Can two atoms be a crystal?












16












$begingroup$


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







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    Can you give a link in your question to an example of what you are talking about?
    $endgroup$
    – Aaron Stevens
    2 days 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
    2 days 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
    2 days ago






  • 1




    $begingroup$
    @denklo That's an answer
    $endgroup$
    – FGSUZ
    2 days 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
    2 days ago


















16












$begingroup$


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







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    Can you give a link in your question to an example of what you are talking about?
    $endgroup$
    – Aaron Stevens
    2 days 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
    2 days 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
    2 days ago






  • 1




    $begingroup$
    @denklo That's an answer
    $endgroup$
    – FGSUZ
    2 days 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
    2 days ago
















16












16








16





$begingroup$


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







share|cite|improve this question











$endgroup$




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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 2 days ago









Qmechanic♦

103k121851177




103k121851177










asked 2 days ago









m137m137

1829




1829








  • 1




    $begingroup$
    Can you give a link in your question to an example of what you are talking about?
    $endgroup$
    – Aaron Stevens
    2 days 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
    2 days 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
    2 days ago






  • 1




    $begingroup$
    @denklo That's an answer
    $endgroup$
    – FGSUZ
    2 days 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
    2 days ago
















  • 1




    $begingroup$
    Can you give a link in your question to an example of what you are talking about?
    $endgroup$
    – Aaron Stevens
    2 days 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
    2 days 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
    2 days ago






  • 1




    $begingroup$
    @denklo That's an answer
    $endgroup$
    – FGSUZ
    2 days 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
    2 days ago










1




1




$begingroup$
Can you give a link in your question to an example of what you are talking about?
$endgroup$
– Aaron Stevens
2 days ago




$begingroup$
Can you give a link in your question to an example of what you are talking about?
$endgroup$
– Aaron Stevens
2 days 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
2 days 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
2 days 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
2 days 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
2 days ago




1




1




$begingroup$
@denklo That's an answer
$endgroup$
– FGSUZ
2 days ago




$begingroup$
@denklo That's an answer
$endgroup$
– FGSUZ
2 days 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
2 days 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
2 days ago












2 Answers
2






active

oldest

votes


















21












$begingroup$

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.






share|cite|improve this answer









$endgroup$





















    0












    $begingroup$

    Why can't it be? This is a matter of definition and whether one is comfortable or not with such a definition, which is determined by one's intuitive feel. Certainly, the papers authors are comfortable with it, otherwise they wouldn't use it.



    To me, perhaps because of my affinity for theoretical mathematics and also computer programming, I see no problem at all with a crystal as having only one repeating unit. I tend to think of such a thing as being most similar to a mathematical set (though perhaps given the identical nature of the repeating units, a "multiset" might be the better choice if one wants to get strict), and a set can have one or even zero elements within it. That said, a "crystal with zero repeating units" is perhaps uninteresting physically, but mathematically even still makes sense, and moreover, a crystal can be abstracted into its set of lattice points which, as just that, a set, is entirely mathematically reasonable to consider as having 1 or even 0 points. In fact, from such a standpoint, the definition that admits 0 points can be "simpler" when one looks at how it is formulated in formal logic.



    Moreover, two atoms constitute only a minimal repeating unit where and when the two atoms are different. If they are the same, then you have actually do have two repeating units in the "lattice".






    share|cite|improve this answer









    $endgroup$













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      2 Answers
      2






      active

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      2 Answers
      2






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      active

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      21












      $begingroup$

      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.






      share|cite|improve this answer









      $endgroup$


















        21












        $begingroup$

        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.






        share|cite|improve this answer









        $endgroup$
















          21












          21








          21





          $begingroup$

          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.






          share|cite|improve this answer









          $endgroup$



          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.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 2 days ago









          Emilio PisantyEmilio Pisanty

          82.8k22200415




          82.8k22200415























              0












              $begingroup$

              Why can't it be? This is a matter of definition and whether one is comfortable or not with such a definition, which is determined by one's intuitive feel. Certainly, the papers authors are comfortable with it, otherwise they wouldn't use it.



              To me, perhaps because of my affinity for theoretical mathematics and also computer programming, I see no problem at all with a crystal as having only one repeating unit. I tend to think of such a thing as being most similar to a mathematical set (though perhaps given the identical nature of the repeating units, a "multiset" might be the better choice if one wants to get strict), and a set can have one or even zero elements within it. That said, a "crystal with zero repeating units" is perhaps uninteresting physically, but mathematically even still makes sense, and moreover, a crystal can be abstracted into its set of lattice points which, as just that, a set, is entirely mathematically reasonable to consider as having 1 or even 0 points. In fact, from such a standpoint, the definition that admits 0 points can be "simpler" when one looks at how it is formulated in formal logic.



              Moreover, two atoms constitute only a minimal repeating unit where and when the two atoms are different. If they are the same, then you have actually do have two repeating units in the "lattice".






              share|cite|improve this answer









              $endgroup$


















                0












                $begingroup$

                Why can't it be? This is a matter of definition and whether one is comfortable or not with such a definition, which is determined by one's intuitive feel. Certainly, the papers authors are comfortable with it, otherwise they wouldn't use it.



                To me, perhaps because of my affinity for theoretical mathematics and also computer programming, I see no problem at all with a crystal as having only one repeating unit. I tend to think of such a thing as being most similar to a mathematical set (though perhaps given the identical nature of the repeating units, a "multiset" might be the better choice if one wants to get strict), and a set can have one or even zero elements within it. That said, a "crystal with zero repeating units" is perhaps uninteresting physically, but mathematically even still makes sense, and moreover, a crystal can be abstracted into its set of lattice points which, as just that, a set, is entirely mathematically reasonable to consider as having 1 or even 0 points. In fact, from such a standpoint, the definition that admits 0 points can be "simpler" when one looks at how it is formulated in formal logic.



                Moreover, two atoms constitute only a minimal repeating unit where and when the two atoms are different. If they are the same, then you have actually do have two repeating units in the "lattice".






                share|cite|improve this answer









                $endgroup$
















                  0












                  0








                  0





                  $begingroup$

                  Why can't it be? This is a matter of definition and whether one is comfortable or not with such a definition, which is determined by one's intuitive feel. Certainly, the papers authors are comfortable with it, otherwise they wouldn't use it.



                  To me, perhaps because of my affinity for theoretical mathematics and also computer programming, I see no problem at all with a crystal as having only one repeating unit. I tend to think of such a thing as being most similar to a mathematical set (though perhaps given the identical nature of the repeating units, a "multiset" might be the better choice if one wants to get strict), and a set can have one or even zero elements within it. That said, a "crystal with zero repeating units" is perhaps uninteresting physically, but mathematically even still makes sense, and moreover, a crystal can be abstracted into its set of lattice points which, as just that, a set, is entirely mathematically reasonable to consider as having 1 or even 0 points. In fact, from such a standpoint, the definition that admits 0 points can be "simpler" when one looks at how it is formulated in formal logic.



                  Moreover, two atoms constitute only a minimal repeating unit where and when the two atoms are different. If they are the same, then you have actually do have two repeating units in the "lattice".






                  share|cite|improve this answer









                  $endgroup$



                  Why can't it be? This is a matter of definition and whether one is comfortable or not with such a definition, which is determined by one's intuitive feel. Certainly, the papers authors are comfortable with it, otherwise they wouldn't use it.



                  To me, perhaps because of my affinity for theoretical mathematics and also computer programming, I see no problem at all with a crystal as having only one repeating unit. I tend to think of such a thing as being most similar to a mathematical set (though perhaps given the identical nature of the repeating units, a "multiset" might be the better choice if one wants to get strict), and a set can have one or even zero elements within it. That said, a "crystal with zero repeating units" is perhaps uninteresting physically, but mathematically even still makes sense, and moreover, a crystal can be abstracted into its set of lattice points which, as just that, a set, is entirely mathematically reasonable to consider as having 1 or even 0 points. In fact, from such a standpoint, the definition that admits 0 points can be "simpler" when one looks at how it is formulated in formal logic.



                  Moreover, two atoms constitute only a minimal repeating unit where and when the two atoms are different. If they are the same, then you have actually do have two repeating units in the "lattice".







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered yesterday









                  The_SympathizerThe_Sympathizer

                  3,774923




                  3,774923






























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                      Alcedinidae

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                      Alcedinidae Martin-pêcheur à dos bleu ( Alcedo azurea ) Classification (COI) Règne Animalia Embranchement Chordata Sous-embr. Vertebrata Classe Aves Ordre Coraciiformes Famille Alcedinidae Rafinesque, 1815 Les Alcédinidés ou Alcedinidae forment une famille d'oiseaux plus connus sous les noms de martins-pêcheurs et martins-chasseurs. Sommaire 1 Description 2 Répartition et habitat 3 Systématique 3.1 Liste alphabétique des genres 3.2 Liste des espèces 4 Chez les Anciens : l'alcyon 4.1 Étymologie (Littré) 4.2 Oiseau « fabuleux » ? 5 Notes 6 Articles connexes 7 Liens externes 7.1 Bibliographie Description | Ce sont des oiseaux compacts de taille petite à moyenne (10 à 46 cm), au bec droit et long, en forme de poignard. Leurs pattes sont courtes, et ils portent un plumage aux couleurs vives. Répartition et habitat | Cosmopolites, ils fréquentent surtout ...
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                      Origin of the phrase “under your belt”?

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                      .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ margin-bottom:0; } 17 1 Today, I found myself discussing what students should have "under their belts" during a lecture, and I wondered to myself if there was some inappropriate undertone here that I might be unaware of. Question : What is the origin of the phrase "under your belt"? A google search revealed some webpages (e.g. [1]) that assert its origin is related to consumption of food -- once a meal has been eaten, it's under your belt (which is a relief). However, with such websites, I have no way to determine fact from "random guy on the internet making stuff up". etymology idioms ...
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