International Journal of Earth Sciences

, Volume 101, Issue 7, pp 1705–1722

Composition, age, and origin of the ~620 Ma Humr Akarim and Humrat Mukbid A-type granites: no evidence for pre-Neoproterozoic basement in the Eastern Desert, Egypt

Authors

    • Department of Mineral Resources and Rocks, Faculty of Earth SciencesKing Abdulaziz University
    • Geosciences DepartmentUniversity of Texas at Dallas
  • Abdel-Kader M. Moghazi
    • Department of Mineral Resources and Rocks, Faculty of Earth SciencesKing Abdulaziz University
    • Department of Geology, Faculty of ScienceAlexandria University
  • Ayman E. Maurice
    • Geology Department, Faculty of ScienceBeni Suef University
  • Sayed A. Omar
    • Nuclear Material Authority
  • Qiang Wang
    • State Key Laboratory of Isotope Geochemistry, Guangzhou Institute of GeochemistryChinese Academy of Sciences
  • Simon A. Wilde
    • Department of Applied GeologyCurtin University
  • Ewais M. Moussa
    • Nuclear Material Authority
  • William I. Manton
    • Geosciences DepartmentUniversity of Texas at Dallas
  • Robert J. Stern
    • Geosciences DepartmentUniversity of Texas at Dallas
Original Paper

DOI: 10.1007/s00531-012-0759-2

Cite this article as:
Ali, K.A., Moghazi, A.M., Maurice, A.E. et al. Int J Earth Sci (Geol Rundsch) (2012) 101: 1705. doi:10.1007/s00531-012-0759-2

Abstract

The Humr Akarim and Humrat Mukbid plutons, in the central Eastern Desert of Egypt, are late Neoproterozoic post-collisional alkaline A-type granites. Humr Akarim and Humrat Mukbid plutonic rocks consist of subsolvus alkali granites and a subordinate roof facies of albite granite, which hosts greisen and Sn–Mo-mineralized quartz veins; textural and field evidence strongly suggest the presence of late magmatic F-rich fluids. The granites are Si-alkali rich, Mg–Ca–Ti poor with high Rb/Sr (20–123), and low K/Rb (27–65). They are enriched in high field strength elements (e.g., Nb, Ta, Zr, Y, U, Th) and heavy rare earth elements (Lan/Ybn = 0.27–0.95) and exhibit significant tetrad effects in REE patterns. These geochemical attributes indicate that granite trace element distribution was controlled by crystal fractionation as well as interaction with fluorine-rich magmatic fluids. U–Pb SHRIMP zircon dating indicates an age of ~630–620 Ma but with abundant evidence that zircons were affected by late corrosive fluids (e.g., discordance, high common Pb). εNd at 620 Ma ranges from +3.4 to +6.8 (mean = +5.0) for Humr Akarim granitic rocks and from +4.8 to +7.5 (mean = +5.8) for Humrat Mukbid granitic rocks. Some slightly older zircons (~740 Ma, 703 Ma) may have been inherited from older granites in the region. Our U–Pb zircon data and Nd isotope results indicate a juvenile magma source of Neoproterozoic age like that responsible for forming most other ANS crust and refute previous conclusions that pre-Neoproterozoic continental crust was involved in the generation of the studied granites.

Keywords

U–Pb zircon datingA-type graniteNeoproterozoicNd isotopesArabian-Nubian Shield

Introduction

Rocks of granitic composition are important components of the continental crust. Based on chemical features and field occurrences, granitic rocks can be divided into S-, I-, M- and A-types (Chappell and White 1974, 1992; Loiselle and Wones 1979; Eby 1990; Chappell 1999). A-type granites are generally considered to be generated in “anorogenic” settings (Loiselle and Wones 1979). Eby (1990, 1992) subdivided A-type granites into two subtypes with different origins and tectonic settings. A1-type granites represent differentiates of OIB-like magmas emplaced in continental rifts or during intraplate magmatism, whereas A2-type granites result from partial melting of mafic lower continental crust. This concept has been widely applied in the study of A-type granites (Black and Liégeois 1993; Han et al. 1997; Wu et al. 2002; Anderson et al. 2003; Li et al. 2007; Zheng et al. 2007; Haapala et al. 2007; Zhao et al. 2008; Shang et al. 2010). Of course, petrogenesis of ANS A-type granites may be more complicated, especially where magmatic fluids are concerned.

The Arabian-Nubian Shield (ANS) consists primarily of Neoproterozoic juvenile crust, which is formed by accretion of several mainly intra-oceanic arcs along ophiolitic sutures (Kröner 1985; Stoeser and Camp 1985; Vail 1985; Quick 1991; Johnson 1998; Ali et al. 2009, 2010a, b; Stern and Johnson 2010) between 900 and 550 Ma as the Mozambique Ocean closed (Stern 1994). Geochronological data suggest that subduction to form the Eastern Desert of Egypt ceased by 615 Ma (Stern 1981, 1994; Stern and Hedge 1985; Kröner 1985; Greiling et al. 1994). Younger igneous rocks are post-collisional and are dominated by felsic plutons known as “younger granites” (El-Gaby 1975; Akaad and Noweir 1980; Greenberg 1981; Harris 1985; Sylvester 1998; Küster and Harms 1998). The younger granites are undeformed and emplaced at shallow levels with typical A-type chemical characteristics (Abdel Rahman and Martin 1990; Katzir et al. 2007a, b; Jarrar et al. 2008; Eyal et al. 2010).

Post-collisional ANS granites are attracting increased economic interest because some plutons, including the Humr Akarem and Humrat Mukbid granite, are associated with high concentrations of rare metals such as Sn, U, Nb, Ta, Y, Zr, and REE (Fig. 1b). These plutons are also of interest because of reports of their young age. Hassanen and Harraz (1996) determined Rb–Sr ages of 527 and 541 Ma, much younger than other late granites of the ANS. These workers also report isotopic evidence that pre-Neoproterozoic crust may have contributed, as recorded by εNd of −2.9 to −6.7. Archean and Paleoproterozoic rocks are structurally intercalated with the juvenile Neoproterozoic rocks in the southern and eastern ANS (Fig. 1a), for example, in the Khida terrane of the southeastern Arabian Shield (Stacey and Hedge 1984; Agar et al. 1992; Whitehouse et al. 2001) and Yemen (Whitehouse et al. 1998). Pre-Neoproterozoic crust is also found along the western flanks of the ANS (Sultan et al. 1994; Abdelsalam et al. 2002; Küster et al. 2008), but such evidence has not previously been reported for rocks from the Eastern Desert of Egypt.
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Fig. 1

a Geological sketch map of NE Africa showing the juvenile Arabian-Nubian Shield, the Saharan Metacraton, and Archean and Paleoproterozoic crust that was mostly remobilized during the Neoproterozic. Location of studied area (Fig. 1b) is marked by a rectangle.b Geological map of the Arabian-Nubian Shield showing the main mineralized granitic plutons including the studied Humr Akarim and Humrat Mukbid granites, modified from Johnson and Woldehaimanot (2003) and Küster (2009)

The results of Hassanen and Harraz (1996) indicate that the two plutons are unusually young (nearly all ANS granitic rocks are older than 560 Ma) and are not juvenile Neoproterozoic crustal additions like all other Eastern Desert basement lithologies. This result challenges our understanding of ANS crustal evolution and need to be tested, which we do here. In this paper, we present new geochemical data, SHRIMP U–Pb zircon ages, and Sm–Nd isotopic compositions for the Humr Akarem and Humrat Mukbid granite plutons. Our data indicate that these granitic bodies are not unusual in terms of age or origin, but unusual alteration may be responsible for their anomalous results.

Field setting and petrography

Rock units in the area that encompasses the Humr Akarim and Humrat Mukbid granite plutons include a metavolcanic–metasedimentary association, metagabbro, gneiss, tonalite–granodiorite, and A-type granite (Fig. 2a) (e.g., Hassanen and Harraz 1996; Abd El-Naby et al. 2000; Saleh et al. 2002). The metavolcanic–metasedimentary association and the metagabbro belong to the island arc stage of ANS crustal evolution. Granitic–gneiss complexes have been interpreted as pre-Neoproterozoic basement (El-Gaby et al. 1988), but recent geochronologic and isotopic results indicate that these rocks are Neoproterozoic, yielding zircon ages of 800–600 Ma (Kröner et al. 1994; Bregar et al. 2002; Andresen et al. 2009). Sm–Nd isotopic studies also indicate that Eastern Desert gneisses are juvenile Neoproterozoic crust (Liégeois and Stern 2010). The tonalite–granodiorite association is predominantly composed of metaluminous calc-alkaline granitic rocks (Saleh et al. 2002) that belong to the 850–614 Ma “Older Granite group” of the Egyptian basement complex (Stern and Hedge 1985; Stern 1994; Beyth et al. 1994). A-type granites are the youngest igneous rocks and occur in two small alkali granite plutons, Humrat Mukbid in the east and Humr Akarim in the west (Fig. 2).
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Fig. 2

a Geological map of the Humr Akarim and Humrat Mukbid areas, Eastern Desert, Egypt. The locations of figures b and c are indicated. b Geologic map of the Humr Akarim pluton, showing the area sampled for this study. c Geologic map of the Humrat Mukbid pluton, showing the location of the area sampled for this study

Humr Akarim occurs as a NE-elongated irregular body of coarse- to medium-grained pink granite that is ~6 km in maximum dimension (Fig. 2b). It intrudes quartzo-feldspathic and volcaniclastic metasedimentary rocks, metamorphosed up to greenschist facies (Geological Map of Egypt 1987). Contacts between the granite and the country rocks are irregular; locally phyllites and schists are hornfelsed. Quartz veins and greisenized quartz veins are common on the north side of the pluton and occur as discontinuous lenses and veins that are 10–50 cm wide and up to several hundred meters long. The veins cut across the metasedimentary rocks and contain cassiterite, molybdenite, beryl, fluorite, and secondary malachite (Abd El-Naby et al. 2000). Some zones of the Humr Akarim granitic body are albitized and greisenized. The albite granite is fine- to medium-grained and whitish.

The Humrat Mukbid pluton intrudes gabbro–diorite–granodiorite and metavolcanic–metasedimentary rocks (Fig. 2c). Contacts are poorly exposed due to weathering and erosion. The pluton is up to 7 km across and consists of two pink granite masses. The rocks of the northern mass are medium-grained and partly albitized and greisenized, with pockets and veins of beryl, pegmatite, and fluorite (Hassanen and Harraz 1996).

Granitic rocks of Humr Akarim and Humrat Mukbid are mineralogically and texturally similar. Both are equigranular and composed dominantly of alkali -feldspar (50%), quartz (30%), plagioclase (15%), and subordinate biotite and muscovite (4%). Zircon, fluorite, apatite, and allanite are the main accessory minerals (~1%), and titanite is locally present. Most alkali feldspars minerals are perthite with fine, linear exsolutions. Some samples show the dendritic intergrowths of quartz in alkali feldspar. Biotite and muscovite are subhedral and interstitial between feldspars but show marked local variations between the two plutons. In Humrat Mukbid, biotite is more abundant than muscovite, whereas in some parts of the Humr Akarim pluton, muscovite exceeds biotite. In the albitized part of Humr Akarim granite, dense albite laths form most of the groundmass as well as poikilitic inclusions in quartz and K-feldspar. Some perthite crystals are rimmed with albite.

Analytical techniques

Ten samples from the least altered, southern parts of Humr Akarim and Humrat Mukbid plutons were collected and analyzed for major and trace element contents and Nd isotopic compositions. Sampling locations are shown in Fig. 2b, c.

Major element oxides (Table 1) were determined using standard X-ray fluorescence (XRF) methods at the Guangzhou Institute of Geochemistry, Chinese Academy of Sciences (GIGCAS). Trace elements (Table 1) were analyzed by inductively coupled plasma mass spectrometry (ICP-MS), using a Perkin-Elmer Sciex ELAN 6000 instrument at the GIGCAS. Analytical procedures are described by Li et al. (2006). Analytical precision for most elements is better than 3%.
Table 1

Major and trace element compositions of granite samples from Humr Akarim and Humrat Mukbid, Eastern Desert, Egypt

Sample

AK-1

AK-2

AK-6

AK-12

AK-14

MK-4

MK-10

MK-15

MK-19

MK-25

SiO2

75.15

77.95

75.50

75.80

74.11

75.72

74.63

74.71

74.98

75.13

TiO2

0.04

0.02

0.03

0.01

0.05

0.06

0.05

0.02

0.04

0.03

Al2O3

14.14

12.17

13.78

13.47

13.83

12.98

13.77

13.63

13.47

14.17

Fe2O3

0.39

0.14

0.41

0.38

0.57

0.93

0.52

0.66

0.70

0.63

MnO

0.04

0.01

0.02

0.03

0.02

0.03

0.02

0.04

0.03

0.02

MgO

0.03

0.03

0.05

0.03

0.07

0.07

0.06

0.02

0.04

0.07

CaO

0.28

0.46

0.45

0.39

0.67

0.44

0.50

0.43

0.45

0.40

Na2O

5.38

3.97

4.27

5.00

4.94

4.45

4.93

5.02

4.90

4.64

K2O

3.36

4.09

4.37

3.80

4.26

4.18

4.24

4.22

4.27

3.96

P2O5

0.007

0.002

0.003

0.000

0.010

0.008

0.009

0.006

0.005

0.003

LOI

0.70

0.63

0.62

0.60

0.97

0.61

0.77

0.69

0.62

0.52

Total

99.52

99.46

99.51

99.50

99.51

99.48

99.50

99.44

99.50

99.60

Sc

0.65

0.60

0.32

0.53

1.12

1.18

1.21

0.70

0.75

0.76

Ti

215

146

156

59

276

274

310

138

207

198

V

3.68

2.12

1.97

1.85

3.10

3.32

3.70

2.46

2.40

2.40

Cr

64.23

84.70

63.37

64.45

93.36

56.23

120.80

94.20

98.70

57.35

Mn

292.40

24.08

111.50

203.90

140.40

152.10

202.90

242.60

169.60

167.50

Co

0.43

0.31

0.26

0.25

0.55

0.48

0.69

0.38

0.50

0.33

Ni

1.46

0.96

0.82

0.81

1.30

0.98

1.53

1.16

1.20

0.81

Cu

4.91

1.27

6.23

2.42

1.78

2.80

2.21

1.21

1.30

1.03

Zn

163.10

46.95

50.68

106.30

119.10

125.00

125.90

182.50

123.30

135.90

Ga

50.7

34.1

33.4

45.9

40.3

39.4

38.0

44.9

39.6

40.6

Ge

3.2

2.9

2.1

2.9

2.6

2.6

3.0

3.4

3.1

3.3

Rb

518.3

298.7

367.4

363.3

280.5

268.8

288.5

366.6

299.6

292.6

Sr

4.2

7.3

6.2

5.3

13.9

11.8

13.1

6.5

8.6

9.6

Y

75.4

71.8

68.3

150

90.5

89.2

104.7

85.6

104.5

78.8

Zr

59.4

95.4

126.7

79.9

128.9

144.2

136.2

132.9

128.4

114.8

Nb

47.1

40.4

53.2

43.9

55.9

60.7

57.6

71.8

58.8

53.3

Ba

4.9

34.6

29.4

7.5

61.2

59.8

101.0

13.4

44.3

44.5

La

8.0

9.0

6.2

10.4

16.7

13.2

13.3

12.0

12.6

20.7

Ce

22.7

17.6

11.4

30.7

29.6

21.1

29.0

32.1

36.9

16.4

Pr

4.6

4.1

3.5

5.6

6.8

5.3

5.3

4.9

5.2

8.3

Nd

16.2

16.7

15.2

23.1

25.2

19.9

19.9

16.7

19.3

32.1

Sm

6.9

6.5

6.0

10.3

7.5

6.1

6.2

5.3

6.1

9.3

Eu

0.05

0.11

0.20

0.05

0.39

0.34

0.30

0.14

0.26

0.35

Gd

6.6

6.9

6.5

11.2

7.1

6.1

6.7

5.4

6.8

7.6

Tb

1.9

1.6

1.4

3.0

1.7

1.6

1.7

1.4

1.7

1.6

Dy

14.0

10.9

10.1

21.9

11.7

11.8

12.8

10.9

12.8

10.3

Ho

3.4

2.6

2.5

5.0

2.8

2.9

3.2

2.7

3.2

2.3

Er

12.0

9.3

9.0

16.7

10.3

10.8

11.6

10.4

11.9

8.7

Tm

2.6

1.9

1.8

3.1

2.1

2.2

2.4

2.3

2.4

1.8

Yb

21.0

15.6

13.2

23.4

17.1

17.9

19.1

20.6

19.5

15.6

Lu

3.5

2.6

2.1

3.7

2.9

3.0

3.1

3.5

3.3

2.7

Hf

9.3

9.1

11.0

10.4

10.5

11.4

11.8

13.8

10.7

10.0

Ta

32.5

14.5

13.2

35.5

9.7

10.5

12.2

13.6

15.4

7.6

Pb

58.8

27.6

22.9

68.5

37.8

42.6

25.9

67.7

38.9

48.7

Th

20.1

26.6

27.7

24.5

23.8

21.2

23.5

27.9

22.8

23.5

U

11.1

12.6

11.0

13.1

5.4

7.1

4.2

6.0

5.7

4.0

(Nb/La)N

5.65

4.31

8.29

4.08

3.23

4.43

4.17

5.79

4.50

2.49

(La/Sm)N

0.75

0.90

0.67

0.65

1.44

1.40

1.39

1.45

1.33

1.44

(La/Yb)N

0.27

0.41

0.34

0.32

0.70

0.53

0.50

0.42

0.46

0.95

(Gd/Yb)N

0.26

0.36

0.41

0.40

0.34

0.28

0.29

0.22

0.29

0.41

Eu/Eu*

0.02

0.05

0.10

0.01

0.16

0.17

0.14

0.08

0.12

0.13

TE1,3

1.30

1.09

1.03

1.26

1.09

1.08

1.16

1.26

1.24

0.87

Major element (wt%) by XRF and trace element (ppm) by ICP-MS, AK = Humr Akarim, MK = Humrat Mukbid

(X/Y)N = chondrite-normalized ratio; Eu/Eu* = ratio of observed Eu contents to that expected if no Eu anomaly is present; TE1,3 = Tetrad Effect after Irber (1999)

Nd isotopic analyses (Table 2) were performed using a Micromass Isoprobe multicollector mass spectrometer (MC-ICP-MS) at GIGCAS, using the analytical procedure described by Li et al. (2006). Rare earth elements were separated using cation columns, and Nd fractions were further separated by HDEHP-coated Kef columns. Measured 143Nd/144Nd ratios were normalized to 146Nd/144Nd = 0.7219. Reported 143Nd/144Nd was adjusted to the Shin Etsu JNdi-1 standard (mean 143Nd/144Nd = 0.512115 ± 11). Two samples from each pluton were reanalyzed using a Finnigan MAT 261 at the University of Texas at Dallas (UTD), using the procedure described by Hargrove et al. (2006). These four samples show slightly lower 143Nd/144Nd than those measured at GIGCAS (Table 2) but these differences do not affect our conclusions. Analytical runs at UTD consisted of 10 blocks of 10 scans each for unknowns and three analyses of the La Jolla Nd standard, which yielded mean 143Nd/144Nd = 0.511859 ± 14.
Table 2

Sm–Nd concentration and isotopic data for granite samples from Humr Akarim & Humrat Mukbid, Eastern Desert, Egypt

Sample

Lithology

Sm (ppm)

Nd (ppm)

147Sm/144Nd

143Nd/144Nd

143Nd/144Nd (initial)

εNd(t) 600 Ma

εNd(t) 620 Ma

εNd(t) 630 Ma

AK-1

Granite

6.91

16.21

0.2575

0.513057 ± 11

0.512011

2.9

3.4

3.6

AK-2

Granite

6.47

16.66

0.2346

0.513046 ± 8

0.512093

4.5

4.7

5.2

AK-2

Granite

6.47

16.66

0.2346

0.513022 ± 14a

0.512069

4.0

4.5

4.8

AK-6

Granite

5.99

15.18

0.2384

0.513153 ± 7

0.512184

6.3

6.8

7.0

AK-12

Granite

10.30

23.11

0.2693

0.513149 ± 8

0.512055

3.7

4.2

4.5

AK-14

Granite

7.49

25.20

0.1798

0.512870 ± 6

0.512140

5.4

5.9

6.1

AK-14

Granite

7.49

25.20

0.1798

0.512853 ± 17a

0.512122

5.0

5.5

5.8

MK-4

Granite

6.09

19.94

0.1846

0.512866 ± 9

0.512116

4.9

5.4

5.7

MK-4

Granite

6.09

19.94

0.1846

0.512849 ± 47a

0.512099

4.6

5.1

5.3

MK-10

Granite

6.18

19.87

0.1880

0.512850 ± 9

0.512086

4.3

4.8

5.1

MK-10

Granite

6.18

19.87

0.1880

0.512808 ± 39a

0.512045

3.5

4.0

4.3

MK-15

Granite

5.31

16.67

0.1925

0.512948 ± 7

0.512166

5.9

6.4

6.7

MK-19

Granite

6.10

19.34

0.1906

0.512911 ± 8

0.512137

5.3

5.8

6.1

MK-25

Granite

9.26

32.07

0.1744

0.512930 ± 7

0.512221

7.0

7.5

7.7

Trace element concentrations and isotopic analysis determined at Guangzhou Institute of Geochemistry (Chinese Academy of Science) using a Micromass Isoprobe multi-collector MC-ICP-MS. a Isotopic analysis conducted at UT Dallas on a Finnigan Mat 261 solid-source instrument. Errors reported for isotopic ratios are 2σ. Mean value of JNDi-1 standard is143Nd/144Nd = 0.512115 ± 11 and LaJolla standard is 143Nd/144Nd = 0.511859 ± 14

Four samples for U–Pb zircon age determinations were collected and analyzed. Zircons were separated at UTD using crushing, heavy liquids, and magnetic separation. Grains from the non-magnetic fractions were hand-picked, mounted on double-sided adhesive tape, and set in Epirez™ resin along with several grains of Sri Lanka zircon standard (CZ3) that has a conventionally measured 206Pb/238U age of 563 Ma (Nelson 1997). The mounted zircons were ground and polished to effectively cut them in half and were imaged by cathodoluminescence (CL) using a scanning electron microscope. U–Th–Pb analyses were performed using the SHRIMP II ion microprobe at Curtin University in Australia following techniques described by Nelson (1997) and Williams (1998) utilizing five-cycle runs through the mass stations. A total of 52 spots on 52 zircons were analyzed, along with 15 analyses of the CZ3 standard, which yielded a 1σ variation in Pb/U of 0.42% during the analytical session. Data were processed using SQUID (Ludwig 2001a) and Isoplot (Ludwig 2001b) software. 206Pb/238U ages are most reliable for young zircons and are utilized here. Analytical results for zircons are listed in Table A3 (supplementary material).

Results

Major and trace element composition

Samples from both granite plutons exhibit similar ranges in major element concentrations (Table 1). They contain high SiO2 (74.1–78.0 wt%) and Na2O (3.97–5.38 wt%) contents with Na2O/K2O ≥1. They fall in the field of alkali feldspar granite in the R1–R2 diagram of de la Roche et al. (1980) (Fig. 3a). The majority of samples have agpatic index (AI = Na + K/Al) between 1.01 and 0.9 (Fig. 3b) and are thus classified as alkaline to slightly peralkaline granites according to Liégeois and Black (1987). The contents of CaO, MgO, TiO2, and P2O5 are very low (mean = 0.45, 0.05, 0.04, and 0.006 wt%, respectively).
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Fig. 3

a Chemical classification for granite samples from Humr Akarim and Humrat Mukbid (de La Roche et al. 1980). b Agpaitic index (AI = Na + K/Al) versus SiO2 diagram showing the alkaline to peralkaline characters of the studied granite. Note that the line with AI = 0.87 (Liégeois and Black 1987) separates alkaline and calc-alkaline granite series

REE contents are high and variable (ΣREE = 89–168 ppm). Chondrite-normalized REE patterns with huge negative Eu anomalies (Fig. 4a; (Eu/Eu* = 0.02–0.17)) similar to other ANS-mineralized granites. They are HREE-enriched (Lan/Ybn = 0.27–0.95, Gdn/Ybn = 0.22–0.41), with high Y contents (68–150 ppm) and weakly fractionated to flat LREE (Lan/Smn = 0.65–1.45). The REE patterns also show negative Ce and Nd anomalies (Ce/Ce* = 0.31–1.0; Nd/Nd* = 0.74–0.94). REE patterns show tetrad effect (TE1,3; Table 1) for most samples >1 according to the quantification method of Irber (1999). The granites have high concentrations of Rb (269–518 ppm), Th (20–28 ppm), and U (4–13 ppm), and low contents of Zr (59–144 ppm) and Hf (9–14 ppm) (Table 1; Fig. 4b). Trace element patterns do not show significant negative Nb anomalies (Nbn/Lan > 1), but show positive U and Th anomalies (Un/Nbn, Thn/Ban > 1) and strongly negative Sr, Ba, Eu, and Ti anomalies.
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Fig. 4

Trace element data for Humr Akarim and Humrat Mukbid granite samples, plotted as: a Rare Earth element (REE) patterns (plotted for comparison are the Katharina granites from Sinai, Egypt, Katzir et al. 2007a; the Ineigi and Humrat Waggat granites from Eastern Desert, Egypt, Mohamed and El-Sayed 2008). b Primitive mantle normalized trace element diagram. (Normalization values of chondrite and primitive mantle are from Sun and McDonough 1989)

The high SiO2 contents and the alkaline to slightly peralkaline characteristics of the studied granites are distinct from the metaluminous calc-alkaline composition of typical I-type granites (Chappell 1999). The 10,000 × Ga/Al ratios in Humr Akarem and Humrat Mukbid granites are 4–7, which is higher than the global average of 3.75 for A-type granites (Whalen et al. 1987). Striking depletions in Ba, Sr, P, Eu, and Ti (Fig. 4a, b) in REE patterns and spider diagrams are also common features of A-type granites (Collins et al. 1982; Whalen et al. 1987; Wu et al. 2002; Bonin 2007). The Humr Akarim and Humrat Mukbid granites lie in the field of within-plate granite (WPG, Fig. 5a) on the Y versus Nb diagram (Pearce et al. 1984). When Ga/Al versus Zr is considered (Whalen et al. 1987), the samples fall into the A-type granite field (Fig. 5b). According to the geochemical subdivision of A-type granites by Eby (1992), the Humr Akarim and Humrat Mukbid granite belongs to A2-type granite (Fig. 5c), associated with mafic melts in the lower continental crust.
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Fig. 5

Tectonic discrimination diagrams for the Humr Akarim and Humrat Mukbid granites, Eastern Desert, Egypt. a Y versus Nb diagram (Pearce et al. 1984), showing that the granites plot in the within-plate field. WPG within-plate granites, ORG ocean-ridge granites, VAG volcanic-arc granites, and syn-COLG syn-collisional granites. b 104Ga/Al versus Zr diagram (Whalen et al. 1987), showing the A-type characteristics of the granites. c Y/Nb versus Rb/Nb diagram (Eby 1992), showing the A2-subtype characteristics of the granites

U–Pb zircon geochronology

Humr Akarim pluton

Sample AK-1 is a medium- to coarse-grained pink granite. Zircons separated from it are euhedral (100–200 μm) and yellow to pale brown (Fig. 6a). U contents vary from 51 to 1281 ppm, Th contents from 15 to 318 ppm, and Th/U from 0.29 to 0.75. One measurement was made on each of twelve grains (Table A3—supplementary material). Three spots (AK-1.6, AK-1.7, and AK-1.8) have high common 206Pb (1.25–2.93%). Spot AK-1.1 is very discordant and records a 206Pb/238U age (137 ± 82 Ma) that is much younger than the other 11 analyses. Two spots (AK-1.10 and AK-1.11) show reverse discordance. The remaining six analyses are concordant and yield a concordia age of 633 ± 7 Ma (2σ, MSWD = 0.56; Fig. 7a).
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Fig. 6

Cathodoluminescence images of zircons from the granitoid samples analyzed during this study. a Humr Akarim granite sample #AK-1. b Humr Akarim granite sample # AK-6. c Humrat Mukbid granite sample # MK-19. d Humrat Mukbid granite sample # MK-25. Location of ion-microprobe area is shown by white circles, scale is 100 μm

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Fig. 7

U–Pb concordia diagrams for SHRIMP–RG data of the granitoid samples analyzed during this study. a Sample AK-1. b Sample AK-6. c Sample MK-19. d Sample MK-25. Error ellipses are 2σ; weighted average age errors quoted at 95% confidence. Analytical data are given in Table A3 (supplementary data)

Sample AK-6 is a medium- to coarse-grained pink granite. Zircons are euhedral (100–200 μm) and yellow to pale brown (Fig. 6b). The U content varies from 85 to 2113 ppm, Th content from 26 to 629 ppm, and Th/U from 0.21 to 0.59. One measurement was made on each of twelve grains (Table A3—supplementary material). Seven analyses were excluded from age calculation because they have high common 206Pb (1.82–3.95%), are discordant, show high U content and record younger 206Pb/238U age, and/or show reverse discordance. The remaining five analyses yield a concordia age of 598 ± 13 Ma (95% conf., MSWD = 2.1; Fig. 7b). If we exclude another spot (AK-6.6) because of high U content (1,773 ppm), the remaining four analyses yield a concordia age of 603 ± 8 Ma (2σ, MSWD = 0.76; Fig. 7b).

Humrat Mukbid pluton

Sample MK-19 is a medium- to coarse-grained pink granite. Zircons are mostly elongate, euhedral (100–200 μm), and yellow to pale brown (Fig. 6c). U content varies from 33 to 686 ppm, Th content from 13 to 926 ppm, and Th/U from 0.33 to 1.35. One measurement was made on each of fifteen grains (Table A3—supplementary material). Four spots (MK-19.2, MK-19.8, MK-19.9, and MK-19.12) have high common 206Pb (1.90–7.41%), spot MK-19.3 has very high common 206Pb (18.58%) and records a much younger 206Pb/238U age (235 ± 5 Ma) than the other 14 analyses, and three spots (MK-19.2, MK-19.4, and MK-19.15) show reverse discordance. Spot MK-19.1 has a higher 206Pb/238U age (703 ± 18 Ma) than the other analyses and may be a xenocryst. The remaining six analyses are concordant and yield a concordia age of 625 ± 8 Ma (2σ, MSWD = 2.5; Fig. 7c).

Sample MK-25 is a medium- to coarse-grained pink granite. Zircons are yellow to pale brown and mostly elongate and euhedral (100–200 μm), although some grains show marginal pitting (Fig. 6d). U content varies from 63 to 540 ppm, Th content from 39 to 270 ppm, and Th/U from 0.19 to 1.51 (average = 0.59). One measurement was made on each of thirteen grains (Fig. 7d; Table A3—supplementary material). Two spots (MK-25.5 and MK-25.13) are discordant, three spots (MK-25.2, MK-25.6, and MK-25.11) show reverse discordance. Spot MK-25.3 is discordant and has a higher 206Pb/238U age (744 ± 11 Ma) than the other 12 analyses and may be a xenocryst. The remaining seven analyses yield a concordia age of 619 ± 8 Ma (95% conf., MSWD = 0.16; Fig. 7d).

In summary, samples AK1 and AK-6 yielded ages range from 634 ± 8 to 598 ± 13 Ma, whereas samples MK-19 and MK-25 yielded ages from 626 ± 8 to 619 ± 8 Ma. These are somewhat older than most ages reported for within-plate alkaline granites in the Arabian-Nubian Shield (608–580 Ma; Be’eri-Shlevin et al. 2009). However, Johnson et al. (2011; p. 56) suggested that post-tectonic A-type granites were emplaced in the ANS as early as the middle Cryogenian (Hamra and Bishah plutons, ~686 and ~678 Ma); nevertheless, the first major pulse of alkali magmatism occurred between 630 and 620 Ma, with the emplacement of plutons in the southern (Asir terrane) and northern (Afif and Midyan terranes) ANS. These granites mark the onset of highly fractionated intraplate, post-tectonic magmatism, and the beginning of a transition from convergent to extensional tectonics that characterized the remaining ANS history (Johnson et al. 2011).

These ages indicate a magmatic emplacement as early as 634 ± 8 Ma and suggest a younger event ~600 Ma, perhaps interaction with F-rich fluids. Alternatively, the intrusion age could be ~600 Ma and the older ages could represent inherited zircons, 630–620 Ma being a typical age for the granodioritic batholiths constituting the country rocks of the studied plutons.

Nd isotope compositions

Samarium and neodymium concentrations and Nd isotopic compositions for 10 whole-rock samples (14 analyses) of granitic rocks from the Humr Akarim and Humrat Mukbid plutons are presented in Table 2. Mean εNd at 600–630 Ma ranges from +4.5 to +5.3, respectively, for Humr Akarim granitic rocks; and from +5.2 to +6.2, respectively, for Humrat Mukbid granitic rocks (Table 2). Because there is little difference in εNd values at 630, 620 and 600 Ma, the intermediate value at 620 Ma is chosen for commodity; εNd at 620 Ma ranges from +3.4 to +6.8 (mean = +5.0) for Humr Akarim granitic rocks; and from +4.8 to +7.5 (mean = +5.8) for Humrat Mukbid granitic rocks (Table 2). These results are plotted against the zircon age (620 Ma) in Fig. 8. These isotopic compositions are close to that expected for juvenile crust of this age according to the depleted mantle model of Nelson and DePaolo (1985). There is no difference on this diagram (Fig. 8) between our samples and other juvenile samples from the ANS juvenile crust (Stern 2002; Liégeois and Stern 2010). If pre-Neoproterozoic crust contributed to the composition of Humr Akarim magmas, it must have been very little considering the sensitivity of Nd isotopes to such input (Küster et al. 2008; Stern 2002; Liégeois and Stern 2010). Nd TDM model ages for samples with 147Sm/144Nd ≤0.165 are regarded as meaningful (Stern 2002). None of the fourteen samples analyzed here had 147Sm/144Nd <0.174 (Table 2); therefore, TDM ages are not reliable and are not reported.
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Fig. 8

Nd isotopic evolution through time for Humr Akarim and Humrat Mukbid granites. The reference line for chondritic uniform reservoir (CHUR) and depleted mantle evolution curves of Goldstein et al. (1984) and Nelson and DePaolo (1985). The field for the ANS juvenile Neoproterozoic crust is from Hargrove et al. (2006), Ali et al. (2009), Moussa et al. (2008), and Stoeser and Frost (2006). Data points for Hafafit and Meatiq granite from Liégeois and Stern (2010)

Discussion

Below we discuss several points including the role of fractional crystallization, fluid–rock interaction, and magma source region in the evolution of the Humr Akarim and Humrat Mukbid A-type granites.

Fractional crystallization versus fluid–rock interaction

The high Rb/Sr (20–123), low K/Rb (27–65), low Zr/Hf (6–15), low La/Nb (0.12–0.39), and very low Eu/Eu (0.02–0.17) all indicate that the Humr Akarim and Humrat Mukbid A-type granites are highly differentiated (Bau 1996). Pronounced negative Eu anomalies require extensive fractionation of feldspar. Plagioclase fractionation should produce negative Sr and Eu anomalies, whereas K-feldspar separation is responsible for the negative Ba anomaly (Wu et al. 2002). The presence of strongly negative Eu, Sr, and Ba anomalies in the studied granites thus indicate fractionation of both plagioclase and K-feldspar. This is further confirmed by the positive correlation between Ba and Sr versus Eu/Eu* (Fig. 9a, b) and negative correlation between K/Rb and Rb (Fig. 9c). Comparing the composition of the Humr Akarem and Humrat Mukbid granites with fractionation vectors for different phases confirms that fractionation of both K-feldspar and plagioclase was important in the evolution of the granites (Fig. 9d). Moreover, Al2O3 negatively correlates with SiO2 (Fig. 9e), consistent with the inference that feldspar removal may have been responsible. Fe-bearing minerals such as biotite, ilmenite, and titanite might have been other fractionating phases as suggested by the negative correlation of SiO2 and FeOt (Fig. 9f).
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Fig. 9

a Eu/Eu* versus Ba diagram. b Eu/Eu* versus Sr diagram. c Rb versus K2O/Rb diagram. d Sr versus Ba diagram, showing that fractionation of K-feldspar and plagioclase played an important role in the evolution of the Humr Akarim and Humrat Mukbid A-type granites (partition coefficients of Sr and Ba are from Arth 1976). e SiO2 versus Al2O3 diagram. f SiO2 versus FeOt diagram

Although fractionation of feldspars and biotite may have caused some of the compositional variation of the studied granites, the tetrad effect on REE patterns (Fig. 4; Table 1) cannot be explained by such fractionation. The tetrad effect can cause a split of chondrite-normalized REE patterns into four rounded segments called tetrads (first tetrad, La–Ce–Pr–Nd; second tetrad, Pm–Sm–Eu–Gd; third tetrad, Gd–Tb–Dy–Ho; fourth tetrad, Er–Tm–Yb–Lu). The segments are either M-shaped (convex) or W-shaped (concave) lanthanide distribution patterns (Masuda et al. 1987). Monecke et al. (2002) mentioned that the tetrad effect in granite lanthanide patterns can be attributed to fractional crystallization during granite differentiation or, to a characteristic of magma–fluid systems that develop during late-stage granite crystallization (McLennan 1994; Kawabe 1995; Irber 1999). Irber (1999) showed that mineral fractionation alone is unlikely to cause the tetrad effect in granitic REE patterns because these could not be generated in Rayleigh fractionation calculations. Therefore, Irber (1999) argued that the tetrad effect of granite samples must have resulted from interaction of the granitic melt with a coexisting fluid at a late stage of crystallization after these split into magma and fluid subsystems. Moreover, Jahn et al. (1993, 2001) emphasized that REE tetrad effects are not common and are most visible in late magmatic differentiates. This effect occurs typically in highly evolved magmatic systems, which are rich in H2O and CO2 and fluid-mobile elements such as Li, B, F and Cl (e.g., London 1986a, b, 1987, 1992, London et al. 1988).

For the studied granites, plotting ratios of K/Rb, Zr/Hf, and Sr/Eu versus the TE1,3 (tetrad effect; Fig. 10) help identify important controls on trace element behavior (Irber 1999). On the K/Rb versus TE1,3 diagram (Fig. 10a), the studied granite samples display a negative correlation, and most samples have TE1,3 > 1 and K/Rb from 50 to 125. Such variation and low K/Rb ratios are considered to indicate mineral growth in the presence of aqueous fluids (Shearer et al. 1985; Clarke 1992). The Zr/Hf ratios range from 6 to 15, much lower than the chondritic ratio of 36.6 (David et al. 2000) and negatively correlate with TE1,3 (Fig. 10b), which is characteristic of petrogenetic systems involving F-bearing fluids (Bau 1996; Irber 1999). The strong decrease in Eu concentrations with tetrad effect is seen in Sr/Eu ratios (Fig. 10c) and shows high value at TE1,3 > 1.10, which is opposite to the trend expected if mineral fractionation is dominant (Irber 1999). Thus, the strong Eu depletion in late stage of granite crystallization may indicate a preferential Eu fractionation into a coexisting aqueous fluid phase (Muecke and Clarke 1981).
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Fig. 10

Tetrad effect (TE1,3) versus a K/Rb, b Zr/Hf, and c Sr/Eu. The straight line mark the chondritic value, and the dashed lines define the boundary to clearly visible tetrad effects (TE1,3 > 1.10) after (Irber 1999)

On the basis of these considerations, it is suggested that crystal fractionation and fluid–rock interaction are the main control of the trace element distribution in the Humr Akarim and Humrat Mukbid granites. Such intense alteration of these granites by late-stage magmatic fluids is likely to have affected zircons and may have led to high contents of common Pb. This alteration may also have been responsible for the anomalous results of Hassanen and Harraz (1996).

Nature and source of the fluids

Implications on the physico-chemical characteristics of the fluids that affected the Humr Akarim and Humrat Mukbid granites can be made on the basis of textures and compositions of the minerals present. The fluids have F-rich composition, as indicated by the widespread occurrence of F-bearing minerals such as fluorite. They have the capacity to transport otherwise fluid-immobile trace elements as indicated by the presence REE-bearing minerals (e.g., zircon, fluorite, allanite, and apatite) in the granite. In addition, in the Qz–Ab–Or–H2O–F haplogranite system, Humr Akarim and Humrat Mukbid granite samples plot close to the minimum melt composition in the presence of fluorine at 2–6 kbar (Fig. 11).
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Fig. 11

Normative composition of the Humr Akarim and Humrat Mukbid granites plotted on the haplogranite Qz–Ab–Or–H2O–F. Dashed line shows the location of minima melt composition at saturated water pressure ranging from 0.5 to 10 kbar (Winkler et al. 1975). Solid line shows the minima melt at 1 kbar with excess H2O at 1%, 2%, 4% F (Manning 1981)

The role of halogens (F and Cl) as complexing agents for REE, Y, and HFSE is widely recognized (e.g., Manning 1981; Gieré 1986; Gieré and Williams 1992; Webster et al. 1989; Keppler and Wyllie 1990, 1991; Charoy and Raimault 1994; Pan and Fleet 1996; Audétat et al. 2000; Webster et al. 2004; Schönenberger and Markl 2008; Agangi et al. 2010). Thermodynamic calculations (Wood 1990a, b; Lee and Byrne 1992) and experimental work (Webster et al. 1989; Bau 1991; Bau and Möller 1992; Haas et al. 1995) show that complexation of trace elements with ligands such as F can significantly increase the solubility of these elements and can be important in natural systems. Two principal genetic models are invoked for the origin of the F-rich fluids: a primary magmatic origin (Mackenzie et al. 1988; Cuney et al. 1992; Clarke et al. 1993; Dostal and Chatterjee 1995) and a secondary metasomatic origin (Higgins et al. 1985; Nurmi and Haapala 1986). In the second hypothesis, a hot hydrothermal fluid, unrelated to the magma, could have leached the trace elements from the host rocks, but we see no evidence that the country rocks were unusually rich in F-rich rocks. For this reason and because the altered nature of the rocks even includes zircon and shows no restriction or concentration toward pluton margins, we favor a magmatic origin for the mineralizing/altering fluids that affected the studied granites. Field evidence for the release of magmatic fluids, represented by greisen and quartz veins, is restricted to the northern parts of both Humr Akarem and Humrat Mukbid plutons, which we largely avoided in this study (Fig. 2b, c). During late magmatic crystallization volatile-rich fluids migrate toward the roof of the pluton, where they react with still hot but subsolidus granite and country rocks (Heinrich 1990). Extensive hydraulic fracturing due to increased fluid pressure occurs concurrently, allowing magmatic fluids to escape and encouraging hydrothermal circulation. This leads to the formation of greisen veins in the granite and nearby country rocks; alteration of magmatic accessory phases is needed to remobilize REE and HFSE (e.g., Förster 2001), but this was not found. The events that can explain the evolution of these rocks are as follows: (1) prolonged crystallization of quartz and feldspar yield a late-stage magmatic fluid enriched in volatiles (H2O, F) and trace elements; (2) during the final stages of magmatic evolution, F dissolved in the magma is concentrated in fluids causing REE and HFSE complexing and mobilization, which subsequently behave as incompatible elements; and (3) interaction of these fluids with the hot, solid granite led to extreme alteration and crystallization of accessory minerals in the interstices between the major mineral phases. This alteration affected even zircon and other isotopic systems.

Magma source

U–Pb zircon ages can help distinguish between magmatic contributions from Neoproterozoic juvenile versus pre-Neoproterozoic crust (Stern et al. 2010). This is because zircons are among the most refractory of minerals, difficult to destroy by dissolution or melting (Tange and Takahashi 2004). Igneous rocks generated by significant interaction with older (non-juvenile) crust invariably contain a mixture of zircons formed within the melt and others inherited from the protolith, older than the igneous rock itself (Stern et al. 2010). However, pre-Neoproterozoic zircons are not found in all ANS igneous rocks; felsic plutonic rocks tend to lack these xenocrystic zircons (Moussa et al. 2008; Andresen et al. 2009), whereas mafic lavas may carry them in abundance (Stern et al. 2010). This presumably reflects different magma compositions and amount of time that magmas and xenocrystic zircons have to interact. Felsic plutonic rocks cool slowly, allowing xenocrystic zircons to dissolve in the magma, whereas unfractionated mafic magmas rise rapidly from the site of melt generation in the mantle through the crust. Magmatic zircons are relatively uncommon in mafic lavas, and xenocrystic zircons have little time to dissolve in the melt. As a result, the proportion of xenocrystic zircon is expected to be greatest in mafic lavas and lowest in felsic plutons (Stern et al. 2010).

Although the ANS is mostly isotopically juvenile, some Neoproterozoic igneous rocks contain zircon inherited from pre-Neoproterozoic sources (Sultan et al. 1990; Hargrove et al. 2006; Ali et al. 2009, 2010b). For example, Sultan et al. (1990) obtained an age of 578 ± 15 Ma for the post-tectonic granite from Nakhil, Eastern Desert of Egypt and reported the presence of inherited zircons possibly as old as 1.6 Ga. Also, Hargrove et al. (2006) studied igneous rocks along the Bi’r Umq suture of Saudi Arabia and showed that any interaction between Neoproterozoic juvenile magmas and pre-Neoproterozoic crust must have been very limited, in spite of the presence of pre-Neoproterozoic zircons. Samples studied by Hargrove et al. (2006) containing pre-Neoproterozoic zircons show slightly lower Nd concentrations, slightly lower initial 143Nd/144Nd, and therefore lower εNd(t) than contemporaneous samples that lack inherited zircon (Hargrove et al. 2006).

Our results found no pre-Neoproterozoic zircons. However, there are a lot of discordant zircons in the studied granites. This is may be due to the presence of slightly older xenocrystic zircons or due to radiation damage in high U zircons that cause these to act as open systems (Ewing et al. 2003; Moussa et al. 2008) subject to gain or loss of U, Pb, and intermediate radiogenic daughter elements. This damage may have been exacerbated by alteration due to circulation of late F-rich, which can dissolve zircons (cf., Watson and Harrison 1983). Combined effects of radiation damage and F-rich magmatic fluids could be responsible for elevated proportions of common Pb in dated zircons.

The calculated initial εNd varies between +3.4 and +7.5 for the Humr Akarim and Humrat Mukbid granitoids, reflecting a relatively young, juvenile Neoproterozoic crustal source for these granites (Dixon and Golombek 1988; Moussa et al. 2008; Hargrove et al. 2006 and Ali et al. 2009, 2010b) or may be because of a younger thermal event (F-fluid rich event modifying Sm/Nd) as discussed above where experimental work (Webster et al. 1989; Bau 1991; Bau and Möller 1992; Haas et al. 1995) show that complexing of trace elements with F can significantly increase the solubility of trace elements in fluids. Alternatively, the large variation in initial εNd (+3.4 to +7.5) may indicate that older components are overshadowed by more primitive material (Sultan et al. 1990).

In summary, the Nd isotopic compositions of Humr Akarim and Humrat Mukbid granitoids are consistent with zircon dating results and indicate juvenile magma sources like most other ANS crustal samples.

Conclusions

The following are the conclusions from our study:
  1. 1.

    Crystallization age for granites from Humr Akarim and Humrat Mukbid, Eastern Desert of Egypt, is ~630–620 Ma. Alternatively, the intrusion age could be ~600 Ma and the older ages being inherited, 630–620 Ma being typical ages for the granodioritic batholiths constituting the country rocks of the studied plutons. We do not confirm the age of 527 and 541 Ma determined using Rb–Sr techniques by Hassanen and Harraz (1996).

     
  2. 2.

    Zircon U–Pb SHRIMP isotopic data indicate the presence of slightly older zircons (~740 Ma, 703 Ma), which may have been inherited from slightly older but still Neoproterozoic crust beneath the studied areas.

     
  3. 3.

    Geochemical data indicate that the studied granitoids are A-type granites formed during a post-collisional phase or within-plate tectonic setting.

     
  4. 4.

    Humr Akarim and Humrat Mukbid granites represent highly fractionated magmas, which evolved an F-rich magmatic fluid in its late stage of evolution as indicated by greisenization and albitization as well as enrichment in HREE and HFSE and by the presence of tetrad effect on REE patterns.

     
  5. 5.

    No evidence for pre-Neoproterozoic crust was found, either in zircon ages or Nd isotopic compositions (strongly positive initial εNd = +3.4 to 7.5).

     
  6. 6.

    Our study does not confirm the εNd values of −2.9 to −6.7 reported by Hassanen and Harraz (1996), or the recalculated εNd values of +0.02 to −5.9 using U–Pb zircon age ~620 Ma (obtained from this study) on the Sm–Nd ratios reported by Hassanen and Harraz (1996). Their results may be explained by the extreme alteration of these rocks.

     

Acknowledgments

This work was supported by NSF-OISE grant #632220 to RJS and a post-doctoral fellowship from Curtin University in Perth, Australia to KAA. The SHRIMP II facility in Perth is operated jointly by Curtin University, the University of Western Australia and the Geological Survey of Western Australia, with support from the Australian Research Council. The authors would like to thank the Guangzhou Institute of Geochemistry, Chinese Academy of Sciences (GIGCAS) for performing the chemical and Nd isotope analyses. We are grateful to Ghaleb Jarrar, Jean-Paul Liégeois and editor Wolf-Christian Dullo for critical reviews that improved this manuscript. This is UTD Geosciences contribution number #1213 and TIGeR publication # 256. This is a JEBEL contribution.

Supplementary material

531_2012_759_MOESM1_ESM.pdf (46 kb)
Supplementary material 1 (PDF 47 kb)

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© Springer-Verlag 2012