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A device for the rapid modal analysis of coarse-grained rocks
283
A Device for the Rapid Modal Analysis of Coarse-Grained Rocks by M. S. BARRATI and G. R. PARSLOW Received 5 February 1965; read 7 January 1966 CONTENTS 1. 2.
page 283
INTRODUCTION MICROSCOPIC METHOD
(a) Sources of Error (b) Time Factor and Expense 3.
MACROSCOPIC METHOD ...
(a) Accuracy (b) Time Factor and Expense
283 284 284 285 288 289 290 290 291
ACKNOWLEDGMENTS '" REFERENCES ... DISCUSSION
ABSTRACT: A device for modal analysis of coarse-grained rocks, using a handoperated mechanical stage, used in conjunction with tabulator, binocular microscope and an etched rock slice, is described. It is considered that the macroscopic method is quicker than, and as accurate as, the microscopic methods of modal analysis of coarsegrained rocks. A study of the errors present in the two types of analysis, macroscopic and microscopic, is made and examples of the former type are given for a collection of granite specimens.
1. INTRODUCTION AN ACCOUNT OF techniques of modal analysis by the measurement of relative areas in thin sections has been given by Chayes (1956). Modern instruments for this purpose may be divided into two types, continuous line integrators such as the Dollar integrating stage (1937) and point counters such as that of Chayes (1949, 1955) and that produced by the James Swift Co. The poor reproducibility of results for coarse-grained rocks by such microscopic methods has led recent workers, Jackson & Ross (1956), Fitch (1959), Smithson (1963), to attempt macroscopic techniques using rock slabs. The subject of this paper is the same, but the object is to give details as to the construction of a simple piece of equipment and an assessment of the accuracy of this type of method of modal analysis.
2. MICROSCOPIC METHOD The point count method of modal analysis commonly used today is to clamp a thin section of a rock to a mechanical stage which is fitted to a polarising microscope. The mechanical stage is connected to a bank of PROC. GEOL. ASS., VOL. 77, PART 3,1966
19
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M. S. BARRATT AND G. R. PARSLOW
electric counters so that each time one of the counter keys is depressed, to record the mineral observed under the cross-wires, the thin section is moved a specific distance along the traverse. A number of traverses is made at equal distances apart and thus minerals are recorded over a grid system of points. A mode is obtained by reducing to a percentage the totals of the different minerals registered on the tabulator. (a) Sources of Error The precision of modal analysis of rocks has been discussed by Chayes & Fairbairn (1951), Barringer (1953), Chayes (1956), Saha (1959), Bayly (1960a and 1960b), Exley (1963), Hasofer (1963), Solomon (1963) and Emerson (1964). As most of these authors point out, the main difficulty is the coarseness of grain of many rocks. It is frequently not possible to obtain a representative mode of a coarse-grained rock from one microscope slide, having an average area of 400 mms, because an insufficient area of rock is measured. To compensate for the inhomogeneity of coarse-grained rocks and the relatively large area covered by individual grains it is necessary to measure the mode over a large surface of rock. Using the Swift point counter, this is achieved by making several thin sections. Point count methods of modal analysis assume that an areal percentage of minerals represents the actual volume percentages in a given rock. Again, in coarse-grained rocks this assumption may be subject to error because of the large size of the mineral grains. This possible error can be reduced, even eliminated, by making several thin sections either from different parts of one hand-specimen or, preferably, from each of several hand-specimens (Emerson, 1964), and averaging the resultant modes. Operator variance, errors made by the operator during an analysis, varies considerably from one operator to another and is probably controlled, to a large extent, by external conditions, such as extraneous noise, at the time of the analysis. The error is caused by the misidentification of minerals and the depressing of wrong tabulator keys. Operator variance usually increases with increasing operator fatigue which in turn is related to the time factor of anyone analysis. (b) Time Factor and Expense
The use of a mechanical stage for the modal analysis of coarse-grained rocks increases the time factor since the choice of gears, in for example the Swift point counter, is such that the greatest distance between points is only 0.3 mm. and therefore about 3000 points would need to be recorded in order to cover an adequate area. The identification of minerals in different optical orientations could increase considerably the time needed
MODAL ANALYSIS OF COARSE-GRAINED ROCKS
285
to complete one analysis. These two factors would therefore tend to increase the operator variance. Chayes (1956) considered that a rock with an I.C. number of 20-25 would need to be measured over an area of 4000 mm 2 if the analytical error is to be maintained at or below 2.0 per cent for the major minerals. The I.C. number of a rock, devised by Chayes, is an arbitrary measure of coarseness obtained by counting the number of mineral boundaries crossed during a 4 em. traverse. As the average slide is rarely more, but often less, than 400 mm", up to ten slides may need to be measured. The preparation and measurement of such a number of slides per sample is very laborious, time-consuming and expensive. Furthermore, Chayes indicates that the measurement area should be greatly increased if the rocks exhibit any structures (flow, etc.). It may be noted that in the presence of a planar structure, such as a simple foliation, the structure should be at 45° to the traverse direction. On the other hand, satisfactory results may be obtained, by the microscopic method, from one thin section of about 400 mm'', when the I.C. number is greater than 55. 3. MACROSCOPIC METHOD The device described below has been designed for maximum accuracy concomitant with speed and economy. Essentially, the method is a macroscopic technique using rock slices, reflected light and a binocular microscope. Fig. 1 shows plan and elevation diagrams of the apparatus. The original piece ofequipment (Plate 15A) was constructed in the Geology Department of the University of Newcastle upon Tyne during 1961. It is relatively cheap and easy to build when compared with Smithson's equipment (1963). The apparatus is a hand-operated stage on which a rock slice can be moved in two directions at right-angles. Movement from one traverse line to another, north-south relative to the microscope cross-wires, is facilitated by the use of a sliding aluminium plate (A) measuring 7 x 14 em. The distance between the traverse lines is measured with the aid of a steel rule (B) mounted on the plate carrier (C). The plate (A) is removable for the easy mounting of the rock slice. The plate carrier (C) travels along two 1 em, diameter rods (D and D /) and is moved, east-west relative to the microscope cross-wires, by turning the handle (E). This handle (E) turns the large bolt (F, 30 em. long and 2 cm. diam.) that runs through the nut (G) fixed to the underside of the plate carrier (C). The bolt (F) is carried on brass bearings (H and H') fitted into the L-shaped brackets (I and 1') forming the ends of the stage. These brackets (I and I') are firmly screwed to a wooden base and the whole apparatus may be clamped to the bench when in use.
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M. S. BARRATT AND G. R. PARSLOW
All the materials used in the construction of the apparatus are easily obtainable and the assembly is fairly simple, without the need for extensive workshop facilities. The rock slice (J), approximately 100 x 100 x 3 mm., can be readily cut from the hand-specimen with a diamond-saw. This rock slice (J) is mounted on the sliding plate (A) with Plasticine using a hand-levelling press. The slice is viewed by reflected light, using a binocular microscope, and the minerals are recorded on an electric tabulator. In smaller institutions or for
c
,
HI
G
E
Fig. 1. Plan and elevation diagrams, not to scale, of the apparatus described
PROC. GEOL. ASS., VOL. 77 (1966)
PLATE 15
A: General view of the modal analysis equipment described in this paper
.
.' ,.
B: A slice of etched granite viewed at x 5 magnification Plagioclase crystals. powdery white and euhedral, enclosed with criss-crossing ridges, are clearly visible. Exsolved albite crystals can also be seen. A small biotite crystal, black with the edge of the plate
,\
..
by reflected light. The by alkali felspar, white rimming the plagioclase cleavage, is visible near
[To face p. 286
MODAL ANALYSIS OF COARSE-GRAINED ROCKS
287
amateur work the electric tabulator can be dispensed with and straightforward manual tabulating used. Even the binocular can be replaced by a simple magnifier which has some fixed reference point in the field of view (i.e. equivalent to the crossed hair-line of the microscope). By turning the handle (E) of the stage continuously or by a measured amount (i.e. one turn, half turn, etc.) the traverse can be that of a continuous line integrator or a point counter. The minerals present in the rock slice can be etched and stained to assist identification. Bailey & Stevens (1960) suggest etching for five minutes in hydrofluoric acid vapour and ten minutes in sodium cobaltinitrate and sodium rhodizonate solutions to stain the alkali and plagioclase felspars yellow and red respectively. The staining technique was dispensed with as it was found to be rather troublesome. The staining technique often stained all the felspars yellow or was removed during the washing process. Perseverance resulted in three out of five slabs taking up the stain each time, but in the present study, the increased time factor was considered to be too high to warrant continuing with it. Instead, the slices were etched 40 per cent hydrofluoric acid for five minutes and the different minerals were found, when viewed by reflected light, to exhibit characteristic etch textures. For instance, in the Cairnsmore of Fleet granite specimens (Parslow, 1964) biotite and chlorite are black with a cleavage; muscovite is yellow with a cleavage; plagioclase is white and powdery; alkali felspar is white with a network of fine ridges and quartz is glassy. The alkali felspar is the deepest etched with plagioclase being less affected and the quartz and micas showing little or no effects of the etching process. Plate 15 B shows that even exsolved rims of albite round plagioclase are readily discernible and that the plagioclase is not so deeply etched as the alkali felspar. The same minerals in other rock types may show slightly different features to those mentioned above, but it is considered that they would still exhibit certain characteristic textures thus facilitating their identification. Etch textures are comparable with normal optical properties; that is to say a person studying a group of rocks will, with practice, be capable of identifying different minerals that have similar etch textures. If a study is being made of rock types other than granite, where two felspars are present, it may be found necessary to adopt the staining technique even though it is rather time-consuming. It may be necessary to vary the etching time when commencing a study of a group of rocks in order to obtain the best possible etch textures. In certain exceptional cases etching may not be necessary. Lappin (personal communication), when using the apparatus for eclogite modes, found that, due to the characteristic mineral colours, a coat of glycerine on the slice was sufficient to assist in identification and that duplicate analyses agreed to ±O.2 per cent per mineral.
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M. S. BARRATT AND G. R. PARSLOW
(a) Accuracy The accuracy of the macroscopic method was estimated using specimens of the Cairnsmore of Fleet granite with the following conclusions. For an average coarse-grained rock (I.C. 20-25), using traverse lines 2 mm. apart and points spaced at 2 mm. intervals (half-turn of the handle on the original apparatus) on the traverse line, a 500 point count gave rather poor results; a 1000 point count gave good results; and a 1500 point count gave excellent results (Table 1). I. Duplicate determinations (A and B) of a granite (CFG125j288) using 500,1000 and 1500 point counts
TABLE
It is considered that either the 1000 or the 1500 point count is sufficiently accurate for most petrological work.
A500 B500 Range (A-B) Al 000 BIOOO Range (A-B) AI500 BI500 Range (A-B)
Quartz
Potash Felspar
Plagioclase Felspar
Biotite + Chlorite
Muscovite
31.0 34.2 3.2 32.6 31.8 0.8 31.6 31.8 0.2
36.4 31.6 4.8 34.0 33.3 0.7 34.3 35.2 0.9
24.8 26.4 1.6 25.6 25.9 0.3 25.5 25.2 0.3
4.4 3.4 1.0 3.9 4.7 0.8 4.6 4.2 0.4
3.4 4.4 1.0 3.9 4.3 0.4 4.0 3.7 0.3
The average ranges (errors) of the different point counts (500, 1000, 15(0) of a selected sample (11 specimens) of the population are compared in Table II with the maximum range found in the selected sample and in the II. Comparison of the average range (error) per specimen for the various point counts (500, 1000, 1500) in a selected sample of 11 specimens with the maximum range between specimens in that sample (A) and the maximum range between specimens in the total population of 150 specimens
TABLE
(B) The results indicate that all point counts are well within the range of the rocks studied. The 1000 or 1500 counts are to be preferred because of their very small ranges (errors).
500 1000 1500 A B
Quartz
Potash Felspar
Plagioclase Felspar
Biotite + Chlorite
Muscovite
3.2 1.4 0.4 11.3 17.9
4.8 1.6 0.9 22.3 24.1
1.6 1.3 1.0 16.2 20.3
1.0 1.0 0.3 6.1 15.6
1.0 0.6 0.3 5.0 10.8
MODAL ANALYSIS OF COARSE-GRAINED ROCKS
289
total population of 150 specimens. Range (error) is defined as the difference between duplicate determinations on a specimen and is a simple measure of analytical error. It can be seen that the ranges (errors) of the point counts are well within the maximum range of the selected group, and of the total population. This indicates that the range exhibited by the total population of granites is due to compositional trends and cannot be accounted for by analytical error. More sophisticated statistics may be applied to measure error but these are only necessary when the range (error) per specimen is very close to the maximum range of the rocks studied, making it difficult to decide whether or not the rocks exhibit any compositional trends. For example, if modal analyses of two specimens of the extreme rock types of the group indicate that the compositional range is large (i.e. the major minerals have a range ~3 per cent) then the above simple statistical technique would be adequate. If, however, the compositional range is similar in magnitude to the range (error) per specimen (i.e. <3 per cent) then further statistical tests would be necessary to define the accuracy of the method within finer limits. In this case, an estimate of the errors could be obtained by using the formula derived by Hasofer (1963) and discussed by Solomon (1963). Alternatively, the two specimens could each be analysed ten or more times and the standard deviations calculated from the results. A comparison of the two sets of standard deviations so obtained will show whether or not the errors (standard deviation) are larger than the small range in composition of the specimens. It will usually be found that the errors are smaller than the compositional range, but if the opposite is the case the method must be modified to decrease these errors. This is achieved by increasing the measurement area, decreasing the grid spacings and checking operator variance. The last mentioned may be checked by the methods suggested by Solomon (368, 1963). (b) Time Factor and Expense
The time per analysis for the 500, 1000 and 1500 point counts is 15, 20 and 35 minutes respectively. The 1000 point count was used when analysing the Cairnsmore of Fleet granite specimens because the increased timefactor of the 1500 point count on 150 specimens outweighed the increase in accuracy. When a small number of specimens is to be analysed or a high degree of accuracy is necessary then the 1500 point count is preferable. Assuming that for an accurate analysis of an average coarse-grained rock six microscope slides, for the microscopic method, would be equivalent to one rock slice of the same area, for the macroscopic method, then the difference in expense between the two methods is immediately obvious. The total cost for six microscope slides (labour, materials, etc.) is at least
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thirty shillings compared with two shillings for a rock slice. This simple-tobuild device will therefore give results that have an accuracy equal to other similar pieces of equipment (Dollar, Chayes, Smithson, etc.) and is considered to be more widely applicable because of its simplicity of construction. It is concluded that this economical method can rapidly give results that are sufficiently accurate for most petrological work. ACKNOWLEDGMENTS
The authors are grateful to D.S.I.R. for providing a grant during the time the work was carried out. Thanks are given to Professor T. S. Westoll for putting the Geology Department of the University of Newcastle upon Tyne at our disposal. Sincere thanks are due to Dr. J. E. Mason and Mr. G. T. Raine of the Geology and Geography Department in Kingston College of Technology and to Dr. C. S. Exley of the University of Keele for their generous help and critical suggestions regarding the presentation of this paper. REFERENCES BAILEY, E. H. & R. E. STEVENS. 1960. Selective Staining of K-feldspar and Plagioclase on Rock Slabs and Thin Sections. Am. Miner., 45, 1020-5. BARRINGER, A. R. 1953. The Preparation of Polished Sections of Ores and Mill Products using Diamond Abrasives, and their Quantitative Study by Point Counting Methods. Trans Instn Min. Metall., 63, 21-41. BAYLY, M. B. 1960a. Errors in Point-Counter Analysis. Am. Miner., 45,447-9. - - - . 1960b. Modal Analysis by Point-Counter-the Choice of Sample Area. J. geol, Soc. Aust., 6, 119-30. CHAYES, F. 1949. A Simple Point Counter for Thin-section Analysis. Am. Miner., 34, 1-11. - - - . 1955. A Point Counter Based on the Leitz Mechanical Stage. Am. Miner., 40, 126-7. - - - . 1956. Petrographic Modal Analysis. - - - & H. W. FAIRBAIRN. 1951. A Test of the Precision of Thin-section Analysis by Point Counter. Am. Miner., 36,704-12. DOLLAR, A. J. 1937. An Integrating Micrometer for the Geometrical Analysis of Rocks. Mineralog. Mag., 24, 577-94. EMERSON, D. O. 1964. Modal Variations within Granitic Outcrops. Am. Miner., 49, 1224-33. EXLEY, C. S. 1963. Quantitative Areal Modal Analysis of Granitic Complexes: a Further Contribution. Bull. geol. Soc. Am., 74, 649-54. FITCH, F. J. 1959. Macro Point Counting. Am. Miner., 44, 667-9. HASOFER, A. M. 1963. On the Reliability of the Point-Counter Method in Petrography. Aust, J. appl. Sci., 14, 168-79. JACKSON, E. D. & D. C. Ross. 1956. A Technique for Modal Analyses of Medium- and Coarse-grained (3-10 mm.) Rocks. Am. Miner., 41, 648-51. PARSLOW, G. R. 1964. The Cairnsmore of Fleet Granite and its Aureole. Ph.D. Thesis, University of Newcastle upon Tyne, SAHA, A. K. 1959. On the Precision of Modal Analyses of Rocks. Q. JI geol. Min. metall. Soc. India, 31, 1-6.
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SMITHSON, S. B. 1963. A Point-Counter for Modal Analysis of Stained Rock Slabs. Am. Miner., 48,1164-6. SOLOMON, M. 1963. Counting and Sampling Errors in Modal Analysis by Point Counter. J. Petrology, 4, 367-82. G. R. Parslow
Geology and Geography Department Kingston College of Technology Kingston-upon-Thames, Surrey
M. S. Barratt Geology Department University of Keele
DISCUSSION MR. D. G. A. WHITTEN suggests that when discussing apparatus and methods of volumetric modal analysis it should not be forgotten that perhaps the simplest possible technique was described by Holmes in his book Petrographic Methods and Calculations (192\). In this he gives an account of the modal analysis of the large slabs of Shap granite which at that time formed the steps of the City and Guilds College in Exhibition Road, South Kensington. The only apparatus required was a straight-edge, a pencil and a tape-measure. Statistically it is probable that the measurements of such large slabs, however crudely done, yielded very good results. The importance of correct identification of the minerals during modal analysis cannot be stressed too strongly. The difficulties which have been mentioned with staining techniques have also been experienced by the speaker. The problem appears to be that in general we are uncertain as to the nature of the material which is actually being dyed, and research on this point would appear necessary. The speaker congratulated the authors on the description of a piece of apparatus which was simple enough for manufacture to be attempted by anyone, even without the facilities of a well-equipped workshop. THE AUTHORS would agree with the speaker that Holmes's technique is often ignored. There are, however, two cases where his method is extremely useful: the analysis of pegmatites, and as a field technique in well-exposed glaciated terrain. Regarding staining, the authors feel that the present staining techniques are adequate but further research into staining techniques would be highly desirable.
A Device for the Rapid Modal Analysis of Coarse-Grained Rocks by M. S. BARRATI and G. R. PARSLOW Received 5 February 1965; read 7 January 1966 CONTENTS 1. 2.
page 283
INTRODUCTION MICROSCOPIC METHOD
(a) Sources of Error (b) Time Factor and Expense 3.
MACROSCOPIC METHOD ...
(a) Accuracy (b) Time Factor and Expense
283 284 284 285 288 289 290 290 291
ACKNOWLEDGMENTS '" REFERENCES ... DISCUSSION
ABSTRACT: A device for modal analysis of coarse-grained rocks, using a handoperated mechanical stage, used in conjunction with tabulator, binocular microscope and an etched rock slice, is described. It is considered that the macroscopic method is quicker than, and as accurate as, the microscopic methods of modal analysis of coarsegrained rocks. A study of the errors present in the two types of analysis, macroscopic and microscopic, is made and examples of the former type are given for a collection of granite specimens.
1. INTRODUCTION AN ACCOUNT OF techniques of modal analysis by the measurement of relative areas in thin sections has been given by Chayes (1956). Modern instruments for this purpose may be divided into two types, continuous line integrators such as the Dollar integrating stage (1937) and point counters such as that of Chayes (1949, 1955) and that produced by the James Swift Co. The poor reproducibility of results for coarse-grained rocks by such microscopic methods has led recent workers, Jackson & Ross (1956), Fitch (1959), Smithson (1963), to attempt macroscopic techniques using rock slabs. The subject of this paper is the same, but the object is to give details as to the construction of a simple piece of equipment and an assessment of the accuracy of this type of method of modal analysis.
2. MICROSCOPIC METHOD The point count method of modal analysis commonly used today is to clamp a thin section of a rock to a mechanical stage which is fitted to a polarising microscope. The mechanical stage is connected to a bank of PROC. GEOL. ASS., VOL. 77, PART 3,1966
19
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M. S. BARRATT AND G. R. PARSLOW
electric counters so that each time one of the counter keys is depressed, to record the mineral observed under the cross-wires, the thin section is moved a specific distance along the traverse. A number of traverses is made at equal distances apart and thus minerals are recorded over a grid system of points. A mode is obtained by reducing to a percentage the totals of the different minerals registered on the tabulator. (a) Sources of Error The precision of modal analysis of rocks has been discussed by Chayes & Fairbairn (1951), Barringer (1953), Chayes (1956), Saha (1959), Bayly (1960a and 1960b), Exley (1963), Hasofer (1963), Solomon (1963) and Emerson (1964). As most of these authors point out, the main difficulty is the coarseness of grain of many rocks. It is frequently not possible to obtain a representative mode of a coarse-grained rock from one microscope slide, having an average area of 400 mms, because an insufficient area of rock is measured. To compensate for the inhomogeneity of coarse-grained rocks and the relatively large area covered by individual grains it is necessary to measure the mode over a large surface of rock. Using the Swift point counter, this is achieved by making several thin sections. Point count methods of modal analysis assume that an areal percentage of minerals represents the actual volume percentages in a given rock. Again, in coarse-grained rocks this assumption may be subject to error because of the large size of the mineral grains. This possible error can be reduced, even eliminated, by making several thin sections either from different parts of one hand-specimen or, preferably, from each of several hand-specimens (Emerson, 1964), and averaging the resultant modes. Operator variance, errors made by the operator during an analysis, varies considerably from one operator to another and is probably controlled, to a large extent, by external conditions, such as extraneous noise, at the time of the analysis. The error is caused by the misidentification of minerals and the depressing of wrong tabulator keys. Operator variance usually increases with increasing operator fatigue which in turn is related to the time factor of anyone analysis. (b) Time Factor and Expense
The use of a mechanical stage for the modal analysis of coarse-grained rocks increases the time factor since the choice of gears, in for example the Swift point counter, is such that the greatest distance between points is only 0.3 mm. and therefore about 3000 points would need to be recorded in order to cover an adequate area. The identification of minerals in different optical orientations could increase considerably the time needed
MODAL ANALYSIS OF COARSE-GRAINED ROCKS
285
to complete one analysis. These two factors would therefore tend to increase the operator variance. Chayes (1956) considered that a rock with an I.C. number of 20-25 would need to be measured over an area of 4000 mm 2 if the analytical error is to be maintained at or below 2.0 per cent for the major minerals. The I.C. number of a rock, devised by Chayes, is an arbitrary measure of coarseness obtained by counting the number of mineral boundaries crossed during a 4 em. traverse. As the average slide is rarely more, but often less, than 400 mm", up to ten slides may need to be measured. The preparation and measurement of such a number of slides per sample is very laborious, time-consuming and expensive. Furthermore, Chayes indicates that the measurement area should be greatly increased if the rocks exhibit any structures (flow, etc.). It may be noted that in the presence of a planar structure, such as a simple foliation, the structure should be at 45° to the traverse direction. On the other hand, satisfactory results may be obtained, by the microscopic method, from one thin section of about 400 mm'', when the I.C. number is greater than 55. 3. MACROSCOPIC METHOD The device described below has been designed for maximum accuracy concomitant with speed and economy. Essentially, the method is a macroscopic technique using rock slices, reflected light and a binocular microscope. Fig. 1 shows plan and elevation diagrams of the apparatus. The original piece ofequipment (Plate 15A) was constructed in the Geology Department of the University of Newcastle upon Tyne during 1961. It is relatively cheap and easy to build when compared with Smithson's equipment (1963). The apparatus is a hand-operated stage on which a rock slice can be moved in two directions at right-angles. Movement from one traverse line to another, north-south relative to the microscope cross-wires, is facilitated by the use of a sliding aluminium plate (A) measuring 7 x 14 em. The distance between the traverse lines is measured with the aid of a steel rule (B) mounted on the plate carrier (C). The plate (A) is removable for the easy mounting of the rock slice. The plate carrier (C) travels along two 1 em, diameter rods (D and D /) and is moved, east-west relative to the microscope cross-wires, by turning the handle (E). This handle (E) turns the large bolt (F, 30 em. long and 2 cm. diam.) that runs through the nut (G) fixed to the underside of the plate carrier (C). The bolt (F) is carried on brass bearings (H and H') fitted into the L-shaped brackets (I and 1') forming the ends of the stage. These brackets (I and I') are firmly screwed to a wooden base and the whole apparatus may be clamped to the bench when in use.
286
M. S. BARRATT AND G. R. PARSLOW
All the materials used in the construction of the apparatus are easily obtainable and the assembly is fairly simple, without the need for extensive workshop facilities. The rock slice (J), approximately 100 x 100 x 3 mm., can be readily cut from the hand-specimen with a diamond-saw. This rock slice (J) is mounted on the sliding plate (A) with Plasticine using a hand-levelling press. The slice is viewed by reflected light, using a binocular microscope, and the minerals are recorded on an electric tabulator. In smaller institutions or for
c
,
HI
G
E
Fig. 1. Plan and elevation diagrams, not to scale, of the apparatus described
PROC. GEOL. ASS., VOL. 77 (1966)
PLATE 15
A: General view of the modal analysis equipment described in this paper
.
.' ,.
B: A slice of etched granite viewed at x 5 magnification Plagioclase crystals. powdery white and euhedral, enclosed with criss-crossing ridges, are clearly visible. Exsolved albite crystals can also be seen. A small biotite crystal, black with the edge of the plate
,\
..
by reflected light. The by alkali felspar, white rimming the plagioclase cleavage, is visible near
[To face p. 286
MODAL ANALYSIS OF COARSE-GRAINED ROCKS
287
amateur work the electric tabulator can be dispensed with and straightforward manual tabulating used. Even the binocular can be replaced by a simple magnifier which has some fixed reference point in the field of view (i.e. equivalent to the crossed hair-line of the microscope). By turning the handle (E) of the stage continuously or by a measured amount (i.e. one turn, half turn, etc.) the traverse can be that of a continuous line integrator or a point counter. The minerals present in the rock slice can be etched and stained to assist identification. Bailey & Stevens (1960) suggest etching for five minutes in hydrofluoric acid vapour and ten minutes in sodium cobaltinitrate and sodium rhodizonate solutions to stain the alkali and plagioclase felspars yellow and red respectively. The staining technique was dispensed with as it was found to be rather troublesome. The staining technique often stained all the felspars yellow or was removed during the washing process. Perseverance resulted in three out of five slabs taking up the stain each time, but in the present study, the increased time factor was considered to be too high to warrant continuing with it. Instead, the slices were etched 40 per cent hydrofluoric acid for five minutes and the different minerals were found, when viewed by reflected light, to exhibit characteristic etch textures. For instance, in the Cairnsmore of Fleet granite specimens (Parslow, 1964) biotite and chlorite are black with a cleavage; muscovite is yellow with a cleavage; plagioclase is white and powdery; alkali felspar is white with a network of fine ridges and quartz is glassy. The alkali felspar is the deepest etched with plagioclase being less affected and the quartz and micas showing little or no effects of the etching process. Plate 15 B shows that even exsolved rims of albite round plagioclase are readily discernible and that the plagioclase is not so deeply etched as the alkali felspar. The same minerals in other rock types may show slightly different features to those mentioned above, but it is considered that they would still exhibit certain characteristic textures thus facilitating their identification. Etch textures are comparable with normal optical properties; that is to say a person studying a group of rocks will, with practice, be capable of identifying different minerals that have similar etch textures. If a study is being made of rock types other than granite, where two felspars are present, it may be found necessary to adopt the staining technique even though it is rather time-consuming. It may be necessary to vary the etching time when commencing a study of a group of rocks in order to obtain the best possible etch textures. In certain exceptional cases etching may not be necessary. Lappin (personal communication), when using the apparatus for eclogite modes, found that, due to the characteristic mineral colours, a coat of glycerine on the slice was sufficient to assist in identification and that duplicate analyses agreed to ±O.2 per cent per mineral.
288
M. S. BARRATT AND G. R. PARSLOW
(a) Accuracy The accuracy of the macroscopic method was estimated using specimens of the Cairnsmore of Fleet granite with the following conclusions. For an average coarse-grained rock (I.C. 20-25), using traverse lines 2 mm. apart and points spaced at 2 mm. intervals (half-turn of the handle on the original apparatus) on the traverse line, a 500 point count gave rather poor results; a 1000 point count gave good results; and a 1500 point count gave excellent results (Table 1). I. Duplicate determinations (A and B) of a granite (CFG125j288) using 500,1000 and 1500 point counts
TABLE
It is considered that either the 1000 or the 1500 point count is sufficiently accurate for most petrological work.
A500 B500 Range (A-B) Al 000 BIOOO Range (A-B) AI500 BI500 Range (A-B)
Quartz
Potash Felspar
Plagioclase Felspar
Biotite + Chlorite
Muscovite
31.0 34.2 3.2 32.6 31.8 0.8 31.6 31.8 0.2
36.4 31.6 4.8 34.0 33.3 0.7 34.3 35.2 0.9
24.8 26.4 1.6 25.6 25.9 0.3 25.5 25.2 0.3
4.4 3.4 1.0 3.9 4.7 0.8 4.6 4.2 0.4
3.4 4.4 1.0 3.9 4.3 0.4 4.0 3.7 0.3
The average ranges (errors) of the different point counts (500, 1000, 15(0) of a selected sample (11 specimens) of the population are compared in Table II with the maximum range found in the selected sample and in the II. Comparison of the average range (error) per specimen for the various point counts (500, 1000, 1500) in a selected sample of 11 specimens with the maximum range between specimens in that sample (A) and the maximum range between specimens in the total population of 150 specimens
TABLE
(B) The results indicate that all point counts are well within the range of the rocks studied. The 1000 or 1500 counts are to be preferred because of their very small ranges (errors).
500 1000 1500 A B
Quartz
Potash Felspar
Plagioclase Felspar
Biotite + Chlorite
Muscovite
3.2 1.4 0.4 11.3 17.9
4.8 1.6 0.9 22.3 24.1
1.6 1.3 1.0 16.2 20.3
1.0 1.0 0.3 6.1 15.6
1.0 0.6 0.3 5.0 10.8
MODAL ANALYSIS OF COARSE-GRAINED ROCKS
289
total population of 150 specimens. Range (error) is defined as the difference between duplicate determinations on a specimen and is a simple measure of analytical error. It can be seen that the ranges (errors) of the point counts are well within the maximum range of the selected group, and of the total population. This indicates that the range exhibited by the total population of granites is due to compositional trends and cannot be accounted for by analytical error. More sophisticated statistics may be applied to measure error but these are only necessary when the range (error) per specimen is very close to the maximum range of the rocks studied, making it difficult to decide whether or not the rocks exhibit any compositional trends. For example, if modal analyses of two specimens of the extreme rock types of the group indicate that the compositional range is large (i.e. the major minerals have a range ~3 per cent) then the above simple statistical technique would be adequate. If, however, the compositional range is similar in magnitude to the range (error) per specimen (i.e. <3 per cent) then further statistical tests would be necessary to define the accuracy of the method within finer limits. In this case, an estimate of the errors could be obtained by using the formula derived by Hasofer (1963) and discussed by Solomon (1963). Alternatively, the two specimens could each be analysed ten or more times and the standard deviations calculated from the results. A comparison of the two sets of standard deviations so obtained will show whether or not the errors (standard deviation) are larger than the small range in composition of the specimens. It will usually be found that the errors are smaller than the compositional range, but if the opposite is the case the method must be modified to decrease these errors. This is achieved by increasing the measurement area, decreasing the grid spacings and checking operator variance. The last mentioned may be checked by the methods suggested by Solomon (368, 1963). (b) Time Factor and Expense
The time per analysis for the 500, 1000 and 1500 point counts is 15, 20 and 35 minutes respectively. The 1000 point count was used when analysing the Cairnsmore of Fleet granite specimens because the increased timefactor of the 1500 point count on 150 specimens outweighed the increase in accuracy. When a small number of specimens is to be analysed or a high degree of accuracy is necessary then the 1500 point count is preferable. Assuming that for an accurate analysis of an average coarse-grained rock six microscope slides, for the microscopic method, would be equivalent to one rock slice of the same area, for the macroscopic method, then the difference in expense between the two methods is immediately obvious. The total cost for six microscope slides (labour, materials, etc.) is at least
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M. S. BARRATT AND G. R. PARSLOW
thirty shillings compared with two shillings for a rock slice. This simple-tobuild device will therefore give results that have an accuracy equal to other similar pieces of equipment (Dollar, Chayes, Smithson, etc.) and is considered to be more widely applicable because of its simplicity of construction. It is concluded that this economical method can rapidly give results that are sufficiently accurate for most petrological work. ACKNOWLEDGMENTS
The authors are grateful to D.S.I.R. for providing a grant during the time the work was carried out. Thanks are given to Professor T. S. Westoll for putting the Geology Department of the University of Newcastle upon Tyne at our disposal. Sincere thanks are due to Dr. J. E. Mason and Mr. G. T. Raine of the Geology and Geography Department in Kingston College of Technology and to Dr. C. S. Exley of the University of Keele for their generous help and critical suggestions regarding the presentation of this paper. REFERENCES BAILEY, E. H. & R. E. STEVENS. 1960. Selective Staining of K-feldspar and Plagioclase on Rock Slabs and Thin Sections. Am. Miner., 45, 1020-5. BARRINGER, A. R. 1953. The Preparation of Polished Sections of Ores and Mill Products using Diamond Abrasives, and their Quantitative Study by Point Counting Methods. Trans Instn Min. Metall., 63, 21-41. BAYLY, M. B. 1960a. Errors in Point-Counter Analysis. Am. Miner., 45,447-9. - - - . 1960b. Modal Analysis by Point-Counter-the Choice of Sample Area. J. geol, Soc. Aust., 6, 119-30. CHAYES, F. 1949. A Simple Point Counter for Thin-section Analysis. Am. Miner., 34, 1-11. - - - . 1955. A Point Counter Based on the Leitz Mechanical Stage. Am. Miner., 40, 126-7. - - - . 1956. Petrographic Modal Analysis. - - - & H. W. FAIRBAIRN. 1951. A Test of the Precision of Thin-section Analysis by Point Counter. Am. Miner., 36,704-12. DOLLAR, A. J. 1937. An Integrating Micrometer for the Geometrical Analysis of Rocks. Mineralog. Mag., 24, 577-94. EMERSON, D. O. 1964. Modal Variations within Granitic Outcrops. Am. Miner., 49, 1224-33. EXLEY, C. S. 1963. Quantitative Areal Modal Analysis of Granitic Complexes: a Further Contribution. Bull. geol. Soc. Am., 74, 649-54. FITCH, F. J. 1959. Macro Point Counting. Am. Miner., 44, 667-9. HASOFER, A. M. 1963. On the Reliability of the Point-Counter Method in Petrography. Aust, J. appl. Sci., 14, 168-79. JACKSON, E. D. & D. C. Ross. 1956. A Technique for Modal Analyses of Medium- and Coarse-grained (3-10 mm.) Rocks. Am. Miner., 41, 648-51. PARSLOW, G. R. 1964. The Cairnsmore of Fleet Granite and its Aureole. Ph.D. Thesis, University of Newcastle upon Tyne, SAHA, A. K. 1959. On the Precision of Modal Analyses of Rocks. Q. JI geol. Min. metall. Soc. India, 31, 1-6.
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SMITHSON, S. B. 1963. A Point-Counter for Modal Analysis of Stained Rock Slabs. Am. Miner., 48,1164-6. SOLOMON, M. 1963. Counting and Sampling Errors in Modal Analysis by Point Counter. J. Petrology, 4, 367-82. G. R. Parslow
Geology and Geography Department Kingston College of Technology Kingston-upon-Thames, Surrey
M. S. Barratt Geology Department University of Keele
DISCUSSION MR. D. G. A. WHITTEN suggests that when discussing apparatus and methods of volumetric modal analysis it should not be forgotten that perhaps the simplest possible technique was described by Holmes in his book Petrographic Methods and Calculations (192\). In this he gives an account of the modal analysis of the large slabs of Shap granite which at that time formed the steps of the City and Guilds College in Exhibition Road, South Kensington. The only apparatus required was a straight-edge, a pencil and a tape-measure. Statistically it is probable that the measurements of such large slabs, however crudely done, yielded very good results. The importance of correct identification of the minerals during modal analysis cannot be stressed too strongly. The difficulties which have been mentioned with staining techniques have also been experienced by the speaker. The problem appears to be that in general we are uncertain as to the nature of the material which is actually being dyed, and research on this point would appear necessary. The speaker congratulated the authors on the description of a piece of apparatus which was simple enough for manufacture to be attempted by anyone, even without the facilities of a well-equipped workshop. THE AUTHORS would agree with the speaker that Holmes's technique is often ignored. There are, however, two cases where his method is extremely useful: the analysis of pegmatites, and as a field technique in well-exposed glaciated terrain. Regarding staining, the authors feel that the present staining techniques are adequate but further research into staining techniques would be highly desirable.