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Distinguishing between octahedral and tetrahedral holes
Complexes formed by lanthanides and actinidesWhat is Nano Zinc Oxide?Structure of KC8Jahn-Teller Distortions in Square Planar Complexes?Polyatomics -How Do They Work?Coordination geometry: why is of Cu(acac)2 square planar?Dissolution of Lithium in MethanolHow does the energy released during a bond formation typically manifest itself on atomic level?
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$begingroup$
I know the question sounds a bit silly and there are many similar answered questions but my 3D visualization (imagination) is very bad. There are some images of octahedral and tetrahedral holes but still there's no easy explanation. Can someone help me?
inorganic-chemistry
asked 9 hours ago
làntèrnlàntèrn
1721 silver badge19 bronze badges
$endgroup$
add a comment |
$begingroup$
I know the question sounds a bit silly and there are many similar answered questions but my 3D visualization (imagination) is very bad. There are some images of octahedral and tetrahedral holes but still there's no easy explanation. Can someone help me?
inorganic-chemistry
asked 9 hours ago
làntèrnlàntèrn
1721 silver badge19 bronze badges
$endgroup$
$begingroup$
Well, the tetrahedral holes are tetrahedral, and the octahedral ones are octahedral. It is not going to be any other way. What is your question, really?
$endgroup$
– Ivan Neretin
8 hours ago
$begingroup$
@Ivan Neretin Nah the problem is there's no picture that the holes are tetrahedral or octahedral. They're just round holes and many balls surround it. If I see the holes from top, will be like seeing pyramid from top or what?
$endgroup$
– làntèrn
8 hours ago
$begingroup$
I know tetrahedral but tetrahedral hole .. Someone should enlarge the hole and shows it is really that tetrahedral.
$endgroup$
– làntèrn
8 hours ago
$begingroup$
If you are in an empty space with 4 atoms as closest neighbors, it is a tetrahedral hole. If 6 atoms a close by, instead, it is a octahedral hole. Now we just need a small 360 $^circ$ camera to fly through crystals to visualize it.
$endgroup$
– Karsten Theis
7 hours ago
$begingroup$
The shape of the holes, taking atoms to be spherical, is not that of a tetrahedron or octahedron. The geometry of closest neighbors is what is described by the terms.
$endgroup$
– Karsten Theis
5 hours ago
add a comment |
$begingroup$
I know the question sounds a bit silly and there are many similar answered questions but my 3D visualization (imagination) is very bad. There are some images of octahedral and tetrahedral holes but still there's no easy explanation. Can someone help me?
inorganic-chemistry
asked 9 hours ago
làntèrnlàntèrn
1721 silver badge19 bronze badges
$endgroup$
I know the question sounds a bit silly and there are many similar answered questions but my 3D visualization (imagination) is very bad. There are some images of octahedral and tetrahedral holes but still there's no easy explanation. Can someone help me?
inorganic-chemistry
inorganic-chemistry
asked 9 hours ago
làntèrnlàntèrn
1721 silver badge19 bronze badges
asked 9 hours ago
làntèrnlàntèrn
1721 silver badge19 bronze badges
asked 9 hours ago
làntèrnlàntèrn
1721 silver badge19 bronze badges
asked 9 hours ago
làntèrnlàntèrn
1721 silver badge19 bronze badges
asked 9 hours ago
làntèrnlàntèrn
1721 silver badge19 bronze badges
1721 silver badge19 bronze badges
$begingroup$
Well, the tetrahedral holes are tetrahedral, and the octahedral ones are octahedral. It is not going to be any other way. What is your question, really?
$endgroup$
– Ivan Neretin
8 hours ago
$begingroup$
@Ivan Neretin Nah the problem is there's no picture that the holes are tetrahedral or octahedral. They're just round holes and many balls surround it. If I see the holes from top, will be like seeing pyramid from top or what?
$endgroup$
– làntèrn
8 hours ago
$begingroup$
I know tetrahedral but tetrahedral hole .. Someone should enlarge the hole and shows it is really that tetrahedral.
$endgroup$
– làntèrn
8 hours ago
$begingroup$
If you are in an empty space with 4 atoms as closest neighbors, it is a tetrahedral hole. If 6 atoms a close by, instead, it is a octahedral hole. Now we just need a small 360 $^circ$ camera to fly through crystals to visualize it.
$endgroup$
– Karsten Theis
7 hours ago
$begingroup$
The shape of the holes, taking atoms to be spherical, is not that of a tetrahedron or octahedron. The geometry of closest neighbors is what is described by the terms.
$endgroup$
– Karsten Theis
5 hours ago
add a comment |
$begingroup$
Well, the tetrahedral holes are tetrahedral, and the octahedral ones are octahedral. It is not going to be any other way. What is your question, really?
$endgroup$
– Ivan Neretin
8 hours ago
$begingroup$
@Ivan Neretin Nah the problem is there's no picture that the holes are tetrahedral or octahedral. They're just round holes and many balls surround it. If I see the holes from top, will be like seeing pyramid from top or what?
$endgroup$
– làntèrn
8 hours ago
$begingroup$
I know tetrahedral but tetrahedral hole .. Someone should enlarge the hole and shows it is really that tetrahedral.
$endgroup$
– làntèrn
8 hours ago
$begingroup$
If you are in an empty space with 4 atoms as closest neighbors, it is a tetrahedral hole. If 6 atoms a close by, instead, it is a octahedral hole. Now we just need a small 360 $^circ$ camera to fly through crystals to visualize it.
$endgroup$
– Karsten Theis
7 hours ago
$begingroup$
The shape of the holes, taking atoms to be spherical, is not that of a tetrahedron or octahedron. The geometry of closest neighbors is what is described by the terms.
$endgroup$
– Karsten Theis
5 hours ago
$begingroup$
Well, the tetrahedral holes are tetrahedral, and the octahedral ones are octahedral. It is not going to be any other way. What is your question, really?
$endgroup$
– Ivan Neretin
8 hours ago
$begingroup$
Well, the tetrahedral holes are tetrahedral, and the octahedral ones are octahedral. It is not going to be any other way. What is your question, really?
$endgroup$
– Ivan Neretin
8 hours ago
$begingroup$
@Ivan Neretin Nah the problem is there's no picture that the holes are tetrahedral or octahedral. They're just round holes and many balls surround it. If I see the holes from top, will be like seeing pyramid from top or what?
$endgroup$
– làntèrn
8 hours ago
$begingroup$
@Ivan Neretin Nah the problem is there's no picture that the holes are tetrahedral or octahedral. They're just round holes and many balls surround it. If I see the holes from top, will be like seeing pyramid from top or what?
$endgroup$
– làntèrn
8 hours ago
$begingroup$
I know tetrahedral but tetrahedral hole .. Someone should enlarge the hole and shows it is really that tetrahedral.
$endgroup$
– làntèrn
8 hours ago
$begingroup$
I know tetrahedral but tetrahedral hole .. Someone should enlarge the hole and shows it is really that tetrahedral.
$endgroup$
– làntèrn
8 hours ago
$begingroup$
If you are in an empty space with 4 atoms as closest neighbors, it is a tetrahedral hole. If 6 atoms a close by, instead, it is a octahedral hole. Now we just need a small 360 $^circ$ camera to fly through crystals to visualize it.
$endgroup$
– Karsten Theis
7 hours ago
$begingroup$
If you are in an empty space with 4 atoms as closest neighbors, it is a tetrahedral hole. If 6 atoms a close by, instead, it is a octahedral hole. Now we just need a small 360 $^circ$ camera to fly through crystals to visualize it.
$endgroup$
– Karsten Theis
7 hours ago
$begingroup$
The shape of the holes, taking atoms to be spherical, is not that of a tetrahedron or octahedron. The geometry of closest neighbors is what is described by the terms.
$endgroup$
– Karsten Theis
5 hours ago
$begingroup$
The shape of the holes, taking atoms to be spherical, is not that of a tetrahedron or octahedron. The geometry of closest neighbors is what is described by the terms.
$endgroup$
– Karsten Theis
5 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
To visualize holes in closest packing of spheres, you need 6 balls (marbles, table tennis balls, etc) of equal size. 3D closest packing can be constructed from 2D layers of closest packed spheres as such:
The light blue layer is on the bottom and the dark blue layer is on top. The holes, tetrahedral or octahedral, are in between layers.
To find a tetrahedral hole, take three balls and arrange them in a triangle to form part of the lower layer. Then place one sphere in the center on top (you have to keep the lower level together somehow or the structure will collapse). Your tetrahedral hole is in the center of the tetrahedron formed by the 4 balls (marked T in the picture).
To find an octahedral hole, you need a helper or glue. Take three balls and arrange them in a triangle. Take another three balls and arrange them in a triangle. Place the two triangles on top of each other, twisted against each other by 60 degrees. This is a octahedron on its side, and in the center is the octahdral hole.
In the picture above, these positions are marked by T and O. You just have to imaging that they are in between the layers, and then you might be able to count nearest spheres. The picture below shows the arrangement of the nearest spheres, only.
If you don't have 6 balls handy, but have two hands handy, you can also do the following. Place thumb, pointer and middle finger together so that the finger tips form a triangle. Point at the center of the triangle with the pointer of the other hand. That's the tetrahedral hole. Now, form a triangle with the finger tips of your other hand. Bring the 6 finger tips together with a little twist so that they "lock in". At the center of the 6 finger tips, you have the octahedral hole.
So, whether you are a visual or a haptic learner (not that that would be a thing), this will do the trick, I hope.
There are some images of octahedral and tetrahedral holes
Actually, I only found images of the spheres representing the atoms, no images of the shape of the space in between. If you squeeze some blue play dough between two layers of marbles, here is what you get:
Within a layer, each indentation is surrounded by six others. The arrows point at the six locations with the largest voids (in the center of triangles formed by the sphere and two of its nearest neighbors in that layer). If you look closely, each indentation has three holes, the contacts with the layer below. The voids take on different shapes depending what is underneath. If a sphere is directly underneath, it is a tetrahedral hole. The shape of this is a tetrahedron with "dented in" faces (far right). If a center of a triangle is directly underneath, it is an octahedral hole. The shape of this is a cube with "dented in" faces (near right; cube and octahedron are complementary archimedian solids: the centers of the faces coincide with the other's vertices and vice versa. A tetrahedron is complementary to itself).
If you shrink the spheres around the atoms to points, you get a space-filling arrangement of tetrehedra and octahedra called a tetrahedral-octahedral honey comb.
answered 6 hours ago
Karsten TheisKarsten Theis
10.1k12 silver badges55 bronze badges
$endgroup$
add a comment |
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$begingroup$
To visualize holes in closest packing of spheres, you need 6 balls (marbles, table tennis balls, etc) of equal size. 3D closest packing can be constructed from 2D layers of closest packed spheres as such:
The light blue layer is on the bottom and the dark blue layer is on top. The holes, tetrahedral or octahedral, are in between layers.
To find a tetrahedral hole, take three balls and arrange them in a triangle to form part of the lower layer. Then place one sphere in the center on top (you have to keep the lower level together somehow or the structure will collapse). Your tetrahedral hole is in the center of the tetrahedron formed by the 4 balls (marked T in the picture).
To find an octahedral hole, you need a helper or glue. Take three balls and arrange them in a triangle. Take another three balls and arrange them in a triangle. Place the two triangles on top of each other, twisted against each other by 60 degrees. This is a octahedron on its side, and in the center is the octahdral hole.
In the picture above, these positions are marked by T and O. You just have to imaging that they are in between the layers, and then you might be able to count nearest spheres. The picture below shows the arrangement of the nearest spheres, only.
If you don't have 6 balls handy, but have two hands handy, you can also do the following. Place thumb, pointer and middle finger together so that the finger tips form a triangle. Point at the center of the triangle with the pointer of the other hand. That's the tetrahedral hole. Now, form a triangle with the finger tips of your other hand. Bring the 6 finger tips together with a little twist so that they "lock in". At the center of the 6 finger tips, you have the octahedral hole.
So, whether you are a visual or a haptic learner (not that that would be a thing), this will do the trick, I hope.
There are some images of octahedral and tetrahedral holes
Actually, I only found images of the spheres representing the atoms, no images of the shape of the space in between. If you squeeze some blue play dough between two layers of marbles, here is what you get:
Within a layer, each indentation is surrounded by six others. The arrows point at the six locations with the largest voids (in the center of triangles formed by the sphere and two of its nearest neighbors in that layer). If you look closely, each indentation has three holes, the contacts with the layer below. The voids take on different shapes depending what is underneath. If a sphere is directly underneath, it is a tetrahedral hole. The shape of this is a tetrahedron with "dented in" faces (far right). If a center of a triangle is directly underneath, it is an octahedral hole. The shape of this is a cube with "dented in" faces (near right; cube and octahedron are complementary archimedian solids: the centers of the faces coincide with the other's vertices and vice versa. A tetrahedron is complementary to itself).
If you shrink the spheres around the atoms to points, you get a space-filling arrangement of tetrehedra and octahedra called a tetrahedral-octahedral honey comb.
answered 6 hours ago
Karsten TheisKarsten Theis
10.1k12 silver badges55 bronze badges
$endgroup$
add a comment |
$begingroup$
To visualize holes in closest packing of spheres, you need 6 balls (marbles, table tennis balls, etc) of equal size. 3D closest packing can be constructed from 2D layers of closest packed spheres as such:
The light blue layer is on the bottom and the dark blue layer is on top. The holes, tetrahedral or octahedral, are in between layers.
To find a tetrahedral hole, take three balls and arrange them in a triangle to form part of the lower layer. Then place one sphere in the center on top (you have to keep the lower level together somehow or the structure will collapse). Your tetrahedral hole is in the center of the tetrahedron formed by the 4 balls (marked T in the picture).
To find an octahedral hole, you need a helper or glue. Take three balls and arrange them in a triangle. Take another three balls and arrange them in a triangle. Place the two triangles on top of each other, twisted against each other by 60 degrees. This is a octahedron on its side, and in the center is the octahdral hole.
In the picture above, these positions are marked by T and O. You just have to imaging that they are in between the layers, and then you might be able to count nearest spheres. The picture below shows the arrangement of the nearest spheres, only.
If you don't have 6 balls handy, but have two hands handy, you can also do the following. Place thumb, pointer and middle finger together so that the finger tips form a triangle. Point at the center of the triangle with the pointer of the other hand. That's the tetrahedral hole. Now, form a triangle with the finger tips of your other hand. Bring the 6 finger tips together with a little twist so that they "lock in". At the center of the 6 finger tips, you have the octahedral hole.
So, whether you are a visual or a haptic learner (not that that would be a thing), this will do the trick, I hope.
There are some images of octahedral and tetrahedral holes
Actually, I only found images of the spheres representing the atoms, no images of the shape of the space in between. If you squeeze some blue play dough between two layers of marbles, here is what you get:
Within a layer, each indentation is surrounded by six others. The arrows point at the six locations with the largest voids (in the center of triangles formed by the sphere and two of its nearest neighbors in that layer). If you look closely, each indentation has three holes, the contacts with the layer below. The voids take on different shapes depending what is underneath. If a sphere is directly underneath, it is a tetrahedral hole. The shape of this is a tetrahedron with "dented in" faces (far right). If a center of a triangle is directly underneath, it is an octahedral hole. The shape of this is a cube with "dented in" faces (near right; cube and octahedron are complementary archimedian solids: the centers of the faces coincide with the other's vertices and vice versa. A tetrahedron is complementary to itself).
If you shrink the spheres around the atoms to points, you get a space-filling arrangement of tetrehedra and octahedra called a tetrahedral-octahedral honey comb.
answered 6 hours ago
Karsten TheisKarsten Theis
10.1k12 silver badges55 bronze badges
$endgroup$
add a comment |
$begingroup$
To visualize holes in closest packing of spheres, you need 6 balls (marbles, table tennis balls, etc) of equal size. 3D closest packing can be constructed from 2D layers of closest packed spheres as such:
The light blue layer is on the bottom and the dark blue layer is on top. The holes, tetrahedral or octahedral, are in between layers.
To find a tetrahedral hole, take three balls and arrange them in a triangle to form part of the lower layer. Then place one sphere in the center on top (you have to keep the lower level together somehow or the structure will collapse). Your tetrahedral hole is in the center of the tetrahedron formed by the 4 balls (marked T in the picture).
To find an octahedral hole, you need a helper or glue. Take three balls and arrange them in a triangle. Take another three balls and arrange them in a triangle. Place the two triangles on top of each other, twisted against each other by 60 degrees. This is a octahedron on its side, and in the center is the octahdral hole.
In the picture above, these positions are marked by T and O. You just have to imaging that they are in between the layers, and then you might be able to count nearest spheres. The picture below shows the arrangement of the nearest spheres, only.
If you don't have 6 balls handy, but have two hands handy, you can also do the following. Place thumb, pointer and middle finger together so that the finger tips form a triangle. Point at the center of the triangle with the pointer of the other hand. That's the tetrahedral hole. Now, form a triangle with the finger tips of your other hand. Bring the 6 finger tips together with a little twist so that they "lock in". At the center of the 6 finger tips, you have the octahedral hole.
So, whether you are a visual or a haptic learner (not that that would be a thing), this will do the trick, I hope.
There are some images of octahedral and tetrahedral holes
Actually, I only found images of the spheres representing the atoms, no images of the shape of the space in between. If you squeeze some blue play dough between two layers of marbles, here is what you get:
Within a layer, each indentation is surrounded by six others. The arrows point at the six locations with the largest voids (in the center of triangles formed by the sphere and two of its nearest neighbors in that layer). If you look closely, each indentation has three holes, the contacts with the layer below. The voids take on different shapes depending what is underneath. If a sphere is directly underneath, it is a tetrahedral hole. The shape of this is a tetrahedron with "dented in" faces (far right). If a center of a triangle is directly underneath, it is an octahedral hole. The shape of this is a cube with "dented in" faces (near right; cube and octahedron are complementary archimedian solids: the centers of the faces coincide with the other's vertices and vice versa. A tetrahedron is complementary to itself).
If you shrink the spheres around the atoms to points, you get a space-filling arrangement of tetrehedra and octahedra called a tetrahedral-octahedral honey comb.
answered 6 hours ago
Karsten TheisKarsten Theis
10.1k12 silver badges55 bronze badges
$endgroup$
To visualize holes in closest packing of spheres, you need 6 balls (marbles, table tennis balls, etc) of equal size. 3D closest packing can be constructed from 2D layers of closest packed spheres as such:
The light blue layer is on the bottom and the dark blue layer is on top. The holes, tetrahedral or octahedral, are in between layers.
To find a tetrahedral hole, take three balls and arrange them in a triangle to form part of the lower layer. Then place one sphere in the center on top (you have to keep the lower level together somehow or the structure will collapse). Your tetrahedral hole is in the center of the tetrahedron formed by the 4 balls (marked T in the picture).
To find an octahedral hole, you need a helper or glue. Take three balls and arrange them in a triangle. Take another three balls and arrange them in a triangle. Place the two triangles on top of each other, twisted against each other by 60 degrees. This is a octahedron on its side, and in the center is the octahdral hole.
In the picture above, these positions are marked by T and O. You just have to imaging that they are in between the layers, and then you might be able to count nearest spheres. The picture below shows the arrangement of the nearest spheres, only.
If you don't have 6 balls handy, but have two hands handy, you can also do the following. Place thumb, pointer and middle finger together so that the finger tips form a triangle. Point at the center of the triangle with the pointer of the other hand. That's the tetrahedral hole. Now, form a triangle with the finger tips of your other hand. Bring the 6 finger tips together with a little twist so that they "lock in". At the center of the 6 finger tips, you have the octahedral hole.
So, whether you are a visual or a haptic learner (not that that would be a thing), this will do the trick, I hope.
There are some images of octahedral and tetrahedral holes
Actually, I only found images of the spheres representing the atoms, no images of the shape of the space in between. If you squeeze some blue play dough between two layers of marbles, here is what you get:
Within a layer, each indentation is surrounded by six others. The arrows point at the six locations with the largest voids (in the center of triangles formed by the sphere and two of its nearest neighbors in that layer). If you look closely, each indentation has three holes, the contacts with the layer below. The voids take on different shapes depending what is underneath. If a sphere is directly underneath, it is a tetrahedral hole. The shape of this is a tetrahedron with "dented in" faces (far right). If a center of a triangle is directly underneath, it is an octahedral hole. The shape of this is a cube with "dented in" faces (near right; cube and octahedron are complementary archimedian solids: the centers of the faces coincide with the other's vertices and vice versa. A tetrahedron is complementary to itself).
If you shrink the spheres around the atoms to points, you get a space-filling arrangement of tetrehedra and octahedra called a tetrahedral-octahedral honey comb.
answered 6 hours ago
Karsten TheisKarsten Theis
10.1k12 silver badges55 bronze badges
edited 3 hours ago
answered 6 hours ago
Karsten TheisKarsten Theis
10.1k12 silver badges55 bronze badges
answered 6 hours ago
Karsten TheisKarsten Theis
10.1k12 silver badges55 bronze badges
answered 6 hours ago
Karsten TheisKarsten Theis
10.1k12 silver badges55 bronze badges
10.1k12 silver badges55 bronze badges
add a comment |
add a comment |
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$begingroup$
Well, the tetrahedral holes are tetrahedral, and the octahedral ones are octahedral. It is not going to be any other way. What is your question, really?
$endgroup$
– Ivan Neretin
8 hours ago
$begingroup$
@Ivan Neretin Nah the problem is there's no picture that the holes are tetrahedral or octahedral. They're just round holes and many balls surround it. If I see the holes from top, will be like seeing pyramid from top or what?
$endgroup$
– làntèrn
8 hours ago
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I know tetrahedral but tetrahedral hole .. Someone should enlarge the hole and shows it is really that tetrahedral.
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– làntèrn
8 hours ago
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If you are in an empty space with 4 atoms as closest neighbors, it is a tetrahedral hole. If 6 atoms a close by, instead, it is a octahedral hole. Now we just need a small 360 $^circ$ camera to fly through crystals to visualize it.
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– Karsten Theis
7 hours ago
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The shape of the holes, taking atoms to be spherical, is not that of a tetrahedron or octahedron. The geometry of closest neighbors is what is described by the terms.
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– Karsten Theis
5 hours ago