X-ray diffraction - Revision history

Cclewley at 13:24, 9 February 2022

2022-02-09T13:24:48Z

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	https://miro.com/app/board/o9J_lpv6cb8=/ (Miro board)		https://miro.com/app/board/o9J_lpv6cb8=/ (Miro board)
	[[Category:~~Visualisation~~ Project ~~Pages~~]]		[[Category:Project pages]]

JacobEdginton: Contributions

2021-12-13T15:07:37Z

Contributions

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	* Jonathan Rackham, Department of Materials. Staff partner from October 2021.		* Jonathan Rackham, Department of Materials. Staff partner from October 2021.
			*Paul Franklyn, Department of Materials. Staff partner from October 2021.

	==Aims & Learning Outcomes==		==Aims & Learning Outcomes==

BenSmith: Caption Carrection

2021-12-13T14:38:44Z

Caption Carrection

← Older revision		Revision as of 14:38, 13 December 2021
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	* In the software the visualisations were created in, snapping to points (i.e. lattice points) was not possible. Adding this would make the Ewald's sphere visualisation easier to understand.		* In the software the visualisations were created in, snapping to points (i.e. lattice points) was not possible. Adding this would make the Ewald's sphere visualisation easier to understand.
	* It was suggested that the user build on their understanding of Fourier by being able to draw a 2D shape and seeing its Fourier transform. This is simple to do in Python, but may have implementation issues in Java Script		* It was suggested that the user build on their understanding of Fourier by being able to draw a 2D shape and seeing its Fourier transform. This is simple to do in Python, but may have implementation issues in Java Script
	[[File:ReciprocalSpaceClip.mp4\|thumb\|316x178px\|2D Reciprocal Space]][[File:3DReciprocalSpaceClip.mp4\|thumb\|316x178px\|3D Reciprocal Space]][[File:EwaldsSphereClip.mp4\|thumb\|316x178px\|~~2D Reciprocal Space~~]][[File:X-Ray_Diffraction(LABELS)_-_配置文件_1_-_Microsoft_Edge_2021-12-13_14-01-25.mp4 \|thumb\|316x178px\|Short & Long Wavelengths]]		[[File:ReciprocalSpaceClip.mp4\|thumb\|316x178px\|2D Reciprocal Space]][[File:3DReciprocalSpaceClip.mp4\|thumb\|316x178px\|3D Reciprocal Space]][[File:EwaldsSphereClip.mp4\|thumb\|316x178px\|Ewald's Sphere]][[File:X-Ray_Diffraction(LABELS)_-_配置文件_1_-_Microsoft_Edge_2021-12-13_14-01-25.mp4 \|thumb\|316x178px\|Short & Long Wavelengths]]
	==Links ==		==Links ==
	Please see videos shown on the right, they provide more detail on the visualisations.		Please see videos shown on the right, they provide more detail on the visualisations.

BenSmith at 14:37, 13 December 2021

2021-12-13T14:37:56Z

← Older revision		Revision as of 14:37, 13 December 2021
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	* In the software the visualisations were created in, snapping to points (i.e. lattice points) was not possible. Adding this would make the Ewald's sphere visualisation easier to understand.		* In the software the visualisations were created in, snapping to points (i.e. lattice points) was not possible. Adding this would make the Ewald's sphere visualisation easier to understand.
	* It was suggested that the user build on their understanding of Fourier by being able to draw a 2D shape and seeing its Fourier transform. This is simple to do in Python, but may have implementation issues in Java Script		* It was suggested that the user build on their understanding of Fourier by being able to draw a 2D shape and seeing its Fourier transform. This is simple to do in Python, but may have implementation issues in Java Script
	[[File:~~EwaldsSphereClip~~.mp4\|thumb\|316x178px\|2D Reciprocal Space]][[File:~~ReciprocalSpaceClip~~.mp4\|thumb\|316x178px\|3D Reciprocal Space]][[File:~~3DReciprocalSpaceClip~~.mp4\|thumb\|316x178px\|~~Ewald's Sphere~~]][[File:X-Ray_Diffraction(LABELS)_-_配置文件_1_-_Microsoft_Edge_2021-12-13_14-01-25.mp4 \|thumb\|316x178px\|Short & Long Wavelengths]]		[[File:ReciprocalSpaceClip.mp4\|thumb\|316x178px\|2D Reciprocal Space]][[File:3DReciprocalSpaceClip.mp4\|thumb\|316x178px\|3D Reciprocal Space]][[File:EwaldsSphereClip.mp4\|thumb\|316x178px\|2D Reciprocal Space]][[File:X-Ray_Diffraction(LABELS)_-_配置文件_1_-_Microsoft_Edge_2021-12-13_14-01-25.mp4 \|thumb\|316x178px\|Short & Long Wavelengths]]
	==Links ==		==Links ==
	Please see videos shown on the right, they provide more detail on the visualisations.		Please see videos shown on the right, they provide more detail on the visualisations.

BenSmith: Clip Captions

2021-12-13T14:33:21Z

Clip Captions

← Older revision		Revision as of 14:33, 13 December 2021
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	* In the software the visualisations were created in, snapping to points (i.e. lattice points) was not possible. Adding this would make the Ewald's sphere visualisation easier to understand.		* In the software the visualisations were created in, snapping to points (i.e. lattice points) was not possible. Adding this would make the Ewald's sphere visualisation easier to understand.
	* It was suggested that the user build on their understanding of Fourier by being able to draw a 2D shape and seeing its Fourier transform. This is simple to do in Python, but may have implementation issues in Java Script		* It was suggested that the user build on their understanding of Fourier by being able to draw a 2D shape and seeing its Fourier transform. This is simple to do in Python, but may have implementation issues in Java Script
	[[File:EwaldsSphereClip.mp4\|thumb\|316x178px]][[File:ReciprocalSpaceClip.mp4\|thumb\|316x178px]][[File:3DReciprocalSpaceClip.mp4\|thumb\|316x178px]][[File:X-Ray_Diffraction(LABELS)_-_配置文件_1_-_Microsoft_Edge_2021-12-13_14-01-25.mp4 \|thumb\|316x178px]]		[[File:EwaldsSphereClip.mp4\|thumb\|316x178px\|2D Reciprocal Space]][[File:ReciprocalSpaceClip.mp4\|thumb\|316x178px\|3D Reciprocal Space]][[File:3DReciprocalSpaceClip.mp4\|thumb\|316x178px\|Ewald's Sphere]][[File:X-Ray_Diffraction(LABELS)_-_配置文件_1_-_Microsoft_Edge_2021-12-13_14-01-25.mp4 \|thumb\|316x178px\|Short & Long Wavelengths]]
	==Links ==		==Links ==
	Please see videos shown on the right, they provide more detail on the visualisations.		Please see videos shown on the right, they provide more detail on the visualisations.

BenSmith at 14:30, 13 December 2021

2021-12-13T14:30:02Z

JacobEdginton: /* Aims & Learning Outcomes */

2021-12-13T14:25:35Z

Aims & Learning Outcomes

← Older revision		Revision as of 14:25, 13 December 2021
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	This visualisation would be used as teaching tools in MATE50005 (Materials Characterisation~~, second year undergraduate~~) lectures as well as self-study tools in lab sessions. It will also be useful in the MATE70001 module (MSc Characterisation course).
			Staff Partner Brief: This visualisation would be used as teaching tools in MATE50005 (Materials Characterisation) lectures as well as self-study tools in lab sessions. It will also be useful in the MATE70001 module (MSc Characterisation course). This visualisation should help students understand the relationship between direct and reciprocal lattices, the features of reciprocal space and how they relate to a crystal’s structure, and how the motion of a diffractometer is related to that of the scattering vector through reciprocal space. They should also be able to evaluate the effect of experimental conditions on the diffraction patterns obtained.

	The students will have knowledge of the following before using this visualisation:		The students will have knowledge of the following before using this visualisation:

JacobEdginton: Video and Links

2021-12-13T14:13:04Z

Video and Links

← Older revision		Revision as of 14:13, 13 December 2021
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	==Design Overview==		==Design Overview==
	The design was split up into four main parts: Fourier transforms, diffraction patterns, reciprocal space, and the Ewald's sphere. The visualisations are shown graphically on the right.		The design was split up into four main parts: Fourier transforms, diffraction patterns, reciprocal space, and the Ewald's sphere. The visualisations are shown graphically on the right, and in video at the bottom of the wiki.

	'''Fourier Transforms'''[[File:ImpVis - Copy.png\|alt=Fourier Analysis & Transform page\|thumb\|424x424px\|Fourier Analysis & Transform page of the visualisation]]Fourier transform are the key mathematical framework for all of crystal X-ray diffraction theory. The Fourier visualisation shows two graphs: a function in the real domain, and the Fourier Transform of that function in the conjugate domain. The user is given control over an adjustable parameter in the function, for instance, for the Gaussian example, the user can control the width. If the play animation button is pressed, this parameter will be continuously varied such that the two graphs move in real time. The user is also given a rest button to return to the original conditions. A feedback button is available so that the design can be further improved. It can be seen that on the left side of the visualisation, there is written text and mathematical formulae that give an explanation of what the user is seeing graphically.		'''Fourier Transforms'''[[File:ImpVis - Copy.png\|alt=Fourier Analysis & Transform page\|thumb\|424x424px\|Fourier Analysis & Transform page of the visualisation]]Fourier transform are the key mathematical framework for all of crystal X-ray diffraction theory. The Fourier visualisation shows two graphs: a function in the real domain, and the Fourier Transform of that function in the conjugate domain. The user is given control over an adjustable parameter in the function, for instance, for the Gaussian example, the user can control the width. If the play animation button is pressed, this parameter will be continuously varied such that the two graphs move in real time. The user is also given a rest button to return to the original conditions. A feedback button is available so that the design can be further improved. It can be seen that on the left side of the visualisation, there is written text and mathematical formulae that give an explanation of what the user is seeing graphically.
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	[[File:EwaldsSphereClip.mp4\|thumb\|316x178px]][[File:ReciprocalSpaceClip.mp4\|thumb\|316x178px]][[File:3DReciprocalSpaceClip.mp4\|thumb\|316x178px]]		[[File:EwaldsSphereClip.mp4\|thumb\|316x178px]][[File:ReciprocalSpaceClip.mp4\|thumb\|316x178px]][[File:3DReciprocalSpaceClip.mp4\|thumb\|316x178px]]
	==Links==		==Links==
			Please see videos shown on the right, they provide more detail on the visualisations.

	https://www.geogebra.org/geometry/ky9yvnft (2D Reciprocal Space)		https://www.geogebra.org/geometry/ky9yvnft (2D Reciprocal Space)

JacobEdginton: General Improvements

2021-12-13T14:11:55Z

General Improvements

Show changes

HansLee: /* Design Overview */

2021-12-12T13:17:58Z

Design Overview

← Older revision		Revision as of 13:17, 12 December 2021
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	'''Diffraction Patterns'''[[File:Diffraction Pattern.png\|alt=Diffraction Pattern page of the visualisation.\|thumb\|Diffraction Pattern page of the visualisation. The lattice in real space is shown on the left, and subsequent diffraction pattern is shown on the right.\|426x426px]]This section of the visualisation aims to connect the lattice geometry of a crystal to the expected X-ray diffraction pattern. The user can choose the lattice type between rock salt, titanium, alumina, and diamond. Each type of lattice will have a different diffraction pattern based on its geometry. The user can choose to show only the basic structure, which consists of only lattice points, or the full structure with the molecular motif.		'''Diffraction Patterns'''[[File:Diffraction Pattern.png\|alt=Diffraction Pattern page of the visualisation.\|thumb\|Diffraction Pattern page of the visualisation. The lattice in real space is shown on the left, and subsequent diffraction pattern is shown on the right.\|426x426px]]This section of the visualisation aims to connect the lattice geometry of a crystal to the expected X-ray diffraction pattern. On the left side, there is text that points out the relation between Fourier transform and diffraction, and prompts the student to try out the visualisation. The screen on the left shows a 2-D projection of the crystal lattice, and the screen on the right shows its X-ray diffraction pattern. The user can choose the lattice type between rock salt, titanium, alumina, and diamond. Each type of lattice will have a different diffraction pattern based on its geometry. The user can choose to show only the basic structure, which consists of only lattice points, or the full structure with the molecular motif.

	The user also has control three other parameters: the wavelength and incident angle of X-rays, and a lattice parameter corresponding to how spaced out the lattice is. When these parameters are changed with the corresponding slider, both screens update in real time.		The user also has control three other parameters: the wavelength and incident angle of X-rays, and a lattice parameter corresponding to how spaced out the lattice is. When these parameters are changed with the corresponding slider, both screens update in real time.

← Older revision		Revision as of 14:30, 13 December 2021
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	~~Staff Partner Brief:~~ This visualisation would be used as teaching tools in MATE50005 (Materials Characterisation) lectures as well as self-study tools in lab sessions. It will also be useful in the MATE70001 module (MSc Characterisation course). This visualisation should help students understand the relationship between direct and reciprocal lattices, the features of reciprocal space and how they relate to a crystal’s structure, and how the motion of a diffractometer is related to that of the scattering vector through reciprocal space. They should also be able to evaluate the effect of experimental conditions on the diffraction patterns obtained.		This visualisation would be used as teaching tools in MATE50005 (Materials Characterisation, second year undergraduate) lectures as well as self-study tools in lab sessions. It will also be useful in the MATE70001 module (MSc Characterisation course).

	The students will have knowledge of the following before using this visualisation:		The students will have knowledge of the following before using this visualisation:

	* Single variable calculus, basic multivariable calculus.		*Single variable calculus, basic multivariable calculus.
	* Understanding of Fourier analysis.		*Understanding of Fourier analysis.
	* Full module on crystallography and electronic states of matter.		*Full module on crystallography and electronic states of matter.
	* Full course on characterisation techniques.		*Full course on characterisation techniques.

	After using this visualisation, students will be able to:		After using this visualisation, students will be able to:

	* Qualitatively describe the relationship between direct and reciprocal lattices.		*Qualitatively describe the relationship between direct and reciprocal lattices.
	* Discuss the features of reciprocal space and how they relate to a crystal’s structure.		*Discuss the features of reciprocal space and how they relate to a crystal’s structure.
	* Relate the motion of a diffractometer to that of the scattering vector through reciprocal space.		*Relate the motion of a diffractometer to that of the scattering vector through reciprocal space.
	* Evaluate the effect of experimental conditions on the diffraction patterns obtained.		*Evaluate the effect of experimental conditions on the diffraction patterns obtained.

	==Design Overview==		==Design Overview==
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	The main goal of this visualisation was to give the user an intuitive understanding of Fourier transformations, without having to rely on solely mathematics. The functions most relevant to the materials course were created in the visualisation: the Gaussian, the Top Hat function, a sinusoid, the Dirac delta, and the Dirac comb [more images to be added].		The main goal of this visualisation was to give the user an intuitive understanding of Fourier transformations, without having to rely on solely mathematics. The functions most relevant to the materials course were created in the visualisation: the Gaussian, the Top Hat function, a sinusoid, the Dirac delta, and the Dirac comb [more images to be added].



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	https://miro.com/app/board/o9J_lpv6cb8=/ (Miro board)		https://miro.com/app/board/o9J_lpv6cb8=/ (Miro board)
	==Design Justification==		==Design Justification ==
	===Assessment Criteria===		===Assessment Criteria===
	'''Education Design'''		'''Education Design'''
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	*The learner should know intuitively what the objectives are of the visualization.		*The learner should know intuitively what the objectives are of the visualization.
	*The user should be able to intuitively understand the function of each interactive element in the visualization.		*The user should be able to intuitively understand the function of each interactive element in the visualization.
	*There should be immediate visual feedback when a learner interacts with the visualization.		* There should be immediate visual feedback when a learner interacts with the visualization.

	===Education Design===		===Education Design===
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	*In order to more easily introduce reciprocal space, the lesson begins with a two-dimensional visualisation. This visualisation is intended to first describe a normal lattice and what it represents, in which the student can then see the corresponding reciprocal lattice, and by interacting with the normal lattice, the student will be able to identify key features of reciprocal space, namely its orthogonality to normal space, and it's reciprocal nature. It is intended to have the specific mathematics described in the left panel. Having now a good understanding in two-dimensions, the student can quickly start to understand the concept in three-dimensions. Although the student may have a good understanding of reciprocal space now, a three-dimensional visual is still much more cluttered. So, the visualisation was limited to only one cell and also introduced each element one by one. As shown on the Miro board, by constructing the visualisation this way, you can highlight the key features, like bringing to attention how a reciprocal lattice vector is at a right-angle to a real lattice plane. A final feature left to bring to light was the lattice's lack of centre, by giving the student to sliders to enlarge and rotate the normal lattice, and see what changes.		*In order to more easily introduce reciprocal space, the lesson begins with a two-dimensional visualisation. This visualisation is intended to first describe a normal lattice and what it represents, in which the student can then see the corresponding reciprocal lattice, and by interacting with the normal lattice, the student will be able to identify key features of reciprocal space, namely its orthogonality to normal space, and it's reciprocal nature. It is intended to have the specific mathematics described in the left panel. Having now a good understanding in two-dimensions, the student can quickly start to understand the concept in three-dimensions. Although the student may have a good understanding of reciprocal space now, a three-dimensional visual is still much more cluttered. So, the visualisation was limited to only one cell and also introduced each element one by one. As shown on the Miro board, by constructing the visualisation this way, you can highlight the key features, like bringing to attention how a reciprocal lattice vector is at a right-angle to a real lattice plane. A final feature left to bring to light was the lattice's lack of centre, by giving the student to sliders to enlarge and rotate the normal lattice, and see what changes.
	*One of the problems in understanding what’s the difference between short/long wavelength is understanding that Ewald’s sphere intersects with very few crystallites when wavelength is large and more crystallite when short. To see this, a good approach would be visualising the Ewald’s sphere for different wavelengths, especially given short wavelength, arcs of the sphere looks like a straight line. This builds up intuition for such phenomenon.		*One of the problems in understanding what’s the difference between short/long wavelength is understanding that Ewald’s sphere intersects with very few crystallites when wavelength is large and more crystallite when short. To see this, a good approach would be visualising the Ewald’s sphere for different wavelengths, especially given short wavelength, arcs of the sphere looks like a straight line. This builds up intuition for such phenomenon.
	===Graphical Design===		=== Graphical Design===
	* A range of shades of blue were implemented. This formed a set of colours that was not visually heavy but was still aesthetically pleasing. Note that the conjugate domain Fourier graph was shown in red. This was gone to give it contrast to the real domain plot: highlighting how the two are different. The text was shown on a light blue pattern with dark text (black).		*A range of shades of blue were implemented. This formed a set of colours that was not visually heavy but was still aesthetically pleasing. Note that the conjugate domain Fourier graph was shown in red. This was gone to give it contrast to the real domain plot: highlighting how the two are different. The text was shown on a light blue pattern with dark text (black).
	* The two screens take up most of the top and centre, which draws the student's attention. The sliders and buttons are placed in a regular pattern below the screens so they are still easy to notice and use, and the screens remain the main focus. The incident angle and wavelength sliders are placed in one column, so it is intuitive to group them together i.e. properties of incident X-rays. The crystal lattice has different colours for different types of particles, so the student can distinguish what the crystal structure looks like without much visual clutter.		*The two screens take up most of the top and centre, which draws the student's attention. The sliders and buttons are placed in a regular pattern below the screens so they are still easy to notice and use, and the screens remain the main focus. The incident angle and wavelength sliders are placed in one column, so it is intuitive to group them together i.e. properties of incident X-rays. The crystal lattice has different colours for different types of particles, so the student can distinguish what the crystal structure looks like without much visual clutter.
	*For both the reciprocal visualisations, different colours where used to distinguish between real and reciprocal lattices. And in two dimensions, in order to highlight the chosen centre and axes, the grid was dotted, keeping both axes filled. Additionally, the visualisation windows were positioned in the centre of the screen in order to draw the students focus onto them, with sliders and such to the right on the same canvas, so that it is clear the interactive elements are directly related to the visuals.		*For both the reciprocal visualisations, different colours where used to distinguish between real and reciprocal lattices. And in two dimensions, in order to highlight the chosen centre and axes, the grid was dotted, keeping both axes filled. Additionally, the visualisation windows were positioned in the centre of the screen in order to draw the students focus onto them, with sliders and such to the right on the same canvas, so that it is clear the interactive elements are directly related to the visuals.
	*It's important to stress the key object in the graphical visualisation, which is the Ewald's sphere. So orange, which is an eye-catching colour is selected for it. Also, thickness of lines(vectors) is chosen to be easily spotted while not blocking too much of crystallite area displayed. It is important that although this is a 2-D visualisation it represents unit cells in 3-D		*It's important to stress the key object in the graphical visualisation, which is the Ewald's sphere. So orange, which is an eye-catching colour is selected for it. Also, thickness of lines(vectors) is chosen to be easily spotted while not blocking too much of crystallite area displayed. It is important that although this is a 2-D visualisation it represents unit cells in 3-D
	===Interaction Design===		===Interaction Design===
	*The Fourier analysis visualization seeks to be interactive via two sliders. They let you control an adjustable parameter in the function we are examining. For instance, in a Gaussian it lets you control sigma and ‘conjugate sigma’ (rho). This gives the user an interactive input, and helps people make the connection between the two parameters (if one is altered so is the other). To add to this, there is an animate button. When pressed, the range of values of a parameter will be swept over. Whilst this is less interactive than manually adjusting the slider, it gives the user a strong overview how a function and its Fourier Transform will change for many different values of a parameter. ensure the user can return to their original state, a reset button will be implemented. This will set the values of the two parameters back to their starting values. In addition, there will be a feedback button. This allows users to submit input and suggest how the visualization might be improved.		*The Fourier analysis visualization seeks to be interactive via two sliders. They let you control an adjustable parameter in the function we are examining. For instance, in a Gaussian it lets you control sigma and ‘conjugate sigma’ (rho). This gives the user an interactive input, and helps people make the connection between the two parameters (if one is altered so is the other). To add to this, there is an animate button. When pressed, the range of values of a parameter will be swept over. Whilst this is less interactive than manually adjusting the slider, it gives the user a strong overview how a function and its Fourier Transform will change for many different values of a parameter. ensure the user can return to their original state, a reset button will be implemented. This will set the values of the two parameters back to their starting values. In addition, there will be a feedback button. This allows users to submit input and suggest how the visualization might be improved.
	*There are several parameters/options that can be changed by the student. Whenever a parameter/option is changed, the two screens update quickly for the student to see how the patterns change with the parameter. To make the controls obvious, there are sliders for adjustable parameters, the drop-down box is marked by a downward arrow and the word "select" next to it, and there is an empty box that can be clicked on to toggle showing the motif.		* There are several parameters/options that can be changed by the student. Whenever a parameter/option is changed, the two screens update quickly for the student to see how the patterns change with the parameter. To make the controls obvious, there are sliders for adjustable parameters, the drop-down box is marked by a downward arrow and the word "select" next to it, and there is an empty box that can be clicked on to toggle showing the motif.
	*For the reciprocal visualisation, any interactive element was highlighted in blue. In order to not clutter the visualisation, any interactive element that could be interacted with indirectly, was left to sliders and toggles outside the visualisation window. To keep the education design element in mind, some interactive elements are only intended to appear after certain events such as reading past a certain point in the left panel or finishing the construction of the three-dimensional visualisation. A feature intended for the student to be able to use is to be able to change their view of the visualisation, and whilst the draft doesn't bring light to this, it can be done by including some extra buttons next to the visual windows, one with a cursor, meant to toggle the users ability to interact with the blue points, and the other with a scroll icon, meant to toggle the students ability to change their perspective.		* For the reciprocal visualisation, any interactive element was highlighted in blue. In order to not clutter the visualisation, any interactive element that could be interacted with indirectly, was left to sliders and toggles outside the visualisation window. To keep the education design element in mind, some interactive elements are only intended to appear after certain events such as reading past a certain point in the left panel or finishing the construction of the three-dimensional visualisation. A feature intended for the student to be able to use is to be able to change their view of the visualisation, and whilst the draft doesn't bring light to this, it can be done by including some extra buttons next to the visual windows, one with a cursor, meant to toggle the users ability to interact with the blue points, and the other with a scroll icon, meant to toggle the students ability to change their perspective.
	*To build up better understanding in how changes in different parameters influences the result it’s better to give more options in changing variables. So, sliders of changing crystal spacing, crystallite radius, wavelength (directly related to radius of Ewald’s sphere) are provided. In designing demo, one variable is included to control the range of graph shown to allow quick display on some computers.		*To build up better understanding in how changes in different parameters influences the result it’s better to give more options in changing variables. So, sliders of changing crystal spacing, crystallite radius, wavelength (directly related to radius of Ewald’s sphere) are provided. In designing demo, one variable is included to control the range of graph shown to allow quick display on some computers.
	==Progress and Future Work==		==Progress and Future Work==
	*All the Geogebra and Desmos visualisations used in the design have been linked on this page (in design and in links)		*All the Geogebra and Desmos visualisations used in the design have been linked on this page (in design and in links)
	*In the software the visualisations were created in, snapping to points (i.e. lattice points) was not possible. Adding this would make the Ewald's sphere visualisation easier to understand.		* In the software the visualisations were created in, snapping to points (i.e. lattice points) was not possible. Adding this would make the Ewald's sphere visualisation easier to understand.
	*It was suggested that the user build on their understanding of Fourier by being able to draw a 2D shape and seeing its Fourier transform. This is simple to do in Python, but may have implementation issues in Java Script		* It was suggested that the user build on their understanding of Fourier by being able to draw a 2D shape and seeing its Fourier transform. This is simple to do in Python, but may have implementation issues in Java Script
	[[File:EwaldsSphereClip.mp4\|thumb\|316x178px]][[File:ReciprocalSpaceClip.mp4\|thumb\|316x178px]][[File:3DReciprocalSpaceClip.mp4\|thumb\|316x178px]]		[[File:EwaldsSphereClip.mp4\|thumb\|316x178px]][[File:ReciprocalSpaceClip.mp4\|thumb\|316x178px]][[File:3DReciprocalSpaceClip.mp4\|thumb\|316x178px]][[File:X-Ray_Diffraction(LABELS)_-_配置文件_1_-_Microsoft_Edge_2021-12-13_14-01-25.mp4 \|thumb\|316x178px]]
	==Links==		==Links ==
	Please see videos shown on the right, they provide more detail on the visualisations.		Please see videos shown on the right, they provide more detail on the visualisations.