# How to plot defects (dislocations and disclinations) in crystals?

How to plot dislocations and disclinations in crystals? like the pictures blow (from Chaikin and Lubensky's book Principles of condensed matter physics). I need to draw several pics of this type. Any help would be appreciated!

• i think this may be easier to do in a 3D application, or a math application like mathematica to be honest Mar 25, 2017 at 18:57
• here is a quick test i did in maya Mar 25, 2017 at 20:10
• @sash thats not what im saying im saying you should be using a software you know that has higher order primitives, like a graphing application or a 3d application you know how to use. Heres the same thing done in illustrator Using same approach. Mar 25, 2017 at 20:50
• Quickest, cheapest and highest quality - draw it with hand :) Mar 25, 2017 at 22:29
• @sash hmm, :/ . Well, in Illustrator for example, despite I am a pro in it, it is very hard to draw such things, way more frustrating and time consuming than just drawing with hand. I mean even without hand drawing skill it would be probably least time consuming way. E.g. start with the simplest image (1st image). Mar 26, 2017 at 14:49

What you really need is a Finite Element Analysis (FEA) application. Not only can the FEA application solve your problem and visualize it. It allows you to somewhat easily solve an arbitrary complex problem for you with some effort.

Image 1: Quick test in Creo, with default meshing. Could be split to your desired grid for more accurate representation.

There are a several free FEA applications or you can use a commercial one (sky is the limit as far as fea application prices go).

• thank. i am now learning 3ds max and blender now. it seems 3d plotting software can do this job quite conveniently
– sash
Mar 27, 2017 at 21:08
• FEA package is for numerical solving of a set of spatial partial differential equations in a given geometry and a given set of boundary values. The drawing (=input the geometry) is something extra. Fea packages import common CAD files. The division to finite elements will be made for the convergence of the solution, not for flashy drawing. In theory there can be selectable the division to cubes, but that's far from optimal. Taking a FEA package to this is like taking an ocean vessel when a small boat is needed.
– user82991
Mar 29, 2017 at 20:35
• @user287001 Thats where your both right and wrong the FEA package solves the shape of the dislocated object. Without you having to draw it, since the points of the mesh are now known dumping the data into a picture is trivial. And nearly every FEA package on earth has a postprocessor that can do it. Even if thats not the case you can dump that data easily into inkscape. Also we are not drawing input geometry we are drawing the output geometry. Mar 29, 2017 at 21:22
• Also while its true that the convegence criteria is what you mesh for, this is sortof a special case. Where each cube represents a crystal structure. Since the underlying model, most often, models one perfect crystall of sorts it will converge to the right solution. Mar 29, 2017 at 21:34
• Seemingly you have done something with FEA. I'm extremely keen to know how you insert the stress or forced displacement onto material so that the result is either twisted structure, the twisting such way that questioner's image is right. I can input the wanted final image into a solid modeller, but forces and torques or forced displacements that would cause it as the result are too much. It could be the opposite forced rotations in the symmetry point+ a good guess of the new non-square form. BTW drawing the mesh onto the surface is anything but a trivial task in Inkscape or Illustrator.
– user82991
Mar 30, 2017 at 0:20

Try at first this. Here Incscape is used without tricks. Comment, can you follow this!

An alternative method due the comments (it's simpler, too)

Copy it by a pen. Do it in Inkscape, because you get consistent lines and errors can be fixed without traces. At first do some preparations

• draw a small rectangle, say 8mm x 8mm or 1/3 inch. Think it to be a square in your grids. Give to it a good stroke width and a light, non-black color; cyan or orange is good. Remove the fill. Select that object when it's ready.
• Doubleclick pen tool icon to get it's options. Select Style of new objects by clicking "Take from selection" Check the boxes Fill, Stroke in the dialog.
• let the snapping be active for paths and nodes.
• Import your original image to Inkscape. Scale it so that one crystal error image fits onto your worksheet (beware distorting the aspect ratio, it can be locked by clicking the lock icon at H/W inspecor)
• select the image, goto Object > Object properties and click Lock and Set. This prevents your reference to move.

Now it's good to save your work, Save it often; once in 5 minutes because Incscape is famous of its ability to crash often.

Practice fast zooming by holding Ctrl + rotating the mousewheel. Practice also fast panning by holding the spacebar and hovering the mouse.

Take the Pen. Zoom BIG, Draw your grids line by line by clicking a node to every crossing in the image.

NOTE: You can keep the zoom big because you can pan as you draw, only hold the Spacebar.

End the new line segment by double click. Fix any errors without waiting as soon as the line segment is ready, use the Node tool. You can move temporarily one node off a little to be able to position another node under it. Otherwise the snapping prevents the fixing.

Some lines are quite tightly curved. You can respect that curvature by clicking extra nodes as you draw or you can add intermediate nodes afterwards by double-clicking the Node tool. Then move the extra nodes to their best positions.

If you delete (=select a node, press DEL) an intermediate node, the line do not straighten. There pops up the curvature handles of the adjacent nodes. They must be adjusted for the best fit.

A skilled user draws the curves straight away by dragging the node handles for the wanted curvature. This is NOT easy, a beginner does better by drawing polylines (=only clicks at new nodes)

When the grid is drawn, change its stroke to the final color, width and line end style. A rounded cap fits a little better.

Then draw the grey shapes that are the shadings in the middle hole. Remove its stroke and arrange it to the background (Object > Lower to Bottom)

Finally select all and Group.

Save different drawings separately and make a composition when all are ready.

• Yes but this is actually the easy part getting the dislocation right is a bit tricky. Especially for the rotation case. Mar 26, 2017 at 17:34
• @joojaa of course it is easy. No use to write on if the questioner can't follow this.
– user82991
Mar 26, 2017 at 17:40
• @sash Sorry, but no 2D drawing programs do anything else, but the tracing, when the object is originally 3D. My first example and its planned sequel with envelope distortion meshes all were also tracings of memorized images - no need to be pointwise accurate due the automatic intermediate lines, but the idea was copied from your pic. The only way to avoid the tracing is to use 3D software. I do not know which one is low cost, flexible enough and still easy to use . Let's wind down this impossible task (=do it by using Inkscape and NO tracing)
– user82991
Mar 26, 2017 at 23:25