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On the quality of representative mineral concentrates
Qeochimics et Coemochimica Acta, 1966, Vol. 30, pp. 546 to 561. Pergamon Press Ltd. Printed in Northern Ireland
On the quality
of representative
mineral
concentrabs
P. C. RICKWOOD Department of Geology, University of Otago, Dunedin, New Zealand (Received23 April 1965) Ah&&-An equation is derived to test the compatibility of an analysis of a mineral with that of its host-rock. It reveals incompatibility in 19 garnet/host-rock pairs of analyses out of 50 pairs published by 8 authors. There are three possible explanations, (1) analytical or printing errors, (2) “garnet” in statements of chemical and/or volume distribution analyses was “garnet plus inclusions”, (3) snalysed material was not representativeof the average garnet. A second equation, derived from the compatibility test, determinesthe maximum purity of the analysed material compatible with (1) and (2). With two exceptions, purity values range from 34 to 90%. For greater accuracy in major element snalyses when mineral homogeneity has not been proven, and particularly when mineral heterogeneity has been demonstrated by means of the electron micro-probe, it may be wiser to analyse high recovery concentratesrather than selectively prepared inclusion-freeconcentrates.
A literature search was made for chemical analyses of garnets and their host-rocks for comparison with similar pairs of analyses of specimens from Connemara, Eire. It wss revealed, surprisingly, that there was incompatibility between analyses in seven of the eight accounts that were found to contain adequate information for the necessary calculations to be made, and that none of the authors reported having made these calculations. This paper describes the compatibility calculation and presents some conclusions drawn from the published data. MATHEMATICAL DERNATION Consider a rock of density D, containing V volume y. of garnet (without inclusions) which has a density d. Let the rock contain W wt y0 of an oxide R,O,, and let the garnet contain X wt y0 of an oxide R,O,. In 100 g of rock there are V . (d/D) g of garnet. But 1 g of garnet contains X/100 g of R,O,, so that in 100 g of rock there are V . (d/D) . (X/100) g of R,O, locked in garnet. However, 100 g of rock contain W g of R,O,. Thus, if the wt y0 of R,O, that is located in all minerals other than garnet is called B, then
B=W-V.;.; Compatibility of analyses can be checked by calculation of B which should always be ~-0. PUBLISHED ANALYSES Compatibility calculrctions were carried out for the oxides CaO, MgO, Fe0 and MnO for the garnet/host-rock pairs of analyses given in eight studies containing 646
Bgn 18
Ch 113
Ch 219
Ch 121 Ch 119
10
11
12 13
982 x034
H 66
19
892
18
17
15 I6
3708
13-B
59.CZ-59
14
16.1
27-CZ-59
8
9
11.1
IO.4
4*1*
4*0*
4-o*
4-o*
14.2
4.17
4.5
4.02
4.02 3.99
3.99
4.06
4.17
4.09
4.1*
4*1* 4-1*
4.1*
4*1*
4.1*
4.1*
d
27.6 2.9
12.6
9.70
6.8
14.3
2.4
2.2
4.0
10
8
5
8*9
13.1
11
4
4.8
7
3
3
4
V
19.8
--_
6
2
1t
2
1
No.
Authors code no.
2.8’
2*8*
2-s*
2+8*
2.67
2.87
2.77
2.77
2.84
2+*
2.76
2.75
2.8”
I.2
1.89
5.91
8.54
8.37
1.58
0.81
0.77
2.04
2.25
l-20
6.3
7.1
1.63
1.34
2.32
2.68
2.72
0.40
O-18
0.42
3.44
3.29 2.95
0.22
3.2
0.85
W
-_. ._______ __.--_.-...-_-_.---..n.d. 2*1(* 2+* n.d. n.d. 2+$* n.d. 2*8* n.d. 2*8* n.d. 2a*
F X
0.31
0.88
1.73
o-54
0.07
0.31
0.15
0.48
0.40
0.17
0.55
1.03
0.95 1.44
2-18
0.33
-0.13
2.96 0.27
2.55
3.12
-0.33
1.69
0.79
-
. B
..^....__----
1.51
0.06
-
W-B
CSO
8.06
0.56
1*50
0*86
1.81
0.15 0.74
0.32
0.71
0.64
0.70
21.3
17.6
11.53
0.06
0.16
0.08
0.09
0.04
0.11
0.00
0.12
0.22
0.05
O-65
2.3
0.37
0.09
o-22
0.17
0.10
0.03
0.06
0.06
0.17
0.11
0.10
1.87
3.74
0.41
0.33
0.47
0.34 0.27
o-14
0.26
O-16
1.06
0.09
0.00
1.35
0.10
0.07
0.10
W-B
1.40
W
MnO
0.35
10.21
..-.__
rc X
Table 1. Compatibility of chemical analyses of garnets with their host rocks 4, R
-0*01 _---.-0.09 _ ._-_.. -0*07 ~_.. .--0.03 __-.__._
0.01
-0.06 --. 0.05
--0*05
-0*10 _.__..__ -0.05 -_@13 --0.06 ~-- 0.04 ^--..__ -1.44
-..0*03 --__.. -0.10
_~
1
z
.F cl
Cl-l121
Ch 119 3708
992
982 1034
H 66
13
14
16
17
19
26.13
27.63 27.96
27.04
27.92 33.30
25.20
28.12 28.48
29.36
23.98
24.30
26.32
34.28
34.13
-
-
n.d. n.d.
6.29
9.51
5.91
8.00
2.50
6.27
2.33
4.47
4.86 6.65
5.35 2.04
0.30
5.61 4.16 4.25
6.26
0.99
-4.52
-2.57
-2.18
I.51 1.74
IO.79
4.90
-0.12
2.68
4.98
2.29
I.21 4.13
6.81
3.5
-1.32
2.11 7.10
1.39 2.07
4.82
9.50
11.38
7.93
7.87
7.68
0.70 0.08
3.56
2.82
1.51
3.86 3.15
2.80 2.42 0.31 1.15
0.09 0.42
0.22
3.67
1.16 0.18
1.85 2.21
1.60
1.39
1.08
0.15 0.01
2.70
3.01
0.43 0.16
0.13
-
n.d. 2.61
-
-
n.d.
3.82 3.60
3.32
0.78 0.84
1.54
I.71
2.19
6.55 4.47
2.39
-
-
n.d.
W-B
n.d.
*
-
W
3.24
r
-
Y
B
W-B
2.0
3.66
4.38
5.36
6.18
8.74
5.63
-
W
Magnetite-hematite-bearing gneiss Magnetite-hematite-bearing gneiss Magnetite-hematite-bearing gneiss
-
Leptynite
-2.16 -0.04
3.55 2.00
Garnet gneiss
Garnet-mica schist Garnet-mica schist
Pelitic schist
Khondalite Khondalite
-1.05
2.71 2.00
Acid granulite
-0.25
Quartz-biotite-garnet gneiss Enderbite
1.31
Meta-ironstone
1.93
0.28 0.15
Metachert
Ihnenite-magnetite-bearing gneiss Ihnenito-magnetite-bearing gneiss
-
2.48
Garnet-chlorite schist Ihnenite-magnetite-bearing gneiss
-
Rock type
-
.
B
801-803). Source of analyses: 1 BARTH(1936,). 2-7 CHINNER(1960). 8-9 COLEMAN and LEE (1963), LEE, COLETUNand ERD (1963). 10 ENGEL and ENQEL(1958,196O). 11-15 HOWIEand SUBRUANIAM(1957). 16-18 LA~~BERT (1959). 19 WYNNE-EDWARDSand Hay (1963).
V = Volume yc of garnet; d = Garnet density; D = Rock density; X = Wt ye of oxide in garnet; W = Wt y. of oxide in rock; B = Wt y. of oxide in the rock that is located in minerals other than garnet; W - B = V . (d/D) . (X/100); n.d. = Not determined; * = Estimated value; t = Garnet volume calculated from chemical analyses and confirmed by Rosiwal analysis. B~LRTH (1936. pp.
18
15
12
Ch 113 Ch 219
27-CZ-59
8
11
13.8
11
7
59-cz-59
10
6
Bgn 18
8
5
9
4
4
10
15.6
3
3
34.00
2
2
n.d.
I X
lt
Authors code no.
1
No.
P. c.
548
J&XCWOOD
enough data. In some cases it was necessary to estinmte gsrnet and/or rock densities. Of 50 publiah~ p&s of snalyses, I9 produced one or more negative values of B (Table 1). Many of these in~mp&tibilities are further increased when other analysed minerals are considered. Errors in the estimates of rock densities are likely to be smaller than those for garnet densities, but an error as large as kO.2 g/ems in the latter would not alter the mineral: rock density rcctioby more than 5 per cent, and this does not significantly alter the majority of the values of B. If the estimates of the garnet densities are lowered by 6.2 g/cm8 then even the most marginal discrepancy between a pair of analyses (16-4InO) still remains. DEDUCTIONS Excluding large measurement errors and printing errors, there are only three explana;tions for the negative values of B. Any or all of these m&y hold and the implications of each will be considered in turn. Hypothah (a) .A fraction of the reported garnet volume is inclusions that were small enough to escape sepcbrateclassifi~tion in the volume distribution analysis. Let us accept that all the me~s~ementa have been accumtely made, that the rock has been carefully powdered and sampled, and that inclusion-free garnet grains have been separated and chemically analysed. Let I’, d, D, X, W and B be the sought true values and V,, d,, D,, X,, W, and B, be the reported values, then from equation (1)
BR=WR-vg.~.~o R (1) - (2) gives B - B, = W - WR Then~derh~the~s(~)~R=~; so that equ&ion (3) reduces to
L),=D;
V
.g.
X,=X;
go
+ VR
-2.2
(3)
R
W,=
W; but V,#V,
B-B,=(V,-v&g and equation (2) becomes W-BB,=V,.D.lOO
d
x
(5)
Thus, V -_== V, NOW
I?*
W-B W - BR
(6)
0,sothat W w
-RB,
(7)
On the quality of representativemineral oonoentrates
649
Hence, the maximum purity of the garnet reported in the volume distribution analysis that is entirely consistent with the given analytical Sgures is: W Te, Maximum pm@
if31
* 100%.
Sgures for each of the 27 discrepancies are given in Table 2.
Table 2. Maximum purities of garnet reported in the volume distribution analyses that are consistent with the given analytical figures* No. 1 2 3 4 6 6 7 8 8 9 9 10 11 12 12 12 13 13 13 14 14 14 15 10 17 I8 19
Authors oode no. 1 2 3 4 8 10 11 27-CZ-69 27-CZ-69 69-(32-69 69-CZ-69 Bgn 18 ch 113 Ch 219 Ch 219 Ch 219 ch 121 ch 121 ch 121 Ch 119 Ch 119 Ch 119 3708 992 982 1034 H 60
Oxide dieorepancy
MaXimun, purity in VR
MhO MIkO MilO
70.0% 0% 61.6% 04.3% 72.3% Sl*S% 90.2 % 81.6% 00.2% 40.0% 34.8% 60.0% 97.6% 70.6% 07.2% 80.6% 0% 47.6% 62.6% 68.1% 68.1% 41.1% 81.8% 90.0% 47.1% 68.2% 06.7 %
MIIO MkO MIIO WI0 l&O Fe0 C&O iUSl0 MIXLO Fe0 IGO Fe0 MgO MnO I?00 MgO C&O Fe0 MgO Mrso XIlO iKIlO MIXlO MIIIO
Sourceofazmlyaes: No.lB~m. 2-7 CHINNER. 8-9Co~~ararrmdL~~; LEE,COLEXAN and EB.D. 10 ENUEL md ENQEL. 11-16 Howm and SWRAMANUM. 16-18 bBKBERT. 19 %~%NNE-~DWARDB~~~~~Y. * Alternatively, these f&wea indicate the order of magnitude of the maximum purity of the &ywd garnet concentratesthat are con&tent with the published data.
For nos. 2 and 13 no manganese oxide is reported in the rocks but O-10 and 0.06 per cent, respectively, should be present to account for the requirements of garnet. The calculated zero per cent purities are absurd so that hypothesis (a) alone is not tenable, and h~oth~~ (b) produces a similar conclusion. Hypothesis (c) (below) can therefore be inferred to operate. However, these incompatibilities constitute speoial Casey where suspicion is cast on the validity of the assumption that no errors have been made. No detection limits are given and the authors make no comments. Maximum purities given by two oxide discrepanoies for the same garnet/host-rook pairs of
550
I?. C.Rzcrrwoo~
analyses were remarkably similar e.g. 8 (l&10)-61.5*/& (FeO)-60-2°/o. None of the authors has specifically reported that garnet in the volume distribution analyses must be taken to mean garnet plus inclusions.
Hypothesis (b) The analysed garnet concentrate was not inclusion-free, Let us accept that all the measurements hsve been accurately made, that the rock has been carefully powdered and sampled, and thst inclusions in minerals were ~p~a~ly recorded in the volume distribution analyses. Then, V, = V; DB = D; W, = W; but d, # d; and X, # X. It can be shown that x
d
X;d,==
W-B W-B,
(9)
For those oxides considered, the rate of change of oxide canoe with iner~~g inclusion percentage will generally be much greater than the r&e of change of garnet density. It is true that for some inclusions these changes will be opposing, but, as a, rough approximation, the purity values in Table 2 indicate the order of magnitude of the maximum purity of the analysed garnet concentrates that are consistent with the published figures. Purities, when claimed, are higher than these calculated figures.
Hypothesis (c) The analysed garnet concentrates are not truly representative of the average garnet in the rocks. If the analyses are error free, and if neither h~thesis (a) nor fb) holds, then one must conclude that in the given rock there does not exist an entity “clear garnet” such that all fmgments of it have the same chemical composition. Such a condition may arise through compositional zoning within crystals, or through the existence of two distinct garnet phases in the rock. Garnets frequently have inclusions concentrated in either the rim or the core. The tendency is to auras only the clear ma;terial,because it is often very difficult, and may be impossible, to carry out separations once the sample has been ground to a sufficiently fine grain size to release all the inclusions. Should there be compositional zoning, then such sampling would be non-representative of the garnet as a whole. Unless crystals are so large as to permit sepamte sampling and analysis of the different zones (LENIN1950), then, at present, the only single positive test-of compositional difference between rims and cores of garnets is electron micro-probe analysis. There are two main criteria according to which one c&n separa.te minerals. (1) By ooncentration of inolusion-free particles, (2) By removal of all di~rete grains of other minerals whilst retaining as much &s possible of the desired miner& A ~on~nt~te prepared by the first procedure could have an average ~rn~i~n of any value between the extreme limits of the ~rn~~n&l ~~~~ty, and could differ greatly from the average oomposition of theminer in the rook. A concentmte prepared by the second procedure will almost always dif&r from the sought average composition, but provided that the weight percentage of retied inclusions is
On the quality of representative mineral concentrates
551
comparable in size to the error of chemical analysis, then the introduced error in the major element analyses will be tolerably small. A small error, always present, is likely to have little effect on the final conclusions of a geochemical investigation, but selectively concentrated minerals could greatly affect such conclusions. The latter may not happen, but the risk is ever present and does not seem worth taking. Acknowledgemnte-Professor L. H. AHRENS (Department of Geochemistry, University of Cape Town, South Africa), Dr C. R. BURCH,C.B.E., F.R.S. (Royal Society Warren Research Fellow, Department of Physics, University of Bristol, England), Professor D. S. COOMBS(Department of Geology, University of Otago, New Zealand) and Mr B. CRUICIESHAXK (Lecturer in Chemistry, University of Bristol, England) kindly read the manuscript and I am grateful to them for their helpful comments. I am indebted to Dr BTJXCH for bringing to my notice the extension of my algebra which led to the derivation of equation (8). Mr P. CARR (Lecturer in Mathematics, College of Science and Technology, Bristol, England) is thanked for checking a number of the calculations. I wish to express my gratitude to the New Zealand Government for the award of a Commonwealth Research Scholarshipduring the tenure of which this paper was written. REPERENCES BARTHT. F. W. (1936) Structural and petrologic studies in Dutchess Co. New York. Part 2. Petrology and metamorphism of the Palaeozoic rocks. Bull. geol. Sot. Am. 4’7, 775-850. CHINNERG. A. (1900) Pelitic gneisseswith varying ferrous/ferricratios from Glen Clona, Angus, Scotland. J. Petrology 1, 178-217. COLEMANR. G. and LEE D. E. (1963) Glaucophane-bearingmetamorphic rock types of the Cazadero Area, California. J. Petrology 4, 260-301. ENC+EL A. E. J. and ENGEL C. G. (1958) Progressive metamorphism and granitization of the major paragneiss, Northwest Adirondack Mountains, New York. Part 1: Total rock. Bull. geol. Sot. Am. 69, 1369-1414. ENGELA. E. J. and ENGEL C. G. (1960) Progressive metamorphism and granitization of the major paragneiss,Northwest Adirondack Mountains, New York. Part 2: Mineralogy. Bull. geol. Sot. Am. 71, l-58. HOWIER. A. and SunA. P. (1957) The paragenesisof garnet in charnockite,enderbite, and related granulites. Miner&g. Msg. 81, 565-586. LAMBERTR. ST. J. (1959) The mineralogy and metamorphism of the Moine Schists of the Morar and Knoydart districts of Inverness-shire. Trane. R. Sot. Ed&b. 88, Pt. 3, 553-588. LEE D. E., COLEMAN R. G. and ERD R. C. (1963) Garnet types from the CazaderoArea, California. J. Petrology 4, 460-492. LEVINS. B. (1950) Genesisof some Adirondack garnet deposits. BUZZ.geol. Sot. Am. 61,519-665. MIYA~HIROA. (1953) Calcium-poor garnet in relation to metamorphism. Geochim. Coemochim. Actu 4, 179-208. WYNNE-EDWBRDSH. R. and HAY P. W. (1963) Coexisting cordierite and garnet in regionally metamorphosed rocks from the Westport area, Ontario. Can. Mineralogiet 7, 453-478.
On the quality
of representative
mineral
concentrabs
P. C. RICKWOOD Department of Geology, University of Otago, Dunedin, New Zealand (Received23 April 1965) Ah&&-An equation is derived to test the compatibility of an analysis of a mineral with that of its host-rock. It reveals incompatibility in 19 garnet/host-rock pairs of analyses out of 50 pairs published by 8 authors. There are three possible explanations, (1) analytical or printing errors, (2) “garnet” in statements of chemical and/or volume distribution analyses was “garnet plus inclusions”, (3) snalysed material was not representativeof the average garnet. A second equation, derived from the compatibility test, determinesthe maximum purity of the analysed material compatible with (1) and (2). With two exceptions, purity values range from 34 to 90%. For greater accuracy in major element snalyses when mineral homogeneity has not been proven, and particularly when mineral heterogeneity has been demonstrated by means of the electron micro-probe, it may be wiser to analyse high recovery concentratesrather than selectively prepared inclusion-freeconcentrates.
A literature search was made for chemical analyses of garnets and their host-rocks for comparison with similar pairs of analyses of specimens from Connemara, Eire. It wss revealed, surprisingly, that there was incompatibility between analyses in seven of the eight accounts that were found to contain adequate information for the necessary calculations to be made, and that none of the authors reported having made these calculations. This paper describes the compatibility calculation and presents some conclusions drawn from the published data. MATHEMATICAL DERNATION Consider a rock of density D, containing V volume y. of garnet (without inclusions) which has a density d. Let the rock contain W wt y0 of an oxide R,O,, and let the garnet contain X wt y0 of an oxide R,O,. In 100 g of rock there are V . (d/D) g of garnet. But 1 g of garnet contains X/100 g of R,O,, so that in 100 g of rock there are V . (d/D) . (X/100) g of R,O, locked in garnet. However, 100 g of rock contain W g of R,O,. Thus, if the wt y0 of R,O, that is located in all minerals other than garnet is called B, then
B=W-V.;.; Compatibility of analyses can be checked by calculation of B which should always be ~-0. PUBLISHED ANALYSES Compatibility calculrctions were carried out for the oxides CaO, MgO, Fe0 and MnO for the garnet/host-rock pairs of analyses given in eight studies containing 646
Bgn 18
Ch 113
Ch 219
Ch 121 Ch 119
10
11
12 13
982 x034
H 66
19
892
18
17
15 I6
3708
13-B
59.CZ-59
14
16.1
27-CZ-59
8
9
11.1
IO.4
4*1*
4*0*
4-o*
4-o*
14.2
4.17
4.5
4.02
4.02 3.99
3.99
4.06
4.17
4.09
4.1*
4*1* 4-1*
4.1*
4*1*
4.1*
4.1*
d
27.6 2.9
12.6
9.70
6.8
14.3
2.4
2.2
4.0
10
8
5
8*9
13.1
11
4
4.8
7
3
3
4
V
19.8
--_
6
2
1t
2
1
No.
Authors code no.
2.8’
2*8*
2-s*
2+8*
2.67
2.87
2.77
2.77
2.84
2+*
2.76
2.75
2.8”
I.2
1.89
5.91
8.54
8.37
1.58
0.81
0.77
2.04
2.25
l-20
6.3
7.1
1.63
1.34
2.32
2.68
2.72
0.40
O-18
0.42
3.44
3.29 2.95
0.22
3.2
0.85
W
-_. ._______ __.--_.-...-_-_.---..n.d. 2*1(* 2+* n.d. n.d. 2+$* n.d. 2*8* n.d. 2*8* n.d. 2a*
F X
0.31
0.88
1.73
o-54
0.07
0.31
0.15
0.48
0.40
0.17
0.55
1.03
0.95 1.44
2-18
0.33
-0.13
2.96 0.27
2.55
3.12
-0.33
1.69
0.79
-
. B
..^....__----
1.51
0.06
-
W-B
CSO
8.06
0.56
1*50
0*86
1.81
0.15 0.74
0.32
0.71
0.64
0.70
21.3
17.6
11.53
0.06
0.16
0.08
0.09
0.04
0.11
0.00
0.12
0.22
0.05
O-65
2.3
0.37
0.09
o-22
0.17
0.10
0.03
0.06
0.06
0.17
0.11
0.10
1.87
3.74
0.41
0.33
0.47
0.34 0.27
o-14
0.26
O-16
1.06
0.09
0.00
1.35
0.10
0.07
0.10
W-B
1.40
W
MnO
0.35
10.21
..-.__
rc X
Table 1. Compatibility of chemical analyses of garnets with their host rocks 4, R
-0*01 _---.-0.09 _ ._-_.. -0*07 ~_.. .--0.03 __-.__._
0.01
-0.06 --. 0.05
--0*05
-0*10 _.__..__ -0.05 -_@13 --0.06 ~-- 0.04 ^--..__ -1.44
-..0*03 --__.. -0.10
_~
1
z
.F cl
Cl-l121
Ch 119 3708
992
982 1034
H 66
13
14
16
17
19
26.13
27.63 27.96
27.04
27.92 33.30
25.20
28.12 28.48
29.36
23.98
24.30
26.32
34.28
34.13
-
-
n.d. n.d.
6.29
9.51
5.91
8.00
2.50
6.27
2.33
4.47
4.86 6.65
5.35 2.04
0.30
5.61 4.16 4.25
6.26
0.99
-4.52
-2.57
-2.18
I.51 1.74
IO.79
4.90
-0.12
2.68
4.98
2.29
I.21 4.13
6.81
3.5
-1.32
2.11 7.10
1.39 2.07
4.82
9.50
11.38
7.93
7.87
7.68
0.70 0.08
3.56
2.82
1.51
3.86 3.15
2.80 2.42 0.31 1.15
0.09 0.42
0.22
3.67
1.16 0.18
1.85 2.21
1.60
1.39
1.08
0.15 0.01
2.70
3.01
0.43 0.16
0.13
-
n.d. 2.61
-
-
n.d.
3.82 3.60
3.32
0.78 0.84
1.54
I.71
2.19
6.55 4.47
2.39
-
-
n.d.
W-B
n.d.
*
-
W
3.24
r
-
Y
B
W-B
2.0
3.66
4.38
5.36
6.18
8.74
5.63
-
W
Magnetite-hematite-bearing gneiss Magnetite-hematite-bearing gneiss Magnetite-hematite-bearing gneiss
-
Leptynite
-2.16 -0.04
3.55 2.00
Garnet gneiss
Garnet-mica schist Garnet-mica schist
Pelitic schist
Khondalite Khondalite
-1.05
2.71 2.00
Acid granulite
-0.25
Quartz-biotite-garnet gneiss Enderbite
1.31
Meta-ironstone
1.93
0.28 0.15
Metachert
Ihnenite-magnetite-bearing gneiss Ihnenito-magnetite-bearing gneiss
-
2.48
Garnet-chlorite schist Ihnenite-magnetite-bearing gneiss
-
Rock type
-
.
B
801-803). Source of analyses: 1 BARTH(1936,). 2-7 CHINNER(1960). 8-9 COLEMAN and LEE (1963), LEE, COLETUNand ERD (1963). 10 ENGEL and ENQEL(1958,196O). 11-15 HOWIEand SUBRUANIAM(1957). 16-18 LA~~BERT (1959). 19 WYNNE-EDWARDSand Hay (1963).
V = Volume yc of garnet; d = Garnet density; D = Rock density; X = Wt ye of oxide in garnet; W = Wt y. of oxide in rock; B = Wt y. of oxide in the rock that is located in minerals other than garnet; W - B = V . (d/D) . (X/100); n.d. = Not determined; * = Estimated value; t = Garnet volume calculated from chemical analyses and confirmed by Rosiwal analysis. B~LRTH (1936. pp.
18
15
12
Ch 113 Ch 219
27-CZ-59
8
11
13.8
11
7
59-cz-59
10
6
Bgn 18
8
5
9
4
4
10
15.6
3
3
34.00
2
2
n.d.
I X
lt
Authors code no.
1
No.
P. c.
548
J&XCWOOD
enough data. In some cases it was necessary to estinmte gsrnet and/or rock densities. Of 50 publiah~ p&s of snalyses, I9 produced one or more negative values of B (Table 1). Many of these in~mp&tibilities are further increased when other analysed minerals are considered. Errors in the estimates of rock densities are likely to be smaller than those for garnet densities, but an error as large as kO.2 g/ems in the latter would not alter the mineral: rock density rcctioby more than 5 per cent, and this does not significantly alter the majority of the values of B. If the estimates of the garnet densities are lowered by 6.2 g/cm8 then even the most marginal discrepancy between a pair of analyses (16-4InO) still remains. DEDUCTIONS Excluding large measurement errors and printing errors, there are only three explana;tions for the negative values of B. Any or all of these m&y hold and the implications of each will be considered in turn. Hypothah (a) .A fraction of the reported garnet volume is inclusions that were small enough to escape sepcbrateclassifi~tion in the volume distribution analysis. Let us accept that all the me~s~ementa have been accumtely made, that the rock has been carefully powdered and sampled, and that inclusion-free garnet grains have been separated and chemically analysed. Let I’, d, D, X, W and B be the sought true values and V,, d,, D,, X,, W, and B, be the reported values, then from equation (1)
BR=WR-vg.~.~o R (1) - (2) gives B - B, = W - WR Then~derh~the~s(~)~R=~; so that equ&ion (3) reduces to
L),=D;
V
.g.
X,=X;
go
+ VR
-2.2
(3)
R
W,=
W; but V,#V,
B-B,=(V,-v&g and equation (2) becomes W-BB,=V,.D.lOO
d
x
(5)
Thus, V -_== V, NOW
I?*
W-B W - BR
(6)
0,sothat W w
-RB,
(7)
On the quality of representativemineral oonoentrates
649
Hence, the maximum purity of the garnet reported in the volume distribution analysis that is entirely consistent with the given analytical Sgures is: W Te, Maximum pm@
if31
* 100%.
Sgures for each of the 27 discrepancies are given in Table 2.
Table 2. Maximum purities of garnet reported in the volume distribution analyses that are consistent with the given analytical figures* No. 1 2 3 4 6 6 7 8 8 9 9 10 11 12 12 12 13 13 13 14 14 14 15 10 17 I8 19
Authors oode no. 1 2 3 4 8 10 11 27-CZ-69 27-CZ-69 69-(32-69 69-CZ-69 Bgn 18 ch 113 Ch 219 Ch 219 Ch 219 ch 121 ch 121 ch 121 Ch 119 Ch 119 Ch 119 3708 992 982 1034 H 60
Oxide dieorepancy
MaXimun, purity in VR
MhO MIkO MilO
70.0% 0% 61.6% 04.3% 72.3% Sl*S% 90.2 % 81.6% 00.2% 40.0% 34.8% 60.0% 97.6% 70.6% 07.2% 80.6% 0% 47.6% 62.6% 68.1% 68.1% 41.1% 81.8% 90.0% 47.1% 68.2% 06.7 %
MIIO MkO MIIO WI0 l&O Fe0 C&O iUSl0 MIXLO Fe0 IGO Fe0 MgO MnO I?00 MgO C&O Fe0 MgO Mrso XIlO iKIlO MIXlO MIIIO
Sourceofazmlyaes: No.lB~m. 2-7 CHINNER. 8-9Co~~ararrmdL~~; LEE,COLEXAN and EB.D. 10 ENUEL md ENQEL. 11-16 Howm and SWRAMANUM. 16-18 bBKBERT. 19 %~%NNE-~DWARDB~~~~~Y. * Alternatively, these f&wea indicate the order of magnitude of the maximum purity of the &ywd garnet concentratesthat are con&tent with the published data.
For nos. 2 and 13 no manganese oxide is reported in the rocks but O-10 and 0.06 per cent, respectively, should be present to account for the requirements of garnet. The calculated zero per cent purities are absurd so that hypothesis (a) alone is not tenable, and h~oth~~ (b) produces a similar conclusion. Hypothesis (c) (below) can therefore be inferred to operate. However, these incompatibilities constitute speoial Casey where suspicion is cast on the validity of the assumption that no errors have been made. No detection limits are given and the authors make no comments. Maximum purities given by two oxide discrepanoies for the same garnet/host-rook pairs of
550
I?. C.Rzcrrwoo~
analyses were remarkably similar e.g. 8 (l&10)-61.5*/& (FeO)-60-2°/o. None of the authors has specifically reported that garnet in the volume distribution analyses must be taken to mean garnet plus inclusions.
Hypothesis (b) The analysed garnet concentrate was not inclusion-free, Let us accept that all the measurements hsve been accurately made, that the rock has been carefully powdered and sampled, and thst inclusions in minerals were ~p~a~ly recorded in the volume distribution analyses. Then, V, = V; DB = D; W, = W; but d, # d; and X, # X. It can be shown that x
d
X;d,==
W-B W-B,
(9)
For those oxides considered, the rate of change of oxide canoe with iner~~g inclusion percentage will generally be much greater than the r&e of change of garnet density. It is true that for some inclusions these changes will be opposing, but, as a, rough approximation, the purity values in Table 2 indicate the order of magnitude of the maximum purity of the analysed garnet concentrates that are consistent with the published figures. Purities, when claimed, are higher than these calculated figures.
Hypothesis (c) The analysed garnet concentrates are not truly representative of the average garnet in the rocks. If the analyses are error free, and if neither h~thesis (a) nor fb) holds, then one must conclude that in the given rock there does not exist an entity “clear garnet” such that all fmgments of it have the same chemical composition. Such a condition may arise through compositional zoning within crystals, or through the existence of two distinct garnet phases in the rock. Garnets frequently have inclusions concentrated in either the rim or the core. The tendency is to auras only the clear ma;terial,because it is often very difficult, and may be impossible, to carry out separations once the sample has been ground to a sufficiently fine grain size to release all the inclusions. Should there be compositional zoning, then such sampling would be non-representative of the garnet as a whole. Unless crystals are so large as to permit sepamte sampling and analysis of the different zones (LENIN1950), then, at present, the only single positive test-of compositional difference between rims and cores of garnets is electron micro-probe analysis. There are two main criteria according to which one c&n separa.te minerals. (1) By ooncentration of inolusion-free particles, (2) By removal of all di~rete grains of other minerals whilst retaining as much &s possible of the desired miner& A ~on~nt~te prepared by the first procedure could have an average ~rn~i~n of any value between the extreme limits of the ~rn~~n&l ~~~~ty, and could differ greatly from the average oomposition of theminer in the rook. A concentmte prepared by the second procedure will almost always dif&r from the sought average composition, but provided that the weight percentage of retied inclusions is
On the quality of representative mineral concentrates
551
comparable in size to the error of chemical analysis, then the introduced error in the major element analyses will be tolerably small. A small error, always present, is likely to have little effect on the final conclusions of a geochemical investigation, but selectively concentrated minerals could greatly affect such conclusions. The latter may not happen, but the risk is ever present and does not seem worth taking. Acknowledgemnte-Professor L. H. AHRENS (Department of Geochemistry, University of Cape Town, South Africa), Dr C. R. BURCH,C.B.E., F.R.S. (Royal Society Warren Research Fellow, Department of Physics, University of Bristol, England), Professor D. S. COOMBS(Department of Geology, University of Otago, New Zealand) and Mr B. CRUICIESHAXK (Lecturer in Chemistry, University of Bristol, England) kindly read the manuscript and I am grateful to them for their helpful comments. I am indebted to Dr BTJXCH for bringing to my notice the extension of my algebra which led to the derivation of equation (8). Mr P. CARR (Lecturer in Mathematics, College of Science and Technology, Bristol, England) is thanked for checking a number of the calculations. I wish to express my gratitude to the New Zealand Government for the award of a Commonwealth Research Scholarshipduring the tenure of which this paper was written. REPERENCES BARTHT. F. W. (1936) Structural and petrologic studies in Dutchess Co. New York. Part 2. Petrology and metamorphism of the Palaeozoic rocks. Bull. geol. Sot. Am. 4’7, 775-850. CHINNERG. A. (1900) Pelitic gneisseswith varying ferrous/ferricratios from Glen Clona, Angus, Scotland. J. Petrology 1, 178-217. COLEMANR. G. and LEE D. E. (1963) Glaucophane-bearingmetamorphic rock types of the Cazadero Area, California. J. Petrology 4, 260-301. ENC+EL A. E. J. and ENGEL C. G. (1958) Progressive metamorphism and granitization of the major paragneiss, Northwest Adirondack Mountains, New York. Part 1: Total rock. Bull. geol. Sot. Am. 69, 1369-1414. ENGELA. E. J. and ENGEL C. G. (1960) Progressive metamorphism and granitization of the major paragneiss,Northwest Adirondack Mountains, New York. Part 2: Mineralogy. Bull. geol. Sot. Am. 71, l-58. HOWIER. A. and SunA. P. (1957) The paragenesisof garnet in charnockite,enderbite, and related granulites. Miner&g. Msg. 81, 565-586. LAMBERTR. ST. J. (1959) The mineralogy and metamorphism of the Moine Schists of the Morar and Knoydart districts of Inverness-shire. Trane. R. Sot. Ed&b. 88, Pt. 3, 553-588. LEE D. E., COLEMAN R. G. and ERD R. C. (1963) Garnet types from the CazaderoArea, California. J. Petrology 4, 460-492. LEVINS. B. (1950) Genesisof some Adirondack garnet deposits. BUZZ.geol. Sot. Am. 61,519-665. MIYA~HIROA. (1953) Calcium-poor garnet in relation to metamorphism. Geochim. Coemochim. Actu 4, 179-208. WYNNE-EDWBRDSH. R. and HAY P. W. (1963) Coexisting cordierite and garnet in regionally metamorphosed rocks from the Westport area, Ontario. Can. Mineralogiet 7, 453-478.