V O L U M E 20, NO. 10, O C T O B E R 1 9 4 8 The following results are typical of the agreement obtained between the Zeisel and the proposed colorimetric method when methanol was the only alcohol present: Zeisel,
70
5.5 4.8
Colorimetric,
70
5.0,5.2
5.0
The procedure here described may be employed to advantage In the determination of methoxyl groups in methyl esters ( 6 ) .
As an example, a sample of dimethyl tartrate was saponified with 4 ml. of 5 S sodium hydroxide. After 3 ml. of distillate had been collected, the latter was diluted and its methanol content de-
965 termined by the procedure described. The results showed 2.0 moles of methanol as compared with a theoretical value of 2 moles. LITERATURE CITED
(1) Boyd and Logan, J . B i d . Cham., 146, 279 (1942). (2) Bricker and Johnson, ISD.ENG.CHEM., AN.4L. ED.,17,400 (1945’ (3) Eegriwe, E., MGcrochim. Acta, 2, 329 (1937). (4) Eegriwe, E., 2. anal. Chem., 110, 22 (1937). (5) MacFayden, D. A , , J . BioZ. Chem., 158, 107 (1945). (6) Snell and Snell, “Colorimetric Methods of Analysis,” Vol. 11, p 17, New York, D. Van Nostrand Co., 1937. (7) U. S.Pharmacopoeia, 12th rev., p. 428. 1932. RECEIVED October 2 5 , 1947.
ELECTRON MICROSCOPE GONIOMETRY A. F. KIRKPATKICK AND EVELYN G.4GNON D.4VIS Stamford Research Laboratories, American Cyanamid Company, Stamford, Conn. The frequent occurrence of unknown crystals in electron microscopical samples presents the problem of their identification. Their relatively small size severely limits the ordinary methods of identification. The silhouette angles observed on the screen or photographic plate are practically all the data available to the electron microscopist. These angles are functions of the interfacial angles of the crystals and the orientation with respect to the screen or plate. The interfacial angles, constants of
T
H h frequent occurrence of unknown crystals in electron microscopical samples presents the problem of identification. The microscopic size of the crystals or the nature of the sample severell limits the ordinary methods of identification. Precipitated materials, pigments, and by-products, such as calcium carbonate, which is used as the illustration in this paper, are an example of the occurrence of microscopic sizes. Crystals associated v i t h other materials in such a manner that separation is not possible, such as crystals attached to fibers or even to other crystals, especially when common ions are present, illustrate the limits due to the nature of the sample. The history of the samples usually limits the number of possibilities and the problem then can be reduced to confirmation of a suspected identity. The authors were presented with the problem of identification of crystals in electron micrographs n ith the suggestion that the silhouette angles, practically all the data available to the electron microscopist, be considered as data for the confirmation of identity. It was then realized that crystallographical concepts could be applied to this problem. ORIGIN AND NATURE OF PROBLEM
Electron micrographs of industrial sludges from the carbon dioxide and sulfuric acid processes for the extraction of cyanamide from crude, commercial calcium cyanamide showed outlines of relatively small crystals (ca. 3 to 5, in breadth). The nature of the sample suggested that the crysta!s might be calcite. The confirmation of this hypothesis by a determination of some physical property was desired. The identification of the crystals as the calcite phase of calcium carbonate was confirmed by the use of electron microscope goniometry. Figure 1 is an electron micrograph of one of the crystals. Its general appearance suggested that the crystal might be one of calcite lying on a rhombohedral face. Figure 3 is an orthographic projection of a calcite crystal showing only the unit rhombohedron, r { 1071 ]. The projection plane is parallel to the face r,(lOil) and the crystal is lying on r6(iOlT).
a suspected compound as obtained from the literature, can be used to calculate the angles of an orthographic projection of the crystal, which is observed with the electron microscope. A comparison of the angles measured with those calculated may establish the identity of the crystal. It may be possible to determine directly axial elements (axial ratios and interaxial angles) and interfacial angles of unknown crystals. This represents the determination of physical constants with the electron microscope.
The solid lines represent the viaible edges, and the dotted lines represent the edges not directly visible. All faces in this form are identical; however, in the projection, faces parallel to the projection plane show their true size, whereas those a t an angle are reduced in size. -4ngle A is the angle between edges T2T6 and w 6 , and showvs the true value. Angle C i p the angle between the projections of edges Tar6 and ~ 3 r d . The plane formed by these edges in space is a t an angle to the projection plane: therefore, the angle between the edges as projected ie different from the true value. The calculation of this angle, from the axial elements and others such as B and C’, is the problem for the electron microscopiht. (In this paper interedge angles arc considered as internal angles.) Donnay and O’Brien (4)showed how the apparent interedge angles of crystals observed with the optical microscope could be correlated with true interfacial angles and the axial element,. They demonstrated how known methods of crystal drawing and B knowledge of the spherical projection and its derivatives, the stereographic and cyclographic projections, could be applied to graphical calculations. In electron microscopy, the silhouette angles of crystals are practically the only determinative data available. In this paper are presented the application of microscope goniometry to the study of electron micrographs and the use of silhouette angles for the determination of physical constants by means of the electron microscope. The calculations follow the methods presented by Donnay and O’Brien (4). Calculation of Angles of Orthographic Projection. Figure 4 is a stereographic projection of a calcite crystal showing only the unit rhombohedron { loill. I t is derived from the interfacial angle (OOOl):(lOil), which is 44”36’ (Dana, 2). This projection was constructed with the use of the Wulff net (Donnay and O’Brien 4). Point C is the projection of the polar axis of the fundamental sphere of projection and of the c crystallographic axis. The three points, UI, a2, and u3,are the positive poles of the three horizontal axes of the hexagonal system. The three points, r l , T P , and (double circles), are the stereographic projections of the face poles which are above the equatorial plane of the fundamental sphere.
966
ANALYTICAL CHEMISTRY
The three points, n, TS, and 18 (single circles), are the poles below the equatorid plane. The great circles connecting these points are the zone circles, the loci of the poles of all faces parallel to a common direction. The great circle, FABC, is the cyclographic projection of face 71, the face which is parallel to the plane of the orthagrsphicprojectian in Figure 3.
angle of 45* from a distance of 15 om. The original magnification on the electron micmscope was 4900X. The length of the orysbl from the vertex at the lower left to that at the upper right N&S calculated to he 4.5 microns. The photographic plate N & S placed in a photographic enlarger and the image was projected onto graph paper. The outlines of
lower left corner i n d h t e the direction of t& lines of trhe graph
Gertexes 'with the vertexes of {he shadow. This relation~dso
is visible over its ehtire length. This shows that the plane of 1.2, and 3 is above the plane o f t h e substrate. The longzdashed lines 3-7, 1-7, and 5-7 then represent edges on the upper side of the arvstal. and the nhort,-dashed lines. 4-8. 6-8. 2-8. edees on the iiwer side of thiwystal. The n o r i d s tokhe edgesare &o shown. This is the orientation of the crystal of calcite as projected in Figure3. ~
Fie:ure 1. EleetrorL Micrograph of Caloite Shadowed with Anti mony at 45" Diagonal 4.5 I"
~~~
I
~~
~
A cyclographie projection of a crystal face is the stereographic projection of a face circle of a spherical projection. A face circle is a great circle of a spherical projection parallel to a crystal face. A cyclographic projection of a cqwtd face is the locus of all points 90" from a face ole. In Fieure 4., FABC is 90" from rl. The graphical solution for the angles of the orthographic projection (Figure 3) is made on the stereographic projection (Figure 4). The interseotions of the eone circles, whose projected inters o d angles are desired, with the cyclographic projection of the face parallel to the plane of the orthographic projection describe mcs which are measures of the projected interirnnsl sneles. Thcir supplements are the anglw dpsired.
Figure% OithographieProjeetion of Calcite Crystal Parallel t o Unit Rhombohedron
~~
Figure 2.
Tracing of E n l a r g e m e n t of Elmtron Micrograph
I n Figure 4, arc A B gives the projected intarsorial angle b e tween Bone circle LH described by the points L, T ~ r2, , H , re, r
