What does x mean in (1-x)A – xB composite materials, molar ratio, weight ratio or volume fraction?












3












$begingroup$


I've been collecting data about ceramic materials and often I get to see composite materials are described as $(1-x)ce{A} - xce{B}$. I am confused what this $x$ means. And I haven't seen any of the papers mention what $x$ is unless %wt is given specifically.



For an example in $(1-x)ce{MgO} - xce{LiF}$ ceramic material, does $x$ mean molar ratio or weight ratio? For me it doesn't make sense to think of $x$ as a volume fraction as most of the times powders of these materials are taken for sintering.




  1. If nothing is mentioned, is it all right to assume $x$ as the molar ratio?


  2. Can we assume volume fraction is equal to molar ratio even in solids or liquids?







physical-chemistry concentration solid-state-chemistry notation







share|improve this question











$endgroup$

















    3












    $begingroup$


    I've been collecting data about ceramic materials and often I get to see composite materials are described as $(1-x)ce{A} - xce{B}$. I am confused what this $x$ means. And I haven't seen any of the papers mention what $x$ is unless %wt is given specifically.



    For an example in $(1-x)ce{MgO} - xce{LiF}$ ceramic material, does $x$ mean molar ratio or weight ratio? For me it doesn't make sense to think of $x$ as a volume fraction as most of the times powders of these materials are taken for sintering.




    1. If nothing is mentioned, is it all right to assume $x$ as the molar ratio?


    2. Can we assume volume fraction is equal to molar ratio even in solids or liquids?







    physical-chemistry concentration solid-state-chemistry notation







    share|improve this question











    $endgroup$















      3












      3








      3





      $begingroup$


      I've been collecting data about ceramic materials and often I get to see composite materials are described as $(1-x)ce{A} - xce{B}$. I am confused what this $x$ means. And I haven't seen any of the papers mention what $x$ is unless %wt is given specifically.



      For an example in $(1-x)ce{MgO} - xce{LiF}$ ceramic material, does $x$ mean molar ratio or weight ratio? For me it doesn't make sense to think of $x$ as a volume fraction as most of the times powders of these materials are taken for sintering.




      1. If nothing is mentioned, is it all right to assume $x$ as the molar ratio?


      2. Can we assume volume fraction is equal to molar ratio even in solids or liquids?







      physical-chemistry concentration solid-state-chemistry notation







      share|improve this question











      $endgroup$




      I've been collecting data about ceramic materials and often I get to see composite materials are described as $(1-x)ce{A} - xce{B}$. I am confused what this $x$ means. And I haven't seen any of the papers mention what $x$ is unless %wt is given specifically.



      For an example in $(1-x)ce{MgO} - xce{LiF}$ ceramic material, does $x$ mean molar ratio or weight ratio? For me it doesn't make sense to think of $x$ as a volume fraction as most of the times powders of these materials are taken for sintering.




      1. If nothing is mentioned, is it all right to assume $x$ as the molar ratio?


      2. Can we assume volume fraction is equal to molar ratio even in solids or liquids?







      physical-chemistry concentration solid-state-chemistry notation




      physical-chemistry concentration solid-state-chemistry notation






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited Feb 12 at 16:59









      andselisk

      16.4k653115




      16.4k653115










      asked Feb 12 at 16:45









      avinavin

      182




      182






















          1 Answer
          1






          active

          oldest

          votes


















          5












          $begingroup$

          Here, $x$ is a variable $(xin[0;1])$ denoting mole fraction of a given constituent in a phase of variable composition (non-stoichiometric compound).
          This is an algebraic way of denoting a given compound from the phase diagram for a solid solution: $x$ corresponds to its abscissa axis.



          And no, volume fraction is not equal to mole fraction and is overall a very inconvenient variable to use, so it's usually being avoided.
          For example, volume fraction would deviate for the different morphologies and allotropes of the same solid, which is not useful for the description of chemical composition, not to mention it's also temperature-dependent.






          share|improve this answer











          $endgroup$









          • 1




            $begingroup$
            Since the OP refers to sintering I don't think that mole fraction can be assumed. In fact the OP mentions that some articles explicitly specify wt %.
            $endgroup$
            – MaxW
            Feb 12 at 17:19










          • $begingroup$
            @MaxW Mole fraction is pretty much a default in the absence of additional remarks. Of course, if there is %wt notation, then it's mass fraction.
            $endgroup$
            – andselisk
            Feb 12 at 17:24










          • $begingroup$
            @MaxW I believe almost all the ceramic compounds are made by sintering. Do you believe 0.8MgO - 0.2LiF could mean weight fractions? Most of the related papers don't mention what x is, although when they do mention about 'weights', they make sure to present it as a percentage, like MgO - 20% LiF. But I'm sure there should be some convention among scientists to understand what x really is unless explicitly specified?
            $endgroup$
            – avin
            Feb 12 at 18:10






          • 2




            $begingroup$
            @avin Again, unless there are any specific notes, $(1-x)ce{MgO} - xce{LiF} ≡ ce{Li_xMg_{(1-x)}O_{(1-x)}F_x}$, so by default $x$ implicates mole fraction.
            $endgroup$
            – andselisk
            Feb 12 at 18:15











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          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          5












          $begingroup$

          Here, $x$ is a variable $(xin[0;1])$ denoting mole fraction of a given constituent in a phase of variable composition (non-stoichiometric compound).
          This is an algebraic way of denoting a given compound from the phase diagram for a solid solution: $x$ corresponds to its abscissa axis.



          And no, volume fraction is not equal to mole fraction and is overall a very inconvenient variable to use, so it's usually being avoided.
          For example, volume fraction would deviate for the different morphologies and allotropes of the same solid, which is not useful for the description of chemical composition, not to mention it's also temperature-dependent.






          share|improve this answer











          $endgroup$









          • 1




            $begingroup$
            Since the OP refers to sintering I don't think that mole fraction can be assumed. In fact the OP mentions that some articles explicitly specify wt %.
            $endgroup$
            – MaxW
            Feb 12 at 17:19










          • $begingroup$
            @MaxW Mole fraction is pretty much a default in the absence of additional remarks. Of course, if there is %wt notation, then it's mass fraction.
            $endgroup$
            – andselisk
            Feb 12 at 17:24










          • $begingroup$
            @MaxW I believe almost all the ceramic compounds are made by sintering. Do you believe 0.8MgO - 0.2LiF could mean weight fractions? Most of the related papers don't mention what x is, although when they do mention about 'weights', they make sure to present it as a percentage, like MgO - 20% LiF. But I'm sure there should be some convention among scientists to understand what x really is unless explicitly specified?
            $endgroup$
            – avin
            Feb 12 at 18:10






          • 2




            $begingroup$
            @avin Again, unless there are any specific notes, $(1-x)ce{MgO} - xce{LiF} ≡ ce{Li_xMg_{(1-x)}O_{(1-x)}F_x}$, so by default $x$ implicates mole fraction.
            $endgroup$
            – andselisk
            Feb 12 at 18:15
















          5












          $begingroup$

          Here, $x$ is a variable $(xin[0;1])$ denoting mole fraction of a given constituent in a phase of variable composition (non-stoichiometric compound).
          This is an algebraic way of denoting a given compound from the phase diagram for a solid solution: $x$ corresponds to its abscissa axis.



          And no, volume fraction is not equal to mole fraction and is overall a very inconvenient variable to use, so it's usually being avoided.
          For example, volume fraction would deviate for the different morphologies and allotropes of the same solid, which is not useful for the description of chemical composition, not to mention it's also temperature-dependent.






          share|improve this answer











          $endgroup$









          • 1




            $begingroup$
            Since the OP refers to sintering I don't think that mole fraction can be assumed. In fact the OP mentions that some articles explicitly specify wt %.
            $endgroup$
            – MaxW
            Feb 12 at 17:19










          • $begingroup$
            @MaxW Mole fraction is pretty much a default in the absence of additional remarks. Of course, if there is %wt notation, then it's mass fraction.
            $endgroup$
            – andselisk
            Feb 12 at 17:24










          • $begingroup$
            @MaxW I believe almost all the ceramic compounds are made by sintering. Do you believe 0.8MgO - 0.2LiF could mean weight fractions? Most of the related papers don't mention what x is, although when they do mention about 'weights', they make sure to present it as a percentage, like MgO - 20% LiF. But I'm sure there should be some convention among scientists to understand what x really is unless explicitly specified?
            $endgroup$
            – avin
            Feb 12 at 18:10






          • 2




            $begingroup$
            @avin Again, unless there are any specific notes, $(1-x)ce{MgO} - xce{LiF} ≡ ce{Li_xMg_{(1-x)}O_{(1-x)}F_x}$, so by default $x$ implicates mole fraction.
            $endgroup$
            – andselisk
            Feb 12 at 18:15














          5












          5








          5





          $begingroup$

          Here, $x$ is a variable $(xin[0;1])$ denoting mole fraction of a given constituent in a phase of variable composition (non-stoichiometric compound).
          This is an algebraic way of denoting a given compound from the phase diagram for a solid solution: $x$ corresponds to its abscissa axis.



          And no, volume fraction is not equal to mole fraction and is overall a very inconvenient variable to use, so it's usually being avoided.
          For example, volume fraction would deviate for the different morphologies and allotropes of the same solid, which is not useful for the description of chemical composition, not to mention it's also temperature-dependent.






          share|improve this answer











          $endgroup$



          Here, $x$ is a variable $(xin[0;1])$ denoting mole fraction of a given constituent in a phase of variable composition (non-stoichiometric compound).
          This is an algebraic way of denoting a given compound from the phase diagram for a solid solution: $x$ corresponds to its abscissa axis.



          And no, volume fraction is not equal to mole fraction and is overall a very inconvenient variable to use, so it's usually being avoided.
          For example, volume fraction would deviate for the different morphologies and allotropes of the same solid, which is not useful for the description of chemical composition, not to mention it's also temperature-dependent.







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited Feb 12 at 17:26

























          answered Feb 12 at 16:56









          andseliskandselisk

          16.4k653115




          16.4k653115








          • 1




            $begingroup$
            Since the OP refers to sintering I don't think that mole fraction can be assumed. In fact the OP mentions that some articles explicitly specify wt %.
            $endgroup$
            – MaxW
            Feb 12 at 17:19










          • $begingroup$
            @MaxW Mole fraction is pretty much a default in the absence of additional remarks. Of course, if there is %wt notation, then it's mass fraction.
            $endgroup$
            – andselisk
            Feb 12 at 17:24










          • $begingroup$
            @MaxW I believe almost all the ceramic compounds are made by sintering. Do you believe 0.8MgO - 0.2LiF could mean weight fractions? Most of the related papers don't mention what x is, although when they do mention about 'weights', they make sure to present it as a percentage, like MgO - 20% LiF. But I'm sure there should be some convention among scientists to understand what x really is unless explicitly specified?
            $endgroup$
            – avin
            Feb 12 at 18:10






          • 2




            $begingroup$
            @avin Again, unless there are any specific notes, $(1-x)ce{MgO} - xce{LiF} ≡ ce{Li_xMg_{(1-x)}O_{(1-x)}F_x}$, so by default $x$ implicates mole fraction.
            $endgroup$
            – andselisk
            Feb 12 at 18:15














          • 1




            $begingroup$
            Since the OP refers to sintering I don't think that mole fraction can be assumed. In fact the OP mentions that some articles explicitly specify wt %.
            $endgroup$
            – MaxW
            Feb 12 at 17:19










          • $begingroup$
            @MaxW Mole fraction is pretty much a default in the absence of additional remarks. Of course, if there is %wt notation, then it's mass fraction.
            $endgroup$
            – andselisk
            Feb 12 at 17:24










          • $begingroup$
            @MaxW I believe almost all the ceramic compounds are made by sintering. Do you believe 0.8MgO - 0.2LiF could mean weight fractions? Most of the related papers don't mention what x is, although when they do mention about 'weights', they make sure to present it as a percentage, like MgO - 20% LiF. But I'm sure there should be some convention among scientists to understand what x really is unless explicitly specified?
            $endgroup$
            – avin
            Feb 12 at 18:10






          • 2




            $begingroup$
            @avin Again, unless there are any specific notes, $(1-x)ce{MgO} - xce{LiF} ≡ ce{Li_xMg_{(1-x)}O_{(1-x)}F_x}$, so by default $x$ implicates mole fraction.
            $endgroup$
            – andselisk
            Feb 12 at 18:15








          1




          1




          $begingroup$
          Since the OP refers to sintering I don't think that mole fraction can be assumed. In fact the OP mentions that some articles explicitly specify wt %.
          $endgroup$
          – MaxW
          Feb 12 at 17:19




          $begingroup$
          Since the OP refers to sintering I don't think that mole fraction can be assumed. In fact the OP mentions that some articles explicitly specify wt %.
          $endgroup$
          – MaxW
          Feb 12 at 17:19












          $begingroup$
          @MaxW Mole fraction is pretty much a default in the absence of additional remarks. Of course, if there is %wt notation, then it's mass fraction.
          $endgroup$
          – andselisk
          Feb 12 at 17:24




          $begingroup$
          @MaxW Mole fraction is pretty much a default in the absence of additional remarks. Of course, if there is %wt notation, then it's mass fraction.
          $endgroup$
          – andselisk
          Feb 12 at 17:24












          $begingroup$
          @MaxW I believe almost all the ceramic compounds are made by sintering. Do you believe 0.8MgO - 0.2LiF could mean weight fractions? Most of the related papers don't mention what x is, although when they do mention about 'weights', they make sure to present it as a percentage, like MgO - 20% LiF. But I'm sure there should be some convention among scientists to understand what x really is unless explicitly specified?
          $endgroup$
          – avin
          Feb 12 at 18:10




          $begingroup$
          @MaxW I believe almost all the ceramic compounds are made by sintering. Do you believe 0.8MgO - 0.2LiF could mean weight fractions? Most of the related papers don't mention what x is, although when they do mention about 'weights', they make sure to present it as a percentage, like MgO - 20% LiF. But I'm sure there should be some convention among scientists to understand what x really is unless explicitly specified?
          $endgroup$
          – avin
          Feb 12 at 18:10




          2




          2




          $begingroup$
          @avin Again, unless there are any specific notes, $(1-x)ce{MgO} - xce{LiF} ≡ ce{Li_xMg_{(1-x)}O_{(1-x)}F_x}$, so by default $x$ implicates mole fraction.
          $endgroup$
          – andselisk
          Feb 12 at 18:15




          $begingroup$
          @avin Again, unless there are any specific notes, $(1-x)ce{MgO} - xce{LiF} ≡ ce{Li_xMg_{(1-x)}O_{(1-x)}F_x}$, so by default $x$ implicates mole fraction.
          $endgroup$
          – andselisk
          Feb 12 at 18:15


















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