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











          Your Answer





          StackExchange.ifUsing("editor", function () {
          return StackExchange.using("mathjaxEditing", function () {
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          });
          });
          }, "mathjax-editing");

          StackExchange.ready(function() {
          var channelOptions = {
          tags: "".split(" "),
          id: "431"
          };
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function() {
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled) {
          StackExchange.using("snippets", function() {
          createEditor();
          });
          }
          else {
          createEditor();
          }
          });

          function createEditor() {
          StackExchange.prepareEditor({
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: false,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: null,
          bindNavPrevention: true,
          postfix: "",
          imageUploader: {
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          },
          onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          });


          }
          });














          draft saved

          draft discarded


















          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fchemistry.stackexchange.com%2fquestions%2f109422%2fwhat-does-x-mean-in-1-xa-xb-composite-materials-molar-ratio-weight-ratio-o%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown

























          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


















          draft saved

          draft discarded




















































          Thanks for contributing an answer to Chemistry Stack Exchange!


          • Please be sure to answer the question. Provide details and share your research!

          But avoid …



          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.


          Use MathJax to format equations. MathJax reference.


          To learn more, see our tips on writing great answers.




          draft saved


          draft discarded














          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fchemistry.stackexchange.com%2fquestions%2f109422%2fwhat-does-x-mean-in-1-xa-xb-composite-materials-molar-ratio-weight-ratio-o%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          -

          Popular posts from this blog

          How to change which sound is reproduced for terminal bell?

          Image
          3 Recently upgrade to 18.10 from 18.04, and using the terminal is becoming annoying: the new alert sound is a drip ( /usr/share/sounds/gnome/default/alerts/drip.ogg ), and the previous one is still located at ( /usr/share/sounds/ubuntu/stereo/bell.ogg ). My issue is that at the gnome-terminal, when autocompleting or pressing left BOTH sounds are reproduced, at the same time. I want to just have ubuntu/stereo/bell.ogg active, not both . At the moment I have been only able to reduce the volume of the alerts (but still both are played), or turn the alerts down (but I dislike both "solutions"). gnome-terminal 18.10 teminal-bell share | improve this question
          Read more

          Title Spacing in Bjornstrup Chapter, Removing Chapter Number From Contents

          Image
          up vote 5 down vote favorite 2 I would like to make it so that the vertical space below the title of each chapter is the same when using the Bjornstrup package (i.e. so that the descenders do not affect the spacing - as shown by the red arrow in the picture below). I think I'm fairly happy with the spacing around "A chapter", so I'd really like titles without descenders (e.g. "Contents") to have the same vertical spacing as "A chapter" below the title. I would also like to remove the large "0" in the contents title. Any help appreciated, as always. documentclass[11pt,a4paper]{book} % Packages[![enter image description here][1]][1] usepackage[left=3.5cm, right=3.5cm, top=4.3cm, bottom=4.25cm]{geometry} usepackage[utf8]{inputenc} usepackage{libertine} usepackage[libertine]{newtx
          Read more

          Can I use Tabulator js library in my java Spring + Thymeleaf project?

          Image
          0 I want to add Tabulator js to my java project. I added tabulator.min.js, tabulator.min.css to resources folder. After that added to my html page these dependencies as recommending in readme.md. <link rel="stylesheet" th:href="@{/css/tabulator.min.css}"> <script type="text/javascript" th:src="@{/js/tabulator.min.js}"></script> Now my tables view all elements, that I have in the html page, but not correct. In the documentation of Tabulator is example how to create header and table, var table = new Tabulator("#example-table", { columns:[ {title:"Name", field:"name", sorter:"string", width:200, editor:true}, {title:"Age", field:"age", sorter:"
          Read more