Dialog Box: Growth Zone Settings [ Sections and Growth Zones Dialog]
Growth model radio buttons. There are three basic growth models; linear, exponential and discontinuous. The last two are considered to be non-linear. For linear growth, the rates are derived from the central distances, and the values in the Total time and Time interval boxes (below) are not used.
Linear growth. If the growth is linear (rates constant with time), and a single crystal or simple twins are being drawn, the calculation of zones is simple. The final shape of the crystal is taken to be specified by the central distances entered in the Forms List dialog (Input1 menu), and it does not have to be recalculated; it is simply rescaled for each successive zone, the scale factors being determined from the Number of zones.
If multiple epitaxial crystals are being drawn, the entire calculation must be repeated for each zone, as for non-linear growth below. Each crystal attains the size determined by the central distance of its forms. The main crystal does this in total time 1.0 - it always has start time 0.0 and end time 1.0. The start and end times of the epitaxial crystals (see Start button below) are given relative to the main crystal. If an epitaxial crystal is given a negative start time, or an end time greater than one, the total growth interval will be extended appropriately.
Non-linear growth. If the growth is by either the exponential or discontinuous models, the increment to the central distance for each form is calculated from the Time interval , using either the Rate Constants in the exponential model or the rates entered for each interval using the Intervals button. The growth of the main crystal starts at time zero, and ends at the Total time specified in the edit box. For epitaxial crystals, each epitaxial crystal starts and ends at the time specified using the Times button at the bottom of the dialog. As in the case of linear growth, the start and end of the growth process will be extended if epitaxial crystals start before or end after the main crystal. However, the start and end times for non-linear growth are absolute (in whatever units you may be using).
The non-linear method, i.e. repetition of the entire calculation for each zone, is always used for epitaxial intergrowth, even if the Linear growth model is selected.
When you click on either the Rate Constants or the Intervals button, you are first presented with the Forms List for Growth-Rate Constants dialog. This simply gives a list of the current forms, for each of which you must specify or confirm the rate constants. Selecting a form from that dialog then presents you with the Exponential Growth-Rate Constants dialog for exponential growth, or the Growth Intervals dialog for discontinuous growth. See help for these dialogs for further information on growth-rate parameters
For proper drawing of epitaxial crystals, the box for Intercrystal edges in the Epitaxial Crystals dialog should usually be checked. Similarly, for interpenetration twins specify the option with intercrystal edges.
When using scaling options (1) or (2) in the Scaling dialog (Input2 menu), it is impossible to scale a non-linear growth-zone drawing before it is completed. However, the overall scale factor for the next calculation is obtained from the last zone. Thus it may be necessary to repeat the calculation with the Calculate command in the File menu, or the Calculate button in the Dialog Bar - Left to get proper scaling. If you are using scaling option (3)- Fixed in./cm. per central distance unit, it is up to you to insure that the drawing does not go off scale.
Linear: number of zones. In linear growth, the crystal will be divided into zones representing equal increments of growth time. Strictly speaking, this number of zones applies only to the host in epitaxial intergrowths; see Times below for the number of zones for guest crystals.
Non-linear: Total time. This is the end time for the main or host crystal if epitaxial crystals are present. Epitaxial guest crystals may actually start before the zero time or after the end or total time for the host crystal - see Times below. The time unit is arbitrary and may be considered to be seconds, hours or any other appropriate unit.
Non-linear: Time interval. An entire calculation will be carried out, and a zone drawn, for each interval.
Marker zones. If you are using wide lines to fill in the growth sectors (see Filling Sectors below), you can insert marker zones of a contrasting color at specified intervals, to show the orientation of growth and the relative rates.
Sector boundaries. If this box is checked, lines are drawn connecting corners in the section which are defined by the same combinations of faces. If a face appears or disappears on a corner between zones, no line is drawn, since this changes the identity of the sector boundary. If you find that too many sectors are thus undefined, the solution is to increase the Number of zones for linear growth, or decrease the Time interval for non-linear growth (see Filling Sectors below).
Pause after each zone. If this box is checked, the calculation will pause after the appearance of each zone outline. Pressing any key will cause the next zone to plot.
Colors for one-face edges. In section, growth sectors are defined by one-face edges (see Sections and Growth Zones). All these edges may be given a single or default color, or you may specify a color for each form, so that sectors may be more easily correlated with external forms. Two-face edges always have the colors specified in the sub-dialogs called with the Line Colors and Patterns/Pens buttons in the Sections and Growth Zones dialog.
Epitaxial crystals - start and end times (Start Button). This allows epitaxial guest crystals to start or end growth at different times relative to the host crystal. For linear growth, the times specified are relative to the main crystal; that is values of 0.0 and 1.0 mean that the epitaxial crystal in question (numbered starting with two for the first guest crystal) starts and ends at the same time as the host. Values of 0.5 and 1.5 mean that the guest crystal starts at half the Total time and ends at half again the Total time after the host crystal has ended.
For linear growth, epitaxial guest crystals reach the full size specified by the central distances of their forms in the time allotted (end minus start), and thus the number of zones will be less than that specified in the Number of zones box if the total time (end minus start) for this crystal is less than one.
For non-linear growth the times are absolute, in whatever time units are currently being used. The ultimate size of each crystal and number of zones is determined by the growth-rate equations.
Filling Sectors. To minimize the problem of undefined sector boundaries, and to make it easier to identify sectors, it may be desirable to make the section lines so close together as to touch or almost touch. This can be done by increasing the Number of zones for linear growth or decreasing the Time interval for non-linear growth; it is made easier by increasing the width of the lines (Line Attributes dialog in the Input2 menu). If the sectors are completely filled in, Marker zones may be used to show the orientation of the growth.