaving the only unknown term 33 WO d WO Vl P 6605-6617 known, leaving the only unknown term WO 2 and WO 3 - Volume vs. Pressure 6605 6617 [2] C b ll Ad J t l “Hi h ff t th i t b ∫∆VdP [2] The WO data was collected at various 31 2 3 [2] Campbell, Andrew J., et. al.; “High pressure effects on the iron– to be ∫∆VdP [2] The WO 2 data was collected at various 31 iron oxide and nickel–nickel oxide oxygen fugacity buffers ” to be ∫∆VdP . [2]. 2 temperatures (300 750 K) and iron oxide and nickel–nickel oxide oxygen fugacity buffers. h d l S 286 (2009) 6 6 temperatures (300-750 K) and 29 Measured Data WO 3 ‐ P2 1 /c Earth and Planetary Science Letters 286 (2009): 556-564 temperatures (300 750 K) and (0 G ) h Cl b h Measured Data 3 1 monoclinic [3] Cottrell Elizabeth et al; "Metal silicate partitioning of tungsten Thi el tion hip bet een ol me nd pressures (0-45 GPa)with NaCl being the 27 ) 300K Isothermal Equations of State monoclinic [3] Cottrell, Elizabeth, et. al; . Metal-silicate partitioning of tungsten This relationship between volume and pressures (0 45 GPa)with NaCl being the 27 ol) 300K Isothermal Equations of State at high pressure and temperature; implications for equilibrium This relationship between volume and pressure calibrant [5] The WO data /mo at high pressure and temperature; implications for equilibrium core formation in Earth " Earth and Planetary Science Letters pressure at a given temperature is known as pressure calibrant [5]. The WO 3 data 25 cc/ WO P2 /a core formation in Earth. Earth and Planetary Science Letters pressure at a given temperature is known as 3 300 K i th l i dt (c WO 3 – P2 1 /a li i 281.3-4 (2009): 275-287. an equation of state was 300 K isothermal compression data 23 me monoclinic 281.3 4 (2009): 275 287. [4] Dorogokupets Peter I Oganov Artem R ; “Ruby metals and an equation of state. was 300 K isothermal compression data. 23 um [4] Dorogokupets, Peter I., Oganov , Artem R.; Ruby, metals, and The published 300 K isothermal equations Vol WO P MgO as alternative pressure scales:A semiemperical The published 300 K isothermal equations 21 V WO 3 ‐ Pm MgO as alternative pressure scales: A semiemperical description of shock wave ultrasonic x ray and of state for each of the WO phases monoclinic description of shock -wave, ultrasonic, x-ray, and of state for each of the WO 3 phases 19 thermochemical data at high temperatures and pressures ” of state for each of the WO 3 phases ([ ] [ ] [ ]) dd b d 19 thermochemical data at high temperatures and pressures. Th A i Ph i l S it 024115 (1 6) (2007) ([1] [4] [7]) needed to be corrected WO ‐ monoclinic The American Physical Society . 024115-(1-6) (2007) ([1], [4], [7]) needed to be corrected, 17 WO 2 monoclinic [5] Fei et al “Toward an internally consistent pressure scale ” (2007) but results match well with the data [5] Fei et al. Toward an internally consistent pressure scale. (2007) P NtA dSi d i 10 1073/ 0609013104 ] but results match well with the data 15 Proc. Nat. Acad. Sci., doi:10.1073/pnas.0609013104.] ll td Th lti b ff 15 0 10 20 30 40 50 Hypothesis [6] Howard Christopher J et al ; “High-temperature phase collected The resulting buffer curves 0 10 20 30 40 50 Hypothesis [6] Howard, Christopher J., et al.; High temperature phase t iti i t t ti id th l t d?” J l f collected. The resulting buffer curves Pressure (GPa) transitions in tungsten trioxide—the last word?” Journal of showed trends that were expected prior Physics: Condensed Matter 14 (2002): 377-387 showed trends that were expected prior Physics: Condensed Matter 14 (2002): 377-387 [] l “C lb fh b 800 to the experiment As the pressure is increased the buffer curves move “up” the A ii d Ih th i d th t [7] Mao, H. K. et al., “Calibration of the ruby pressure gauge to 800 to the experiment. As the pressure is increased, the buffer curves move “up” the As pressure is increased I hypothesized that kbar under quasi hydrostatic conditions ” Journal of to the experiment. As the pressure is increased, the buffer curves move up the hf b h h d Of h O h h l 2 / O As pressure is increased, I hypothesized that kbar under quasi-hydrostatic conditions. Journal of graph for both phases tested Of the various WO 3 phases the monoclinic P2 /c WO 3 the WO and the WO buffer curves will increase Geophysical Research v.91, no. B5, (1986) 4673-4676 graph for both phases tested. Of the various WO 3 phases, the monoclinic P2 1 /c WO 3 the WO 2 and the WO 3 buffer curves will increase Geophysical Research v.91, no. B5, (1986) 4673 4676 [8] Righter Kevin et al ; "Metal silicate partitioning of siderophile phase was used for fO buffer calculations because thermal data were available for it 2 3 ti il t ith tt th [8] Righter , Kevin, et al.; . Metal-silicate partitioning of siderophile phase was used for fO 2 buffer calculations because thermal data were available for it at similar rates with respect to one another, elements and core formation in the early Earth." Annual 2 d it d th id t f th th h W l lt th fO at similar rates with respect to one another, elements and core formation in the early Earth. Annual Review of Earth and Planetary Sciences 31 (2003): 135 174 and it coverd the widest pressure range for the other phases We calculate the fO 2 thus maintaining a consistent log(fO ) distance Review of Earth and Planetary Sciences 31 (2003): 135-174. and it coverd the widest pressure range. for the other phases. We calculate the fO 2 thus maintaining a consistent log(fO 2 ) distance buffer curves by inputting pressure temperature and molar volume into the Birch 2 between them buffer curves by inputting pressure, temperature and molar volume into the Birch between them. Murhaghan equation of state: Murhaghan equation of state: Murhaghan equation of state: () 3 /2 [( /) 7/3 ( /) 5/3 ]{ 3/ ( ' )[ ( /) 2/3 ]} [2] P(V) = 3K 0 /2 [(V 0 /V) 7/3 - (V 0 /V) 5/3 ]{1+3/4(K 0 ' – 4)[ (V 0 /V) 2/3 – 1]} [2] P(V) = 3K 0 /2 [(V 0 /V) (V 0 /V) ]{1+3/4(K 0 4)[ (V 0 /V) 1]} [2]
Transcript of W-WO and WdW-WO OFitRltihitHihT t dPOxygen Fugacity ...W-WO 2 and WdW-WO 3 OFitRltihitHihT t...
W WO d W WO O F it R l ti hi t Hi h T t d PW-WO and W-WO Oxygen Fugacity Relationship at High Temperature and PressureW-WO2 and W-WO3 Oxygen Fugacity Relationship at High Temperature and PressureW WO2 and W WO3 Oxygen Fugacity Relationship at High Temperature and Pressure2 3TJ DTJ DeaneTJ Deane
Advisor: Dr Andrew CampbellAdvisor: Dr. Andrew CampbellAdvisor: Dr. Andrew Campbell
Introduction Experiment ConclusionIntroduction Experiment Conclusionp
ffUnderstanding different thermodynamic (b) (a)Understanding different thermodynamic 2”(b) (a)WWO2 - WWO3 Buffer Curve Comparison
properties of materials is important for a Thermocouple to WWO2 - WWO3 Buffer Curve Comparisonproperties of materials is important for a measure temperature 10p p p
i t f T t i d t lof sample
10
variety of reasons Tungsten is a moderately Wires connectingp
2 5variety of reasons. Tungsten is a moderately Wires connecting power supply to ”
5
siderophile element considered to be found inpower supply to heatersiderophile element considered to be found in heater 0p
both the o e nd ili te po tion of the2 WWO3 - 40 GPaboth the core and silicate portions of the ” (c) -5
WWO3 40 GPaWWO2 40 GPboth the core and silicate portions of the
2 (c) -5 WWO2 - 40 GPa
Earth x-ray”102) WWO3 - 20 GPaEarth. x ray
beam -10O2
WWO2 - 20 GPabeam
g(fO WWO2 - 20 GPa
WWO3 0 GPH t ( ) i l ti bl k
-15og WWO3 - 0 GPa
U d t di h t t b h dHeater (a), insulating block
15lo WWO2 - 0 GPaUnderstanding how tungsten behaves under
( ), g(b) and diamond anvil cell 20Understanding how tungsten behaves under
Detector(b), and diamond anvil cell -20
high temperature and pressure conditions canDetector (c) that were used tohigh temperature and pressure conditions can (c) that were used to
generate temperature and-25g p p
help to le d to bette nde t nding of hogenerate temperature and
help to lead to a better understanding of how pressure -30help to lead to a better understanding of how f
pressure 30
and under what conditions the core formed Sample along the x-ray beam line during trip to 35and under what conditions the core formed. Sample along the x ray beam line during trip to NSLS i B kh N Y k J l 2009
-35NSLS in Brookhaven New York, July 2009 0.0004 0.0006 0.0008 0.001 0.0012 0.0014, y 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
1/T (1/K)F ll d t di th t t id b ff
1/T (1/K) Fully understanding the tungsten oxide buffer X ray diffraction experiments were conducted at the National Synchrotron Light SourceFully understanding the tungsten oxide buffer X-ray diffraction experiments were conducted at the National Synchrotron Light Source system is essential for scientists who would
y p y g(NSLS) i B kh N Y k A hi h d di t d t th lsystem is essential for scientists who would By calculating the difference in(NSLS) in Brookhaven New York. A high powered x-ray was directed at the sampley
e t ng ten o ide me n of ont ollingBy calculating the difference in (NSLS) in Brookhaven New York. A high powered x ray was directed at the sample
use tungsten oxide as a means of controllingy g
f it b t WO dwhich was held within a diamond anvil cell to generate high pressures and surroundeduse tungsten oxide as a means of controlling f
oxygen fugacity between WO3 andwhich was held within a diamond anvil cell to generate high pressures and surrounded oxygen fugacity within their experiments
oxygen fugacity between WO3 and g g pby individually constructed heaters to generate high temperatures Multiple diffractionoxygen fugacity within their experiments. WO we find that the ΔfO is alwaysby individually constructed heaters to generate high temperatures. Multiple diffraction WO2 we find that the ΔfO2 is always by individually constructed heaters to generate high temperatures. Multiple diffraction
k i P T di i d l d d i h l2 2
positive indicating the fO of WO ispatterns were taken at varying P-T conditions and analyzed to determine the molarC t h t th t t hi h
positive, indicating the fO2 of WO3 is patterns were taken at varying P T conditions and analyzed to determine the molar Current research suggests that at high
pos t e, d cat g t e O2 o O3 sti ll hi h th th t f WOvolumes of each of the phases presentCurrent research suggests that at high continually higher than that of WO2
volumes of each of the phases present. pressures W4+ becomes more stable than W6+ continually higher than that of WO2
p ppressures W4+ becomes more stable than W6+
for this pressure temperatureA tpin ili te melt oe i ting ith
for this pressure – temperature A computer programin silicate melts coexisting withp p
i Thi i di t th t WO hA computer program in silicate melts coexisting with regime. This indicates that WO2 hascalled Fit2D reads themetal [3]
regime. This indicates that WO2 has called Fit2D reads the metal. [3]. a lower Gibbs free energy in thisdiffraction patterns a lower Gibbs free energy in this diffraction patterns gregime making it the more stable
d act o patte st t b th d t tGibb f dG SdT VdP
regime, making it the more stable output by the detectorGibbs free energy : dG = -SdT + VdPeg e, a g t t e o e stab eh Thi ΔfO i i i l
output by the detector Gibbs free energy : dG SdT + VdP phase This ΔfO2 is increasinglyand turns them into- for fixed T : dG = VdPphase. This ΔfO2 is increasingly and turns them into - for fixed T : dG = VdP more positive as the pressure isl t f 2 th t l more positive as the pressure is plots of 2-theta angle p pi d i WO i b i
plots of 2 theta angle
fincreased, meaning WO2 is becomingvs peak intensity WeRelating Gibbs free energy and oxygenincreased, meaning WO2 is becoming vs. peak intensity. We Relating Gibbs free energy and oxygen more and more stable at increasingassign each peak afugacity:more and more stable at increasing assign each peak a fugacity:
gpressure supporting the results
ass g eac pea ah d t f
g yG RTl fO
pressure, supporting the results phase and a set ofG(O2) = RTlnfO2p essu e, suppo t g t e esu tsf d ith [3] hil di i
phase and a set of G(O2) RTlnfO2 found with [3] while disproving myMiller indices which( ) found with [3], while disproving my Miller indices which hypothesisd t i th lUnde t nding th t fo the t ng tenhypothesis. determine the molarUnderstanding that for the tungsten –ypdetermine the molar Understanding that for the tungsten
volume of a particulartungsten oxide system volume of a particular tungsten oxide system phase for thatx/2G G G phase for that x/2G(O2) = G(WOx) - G(W)p ase o t atdiff ti tt
/ (O2) (WOx) (W) diffraction patterndiffraction pattern.
Therefore along an isothermTherefore, along an isothermReferences
, gRTlnfO RTlnfO + ∫∆VdP ReferencesRTlnfO2(P T) = RTlnfO2(1 bar T) + ∫∆VdP ResultsRTlnfO2(P,T) RTlnfO2(1 bar, T) + ∫∆VdP
fResults
[1] Bouvier P et al ; “X-ray diffraction study of WO3 at high- where the oxygen fugacity at 1bar isResults
[1] Bouvier, P. et al.; X ray diffraction study of WO3 at high ” J l f Ph i C d d M tt 14 (2002)
where the oxygen fugacity at 1bar is pressure.” Journal of Physics: Condensed Matter 14 (2002) known leaving the only unknown term
33WO d WO V l P
p y ( )6605-6617known, leaving the only unknown term WO2 and WO3 - Volume vs. Pressure 6605 6617
[2] C b ll A d J t l “Hi h ff t th i
, g yt b ∫∆VdP [2] The WO data was collected at various 31
2 3
[2] Campbell, Andrew J., et. al.; “High pressure effects on the iron–to be ∫∆VdP [2] The WO2 data was collected at various 31 [ ] p , , ; g piron oxide and nickel–nickel oxide oxygen fugacity buffers ”
to be ∫∆VdP. [2]. 2temperatures (300 750 K) and iron oxide and nickel–nickel oxide oxygen fugacity buffers.
h d l S 286 (2009) 6 6temperatures (300-750 K) and 29 Measured DataWO3 ‐ P21/c Earth and Planetary Science Letters 286 (2009): 556-564temperatures (300 750 K) and
(0 G ) h Cl b hMeasured Data 3 1/
monoclinic y ( )[3] Cottrell Elizabeth et al; "Metal silicate partitioning of tungstenThi el tion hip bet een ol me nd pressures (0-45 GPa)with NaCl being the 27) 300K Isothermal Equations of State
monoclinic[3] Cottrell, Elizabeth, et. al; . Metal-silicate partitioning of tungsten This relationship between volume and pressures (0 45 GPa)with NaCl being the 27
ol) 300K Isothermal Equations of State
at high pressure and temperature; implications for equilibriumThis relationship between volume and
pressure calibrant [5] The WO data /mo
at high pressure and temperature; implications for equilibrium core formation in Earth " Earth and Planetary Science Letterspressure at a given temperature is known as pressure calibrant [5]. The WO3 data 25cc
/
WO P2 /a core formation in Earth. Earth and Planetary Science Letterspressure at a given temperature is known as p [ ] 3300 K i th l i d t
(c WO3 – P21/a li i 281.3-4 (2009): 275-287.an equation of state was 300 K isothermal compression data 23m
e monoclinic 281.3 4 (2009): 275 287. [4] Dorogokupets Peter I Oganov Artem R ; “Ruby metals andan equation of state. was 300 K isothermal compression data. 23
um [4] Dorogokupets, Peter I., Oganov, Artem R.; Ruby, metals, and qThe published 300 K isothermal equations Vo
l
WO P MgO as alternative pressure scales: A semiempericalThe published 300 K isothermal equations 21V WO3 ‐ Pm MgO as alternative pressure scales: A semiempericaldescription of shock wave ultrasonic x ray and
p qof state for each of the WO phases monoclinic description of shock-wave, ultrasonic, x-ray, and of state for each of the WO3 phases 19
thermochemical data at high temperatures and pressures ”of state for each of the WO3 phases ([ ] [ ] [ ]) d d b d
19thermochemical data at high temperatures and pressures. Th A i Ph i l S i t 024115 (1 6) (2007)([1] [4] [7]) needed to be corrected WO ‐monoclinic The American Physical Society. 024115-(1-6) (2007)([1], [4], [7]) needed to be corrected, 17 WO2 monoclinic y y ( ) ( )
[5] Fei et al “Toward an internally consistent pressure scale ” (2007)but results match well with the data [5] Fei et al. Toward an internally consistent pressure scale. (2007) P N t A d S i d i 10 1073/ 0609013104 ]
but results match well with the data 15 Proc. Nat. Acad. Sci., doi:10.1073/pnas.0609013104.]ll t d Th lti b ff
150 10 20 30 40 50Hypothesis , /p ]
[6] Howard Christopher J et al ; “High-temperature phasecollected The resulting buffer curves 0 10 20 30 40 50Hypothesis [6] Howard, Christopher J., et al.; High temperature phase t iti i t t t i id th l t d?” J l f
collected. The resulting buffer curves Pressure (GPa)ypo
transitions in tungsten trioxide—the last word?” Journal of showed trends that were expected prior( )
gPhysics: Condensed Matter 14 (2002): 377-387showed trends that were expected prior Physics: Condensed Matter 14 (2002): 377-387
[ ] l “C l b f h b 800
p pto the experiment As the pressure is increased the buffer curves move “up” theA i i d I h th i d th t [7] Mao, H. K. et al., “Calibration of the ruby pressure gauge to 800 to the experiment. As the pressure is increased, the buffer curves move “up” theAs pressure is increased I hypothesized that [ ] , , y p g g
kbar under quasi hydrostatic conditions ” Journal ofto the experiment. As the pressure is increased, the buffer curves move up the
h f b h h d Of h O h h l 2 / OAs pressure is increased, I hypothesized that
kbar under quasi-hydrostatic conditions. Journal of graph for both phases tested Of the various WO3 phases the monoclinic P2 /c WO3the WO and the WO buffer curves will increase Geophysical Research v.91, no. B5, (1986) 4673-4676graph for both phases tested. Of the various WO3 phases, the monoclinic P21/c WO3the WO2 and the WO3 buffer curves will increase Geophysical Research v.91, no. B5, (1986) 4673 4676[8] Righter Kevin et al ; "Metal silicate partitioning of siderophile
3 3phase was used for fO buffer calculations because thermal data were available for it
2 3t i il t ith t t th [8] Righter, Kevin, et al.; . Metal-silicate partitioning of siderophilephase was used for fO2 buffer calculations because thermal data were available for it at similar rates with respect to one another,
elements and core formation in the early Earth." Annualp 2
d it d th id t f th th h W l l t th fOat similar rates with respect to one another,
elements and core formation in the early Earth. Annual Review of Earth and Planetary Sciences 31 (2003): 135 174and it coverd the widest pressure range for the other phases We calculate the fO2thus maintaining a consistent log(fO ) distance Review of Earth and Planetary Sciences 31 (2003): 135-174. and it coverd the widest pressure range. for the other phases. We calculate the fO2thus maintaining a consistent log(fO2) distance
buffer curves by inputting pressure temperature and molar volume into the Birchg g 2
between them buffer curves by inputting pressure, temperature and molar volume into the Birch between them. y p g p , pMurhaghan equation of state:
bet ee t eMurhaghan equation of state:Murhaghan equation of state:( ) 3 /2 [( / )7/3 ( / )5/3]{ 3/ ( ' )[ ( / )2/3 ]} [2]P(V) = 3K0/2 [(V0/V)7/3 - (V0/V)5/3]{1+3/4(K0' – 4)[ (V0/V)2/3 – 1]} [2]P(V) = 3K0/2 [(V0/V) / (V0/V) / ]{1+3/4(K0 4)[ (V0/V) / 1]} [2]
