Can two atoms be a crystal?
$begingroup$
In the physics literature, you can often find the term "two-ion crystal", when talking about two ions that are confined in a e.g. Paul trap. How is this possible? Shouldn't a crystal be a structure which repeats in space multiple (>2) times? Otherwise, what are the necessary requirements to define something as a crystal?
EDIT: one of the first ≈5k results found by Googling "two-ion crystal" https://arxiv.org/abs/1202.2730
solid-state-physics atomic-physics terminology crystals ion-traps
edited 8 hours ago
Qmechanic♦
103k121851175
asked 12 hours ago
m137m137
1578
$endgroup$
|
show 2 more comments
$begingroup$
In the physics literature, you can often find the term "two-ion crystal", when talking about two ions that are confined in a e.g. Paul trap. How is this possible? Shouldn't a crystal be a structure which repeats in space multiple (>2) times? Otherwise, what are the necessary requirements to define something as a crystal?
EDIT: one of the first ≈5k results found by Googling "two-ion crystal" https://arxiv.org/abs/1202.2730
solid-state-physics atomic-physics terminology crystals ion-traps
edited 8 hours ago
Qmechanic♦
103k121851175
asked 12 hours ago
m137m137
1578
$endgroup$
1
$begingroup$
Can you give a link in your question to an example of what you are talking about?
$endgroup$
– Aaron Stevens
11 hours ago
2
$begingroup$
I mean, is a taco a sandwich? It seems they're using "crystal" in a different way than most do, but there's no law against that.
$endgroup$
– knzhou
11 hours ago
1
$begingroup$
The necessary requirenment for a crystal is that it is periodic along it's lattice vectors. I.e. there exists at least one vector $v$ so that a translation along it conserves the system (btw. the number of such lineraly independent vektors defines the dimension of the crystal), by which i mean the observables, for instance the electron density within a solid in equilibrium: $rho(x + n v) = rho(x)$, $n inmathbf{N}$. This is by no means true for two isolated ions.
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– denklo
11 hours ago
1
$begingroup$
@denklo That's an answer
$endgroup$
– FGSUZ
11 hours ago
2
$begingroup$
@denklo That's an interesting definition; it's particularly notable in that it leaves out all real materials, so that (under that definition) crystals don't exist in the real world. (Among other shortcomings, such as leaving out quasicrystals, which are accepted as crystals by, say, the American Crystallographic Association, and other institutions whose opinions are generally regarded as important in this area.)
$endgroup$
– Emilio Pisanty
11 hours ago
|
show 2 more comments
$begingroup$
In the physics literature, you can often find the term "two-ion crystal", when talking about two ions that are confined in a e.g. Paul trap. How is this possible? Shouldn't a crystal be a structure which repeats in space multiple (>2) times? Otherwise, what are the necessary requirements to define something as a crystal?
EDIT: one of the first ≈5k results found by Googling "two-ion crystal" https://arxiv.org/abs/1202.2730
solid-state-physics atomic-physics terminology crystals ion-traps
edited 8 hours ago
Qmechanic♦
103k121851175
asked 12 hours ago
m137m137
1578
$endgroup$
In the physics literature, you can often find the term "two-ion crystal", when talking about two ions that are confined in a e.g. Paul trap. How is this possible? Shouldn't a crystal be a structure which repeats in space multiple (>2) times? Otherwise, what are the necessary requirements to define something as a crystal?
EDIT: one of the first ≈5k results found by Googling "two-ion crystal" https://arxiv.org/abs/1202.2730
solid-state-physics atomic-physics terminology crystals ion-traps
solid-state-physics atomic-physics terminology crystals ion-traps
edited 8 hours ago
Qmechanic♦
103k121851175
asked 12 hours ago
m137m137
1578
edited 8 hours ago
Qmechanic♦
103k121851175
asked 12 hours ago
m137m137
1578
edited 8 hours ago
Qmechanic♦
103k121851175
edited 8 hours ago
Qmechanic♦
103k121851175
edited 8 hours ago
Qmechanic♦
103k121851175
103k121851175
asked 12 hours ago
m137m137
1578
asked 12 hours ago
m137m137
1578
asked 12 hours ago
m137m137
1578
1578
1
$begingroup$
Can you give a link in your question to an example of what you are talking about?
$endgroup$
– Aaron Stevens
11 hours ago
2
$begingroup$
I mean, is a taco a sandwich? It seems they're using "crystal" in a different way than most do, but there's no law against that.
$endgroup$
– knzhou
11 hours ago
1
$begingroup$
The necessary requirenment for a crystal is that it is periodic along it's lattice vectors. I.e. there exists at least one vector $v$ so that a translation along it conserves the system (btw. the number of such lineraly independent vektors defines the dimension of the crystal), by which i mean the observables, for instance the electron density within a solid in equilibrium: $rho(x + n v) = rho(x)$, $n inmathbf{N}$. This is by no means true for two isolated ions.
$endgroup$
– denklo
11 hours ago
1
$begingroup$
@denklo That's an answer
$endgroup$
– FGSUZ
11 hours ago
2
$begingroup$
@denklo That's an interesting definition; it's particularly notable in that it leaves out all real materials, so that (under that definition) crystals don't exist in the real world. (Among other shortcomings, such as leaving out quasicrystals, which are accepted as crystals by, say, the American Crystallographic Association, and other institutions whose opinions are generally regarded as important in this area.)
$endgroup$
– Emilio Pisanty
11 hours ago
|
show 2 more comments
1
$begingroup$
Can you give a link in your question to an example of what you are talking about?
$endgroup$
– Aaron Stevens
11 hours ago
2
$begingroup$
I mean, is a taco a sandwich? It seems they're using "crystal" in a different way than most do, but there's no law against that.
$endgroup$
– knzhou
11 hours ago
1
$begingroup$
The necessary requirenment for a crystal is that it is periodic along it's lattice vectors. I.e. there exists at least one vector $v$ so that a translation along it conserves the system (btw. the number of such lineraly independent vektors defines the dimension of the crystal), by which i mean the observables, for instance the electron density within a solid in equilibrium: $rho(x + n v) = rho(x)$, $n inmathbf{N}$. This is by no means true for two isolated ions.
$endgroup$
– denklo
11 hours ago
1
$begingroup$
@denklo That's an answer
$endgroup$
– FGSUZ
11 hours ago
2
$begingroup$
@denklo That's an interesting definition; it's particularly notable in that it leaves out all real materials, so that (under that definition) crystals don't exist in the real world. (Among other shortcomings, such as leaving out quasicrystals, which are accepted as crystals by, say, the American Crystallographic Association, and other institutions whose opinions are generally regarded as important in this area.)
$endgroup$
– Emilio Pisanty
11 hours ago
1
1
$begingroup$
Can you give a link in your question to an example of what you are talking about?
$endgroup$
– Aaron Stevens
11 hours ago
$begingroup$
Can you give a link in your question to an example of what you are talking about?
$endgroup$
– Aaron Stevens
11 hours ago
2
2
$begingroup$
I mean, is a taco a sandwich? It seems they're using "crystal" in a different way than most do, but there's no law against that.
$endgroup$
– knzhou
11 hours ago
$begingroup$
I mean, is a taco a sandwich? It seems they're using "crystal" in a different way than most do, but there's no law against that.
$endgroup$
– knzhou
11 hours ago
1
1
$begingroup$
The necessary requirenment for a crystal is that it is periodic along it's lattice vectors. I.e. there exists at least one vector $v$ so that a translation along it conserves the system (btw. the number of such lineraly independent vektors defines the dimension of the crystal), by which i mean the observables, for instance the electron density within a solid in equilibrium: $rho(x + n v) = rho(x)$, $n inmathbf{N}$. This is by no means true for two isolated ions.
$endgroup$
– denklo
11 hours ago
$begingroup$
The necessary requirenment for a crystal is that it is periodic along it's lattice vectors. I.e. there exists at least one vector $v$ so that a translation along it conserves the system (btw. the number of such lineraly independent vektors defines the dimension of the crystal), by which i mean the observables, for instance the electron density within a solid in equilibrium: $rho(x + n v) = rho(x)$, $n inmathbf{N}$. This is by no means true for two isolated ions.
$endgroup$
– denklo
11 hours ago
1
1
$begingroup$
@denklo That's an answer
$endgroup$
– FGSUZ
11 hours ago
$begingroup$
@denklo That's an answer
$endgroup$
– FGSUZ
11 hours ago
2
2
$begingroup$
@denklo That's an interesting definition; it's particularly notable in that it leaves out all real materials, so that (under that definition) crystals don't exist in the real world. (Among other shortcomings, such as leaving out quasicrystals, which are accepted as crystals by, say, the American Crystallographic Association, and other institutions whose opinions are generally regarded as important in this area.)
$endgroup$
– Emilio Pisanty
11 hours ago
$begingroup$
@denklo That's an interesting definition; it's particularly notable in that it leaves out all real materials, so that (under that definition) crystals don't exist in the real world. (Among other shortcomings, such as leaving out quasicrystals, which are accepted as crystals by, say, the American Crystallographic Association, and other institutions whose opinions are generally regarded as important in this area.)
$endgroup$
– Emilio Pisanty
11 hours ago
|
show 2 more comments
1 Answer
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$begingroup$
Coulomb crystals are the structures formed by ions in a trap when they are sufficiently cold: once they stop jiggling around, they come down to equilibrium positions which need to balance the need to get down to the center of the trap, where the trapping potential is at its minimum, with the mutual repulsion between the ions.
This usually results in an orderly stacking of the ions, often with very clear local symmetries in a bunch of places. Here's one example, formed in an elongated ion trap (with experiment on the left and a simulation on the right; the lines are blurry because the whole thing is rigidly rotating about its vertical axis):
Image source
Within an ion-trapping context, the phrase "two-ion crystal" is a perfectly natural phrase to use for the case where you have coulomb-crystal dynamics, with a trapping potential and a Coulomb repulsion balancing out to give the equilibrium positions, and you have $N=2$ ions in the structure. If the phrase doesn't make sense to you, then that's just an indication that you're not within that text's intended audience.
Now, is the word "crystal" being used correctly here? The real answer is that it doesn't matter, at all: this is unambiguous notation, and lack of ambiguity is the single requirement that we make of notation.
answered 11 hours ago
Emilio PisantyEmilio Pisanty
82.6k22200415
$endgroup$
add a comment |
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$begingroup$
Coulomb crystals are the structures formed by ions in a trap when they are sufficiently cold: once they stop jiggling around, they come down to equilibrium positions which need to balance the need to get down to the center of the trap, where the trapping potential is at its minimum, with the mutual repulsion between the ions.
This usually results in an orderly stacking of the ions, often with very clear local symmetries in a bunch of places. Here's one example, formed in an elongated ion trap (with experiment on the left and a simulation on the right; the lines are blurry because the whole thing is rigidly rotating about its vertical axis):
Image source
Within an ion-trapping context, the phrase "two-ion crystal" is a perfectly natural phrase to use for the case where you have coulomb-crystal dynamics, with a trapping potential and a Coulomb repulsion balancing out to give the equilibrium positions, and you have $N=2$ ions in the structure. If the phrase doesn't make sense to you, then that's just an indication that you're not within that text's intended audience.
Now, is the word "crystal" being used correctly here? The real answer is that it doesn't matter, at all: this is unambiguous notation, and lack of ambiguity is the single requirement that we make of notation.
answered 11 hours ago
Emilio PisantyEmilio Pisanty
82.6k22200415
$endgroup$
add a comment |
$begingroup$
Coulomb crystals are the structures formed by ions in a trap when they are sufficiently cold: once they stop jiggling around, they come down to equilibrium positions which need to balance the need to get down to the center of the trap, where the trapping potential is at its minimum, with the mutual repulsion between the ions.
This usually results in an orderly stacking of the ions, often with very clear local symmetries in a bunch of places. Here's one example, formed in an elongated ion trap (with experiment on the left and a simulation on the right; the lines are blurry because the whole thing is rigidly rotating about its vertical axis):
Image source
Within an ion-trapping context, the phrase "two-ion crystal" is a perfectly natural phrase to use for the case where you have coulomb-crystal dynamics, with a trapping potential and a Coulomb repulsion balancing out to give the equilibrium positions, and you have $N=2$ ions in the structure. If the phrase doesn't make sense to you, then that's just an indication that you're not within that text's intended audience.
Now, is the word "crystal" being used correctly here? The real answer is that it doesn't matter, at all: this is unambiguous notation, and lack of ambiguity is the single requirement that we make of notation.
answered 11 hours ago
Emilio PisantyEmilio Pisanty
82.6k22200415
$endgroup$
add a comment |
$begingroup$
Coulomb crystals are the structures formed by ions in a trap when they are sufficiently cold: once they stop jiggling around, they come down to equilibrium positions which need to balance the need to get down to the center of the trap, where the trapping potential is at its minimum, with the mutual repulsion between the ions.
This usually results in an orderly stacking of the ions, often with very clear local symmetries in a bunch of places. Here's one example, formed in an elongated ion trap (with experiment on the left and a simulation on the right; the lines are blurry because the whole thing is rigidly rotating about its vertical axis):
Image source
Within an ion-trapping context, the phrase "two-ion crystal" is a perfectly natural phrase to use for the case where you have coulomb-crystal dynamics, with a trapping potential and a Coulomb repulsion balancing out to give the equilibrium positions, and you have $N=2$ ions in the structure. If the phrase doesn't make sense to you, then that's just an indication that you're not within that text's intended audience.
Now, is the word "crystal" being used correctly here? The real answer is that it doesn't matter, at all: this is unambiguous notation, and lack of ambiguity is the single requirement that we make of notation.
answered 11 hours ago
Emilio PisantyEmilio Pisanty
82.6k22200415
$endgroup$
Coulomb crystals are the structures formed by ions in a trap when they are sufficiently cold: once they stop jiggling around, they come down to equilibrium positions which need to balance the need to get down to the center of the trap, where the trapping potential is at its minimum, with the mutual repulsion between the ions.
This usually results in an orderly stacking of the ions, often with very clear local symmetries in a bunch of places. Here's one example, formed in an elongated ion trap (with experiment on the left and a simulation on the right; the lines are blurry because the whole thing is rigidly rotating about its vertical axis):
Image source
Within an ion-trapping context, the phrase "two-ion crystal" is a perfectly natural phrase to use for the case where you have coulomb-crystal dynamics, with a trapping potential and a Coulomb repulsion balancing out to give the equilibrium positions, and you have $N=2$ ions in the structure. If the phrase doesn't make sense to you, then that's just an indication that you're not within that text's intended audience.
Now, is the word "crystal" being used correctly here? The real answer is that it doesn't matter, at all: this is unambiguous notation, and lack of ambiguity is the single requirement that we make of notation.
answered 11 hours ago
Emilio PisantyEmilio Pisanty
82.6k22200415
answered 11 hours ago
Emilio PisantyEmilio Pisanty
82.6k22200415
answered 11 hours ago
Emilio PisantyEmilio Pisanty
82.6k22200415
answered 11 hours ago
Emilio PisantyEmilio Pisanty
82.6k22200415
82.6k22200415
add a comment |
add a comment |
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1
$begingroup$
Can you give a link in your question to an example of what you are talking about?
$endgroup$
– Aaron Stevens
11 hours ago
2
$begingroup$
I mean, is a taco a sandwich? It seems they're using "crystal" in a different way than most do, but there's no law against that.
$endgroup$
– knzhou
11 hours ago
1
$begingroup$
The necessary requirenment for a crystal is that it is periodic along it's lattice vectors. I.e. there exists at least one vector $v$ so that a translation along it conserves the system (btw. the number of such lineraly independent vektors defines the dimension of the crystal), by which i mean the observables, for instance the electron density within a solid in equilibrium: $rho(x + n v) = rho(x)$, $n inmathbf{N}$. This is by no means true for two isolated ions.
$endgroup$
– denklo
11 hours ago
1
$begingroup$
@denklo That's an answer
$endgroup$
– FGSUZ
11 hours ago
2
$begingroup$
@denklo That's an interesting definition; it's particularly notable in that it leaves out all real materials, so that (under that definition) crystals don't exist in the real world. (Among other shortcomings, such as leaving out quasicrystals, which are accepted as crystals by, say, the American Crystallographic Association, and other institutions whose opinions are generally regarded as important in this area.)
$endgroup$
– Emilio Pisanty
11 hours ago