What is an isotope?

A Nuclide Z X Z = atomic number = number of protons A = mass number = number of nucleons (protons + neutrons) N = neutron number = number of neutrons, i.e. N = A–Z

The same Z – isotopes The same A – isobars Vojtěch Janoušek:

Radiogenic isotope geochemistry Relative atomic mass • Dalton (or atomic mass unit - a.m.u.) and geochronology = 1/12 of the mass of 12C

Periodic table of elements Radioactive decay

D.I. Mendeleev Decay constant λ reflects the stability of atoms = what is the proportion of atoms that decay in given time t NNe 0

t D  D0  Ne 1

Half-life t1/2 = how long it takes for half of the atoms to decay

ln20693 . t 1  2 

1 Types of radioactive decay Types of radioactive decay

-β decay 87 Rb 87Sr 176 Lu  176 Hf 187  187 α decay Re Os

147Sm 143Nd +β decay

Types of radioactive decay Example of branched decay

Spontaneous fission

2 Example of decay chain (238U) Calculating age and initial ratio

• Radioactive isotope (87Rb, 147Sm, ...) • Radiogenic isotope (87Sr, 143Nd, ...) • Stable isotope (86Sr, 144Nd, ...)

• R (radioactive isotope to stable) e.g., (87Rb/86Sr) , (147Sm/144Nd)

I (radiogenic isotope to stable) e.g., (87Sr/86Sr), (143Nd/144Nd)

Calculating age and initial ratio Radiogenic/radioactive/stable isotopes

t 143 143 I  I i  Re 1  Nd Nd   144  144  1 Nd Nd i 143 143 147 t  ln 1 Nd Nd Sm t 147 144  144  144 e 1   Sm  Nd Nd i Nd    144 Nd  87 87 87 Sr Sr Rb t 86  86  86 e 1 Sr Sr i Sr 176 Hf 176 Hf 176 Lu   et 1 177 Hf 177 Hf 177 Hf i 1  I  Ii  187 187 187 t  ln 1 Os Os Re t  R 186  186  186 e 1   Os Os i Os Treatise on Geochemistry kap. 3.08: Geochronology and etc. Thermochronology in Orogenic Systems (K. V. Hodges)

3 Rb–Sr method Sr isotopes

Rubidium rubidium strontium 87Rb is –β radioactive: • Alkali, lithophile element Isotopic composition (%) λ = 1.42 . 10–11 yr–1 85Rb 72.1654 84Sr 0.56 87 87 0 • Substitutes for K Rb Sr 1e   Q 87 86 (Steiger & Jäger 1977) (K-feldspars, micas, some clay Rb 27.8346 Sr 9.86 87 minerals, evaporites…) Sr 7.0 88 Sr 82.58 87 87 87 Sr Sr Rb t Relative atomic weight 86  86  86 e 1 Sr Sr i Sr Rb 85.46776 84Sr 83.9134 Strontium 86Sr 85.9092 • Alkaline earth; ion radius 87 87 87Sr 86.9088  Sr Sr    somewhat greater than that 86  86 of Ca, substitutes for Ca 88Sr 87.9056 1  Sr Sr i  t  ln 87 1 (plagioclase, carbonates, apatite…),   Rb    sometimes also K (K-feldspars)  86 Sr  • Rb is strongly incompatible element, thus its amount and Rb/Sr ratio rise with fractionation (esp. high in pegmatites)

Rb–Sr method Isochrons

Approx. blocking temperatures Possible applications Initial ratios are obtained for Rb–Sr system:  87 Sr 87 Sr  • Cooling of plutonic rocks (blocking • Mineral lacking the radioactive element   orthoclase 320 ºC 86  86 temperatures << solidus), crystallization of (e.g., apatite – contains nearly no Rb) 1 Sr Sr i biotite 350 ºC t  ln 1 volcanic rocks (quick solidification) • Mineral extremely rich in radioactive element,  87  muscovite 450–500 ºC  Rb soon dominated by the radiogenic component   • Dating of mineralization (using cogenetic  86 Sr  minerals – muscovite, biotite, adularia) Mezger (1990) (e.g. lepidolite – rich in Rb)

Isochron method Appropriate material for Rb–Sr dating The samples define an isochron, if they:  Mineral isochrons from plutonic rocks • are cogenetic (identical source – thus share the same initial ratios) o K-rich minerals (high Rb/Sr): K-feldspars (orthoclase, adularia), micas (muscovite, biotite, lepidolite), leucite • were contemporaneous (the same age) o Combined with Ca-rich minerals that are rather Rb poor (low Rb/Sr ratio): • formed closed isotopic system throughout plagioclase, apatite, ilmenite, amphibole, pyroxene their history  Whole-rock samples • (there is a sufficient spread in compositions, i.e. in 87Rb/86Sr ratios)

4 Isochrons Sm–Nd method

Samarium and neodymium samarium neodymium 87Sr 87 Sr 87 Rb t • Light Rare Earth Elements (LREE) Isotopic composition(%) 86  86  86 e 1 Sr Sr Sr • LREE form own minerals i 144Sm 3.1 142Nd 27.13 Biotite (monazite, allanite, bastnäsite); 147Sm 15.0 143Nd 12.18 •Substitute for Ca2+ a Th4+ in 148Sm 11.3 144Nd 23.80 y = a + bx rock-forming minerals (mainly 149Sm 13.8 145Nd 8.30 plagioclase, biotite, apatite) K-feldspar 150Sm 7.4 146Nd 17.19 • Incompatible elements, i.e. 152 148 Amphibole Sm 26.7 Nd 5.76 concentrations of Sm and Nd 154Sm 22.7 150Nd 5.64 increase with geochemical Plagioclase fractionation

Geochronologically significant is decay of 147Sm:

147  143 1 Sm Nd intercept a slope b ~ age t  lnb 1 Initial ratio 143 143 147 –12 –1  Nd Nd Sm t λ = 6.539 × 10 yr 144  144  144 e 1 (Lugmair & Marti 1978) Nd Nd i Nd

Sm–Nd method Sm–Nd method

Possible dating applications • Cooling of basic intrusions • Evolution of terrestrial Nd is explained by the model of a primitive mantle reservoir with Sm/Nd ratio of chondritic meteorites, so-called CHUR • Crystallization of basic volcanic rocks (rapid cooling) – (Chondritic Uniform Reservoir or Bulk Earth: DePaolo 1988) with present-day they are difficult to date by the Rb/Sr and U/Pb methods (especially if very old, partly altered and do not contain zircon) isotopic composition: 147 144 • Dating high-grade metamorphism Sm/ NdCHUR = 0.1967 143 144 (granulite- and eclogite-facies) Nd/ NdCHUR = 0.512638 (Jacobsen & Wasserburg 1980)

Appropriate material for Sm–Nd dating  Minerals from (ultra-)basic igneous rocks SA pyroxene, amphibole, plagioclase, ilmenite, apatite, 143Nd monazite, zircon… 144 143 144 i Nd 4  Garnet (+ Cpx) in metamorphic rocks Small differences in Nd/ Nd  i 110 Nd CHUR  Whole-rock samples ratios → initial composition of 143Nd the Nd is normally expressed  144 using the ε notation Nd Nd i

Where: index „i“ denotes initial ratio, SA = sample

5 Nd isotopes Nd model ages

trivalent REE – lanthanide Sm/Nd decreases during differentiation , Model age = moment in the past contraction, Nd shows greater ionic thus mantle develops higher 143Nd/144Nd when Nd isotopic composition of the radius than Sm and thus the ratios than crust sample was identical with that of some Sm/Nd decrease during geochemical model reservoir (most often CHUR or fractionation; this fractionation is still Depleted Mantle — DM). comparably limited

Parcial melting of CHUR Melt — depleted in Sm, Sm/Nd ratio is lower than that of CHUR Residue — enriched in Sm, higher Sm/Nd ratio The melt-depleted mantle domains develop, over time, 143Nd/144Nd greater than CHUR (so-called Depleted Mantle, DM – DePaolo 1988) Isotopic provinces of the Western U.S. based on

crustal residence times (ΤDM) (Bennett and DePaolo 1987)

Lu–Hf method Lu–Hf method

Lutetium lutetium hafnium Appropriate material for Lu–Hf dating • The heaviest among REE Isotopic composition (%) • Usage analogous to the Sm–Nd method • Enters the crystal structure of • Shorter half life and higher Lu/Hf ratios of common rocks and minerals result many accessories: allanite, 175Lu 97.4 174Hf 0.16 in greater variability of the Hf isotopic composition (= advantage) monazite, apatite and titanite 176Lu 2.6 176Hf 5.2 177Hf 18.6 178 Hafnium Hf 27.1 Mineral phases in igneous and metamorphic rocks 179Hf 13.7 • Transition metal 180Hf 35.2 • High Lu/Hf: titanite, apatite, monazite, allanite • Geochemical behaviour strongly •LowLu/Hf: zircon = ideal mineral for Hf isotopic studies: resembles Zr, for which it readily substitutes in accessory minerals – Hf substitutes into the crystal lattice (and is thus relatively immobile) (zircon) – High concentrations of Hf and low Lu/Hf ratios in zircon require (almost) 176 • Lu shows branched decay: no age correction for the initial ratios 1 -β emission l = 1.94 × 10–11 yr –1 – Is often combined with in situ U–Pb dating, (97 % of decays) mostly using LA ICP-MS 176 Lu  176 Hf   (Patchett & Tatsumoto 1980) Whole-rock samples 2 Electron capture (3 % of decays) no geochronological meaning • Acid as well as basic (Lu/Hf ratio decreases with geochemical fractionation)

6 Lu–Hf method Lu–Hf method

Petrogenesis of igneous rocks Small differences in 176Hf/177Hf → initial ratios of Hf isotopes are usually expressed as: Isotopic evolution of Hf in a chondritic reservoir, in an igneous rock, formed by its partial melting, and in residue of this partial melting 176 SA (Faure 1986) Hf 177 i Hf i 4  Hf 110 176 CHUR Hf 177 Hf i

Where: index „i“ = initial ratio, SA = sample, CHUR = Chondritic Uniform Reservoir

εHf < 0: rock originated from (or assimilated significant amount of) material with Lu/Hf lower than CHUR (e.g., old crustal rocks).

εHf > 0: rock comes from a source with high Lu/Hf (e.g. mantle domains impoverished in incompatible elements due to previous partial melting – 176 177 176 177 Lu/ HfCHUR = 0.0334 a Hf/ HfCHUR = 0.28286 Depleted Mantle = DM) (Patchett & Tatsumoto 1980)

K–Ar and Ar–Ar methods K–Ar and Ar–Ar methods

Potassium potassium argon • Alkali metal 40K is radioactive with branched decay Isotopic composition (%) • Lithophile element th 1. -β emission (88.8 % of decays) (8 most common 39K 93.2581 36Ar 0.337 in the Earth‘s crust) 40 38 K 0.01167 Ar 0.063 40 40 0 –10 –1 K Ca e λβ = 4.962 . 10 yr • Three naturally occurring 41K 6.7302 40Ar 99.600 1 39 40 41 isotopes: K, K, K Relative atomic mass 2. Electron capture (11.16 % of decays) A (K) 39.098304 A (Ar) 39.9476 r r 40 0 40 –10 –1 K 1e Ar   λEC = 0.581 . 10 yr Argon

nd •2most common noble gas 3. +β emission (0.001 % of decays) • Three naturally occurring 40 K40Ar 0e  2 isotopes: 36Ar, 38Ar, 40Ar 1

Total decay constant for 40K: –10 –1 λ = λEC + λβ = 5.543 . 10 yr

7 K–Ar method K–Ar method

Reasonable age by the K–Ar method Argon loss is caused usually by: can be obtained if: • Regional metamorphism (increased P–T, recrystallization)  Mineral has represented a closed • Increased T or even partial melting due to contact metamorphism system for 40Ar and potassium throughout the history • Inability of the crystal lattice to retain Ar (even at low P–T)  Amount of extraneous 40Ar is negligible • Chemical weathering and hydrothermal alteration or can be reasonably corrected for • Dissolution and reprecipitation of the evaporites  Potassium isotopic composition is • Mechanical breakage of the minerals (even gridding!) normal and has not changed due to • Lattice damage by the radioactive decay fractionation (relatively light element)

39 1 39 1 19 K  0 n18 Ar1p

K–Ar method Ar–Ar method

Non-radiogenic Ar Ar–Ar method • Modification of the classic K–Ar technique Extraneous Ar • Sample irradiation by fast neutrons in a nuclear reactor: • Inherited Ar (originated in the rock by radioactive decay before the dated event) 39 39 • Excess Ar K (n,p) Ar, i.e.: (captured by minerals due to diffusion from surroundings) • Ar can be captured esp. by minerals with large hollows in their structure (beryl, cordierite, tourmaline, often also pyroxene) 39 1 39 1 19 K  0 n18 Ar1p Atmospheric Ar • Ar gained from atmosphere (adsorption at the grain boundaries, microcracks) • Thus produced 39Ar is analysed in the same fraction as 40Ar → it eliminates the problems with sample inhomogeneity, easier analytics • Incremental heating technique or laser ablation: – useful for samples that suffered a partial Ar loss –(in situ measurement)

8 Ar–Ar method Re–Os method

Using Ar–Ar method of dating Rhenium rhenium osmium • Fresh, unaltered samples • Transition metal Isotopic composition (%)

• Binary plots of fraction of the • Rare in rock-forming minerals, 185Re 37.4 184Os 0.02 released Ar (0–100 %) vs. 40Ar/39Ar more common in sulphides or 187Re 62.6 186Os 1.58 REE minerals • Dating of volcanic rocks, including 187Os 1.6 pyroclastics (phenocrysts of K-rich 188Os 13.3 minerals, e.g. K-feldspar, micas, 189Os 16.1 amphibole) – stratigraphy Osmium 190Os 26.4 192Os 41.0 • Low blocking temperatures of Ar–Ar • Transition metal from the Pt group system in minerals – ‚cooling ages‘ (PGE) • Bothe elements are chalcophile and siderophile, i.e. are concentrated in Approx. blocking temperatures for sulphidic phase (with iron) K(Ar)–Ar system: amphibole 500–450 ºC 187Re is -β radioactive: muscovite 350–400 ºC 187 Re 187Os biotite 300 ºC

microcline 150–200 ºC –11 –1 Amphibole from metagabbro, Mariánské Lázně l = 1.64 × 10 yr (Lindner et al. 1989) Mezger (1990) Complex, Czech Rep. (Dallmeyer & Urban 1998)

Re–Os method Re–Os method

Isochron method Evolution of terrestrial Os • Present-day CHUR composition:

187 187 187 187 186 Os Os Re t Re/ OsCHUR = 3.3 186  186  186 e 1 187 186 Os Os i Os Os/ OsCHUR = 1.06 (Walker et al. 1989)

• Re is incompatible element, Possible application i.e. is concentrated in melt • Dating of sulphide deposits • Os is strongly compatible element, and thus remains in • Dating of iron meteorites the residue after melting 6 • Geochronology and petrogenesis of • During differentiation, the ultrabasic rocks (esp. Precambrian) Re–Os isochron for komatiites from Monro Re/Os ratio increases, and Township (Walker et al. 1989) therefore the mantle develops • Mineral phases rich in Re and Theoretical evolution of Os isotopes in to (much) lower 187Os/186Os poor in Os chondritic mantle and continental crust then the crust • Especially sulphides – molybdenite, PGE minerals (Allegre & Luck 1980) http://www.geo.cornell.edu/geology/classes/Geo656/656home.html http://www.geo.cornell.edu/geology/classes/Geo656/656home.html

9 Pb isotopes U–(Th)–Pb dating of accessory phases

Uranium uranium lead Concordant ages • With Th belong to actinides Isotopic composition (%) t(207Pb/206Pb) = t(207Pb/235U) = t(206Pb/238U) = t(208Pb/232Th) • Three naturally occurring isotopes 234U 0.0057 204Pb 1.4 235 206 • 235U and 238U are radioactive and U 0.7200 Pb 24.1 238 207 form decay chains with 207Pb U 99.2743 Pb 22.1 Discordant ages 208 206 Pb 52.4 and Pb as end products • Lead loss from damaged crystal lattice 234 • U is intermediate product of the • Gain of U or Th 238U decay chain 238U  206 Pb Thorium 235 207 Concordia = a curve onto which fall all the • Six naturally occurring isotopes; U  Pb concordant analyses: only 232Th has a long half-life 238U/235U = 137.88 t(207Pb/235U) = t(206Pb/238U) • 232Th forms a decay chain with 208Pb as an end product 232Th 208 Pb • Isotopes 227, 228, 230, 231 and 204Pb is non-radiogenic isotope 234 are intermediate members of 238U decay chains of 232Th, 235U and 238U   204Pb

Concordia diagram Interpretation of discordant data

Wetherill graph 207Pb* /235U–206Pb*/238U (Concordia diagram) • Used for U-rich accessories: zircon, monazite, titanite, apatite, rutile…) • 207Pb*, 206Pb*= radiogenic Pb (corrected for non- radiogenic, ‚common‘ lead) e.g. by model of Stacey & Kramers (1975)

206 Pb*  e1t 1 238U (Parrish & Noble 2003) 207 Pb*  e2t 1 235U

10 Internal structure of the zircon crystals SHRIMP

Corfu et al. (2003) • BSE (back-scattered electrons) SHRIMP = Sensitive High-resolution Ion MicroProbe • CL (cathodoluminescence) • in-situ analysis, secondary beam of Pb ions triggered by bombardment of the sample by light ions (such as oxygen) (SIMS)

Advantages • Dating directly in the thin section • Dating of individual zones of zircon crystals • (In combination with CL, BSE) – dating zircons with complex inheritance, from polymetamorphic terrains with complex history • High spatial resolution (~10–20 μm)

Disadvantages • Complex instrumentation (interferences) • Slow (1 pt. ~ 30 min.) • Expensive, not easily accessible

 LA ICP-MS Dating monazite by electron microprobe



LA ICP-MS Chemical dating of monazite by electron microprobe (Suzuki et al. 1994) (Laser-Ablation Inductively-Coupled Plasma Mass-Spectrometry) Th U U Advantages Pb  e 232t 1208  0.9928e 238t 1206  0.0072e235t 1207 • Dating directly in the thin section 232 238.04 238.04

• Dating of individual zones of zircon crystals (Montel et al. 1996) • Much cheaper than SHRIMP Advantages • Much quicker (1 pt. ~ several min) • Dating directly in the thin section • Extremely quick and cheap method, ideal for study of unknown Disadvantages (polymetamorphic) terrains, sediment provenance • Complex instrumentation • High spatial resolution several μm) • Lower spatial resolution than SHRIMP Disadvantages • Imprecise • All Pb is considered to be radiogenic (no correction on ‘common lead’ can be applied)

Comparison of SHRIMP (SIMS) and LA ICP-MS dating of zircon (Košler & Sylvester 2003)

11 Fission track method

Accumulation of spontaneous • Method based on natural decay of fission tracks uranium by spontaneous fission of 238U. Polished section • Counting the number of fission tracks in through crystal natural sample. It is proportional to the U concentration, age and the well-known Spontaneous tracks etched decay constant. Surface Confined • The U concentration is obtained from the External mica proportion of induced fission-tracks after detector attached

irradiation with thermal neutrons in a Thermal neutron nuclear reactor or is measured directly irradiation, induced fission (e.g. by LA ICP MS). tracks register in detector

• Dating cooling of accessory minerals, Induced tracks etched e.g. apatite, zircon, titanite only in detector

Plan view of several crystals

B Mirror B C image C

A A Grain mount showing External detector showing (Goncalves et al. 2005) spontaneous tracks in induced tracks defining the individual grains grain outlines

Processes determining/modifying the Using Sr–Nd isotopes I. – magma sources composition of magmatic rocks

Low Rb/Sr Low Sm/Nd Closed system High Rb/Sr The magma develops without

εNd < 0 High Sm/Nd any exchange of material with

the surroundings (

r r S

Rock originated from (or S

6 6

8 8

/ / r

r Crustal S

assimilated much material • Fractional crystallization, S

7

7 8 8 contaminant derived from) a source with crystal accumulation…

Sm/Nd ratio lower than Pristine SiO2 • Isotopic composition still melt CHUR (e.g., old crust) UPPER reflects that of the source CRUST Young Pristine εNd > 0 melt Open system ab Rock comes form a source Isotopic composition of the 1/Sr 1/Sr with high Sm/Nd source is not preserved as a result of: (e.g., mantle depleted by Old Development of 87Sr/86Sr composition in a fractionating the previous extraction of crust  Hybridization mantle-derived igneous suite. a Closed-system fractional basaltic magma; (magma mixing) crystallization, b Contamination, followed by closed-system LOWER High Rb/Sr fractionation (after Briquet & Lancelot 1979) Depleted Mantle = DM) CRUST Low Sm/Nd  Contamination by country rocks (often in the form of AFC)  Late alterations http://www.geo.cornell.edu/geology/classes/Geo656/656home.html

12 Pb isotopes Using Sr–Nd isotopes II. – binary mixing

(Sr / Nd) > (Sr / Nd) 1 21

• Continental crust shows much higher average U, Th and Pb α = concentrations than mantle (> 10 ppm Pb in continental 10

α Nd = crust vs. < 1 ppm Pb in Earth‘s mantle); 2 144 α = 1 Nd α = 143 0 • This in principle applies also to oceanic crust, including the .5

marine sediments α = 0.1

0.5110 0.5115(Sr 0.5120/ Nd) 0.5125 0.5130 21 < (Sr / Nd) 2 • Therefore, Pb isotopes = highly 0.704 0.706 0.708 0.710 0.712 sensitive indicator of crustal 87Sr 86Sr contamination

• Currently 93.7% of natural U is 238U, therefore the 206Pb/204Pb is the ratio of choice to examine the crustal contamination of mantle- derived magma

(A: Sr = 400 ppm; B: Sr = 100 ppm) (A: Sr = 100 ppm, Nd = 2 ppm; B: Sr = 200 ppm, Nd = 20 ppm)

Using Sr–Nd isotopes III. – AFC Diffusion

• Composition of the Assimilant r = 0.2Assimilant r = 0.5 1. Grain-boundary diffusion resulting magma does

Sr D Sr D • (relatively quick) transport in fluid phase D D D

6 D D

= 8 86 = =

= = not plot onto a tie line = =

0 0 0 2 1 2 1 . . . 9 9 7 Sr Sr

between both end 7 8 87 .7 D = 0 1 2. Volume diffusion members, unlike in the D = 0.0 = 0.001 .001 D case of binary mixing. Initial liquid D = 0 Initial liquid • (relatively slow) material transport through the crystal lattice 0.700 0.710 0.720 0.700 0.710 0.720 0 200 400 600 0 200 400 600 • compensates the gradient of concentration, temperature or chemical potential Sr (ppm) Sr (ppm) • speeded up by the presence of crystal lattice imperfections (dislocations, vacancies)

Initial liquid Assimilant r = 0.8Assimilant r = 1.5 DNd = 0.01, D Sr = 2 r = 0.1 Fick‘s (First) Law: c D D D r = 0.2 Sr Sr D D 6 D D D = = = = 8 86 J  D = = = 2 1 0 0 = 0 . Nd 0 . 0 0 2 1 . . 5 Sr 7 Sr 1 0 144 7 .01 1 x 8 0 87 D = Nd r = 0.5 01 143 0.0 D = J = material flux, D = diffusion coefficient, c = concentration, x = distance Initial liquid Initial liquid r = 1.5 c

r = 0.1 0.700 0.710 0.720 0.700 0.710 0.720 ( = concentration gradient) r = 0.2 r = 0.5 Assimilant 0 200 400 600 0 200 400 600 x DNd = 2, D Sr = 0.01 Sr (ppm) Sr (ppm)

0.51050.702 0.5110 0.5115 0.5120 0.704 0.5125 0.5130 0.5135 0.706 0.708 0.710 0.712 0.714 0.716

87Sr 86Sr

13 Diffusion Blocking temperatures

Diffusion coefficient depends on: TO P, T, a H 2O, fO2, anisotropy of the lattice, porosity… Blocking/closure temperatures Arrhenius equation: • Closure of isotopic system (relative to both the parent and Ea / RT TC D  D0e daughter isotopes) Temperature • Usage: PTt paths Ea lnDD ln 0 RT Open system P: parent nuclide (Dodson 1973, 1976) e.g. 147Sm, 87Rb D = diffusion coefficient  Linear decrease in temperature D: daughter nuclide 2 –1 143 87 D0 = frequency factor (m s )  Cooling mineral exchanges D/P e.g. Nd, Sr E = activation energy (J mol–1) isotopes with the rest of rock, A that acts as an infinite reservoir T = temperature (K) R = Universal Gas Constant (R = 8.31441 J mol–1 K–1)

Time

Blocking temperatures Blocking temperatures

Mineral Isotopic system Closure T RE/ A TC  A D0 Zircon U – Pb > 800 ºC ln 2 a Baddeleyite U – Pb > 800 ºC Monazite U – Pb ≈ 700 ºC a = characteristic diffusion size Titanite U – Pb ≈ 600 ºC (~ grain radius) A = geometry factor (sphere = 55, Garnet U – Pb > 550 ºC cylinder =27, plate = 8.7) Garnet Sm – Nd > 550 ºC = time constant (with which the Amphibole K – Ar ≈ 500 ºC diffusion coefficient diminishes) Muscovite Rb – Sr ≈ 500 ºC Blocking temperature is not a Plagioclase Rb – Sr ≈ 450 ºC constant but depends on: Muscovite K – Ar ≈ 350 ºC •Mineral Apatite U – Pb ≈ 350 ºC •Grain size Biotite Rb – Sr ≈ 300 ºC • Shape of the grain Biotite K – Ar ≈ 280 ºC Cooling curve for Glen Dessary syenite (Scotland), K-feldspar K – Ar ≈ 200 ºC • Cooling rate based on distinct blocking temperatures for various minerals and isotopic systems (van Breemen et al. 1979).

14 References and further reading References and further reading

ALBARÈDE F. 1995. Introduction to the Geochemical Modeling. Cambridge University Press. FAURE, G. 1986. Principles of Isotope Geology. J. Wiley & Sons, Chichester. ALLÈGRE, C. J., 2008. Isotope Geology. Cambridge University Press. FAURE, G. & MENSING, T. M. 2004. Isotopes: Principles and Applications. J. Wiley, New Jersey. ALLÈGRE, C. J. & LUCK, J. M., 1980. Osmium isotopes as petrogenetic and geological tracers. GEYH, M.A. & SCHLEICHER, H. 1990. Absolute Age Determination. Springer, Berlin. Earth Planet. Sci. Letters, 48, 148-154. GONCALVES, P., WILLIAMS, M. L. & JERCINOVIC, M. J., 2005. Electron-microprobe age mapping BENNETT, V. C. & DEPAOLO, D. J., 1987. Proterozoic crustal history of the western United States as of monazite. Am. Miner., 90, 578-585. determined by neodymium isotopic mapping. Geological Society of America Bulletin, 99, 674-685. JACOBSEN S.B. & WASSERBURG G.J. 1980. Sm–Nd evolution of chondrites. Earth Planet. Sci. Lett. BRIQUEU, L. & LANCELOT, J., 1979. Rb–Sr systematics and crustal contamination trends for calc- 50: 139–155. alkaline igneous rocks. Earth and Planetary Science Letters, 43, 385-396. KOŠLER, J. & SYLVESTER, P. J. 2003. Present trends and the future of zircon in geochronology: Laser CORFU, F. et. al. 2003. Atlas of zircon textures. In: HANCHAR, J. M. & HOSKIN, P. W. O. (eds): ablation ICPMS.- In: HANCHAR, J. M., & HOSKIN, P. W. O. (eds) : Zircon. Reviews in Mineralogy Zircon. Reviews in Mineralogy and Geochemistry 53, Washington, 469-503. and Geochemistry 53, Washington, 243-275. DALLMEYER, R. D. & URBAN, M., 1998. Variscan vs Cadomian tectonothermal activity in LINDNER, M. et al. 1989. Direct determination of the half-life of 187Re. Geochim. Cosmochim. Acta, 53, northwestern sectors of the Teplá-Barrandian Zone, Czech Republic: constraints from 40Ar/39Ar 1597–1606. ages. Geol. Rdsch., 87, 94-106. LUDWIG, K. R., 2003. Isoplot/Ex version 3.00. A geochronological toolkit for Microsoft Excel, User's DEPAOLO, D.J. 1988. Neodymium Isotope Geochemistry. Springer, Berlin. Manual: Berkeley Geochronology Center Special Publication No. 4. DICKIN, A.P. 1995. Radiogenic Isotope Geology. Cambridge University Press. LUGMAIR G.W. & MARTI K.1978. Lunar initial 143Nd/144Nd: differential evolution line of the lunar DODSON, M. H., 1973. Closure temperature in cooling geochronological and petrological systems. crust and mantle.– Earth Planet. Sci. Lett. 39, 349–357. Contr. Mineral. Petrol., 40, 259–274. MCDOUGALL, I. & HARRISON, T. M., 1988. Geochronology and Thermochronology by the 40Ar/39Ar DODSON, M. H., 1976. Kinetic processes and thermal history of slowly cooling liquids Nature, 259, Method. Oxford University Press. 551–553. MEZGER, K., 1990. Geochronology in granulites. In: Vielzeuf, D. & Vidal, P. (eds): Granulites and Crustal Evolution. Kluwer, Dordrecht, 451-470.

References and further reading Web links

MONTEL, J. M. et al. 1996. Electron microprobe dating of monazite. Chemical Geology, 131, 37-53. • Geochemistry 455 (W.M. White, Cornell University) PARRISH, R. R. & NOBLE, S. R., 2003. Zircon U-Th-Pb Geochronology by Isotope Dilution - http://www.geo.cornell.edu/geology/classes/geo455/Geo455.html Thermal Ionization Mass Spectrometry (ID-TIMS). In: HANCHAR, J. M & HOSKIN, P. W. O. (eds): Zircon. Reviews in Mineralogy and Geochemistry 53, Washington, 183-213. • Igneous and metamorphic geology (J. D. Winter, Whitman University) PATCHETT, P. J. & TATSUMOTO, M. 1980. A routine high-precision method for Lu–Hf isotope http://www.whitman.edu/geology/winter/JDW_PetClass.htm geochemistry and chronology. Contrib. Mineral. Petrol., 75, 263-267. ROLLINSON H.R. 1993. Using Geochemical Data: Evaluation, Presentation, Interpretation. • Isotopic Geology 656 (W.M. White, Cornell University) Longman, London. http://www.geo.cornell.edu/geology/classes/Geo656/656home.html STACEY, J. & KRAMERS, J., 1975. Approximation of terrestrial lead isotope evaluation by a two- • Dickin – Radiogenic Isotopes Geology stage model. Earth and Planetary Science Letters, 26, 207-221. http://www.onafarawayday.com/Radiogenic/ STEIGER R.H. & JÄGER E. 1977. Subcommission on geochronology: convention on the use of decay • Flashed teaching resources in geology from the constants in geo- and cosmochronology. Earth Planet. Sci. Lett. 36, 359–362. University of Tromsø, Norway SUZUKI, K., ADACHI, M. & KAJIZUKA, I., 1994. Electron microprobe observations of Pb diffusion http://ansatte.uit.no/kku000/webgeology/ in metamorphosed detrital monazites. Earth and Planetary Science Letters, 128, 391-405. VAN BREEMEN, O. et al. 1979. Age of the Glen Dessary Syenite, Inverness-shire: diachronous Palaeozoic metamorphism Across the Great Glen. Scottish Journal of Geology, 15, 49-62. WALKER, R. J. et al. 1989. Os, Sr, Nd, and Pb isotope systematics of southern African peridotite xenoliths: implications for the chemical evolution of subcontinental mantle. Geochim. Cosmochim. Acta, 53, 1583-1595.

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