January, 1941
INDUSTRIAL AND ENGINEERING CHEMISTRY
through the points in such a way that it was similar to the binary n-propanol-water curve and also to the other constantnitromethane ternary curves. Using a method similar to the plotting of Figure 6 from Figure 5, the triangular chart of Figure 9 was drawn from the n-propanol and the water equilibrium diagrams. The curved lines represent constant weight per cent n-propanol or water in the equilibrium vapors. The compositions of the boiling liquids are represented by the coordinates of the triangle. The end points of the vapor curves are taken directly from a pair of binary equilibrium diagrams shown in Figure 4, so it may be seen how necessary their determination is. To find the composition of the vapor in equilibrium with a liquid containing 35 per cent nitromethane, 35 per cent npropanol, and 30 per cent water, we interpolate between the vapor curves and find that there is 32.5 per cent n-propanol and 19.1 per cent water in the vapor. The rest of the vapor, 48.4 per cent, must be nitromethane. This diagram indicates the formation of a ternary azeotrope whose composition is 55.9 per cent nitromethane, 26.6 per cent n-propanol, and 17.5 per cent water. It is a minimum boiling mixture, with a boiling point of 82.3’ C. as determined in the Swietoslawski ebulliometer a t 760 mm. This temperature is much lower than the boiling point of any of the three components and is also lower than that of any of the three binary azeotropes. If, in the series of reactions involved in preparing nitromethane by nitration, n-propanol should be used as a solu-
95
bilizer, the product would be a ternary mixture of n-propanol, nitromethane, and water, possibly containing only a small amount of nitromethane. It should be possible to recover the nitromethane from such a mixture by a process analogous to the Keyes process for preparing absolute ethanol by the addition of benzene. The azeotrope lies just outside the two-phase region of Figure 1, and by the addition of water or a water-rich ternary mixture, a heterogeneous mixture would be produced. This would separate into two layers, one rich in water, the other containing about 90 per cent nitromethane. The latter could then be rectified by batch distillation to pure nitromethane, the water and n-propanol being removed as the ternary or binary azeotrope.
Literature Cited (1) Baker, E. M., Chaddock, R. E., Lindsay, R. A., and Werner, R. C., IND.ENQ.CHEM.,31, 1263-5 (1939). ( 2 ) Baker, E. M., Hubbard, R. 0. H., Huguet, J. H., and Michalowski, S. S., I b i d . , 31, 1260-2 (1939). (3) Carey, J. S., and Lewis, W. K., I b i d . , 24, 882 (1932). (4) Carveth, H. R., J.Phys. Chem., 3, 193 (1899). (5) Landolt-Bornstein, Physikalische-Chemische Tabellen (1923). (6) Lange, N. A., Handbook of Chemistry, p. 432 (1937). (7) Lecat, M., 2. unorg. allgem. Chem., 186, 119 (1930). (8) Schumacher, J. E., personal communication, April 12, 1940. (9) Swietoslawski, W., “Ebulliometry”, pp. 4-7, New York, Chemical Pub. Co., 1937. (10) Timmermans, 2.physik. Chem., 58, 29 (1907). FROM a master’s thesis presented by A. R. Fowler.
Color Characteristics of Cement L. R. DAWSONl AND R. V. ANDES2 A quantitative method for the determination and comparison of the color characteristics of standard portland and several special cements and other substances is described. I t is based on measurements made with a Zeiss Pulfrich photometer. The color or hue of the standard portland cements investigated varies over relatively narrow limits from nearly neutral gray through yellow or tan to a reddish brown. The average reflectivity or lightness ranges from 15.0 to 35.1, as compared to a baryta plate as 100. This value for white cements is of the order of 75. Specific surface and ferric oxide content affect the average reflectivity. Increase in specific surface and decrease in ferric oxide content increase the average reflectivity or lightness. Apparently, a change in specific surface does not essentially alter the color or hue.
I
NTEREST in the color of cement is becoming increasingly evident. Since color is largely subjective (6), many fruitless arguments have resulted from differences in opinion as to the “color” of various cements based on purely visual observation. The study here presented attempts to compare the color characteristics of cement in a more objective manner, based on quantitative measurements made by a photometer. One 2
Present address, Louisiana Polytechnic Institute, Ruston, La. Present address, Westvaco Corporation, Charleston, W. \‘a.
Universal Atlas Cement Company, Buffington Plant, Gary, Ind.
T. D. TIEMANN Atlas Lumnite Cement Company, Buffington Plant, Gary, Ind.
hundred standard portland cements as well as several special cements, including white, colored, and aluminous types, were investigated. It is not to be construed from the results presented that all of the many variations occurring in the color of hydrated products, such as mortar and concrete, are directly attributable to the cement alone; in particular, variations in the lightness (value or reflectivity) as shown by the work of Dunagan (a) are more often caused by other factors such as surface treatment, curing procedure, and moisture content than by the color characteristics of the particular cement employed. Shades or tints of color, in the absence of coloring pigments and exposed colored aggregate, are, however, definitely related to the color characteristics of the cement, particularly t o the hue. Therefore this paper is presented with the realization that the study is not entirely complete but with the hope that it will give a representative survey of the color of cements, provide a rapid and dependable quantitative method for determining and controlling the uniformity of color in cement products, and stimulate further investigation in this increasingly important field.
96
Vol. 33, No. 1
INDUSTRIAL AND ENGINEERING CHEMISTRY
Equipment and Method The equipment used consisted of a Zeiss Pulfrich photometer equipped with a sphere reflectometer and a set of seven K-filters. The filters had the following effective wave lengths in millimicrons : K1 630
K3
K2 650
563
K4 536
K5
K6
K7
510
480
460
A standard baryta plate was used as a basis of comparison. This plate is very close to magnesium carbonate in total reflectivity and color characteristics. The method employed consisted of the determination of the percentage of light reflected from the sample under observation in terms of the light reflected from the baryta plate taken as 100 for each of the seven filters. These values appear in the tables, for each of the seven filters, under the columns headed “reflectivity”. The value X is the reflectivity at a wave length of 600 millimicrons and was obtained graphically from the reflectivity curve (effective wave length plotted against reflectivity). The average reflectivity, R, is the arithmetical average of the above eight values and gives a measure of the general lightness, or in terms of Munsell (6), the “value” of the sample. The color percentages (red,, yellow, green, and blue) were obtained by dividing by the total reK2 flectivity (the sum of reflectivities K1 K3 K4 K5 K6 K7 X ) the K2 for the red, combined reflectivities of K1 X 4- K3 for the yellow, K4 K5 for the green, K7 for the blue, and expressing the and K6 result as a percentage of the total reflectivity. This method was chosen since the average wave lengths obtained for the four combinations above (red 640, yellow 582, green 523, blue 470 millimicrons) are close to the value given in the Handbook of Chemistry and Physics (4) and in other sources as representative wave lengths of these four colors.
+
+
+
+
+ ++
++
+
TABLE I. COLORCHARACTERISTICS OF STANDARD Sur-
Cement
No. 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
K1 25 28 25 27 28 31 18 29 24 20 29 27 33 34 27 33 22 25
K2 26 29 26 28 29 31 18 30 25 20 30 28 35 35 27 34 22 26 18 19 32 32
K3 22 25 22 23 25 28 16 26 21 18 25 25 31 32 24 30 20 23 17 29
Reflectivity K4 K 5 K 6 K 7 20 19 16 14 23 21 18 16 21 19 16 1 5 22 21 18 17 24 21 18 16 25 22 20 18 15 14 12 10 24 23 19 18 21 19 17 15 17 16 14 11 24 23 21 20 24 21 18 17 29 27 23 20 30 27 21 20 23 21 18 17 29 27 22 21 19 17 15 14 22 20 18 16 15 14 13 12 27 28 22 20
26 26 26 27 25 25 19 20 37 38 35 35 27 27 33 33 29 30 39 39 30 40 22 28 33 33 27 22 35 25
24 24 23 18 36 33 25 31 28 37
23 22 19 24 22 19 22 21 18 17 16 15 34 30 26 32 30 24 24 23 19 29 27 24 26 24 21 35 33 28
The data obtained are shown in Tables I to IV. Table I presents the data for the standard portland cements from 1 t o 100; for three white cements, W1, W2, and W3; for a green and a red cement, G and R, respectively; and for three aluminous cements, A l , A2,and A3. Table I1 shows the color analyses of several ,well-known chemical substances as well as of nine standard neutral gray Munsell color disks. Table I11 shows the variations in color characteristics with change in specific surface obtained by grinding three different portland cements, generally representative in color characteristics, in a laboratory pebble mill. Table IV shows the relation of average reflectivity R to the average ferric oxide content for ten groups in t,he order of decreasing reflectivity. This table was compiled from the data of Table I.
Color Characteristics If a neutral gray is analyzed for color characteristics (Table 11), i t will be found that the reflectivities a t each of the eight wave lengths will be equal and hence that the four color percentages will each be equal numerically to 25. One neutral gray will differ from another only in total reflectivity or average reflectivity R; the lighter the gray, the higher the value R. I n the Munsell system (5) No. 0 is black and No. 10 is white. The more important color characteristics of the standard cements appear in Table I. First, i t is obvious that none of the cements examined exhibits a color or “hue” equivalent
17 18 17 13 24 22 18 22 20 26
face. . -Color PercentagesFerOs, S q . Red Yellow Green Blue 70 Cm./G.
X
R
24 27 24 25 27 30 17 28 23 19 27 26 32 34 26 31 21 24 18 31
20.8 23.4 21.0 22.4 23.5 25.6 15.0 24.6 20.6 16.8 24.9 23.2 28.8 29.1 22.9 28.4 16.3 21.7 15.8 27.3
25 22.8 25 2 3 . 1 24 21.9 19 1 7 . 1 37 3 2 . 7 34 30.6 26 23.6 32 28.9 29 25.9 38 34.4
30.7 30.5 30.4 30.3 30.3 30.2 30.0 29.9 29.8 29.8 29.7 29.6 29.6 29.6 29.6 29.5 29.4 29.4 29.4 29.4
18.1 4 . 0
27.7 27.8 27.4 26.5 27.7 28.3 27.5 27.4 26.6 27.5 26.1 27.4 29.4 28.3 27.3 26.9 27.3 27.1 27.8 27.5
23.5 23.5 23.8 23.8 23.9 23.0 24.2 23.9 24.2 24.1 23.6 24.2 24.3 24.5 24.0 24.7 24.0 24.2 23.0 23.8
18.2 18.4 19.4 18.1 18.5 18.3 18.8 19.4 18.6 20.6 18.8 18.7 17.6 19.1 18.9 19.3 19.3 19.8 19.3
3.6 2.8 2.3 3.7 3.6 5.2 2.6 3.1 3.5 2.3
28.6 26.9 28.6 2 6 . 5 28.6 2 6 . 8 2 8 . 6 26.7 28.6 27.9 28.6 2 7 . 3 2 8 . 6 26.9 28.5 2 7 . 3 28.5 2 7 . 5 28.4 27.2
24.7 24.9 24.6 24.2 24.4 21j.3 24.9 24.3 24.2 24.7
20.8 20.0 20.0 20.5 19.1 18.8 19.6 19.9 19.8 19.7
3.1 2.7 3.4 2.8 2.5 2.3 2.8 2.2 2.3 2.6 2.4 2.3 3.7 3.0 2.2 2.3 2.9 3.4 2.6 2.8
1980 1920 1750 1616 1648 1905 1840 1623 1798 1750 1630 2115 2 . 1 1918 2 . 7 1555 3 . 1 1715 2 . 2 1713 3 . 2 1723 3 . 6 1663 3 . 7 1823 3 . 0 1930
1698 1943 1602 1538 1680 1741 1530 1835 1708 1830 1775 1705 1588 1675 1705 1723 1673 1855 18,55 1740
to a true neutral gray since the color percentages for any one cement are not equal. Without exception the blue for every cement is considerably less than 25.0 per cent, while the red and yellow are each greater than 25.0 per cent. The green is in most instances close to, although generally slightly less than, 25.0 per cent. Hence it follows that the hue or color of the standard cements is more yellow to brown than a true neutral gray. (Brown is a red or yellow of low luminosity, 6.) This same general deficiency in the blue and excess in the red and yellow may be seen in the ferric oxide, sulfur, and potassium chromate of Table TI. The materials of this table have been visually designated in color by several individuals as: ferric oxide, orange red; sulfur, pale yellow; potassium chromate, canary yellow; chrome green, green; cupric acetate, bluegreen; cobalt blue, deep blue or purple-blue. I t is interesting to note that the absorption of a band of light 400 A. wide, moving from a wave length of 4000 to one of 5000 A. in the spectrum results in residual light varying from lemon yellow to orange in color ( 3 ) . The range of color or “hue” variation throughout the entire hundred standard cements is relatively small. The red varies between the limits of 26.7 t o 30.7 per cent, and the blue from 22.9 to 17.6 per cent. It is perhaps
INDUSTRIAL AND ENGINEERING CHEMISTRY
January, 1941
PORTLAND AND SPECIAL CEMENTS CementReflectivity No. K 1 K 2 K 3 K4 K5 K6 IZ7 X
L
71 72 73 74 75 76 77 78 79 80
23 30 30 25 27 25 23 20 25 28
23 30 31 25 27 24 23 20 25 28
21 29 29 24 26 24 22 19 24 28
22 19 17 28 27 21 28 26 23 23 22 19 25 24 20 23 21 18 21 20 17 19 17 15 23 22 19 26 25 21
R
-
Sur-
faae, -Color PeroentagesFenOa, Sq. Red Yellow Green Blue % Cm./G. 1400 1760 1813 1655 1895 1755 1793 1635 1788 2065 1710 1645 1765 1955 1705 1713 1813 1667 1768 1695
17 20 22 18 18 17 17 15 18 19
1653 1735 1648 1883 1795 1705 1983 1728 1715 1645 1820 1710 1655 1614 1733 1633 1698 1530 1835 1788
91 92 93 94 95 96 97 98 99 100
97
significant in this connection that the green and yellow colors in general remain relatively constant (green 23.0 to 25.5 per cent, yellow 26.1 to 28.3 per cent) and that the greater color variation is in the red and the blue. An increase in the red is generally accompanied by a corresponding decrease in the blue. The white cements more nearly approach a neutral gray than do the standard types, although they also indicate a deficiency in the blue. The average reflectivity R (a measure of the lightness of a substance) of the standard cement series ranges from 15.0 to 35.1. This value for the baryta plate is 100, for white cements of the order of 75, and for a Munsell neutral gray No. 1 only 2.0. Although a cement cannot be visually compared to a Munsell disk because of differences in such characteristics as surface texture, i t may be seen that the lightness as measured by the average reflectivities falls in the range of Munsell values of 4 to 7. Various types of carbon black are of a low order, generally near 1.0.
Causes of Color Variation
No particular attempt was made in this introductory study t o determine the actual causes of the differences in color characteristics exhibited among the various cements. However, W-1 78 78 77 76 74 73 72 78 75.7 25.8 25.6 24.7 23.0 during the investigation a few significant feaW-2 81 81 81 80 79 74 72 81 78.7 25.8 2 5 . 8 25.3 23.1 tures became evident and are therefore preW-3 74 73 74 74 75 73 71 74 73.5 2 5 . 0 25.2 25.3 24.5 G 13 11 20 26 28 19 15 16 18.5 1 6 . 2 24.3 36.5 23.0 sented. Undoubtedly many factors contribute 2 3 . 7 1 6 . 2 17.2 23.2 42.9 16 16 26 38 42 18 1 5 15 R to the color characteristics of a cement, among 9 12 10.5 27.4 2 7 . 4 2 3 . 8 21.4 9 A-1 12 11 11 10 10 which might be mentioned composition, burning 14 14 13 13 13 12 12 14 1 3 . 1 26.7 25.7 24.8 22.8 A-2 A-3 45 45 43 42 43 40 38 44 4 2 . 5 2 6 . 4 25.6 25.6 23.0 and cooling treatment, and specific surf&ce. The effect oi composition and surface may apparently be overCOLORDISKS CHARACTERISTICS OF CHEMICALS AND MUNSELL TABLE 11. COLOR shadowed frequently by the -Color PeraentageaReflectivity burning and cooling oondiRed Yellow Green Blue Material K1 K2 K3 K4 K5 K6 K7 X R tions. No definite correla6.5 5.5 5.5 5 . 0 23 1 5 . 8 5 3 . 8 28.5 9.4 8.3 35 13 33 Ferric oxide tion could be drawn between 91 68 54 82.5 27.7 27.4 26.4 18.5 91 90 88 86 92 Sulfur (powder) 5 . 0 79 10 5 7 . 5 34.0 33.7 2 9 . 1 3.2 76 60 79 79 78 Potassiumchromate the composition and color or 7.5 5.0 3.5 6 . 0 11.1 1 8 . 8 4 4 . 0 2 6 . 1 9.5 11.5 2.8 2.5 5.5 Chrome green 6 . 0 17.0 1 7 . 0 1 2 . 0 2.2 7.5 6.0 7.738.248.1 1.9 1.7 2.5 Cu ric acetate hue. 6 . 0 1 3 . 0 23.0 2 3 . 0 5 . 0 1 0 . 9 15.0 1 0 . 4 21.8 62.8 5.0 8.0 4.0 Co%alt blue However, a definite correMunsellneutralgray disks lation between ferric oxide 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 1 2.0 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 2 3.5 content and average reflec6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 3 6.5 tivity R was found and is 4 10.0 1 0 . 0 1 0 . 0 10.0 10.0 10.0 1 0 . 0 10.0 1 0 . 0 5 18.0 1 8 . 0 1 8 . 0 18.0 1 8 . 0 1 8 . 0 18 0 1 8 . 0 18 0 shown in Table IV. This 6 27.0 27.0 27.0 27.0 27.0 2 7 . 0 27:O 27 0 2710 7 36.0 36.0 3 6 . 0 3 8 . 0 36.0 36.0 36.0 36.0 36.0 table represents an analysis of 8 5 0 . 0 5 0 . 0 50.0 50.0 50.0 50.0 50.0 5 0 . 0 5 0 . 0 the data in Table I by aver9 70.0 70.0 70.0 70.0 70.0 70.0 70.0 70.0 70.0 ages. The cements were arranged in decreasing order of reflectivity R, and the average TABLE 111. EFFECTOR SPECIFICSURFACE ON THE COLOR R, ferric oxide content, and CHARACTERISTICS OF THREE PORTLAND CEXENTS specific surface were determined for each proup * of ten cements. On the average, an increase in su2ce, ferric oxide content of 1 per cent is accompanied Cement Reflectivity --Color Percentages--Sq. No. K I K2 K 3 K4 X 5 X 6 K 7 X R Red Yellow Green Blue Cm./G. by a decrease in the value of R of approxila 30 31 27 24 23 21 19 29 2 5 . 5 29.9 27.4 23.1 1 9 . 6 1315 mately 12 units. lb 33 34 30 28 27 24 22 32 2 8 . 7 29 1 27.0 23.9 2 0 . 0 2045 lo 35 37 32 30 29 26 24 34 30.9 29.2 26.8 23.8 20.2 2380 The effect of variation’in specific surface on the Id 40 41 36 34 32 29 27 38 3 4 . 6 29.2 2 6 . 7 23.8 20.4 2885 color characteristics of three generally represen2a 27 27 26 25 24 22 20 27 2 4 . 8 27.2 26.8 24.8 21.2 1325 tative standard cements is shown in Table 111. 2b 31 31 30 30 29 25 23 31 2 8 . 8 2 7 . 0 2 6 . 5 25 6 20.9 1965 20 37 36 35 35 33 29 28 36 33.6 27.1 2 6 . 4 2513 21.2 3030 The increase in average reflectivity R caused by 3s 23 23 21 20 18 16 15 22 1 9 . 8 29.2 27.2 2 4 . 0 19.6 1315 an increase in specific surface is different for the 3b 25 25 22 21 19 18 16 24 2 1 . 2 29.4 2 7 . 1 2 3 . 5 20.0 2365 three samples shown but, on the average, is of 30 28 28 26 25 24 20 18 27 2 4 . 5 28.6 27.1 24.9 19.4 2980 the order of approximately 0.4 for each increase 7
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INDUSTRIAL AND ENGINEERING CHEMISTRY
98
OF AVERAGE REFLECTIVITY TO FERRIC TABLEIV. RELATION OXIDECONTEXT
Group
Av. Reflectivity R
Ferric Oxide, ’%
32.3 29.0 27.4 26.3 25.2 23.5 23.0 22.2 20.6 17.4
2.3 2.4 2.8 2.6 2.6 2.9 2.9 3.2 3.3 3.5
Sp. Surface Sq. Cm./G: 1842 1728 1718 1728 1709 1742 1720 1748 1751 1737
in surface of 100 sq. cm. per gram. The color percentages remain essentially constant, despite the change in surface, which indicates that the main effect of surface change is apparently one of lightness rather than hue. Based on these observations, it is indicated that small variations in ferric oxide content are more effective in changing the average reflectivity, or lightness, of a cement than relatively large changes in specific surface.
Vol. 33, No. 1
Aclrnowledgment The authors express their gratitude to D. I. Elder and other members of the staff of the Universal Atlas Cement Company’s Research Laboratory for their helpful cooperation. Thanks are due W. V. Friedlaender of the research staff for his help and comments, and t o L. L. Huspek, of the company’s Central Laboratory for several of the specific surface determinations.
Bibliography (1) Duff, W. A., Textbook of Physics, Philadelphia, P. Blakiston’s Son and Go., 1926. (2) Dunagan, W. M., Iowa Eng. Expt. Sta., Bull. 139 (1938). (3) Fairbanks, E. E., “Litboratory Investigation of Ores”, 1 s t ed. (Chap. IV, “Practical Photomicrography”, Loveland and Trivelli), New York, McGraw-Hill Book Co., 1928. (4) Hodgman, C. D., Handbook of Chemistry and Physics, 20th ed., Cleveland, Chemical Rubber Publishing Co., 1925. (5) Munsell, A. H., “Munsell Book of Color”, Baltimore, Munsell Color Co., Inc., 1929. (6) Spinney, L. B., Textbook of Physics, 4th ed., New York, Macmillan Go., 1931. (7) Watson, W., Textbook of Physics, London, Longmans, Green and Co., 1927.
Application of the System Sodium Chloride-Sodium Nitrite-Sodium Nitrate to Meat Curing X-Ray and Microscopic Studies GEORGE L. CLARK
LLOYD A. HALL
University of Illinois, Urbana, 111.
I
N SPITE of the fact that three very common sodium salts
are involved, little work was reported in the literature concerned with studies of the three-component system sodium chloridesodium nitrite-sodium nitrate. There should be considerable interest in the fundamental study of such a system on its own account, but great weight is added t o the desirability of knowledge of the system in view of the fact that these three salts, either in simple solution, simple solid mixture, or specially blended, are used for the curing of meats. Thousands of tons of these salts in various proportions, either as a physical mixture or as an intimately deposited crystalline mass from solution or from melts, and in solution and as a dry cure are used each year in the meat-packing industry. A thorough search has failed to reveal in the literature any report of an analysis of the ternary system. There are a few scattered observations on binary systems involving the three salts, but the general supposition seems to be that no chemical compound formation and no solid solubility are involved. Several x-ray studies, particularly by Thomas and Wood (S), have demonstrated that binary mixtures-for example, sodium chloride and potassium nitrate, or vice versa-when melted together bring about rearrangement of ions, and x-ray patterns disclose the presence, in addition to the t v o original
The Griffith Laboratories, Chicago, Ill.
salts, of sodium nitrate and potassium chloride. The three salts under consideration crystallize in three different systems and, under normal conditions, would be expected t o show only faint relations t o one another; or indeed it might be expected that they would be essentially incompatible. The essential data on crystal structures are as follows: Salt Crystal System Unit Cell Dimensions. i. NaCl NaN09 NaNOs
Cubic Orthorhombic Rhombohedral
a0
a a
-
= 5.628 E
3.55, b 6.32, OL
-
E
5.56, c 47’1.5’
-
5.38
As a matter of fact, however, the three structures are more closely related than a t first appears. Both the planar anions NOT and K O p can be considered t o replace C1- in the NaCl lattice with some distortion resulting in the orthorhombic and rhombohedral structures. From a melt or concentrated solution of these three salts crystallizes a solid material, the identification and properties of which are the subject of this investigation in relation to powders formed from mixing or grinding together in a physical mixture the three individual salts. There are a t least two fundamental methods of approach to the identification of the mixed crystals-namely, that of x-ray diffraction analysis of the powders and a microscopic study, particularly in polarized
