78jjjjjxT:44,`x *8j INSTRUCTIONS for the CRYSTAL STEREOGRAPHIC PROJECTION PROGRAM Version 2.29 PUBLIC DOMAIN SOFTWARE by Tom Kosel Univ. Notre Dame (219) 631-5642 kosel@saturn.ece.nd.edu October 6, 1993 Acknowledgements I wrote the sterographic projection software described herein for the love of the subject, and as a teaching and research tool. I am thankful for the guidance of Prof. Gareth Thomas of Univ. of California, Berkeley for my original introduction to the subject, and to B.D. Cullity of Notre Dame, whose most excellent text on x-ray diffraction and crystallography formed the basis for my introduction to stereographic projection and my later opportunity to convey it as well as I might to students at Notre Dame. I am also thankful to those individuals, universities, and research laboratories who supported my efforts by their purchase of site licenses for the earlier, non-public domain versions of the software. Thomas H. Kosel Apple and MacPaint are registered trademarks of Apple Computer, Inc. Microsoft QuickBASIC is a trademark of Microsoft Corporation. The program was compiled using the Microsoft QuickBASIC Compiler, v. 1.00B. T.H. KOSEL AND APPLE COMPUTER, INC. MAKE NO WARRANTIES, EITHER EXPRESS OR IMPLIED, REGARDING THE ENCLOSED COMPUTER SOFTWARE PACKAGE, ITS MERCHANTABILITY OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. THE EXCLUSION OF IMPLIED WARRANTIES IS NOT PERMITTED BY SOME STATES. THE ABOVE EXCLUSION MAY NOT APPLY TO YOU. THERE MAY BE OTHER RIGHTS THAT YOU MAY HAVE WHICH VARY FROM STATE TO STATE. Introduction This instruction manual is arranged in the order of the menus which appear on the screen during operation of the programs. A few menu options operate slightly differently depending on the currently defined crystal shape (cubic, hexagonal or general), and these differences are stated under the appropriate options. The principal difference is that if a noncubic crystal is in use, the program differentiates between poles and directions, and either 3-axis Miller indices or 4-axis Miller-Bravais indices can be used for hexagonal crystals (see the Edit menu). The program is compiled with the Microsoft QuickBASIC Compiler, version 1.00B, and is a true double-clickable application. You should read the Dialog Boxes section of the instructions before running the program, and the description of the Clear and Revert selections of the File Menu. The rest is believed to be more or less self-explanatory. You should also know that the program is only ready to accept menu selections when the Arrow Cursor is visible. During all subroutines, the Crosshair Cursor is visible, and the menus are disabled. Keyboard input is required at several points in the program, either for entering indices (see Data Entry Dialog box) or for decisions by the user. The latter are handled by single-key inputs. For instance, the response to the question "Draw circle? (Y/N)" must be either an upper or lower case Y or N. Other characters will be ignored. The program does not wait for you to hit the return or enter key for such input. Since all keystrikes are recorded in an input buffer, it is not advisable to hit keys unless keyboard input is requested, since if you hit an extra "y" and the program comes to a decision for which this is an appropriate response, the program will use the "y" stored in the input buffer to decide what to do. Nearly all questions require Y/N (yes/no) responses. Note that the current selection checked in the Pole Entry Dialog Box or the Pole/Direction Dialog Box can be approved simply by hitting the space bar, but that other keys are ignored. The same is true for the Shape/Circles/Orientation dialog box in the Save and Recall routines. Microsoft provides the following command-key controls over program execution: Command-Period(.): Terminates program execution, after displaying a message. Command X, C and V will cut, copy and paste during some keyboard input operations. Dialog Boxes There are three dialog boxes used frequently in the program which allow entry of appropriate information. Some data entry is done in the main drawing window, when the drawing is to be erased shortly after the input. Pole/Direction Dialog Box This box contains two "radio buttons" which allow the user to select whether the next vector to be input is to be a pole or a direction in a noncubic crystal. (Poles and directions of the same indices do not in general coincide in noncubic systems.) Simply click the mouse on the appropriate button. If you want to use the currently highlighted button, you can simply hit the space bar to save time. Pole Entry Dialog Box This box contains check boxes for the four ways in which the user can select a pole at any point needed in the program. The options are: hkl This allows typing in the hkl indices of the pole/direction. Mouse Allows selection of pole by clicking mouse inside projection. N-S/E-W Allows selection of pole by typing the north-south (N-S) and east-west (E-W) coordinates on a standard meridional Wulff net with its north pole assumed at the top of the projection. If the N-S coordinate entered is negative, the pole is assumed south of the equator rather than north, and if the E-W coordinate is negative the pole is assumed to be on the west side rather than the east. Existing Allows selection of an already-drawn pole by clicking near it with the mouse. The program takes dot products of the direction corresponding to the clicked location with the set of poles already plotted and chooses the closest one in terms of angle. Cancel Allows you to return to the main menu without completing whatever subroutine (menu selection) you were working in. Simply click inside the box next to the desired mode of entry. The Pole Entry Dialog Box also has the hidden option that instead of having to click the desired option with the mouse, you can simply hit the space bar if the option desired is the same as the one marked in the dialog box. This selects the marked option, and saves a great deal of time since you will often keep using the same entry mode over. Data Entry Dialog Box This is a dialog box which appears at the upper left corner of the main drawing window to allow data input for various routines without encroaching on the drawing window. Enter data exactly as requested; in particular, when asked to "Enter h,k,l", you must enter the indices separated by commas, all on the same line. File Menu Print This prints the current projection at the desired size on either the Apple ImageWriter or Apple LaserWriter (depending on which printer driver is installed in your system file). This option uses the Revert routine to print; it will therefore not print any labels you may have placed on the screen using options in the Edit menu. Upon selecting the Print option, the user is asked whether he wants to use the ImageWriter or LaserWriter, since different Aspect Ratios and size conversions are used for these; the printer actually called will depend on which is selected using Chooser. Next, the user is asked for the desired Aspect Ratio, which determines the circularity of the printed projection. The default Aspect Ratios are automatically used if you simply hit the return key. The default values give true circles on the author's printers, but you may need to experiment to get true circles on your own printer. See Aspect Ratio under the Edit menu. The user is next asked to enter the desired diameter in cm (on the paper); the size of the projection on the screen before printing has no effect on printed size. The user is then asked to enter any single line of information he would like to have printed underneath the projection, for identification purposes. You may want to enter information for bookeeping purposes; if not, just hit return. The program will automatically print a line giving the crystal shape, if cubic or hexagonal, underneath the user-input line. The familiar page setup and print selection dialog boxes for your printer are then presented. Use font substitution on the LaserWriter; the 9-point Geneva will be converted to 9-point Helvetica. Print Screen This selection is no longer functional due to compiler changes. Clear Starts a new file containing the list of circles and poles drawn on the projection, and immediately clears the screen. Each pole/direction (up to 1000) drawn subsequently by routines in the Plot menu is saved in an internal memory file (hereafter calle the revert file) with information as to whether it was labeled, whether its circle was drawn, etc. If more than 1000 poles are drawn, only the first 1000 are saved in the revert file. A message is displayed on the screen when a pole is plotted but not saved in the revert file. See also: New File, Revert, Save, Recall (File menu) New File Starts a new revert file without clearing the screen. See also: Clear, Revert, Save, Recall (File menu) Revert Erases screen and redraws the circles/poles/directions in the current file of circles. Note that this will work in any orientation, so that you can move to a new orientation and redraw the same set of circles etc. even if you have derived an irrational pole by some complicated procedure. If the current file is empty (no circles drawn since last selection of New File or Clear) then the reversion simply clears the screen and draws the basic circle. Only poles plotted by means of options in the Plot menu are added to the revert file. Poles can be removed from the Revert list by means of the Pole/circle option of the Edit menu, which also allows you to specify whether the indices and circle for the pole are drawn. See also: Clear, New File, Save, Recall (File menu) Pole/circle (Edit Menu Save (to disk) Saves current information (either the crystal Shape, the revert file of Circles and poles, or the Orientation) in a file on the disk. A dialog box appears allowing the user to select whether to save the Shape, Circles or Orientation; hitting the space bar will automatically approve the currently selected item. The file name is next specified by the user by keyboard input. It's best to use an alphanumeric name like "standard cube" for these files. Shape, Circles and Orientation files are distinguished by the program when being retrieved later using Recall. See also: Recall (File menu) Recall (from disk) Recalls a previously saved Shape, list of Circles or Orientation from the disk. The disk file name is selected from the usual dialog box; only files of the correct type are displayed. Folder names are also displayed so that you can search in other folders. The screen is automatically cleared and the projection is redrawn. See also: Save (File menu) Quit Ends the program, returning the user to the Finder. Plot Menu Each pole plotted with an option from this menu is added to the revert list. Pole/Circle Allows you to plot any pole or circle by selecting it by any of the four methods in the Pole Entry Dialog Box. If the crystal is noncubic, the Pole Entry Dialog Box is preceded by the Pole/Direction Dialog Box, which you use to specify whether the point to be plotted is to be a pole or direction. (Poles and directions of the same indices do not generally coincide in noncubic systems.) The user is also asked whether he wants to draw the great circle normal to the selected pole or direction. The choices of whether to draw the circle, or to include the indices as a label for the pole, can be changed using the Pole/circle option of the Edit menu, which also allows you to remove the pole from the Revert list. See Also: Dialog Boxes section of manual Clear, New File, Revert (File Menu) Pole/circle (Edit Menu) Standard circles/poles Draws the standard set of circles and poles, including all {100} and {110} poles and their circles. If the crystal is hexagonal, the standard set includes all {2-1-10} , {10-10}, {10-11} circles and poles plus (0001). The circles of some planes may be drawn through the indices of other planes. This can be cleaned up later using the Relabel option of the Edit menu, and the projection is automatically relabeled during the Revert operation of the File menu. All {111} poles Draws the directions or poles of indices 111, -111, 1-11 and 111. If the crystal is noncubic, the Pole/Direction Dialog box appears, to allow the user to choose between poles and directions. The user is asked whether the circles are also to be drawn. In hexagonal crystals, the All {111} Poles option is not useful since it adds only two new poles to the standard set, and the members of the "family" {111} do not have similar Miller-Bravais indices, spacings or angles with [0001]. All {hkl} poles Permutes the indices and minus signs to obtain all 24 possible permutations, all of which are plotted even though in noncubic crystals they may not be of equivalent d-spacing or atomic arrangement. In noncubic crystals, the Pole/Direction Dialog box appears first. Then the user is asked for the indices (h,k,l), whether the poles are to labeled, and whether the circles are to be drawn. If the crystal is hexagonal, the program converts to 4-axis indices and permutes the first three indices, to obtain the set of 12 possible members of the most general family. Choice of a low-index family will cause some of the poles to be plotted (and saved to the revert file) more than once. If for some reason you need to frequently plot a family such as {112}, you could type in the twelve permutations of this (in cubic) once and then Save it as a file of circles. Pole on circle This allows the user to specify a pole/direction to plot on an existing great circle at a specified angle from another pole known to be on the same great circle. For instance, you could plot the new orientation of the tensile axis of a single crystal after it rotates a known number of degrees towards the Burgers vector of a single slip system. The user first specifies which great circle he wants by clicking near it on the projection (see Circle option of Identify menu). Then he must select which pole to measure from on this great circle, using the Pole Entry Dialog Box, after which he enters the number of degrees the resultant pole is to be from the first pole. If the angle entered is positive, the first pole is rotated in a clockwise sense about the normal to the great circle, looking along the normal towards the center of the projection. If a negative angle is entered, the rotation sense will be counterclockwise. Since the resultant pole may be irrational, its indices are not labeled on the projection. They can be determined using the "hkl via mouse" selection of the Identify menu. If the user chooses the first pole lying on the circle by picking the "mouse" option of the Pole Entry Dialog Box, the program uses a special procedure. Since the pole chosen by the mouse may not lie exactly on the mathematical great circle, the program constructs a new pole which does. This new pole lies at the intersection of a great circle which is calculated but not drawn; this circle contains both the pole of the original great circle and the pole which was chosen using the mouse.  Figure 1. Illustration of the procedure used in "Pole on circle" for determining the position of a starting pole selected using the mouse option. Suppose the user chooses the 111 circle and then chooses a pole lying on it via the "mouse" option of the Pole Entry Dialog box. If he clicks at point M in the drawing in Figure 1, the program constructs a point M' which lies exactly on the 111 circle. This is done by first calculating the indices of circle A which contains both points M' and the pole 111. Circle A and its pole, which are shown in Figure 1 for illustration, are not normally drawn. Pole B was constructed on the 111 circle at 60 from the point M'. The "Pole on circle" procedure adds poles M' and B to the revert file, plus the circle of B if requested; M is not added. If the crystal is noncubic and the circle on which a pole is to be constructed is that of a pole, then the program asks the user for input of a direction; and if the circle is that of a direction the user is asked for a pole on it. This is because the zone law (the plane (hkl) belongs to the zone [uvw] if hu + kv + lw = 0) holds for any crystal system. The user can therefore always choose the indices of some direction which lies on the circle of a pole hkl; e.g. -kh0 or 0-lk will work. Since there is no corresponding simple law for the indices of a pole which lies perpendicular to another pole, in a general crystal it is unlikely that any pole of low indices will lie on a given great circle, even if it is that of a low-index plane. The Pole on Circle routine was intended for construction of a pole at some given angle from some known pole or direction lying on the circle. For instance, in a cubic crystal one could construct the pole at 30 from a {110} pole on a {111} circle; one can see from the Thompson tetrahedron that this must be a {112} pole, and this can be checked using the "hkl via mouse" selection of the Identify menu. See Also: Dialog Boxes section of manual Circle, hkl via mouse (Identify menu) Cross product Allows the user to draw the pole and circle (if desired) of the plane which contains two given poles or directions. The user is prompted to choose two poles or directions using the Pole Entry Dialog Box, after which the pole or direction is drawn with or without its circle as specified by the user. Since the resultant pole may be irrational, its indices are not labeled on the projection. They can be determined using the "hkl via mouse" selection of the Identify menu. See Also: Dialog Boxes section hkl via mouse (Identify menu) Identify Menu hkl via mouse Allows identification of any pole on any projection by clicking on it with the mouse. The program calculates the decimal indices, and also gives approximate integer indices and the deviation (in degrees) of the integer-index pole from that of the true decimal pole. The precision of the conversion to integers can be altered using the Index Precision option of the Edit menu. hkl via Wulff coords Identifies any pole by typing in the north-south (N-S) and east-west (E-W) coordinates on a Wulff net with its north pole assumed at the top of the projection. If the N-S coordinate entered is negative, it implies that the pole is south of the equator rather than north, and if the E-W coordinate is negative the pole is on the west side rather than the east. The program calculates the decimal indices, and also gives approximate integer indices and the deviation (in degrees) of the integer-index pole from that of the true decimal pole. The precision of the conversion to integers can be altered using the Index Precision option of the Edit menu. Existing Pole While it may seem strange to want to identify an already plotted pole, this is helpful if the pole was plotted without displaying its indices, as with the Cross Product or Pole on Circle routines. Click near the pole of interest, and the program determines the pole which is closest to the clicked point and displays its true indices. These may be either decimal or integer indices, depending on how the pole was originally defined. Circle Identifies any circle already drawn on the projection by clicking close to it with the mouse. The program determines the drawn circle to which the clicked point is closest in terms of angle, so the point need not lie on the circle. In fact, if it lies exactly on the circle, the point will appear to have been erased after clicking. Intersection Identifies the direction at the intersection of any two circles already drawn on the projection. This uses the Circle option just described to specify the circles. According to the zone rule, the indices of the direction at the intersection of any two circles is given by the "cross product" of the circle indices. The indices of the intersection are plotted under it on the projection only if requested by answering "y" to the question "Label pole? (Y/N)". The pole can be saved in the revert list if requested by answering "y" to the question "Save in revert list? (Y/N)". Rotate Menu Pole Prompts the user to select two poles, A and B, via the Pole Entry Dialog Box. Pole B will be rotated about axis pole A by the amount specified by the user. The rotation of B will be clockwise about A looking along A towards the center of the sphere if the angle specified is positive, or counterclockwise if negative. The user decides whether or not to draw the rotation circle; if not, only a dotted line consisting of 20 points is drawn. Since this option is intended primarily for demonstration purposes, the positions of poles A and B and the endpoint of the rotation are not added to the revert list. Crystal Rotates the crystal coordinate system about the specified pole by the specified angle. The sense of the rotation angle is that just described in the Pole option of the Rotate menu. The projection is erased and the existing set of circles and poles is automatically redrawn in the new orientation. The routine may be of interest for demonstrating the rotation axes of crystals in courses dealing with symmetry. It is also useful for constructing projections or altering their orientation slightly. Tutorial This provides a stepwise tutorial instructing the user on two methods (1 and 2) of rotating one pole B about another pole A (the rotation Axis) at a general location, using a Wulff net. In Method 1, the user moves the axis pole A to the outer (basic) circle and performs the rotation operation by moving pole B along a parallel (or the equator) of the Wulff net. In Method 2, he moves A to the center of the projection and rotates B along a circle centered at the center of the projection. The user can choose pole locations A and B using the Pole/Direction Dialog Box, and is given prompts explaining how to perform the next graphical step. The intended method of use is for the user to define the problem, draw the starting locations of A and B on paper, and follow the steps on paper using the computer display to verify the correctness of his construction. At the end of the operation, he is allowed to repeat the same rotation using the other option if he desires. Orientation Menu New Allows selection of a new orientation. The central pole or direction is first chosen via the Pole Entry Dialog Box, after which the user is allowed to choose the east pole automatically or by user specification. In noncubic crystals, remember that you can always pick a direction which is normal to a central pole by using the zone rule (zero "dot product"). It may be simpler to allow the automatic choice of east pole to be made, and then to rotate the crystal about the central pole to any desired new orientation. The projection is erased. If desired, the existing set of circles can redrawn by choosing Revert from the file menu. Mirror Pole Provides the mirror image of a pole through a plane whose normal is selected with the Pole Entry Dialog Box. The pole to be mirrored is also selected via the Pole Entry Dialog Box. If another pole is also to be mirrored through the same plane, the user can proceed to the next pole by hitting the space bar; he must hit any other key to end the routine. Neither the poles to be mirrored or their mirror poles are added to the revert list. You could do this manually by using the Plot pole/circle option of the Plot menu, and specifying the pole to be plotted by using the mouse to click on the pole of interest. Mirror Crystal Constructs the mirror image of the entire crystal through a plane whose normal is selected via the Pole Entry Dialog Box. The projection is erased and the standard set of circles is drawn in the mirror orientation. Note that the coordinate system of the mirror orientation will be left-handed. You can return to a right-handed system by another mirror operation or by selecting the New option of the Orientation menu. Compare This routine measures angles between any pair of poles or directions, each belonging to one of two projections (A and B) of different orientation. At present, no provision has been made to allow A and B to be from different crystal structures. The routine can be used, for instance, to measure the angle between [111]A and [321]B if the unit cells of both grains A and B have the same shape. The routine operates by placing both projections A and B side by side on the screen, and allowing the user to select a pole from A and one from B usingthe Pole Entry Dialog Box. Begin by saving orientation B and the desired set of circles and poles for B on disk using Save Orientation and Save Circles. (Saving the circles is not necessary if you are satisfied to have the same circles for both grains.) Next, construct a projection of grain A, or use Recall Orientation and Recall Circles to retrieve it from disk. If you want to be able to return to orientation A later, save it using the Save Orientation option since the Compare routine reverts to B when it is exited. Now, choose Compare from the Orientation menu. Projection A will be redrawn on the left side of the screen using whatever orientation and circles/poles you had on the screen before choosing Compare. You are then prompted to choose orientation B from a disk file (see Recall Orientation). Next, you are asked whether you want to use a set of circles already stored on the disk ("Use circles from disc? (Y/N)"). If you want the same circles for B as for A, hit "n" for no, or hit "y" for yes and then choose a file name. B will now be drawn on the right side of the screen. The system now displays the Pole Entry Dialog box and writes "Crystal A" under the left projection to remind you that you are to pick a pole/direction from that crystal. Once this is done, you choose a pole/direction from B, and the angle between the two is printed at the upper left corner of the screen. You can then either do another pair or exit the routine, in which case orientation B will be redrawn on the screen at the center. It is best not to choose to exit the routine by using the Cancel option of the Pole Entry Dialog Box, since you will be returned to the main screen with the center and radius set as for orientation B in compare (i.e. you will get a small projection on the right side of the screen and will have to restart the program or enter and exit Compare to rectify it). Two-Pole This allows you to define the orientation by specification of the positions of any two poles or directions on the projection. The pole positions are specified using their Wulff net coordinates. For instance, an 001 cubic projection could be constructed either by specifying that 100 was at -90 North and 010 was at 0 North, 90 East; or by specifying that 110 was at -45 North, 90 East and 111 was at -35.26 North, 45 East. The intention is to provide a means of transfering any orientation already known from, for example, the solution of a Laue pattern, into the computer. The routine should also be useful in defining orientations corresponding to Kikuchi or electron channeling patterns. You may find it useful to experiment with the routine by first defining an arbitrary orientation, and then using the Wulff Coordinates option of the Measure menu to find the locations of two arbitrary poles. This was the procedure used in debugging the routine. The definitive check of the correctness of the Two-pole result is that the decimal indices of the center, south and east poles be exactly the same in the orientation specified by Two-pole as originally. Upon choosing the Two-pole menu item, the user is asked to first enter the indices of the first pole, and then its Wulff coordinates. You should pick the most accurately known pole/direction as the first, since the exact position of the second pole/direction can be adjusted as described shortly. The indices and position of the second pole are next entered. Now the routine prints the error (in degrees) between the calculated angle between the two poles and the actual angle between the positions specified via Wulff coordinates. The user is asked to decide whether to correct the error. It is strongly advised that you choose to correct the error by hitting "y", since if you do not, the angles between poles on the resulting projection will not be accurate. This is because the routine operates by calculating the indices of the center, south and east poles of the projection based on the angles between these poles and the two positions specified by the Wulff coordinates (by simultaneuous solution of dot-product equations). If the angle between the Wulff-specified positions is not exactly the same as the true angle between the hkl poles specified, you will create a non-true projection just as you would graphically. The correction feature places pole 2 at exactly the correct number of degrees from pole 1 on the great circle which contains the input poles 1 and 2. Pole 1 is never moved, and should therefore be the one known most accurately. If the correction routine is invoked, the resulting projection will be angle-true. The reason for not having the program automatically correct pole 2 is that you might accidentally provide incorrect indices or Wulff coordinates, which would be recognizable by a large error to be corrected. After pole 2 is entered and corrected, the screen is cleared and the standard set of circles is automatically drawn in the new orientation. Note that you can draw a projection which has pole 1 at exactly the desired location, and then rotate it about pole 1 later using the "Crystal" option under the Rotate menu. Laue See file "Crystal 2.29 update" Measure Menu Angle between poles Calculates the angle between any pair of poles or directions chosen by using the Pole Entry Dialog Box. Wulff Coordinates Determines the Wulff net coordinates of any pole chosen using the Pole Entry Dialog Box, according to the scheme in the N-S/E-W option of the Pole Entry Dialog Box description. Edit Menu Pole/circle Allows you to delete or add labeling of a given pole, and to choose whether or not to have its great circle drawn. Diameter Enlarges the projection diameter specified by the user, in cm. The original standard size (9 cm) can be obtained by hitting return without entering any number. The new projection will not always fit on the screen; only the central part which fits is then drawn, since the expansion is always about the center of the projection. Aspect Ratio Aspect ratio refers to the circularity of the basic circle (and all the arcs of great circles). The drawing is actually an oval with arcs of ovals. A perfect circle on the screen will not print as a perfect circle on the ImageWriter. The Aspect Ratio needed on the screen to create a true circle on the printer using the Print Screen option of the File menu is quite close to one with the newer Apple System files (System v 3.2 and associated ImageWriter file), but if you should use the program with older system files a ratio of 0.9079 is needed. Since the exact ratio may vary from printer to printer, I have made it adjustable. The built-in ratio (1.0184) which works for my ImageWriter is selectable at any time by simply hitting the return key in response to the prompt line. Try setting the ratio at 0.5 or 1.5 to see the effect. The Aspect Ratio for the Print option of the File menu is user-selected inside that routine, with default values. If you need to adjust the Aspect Ratio for the Print or Print Screen options, first make a test print with the aspect ratio set equal to 1.0. Now measure the width and height of the resulting outer oval, and compute the ratio of width to height. This value should give the correct Aspect Ratio to enter for your printer. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Cell Shape This is the option you use in order to define a new unit cell shape. The options are C for cubic, H for hexagonal and G (or any key other than C or H) for any general crystal system. If you select C, no other input is required. For this or any other system, a standard 001 projection is drawn with the standard set of circles and poles, so that you immediately verify your choice of crystal visually. If you choose H for hexagonal, the c/a ratio is requested. If you choose the general shape option, you must enter values for the lattice parameters a, b and c and then for a, b and g. Once you have defined a cell shape, you will probably want to save it for future use using Save from the File menu. Hex I/O modes This routine allows you to independently select the index input mode and output mode as either 3-axis (Miller) or 4-axis (Miller-Bravais). You can have your inputs as 3-axis at the same time that the screen labeling (output mode) is 4-axis or vice-versa. You can at any time change the output mode to either 3-axis or 4-axis. You must then revert to see the projection with the new index mode. You are first asked whether it is the input or output mode which you wish to change. Then you hit either the 3 or the 4 key to select the mode. Index Precision This adjusts the precision with which the "hkl via mouse" and "hkl via Wulff coords" options of the Identify menu convert from decimal to integer indices. The integers are found by multiplying the decimal indices by larger and larger integers until all three indices come within some amount D of being integers. The value of D can be adjusted by the user with the Integer Precision routine. The prompt value given in parentheses is the current value. The original value at startup is 0.1. Using larger values of D will result in smaller but less accurate integer indices; smaller D's will give more accurate but larger integer indices. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Relabel Relabels all poles already labeled without redrawing their circles. This is to clean up the drawing before printing, since circles will often pass through previously drawn indices. The relabeled indices lie on a clear background. Relabeling is automatically performed during reversion. Eraser Provides a MacPaint-like eraser. (MacPaint is an Apple Trademark.) The small square cursor which appears becomes an eraser upon pressing the mouse button, and remains so as the mouse is moved until the mouse button is released, which ends the routine. This is useful for cleaning up drawings to be printed with the Print Screen option of the File menu. See Also: Label, Move, Copy (Edit menu) Label Allows printing of a label typed by the user at any point specified on the projection by clicking the mouse. This is useful for drawings to be printed with the Print Screen option of the File menu. You must click the mouse at the point where you want the lower left corner of the text to begin before typing the label. The labels are specified to always be 9-point bold Geneva. You should choose any blank area of the screen to put the label, and then move it to exactly where you want it using Move or Copy from the Edit menu. You can always erase an unwanted label using Eraser. See Also: Eraser, Move, Copy (Edit menu) Move Allows the user to move any rectangular portion of the screen image wherever he wants. This is intended for moving labels, and is useful for drawings to be printed with the Print Screen option of the File menu. "Objects" such as labels can be selected by drawing a box around them exactly as in MacPaint (Apple trademark), by holding down the mouse button and moving the mouse until the box surrounds the object as desired, at which time the mouse button should be released. If the box drawn on the first try is not suitable, start a new one anywhere outside the first one. If the box is in the position desired after the first try, then release the mouse button and "select" the object by pressing the mouse button while the cursor is inside the box. Then the object can be "dragged" to the desired location, and the mouse button released to permanently place it there. When the button is released, the original object selected will replace any underlying image, but this only happens after releasing the button. The reason that this has been done this way is so that labels typed in a blank screen area can be placed on the projection at any point, and any underlying line will be automatically erased out to the edges of the selection box. If the screen was blank around the original object, the label will be on a white background. It is important to allow the desired amount of white space around the label when selecting it. See Also: Eraser, Label, Copy (Edit menu) Copy This operates exactly as does the Move option, except that the original object is not erased. This allows you to make multiple copies of objects easily. Note that this menu option is NOT equivalent to the normal Copy option which copies text or graphics to the clipboard. See Also: Eraser, Label, Move (Edit menu) Line This is the Crystal equivalent of the elastic straight line from MacPaint (Apple trademark). This may be useful for drawings to be printed with the Print Screen option of the File menu. It could be used, for instance, to construct the trace of a plane. Move the cursor to the desired starting point of the line, press the mouse button, and move the cursor to the desired endpoint. When the mouse button is released (and the cursor is moved one or more pixels), the user is ased whether the line is as desired: "OK? (Y/N)". Hitting y or Y causes the line to become permanent, while any other key causes it to be erased. 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