GEOS 425 Whole Earth Geochem BSU Final Review

What defines a trace element?
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Blundy and Wood ModelD(initial)*exp(4pi*(young's)*(atomsinmole)*(optimal_radius)/2*(exchange radius - optimal)^2*1/3(exchange - optimal)^3))/(R*T)Equilibrium (batch) meltingMelt always in eq with solids. C(l)/C(s) = 1/(D(1-F) + F)Fractional meltingMelt and solids not in eq: C(l)/C(i) = (1/D)*(1-F)^(1/D-1)Accumulated fractional meltaccumC(l)/C(i) = (1-(1-F)^(1/D))/F (EQUALS batch melt!)Eq (batch) crystallizationSolids in eq with const. melt. C(l)/C(i) = 1/(DX+1(1-X)) and C(s) = DC(l)Fractional crystallization (instantaneous melt)Solids not in eq. with const. melt C(l)/C(i) = (1-X)^(D-1)Fractional crystallization (instantaneous solid)C(s)/C(i) = D(1-X)^(D-1)Aggregate frac. crystalaggC(s)/C(i) = (X^D)/X (EQUALS batch crystal)Valley of stabilitystable nuclides have nearly even numbers of proton and neutrons; however, electrostatic repulsion of protons is buffered by excess neutrons, giving the valley of stability its curvatureIstopes and isobarsIsotopes=same element (Z), different # of N. Isobars = isotopes of roughly same mass, can throw off a mass specGamma decayemission of high energy (and frequency) photonSpontaneous Fissionsplitting of U-235,238 Th-232 into two or more mod. heavy daughters (which decay by B-minus)Alpha decayEmission of helium nucleus (alpha particle)Beta minusemission of an alectron and associated conversion of a neutron to a protonPositron Decay (Beta Plus)emission of a positron and assoicated onversion of a proton to a neutronElectron captureAddition of an electron to a nucleus, with accompanying conversion of a proton to a neutronDecay constantProportionality constant of probability nuclide will decay, Costant = ln(2)/(t-1/2)Half life (t-1/2)Time it takes for half of the parent nuclides to undergo decay t-1/2 = ln(2)/decay constantEquation for parent decayN = N(i)*exp(-decay*t) to back track to inital N(i) = N*exp(+decay*t)Equation for daughter generationD*= N(i)(1-exp(-decay*t)Age equationt = 1/(decay)*ln((D-D(i))/N + 1) = 1/(decay)*ln(D*/N + 1)1st tenet of geochron1). Rock or mineral system has neither gained nor lost either parent or daughter atoms so that the D*/N has only been changed due to rad. decay2nd tenet of geochron2). It must be possible to assign a realistic value to D(i) (easier when D*>>D(i))3rd tenet of geochron3). The value of decay constant must be known accurately and should be appropriate to the timescales being considered4th tenet of geochronThe measurements of D and N must be accurate and representative of the rock or mineral to be datedModel agesIf D(i) << D*, D* ~ D, age is insensitive to D(i), so can ignore D(i) or assume DK-Ar model datingUses 40K-40Ar ratios, since Ar is a gas which is easily lost from high temp minerals and magmasZircon U-PbU-238/Pb-206 and U-235/Pb-207 in zircons exclude D(i), (Pb) while incoprorating N, thus allowing for D(0) << D*Isochrons: example Rb-SrIf D(0-initial) is high? Isochron plot with 87Sr/86Sr vs. 87Rb/86SrLinear equation of Rb-Sr87/86Sr(t) = (87/86Sr)(i) + (87Rb/86Sr)(exp(decay*t)-1)87Sr/86Sr of Earth systemsBABI (initial) ->over time -> high Rb/Sr in crust created at 3.8 Ga and low Rb/Sr depleted at 3.8 GaSr in hydrosphereSeawater Sr is a mixture of three sources: 1) continental-derived Sr (relatively high 87Sr/86Sr); 2) mantle-derived Sr from the mid-ocean ridge system (relatively low 87Sr/86Sr); 3) recycled Sr from Phanerozoic marine carbonates (relatively low 87Sr/86Sr)