Two x-axis (Arrhenius plots)

I would like to create an Arrhenius plot. Arrhenius plots are made by plotting k versus 1/T. I have poached a photo of a “typical” Arrhenius plot from the web (see image). Because 1/T is an inconvenient unit it is typical to the temperature (T) on the top x axis.

How do I put in a second (top) x-axis? Note the non-linaear scale.

My variables are k, T and T_reciprocal.

Answer 1

[Chunru]

Not sure your equation. But you can modify the following to produce the plot:

x = linspace(2.5, 4, 20);       % x corrdinate
y = 20.2 -1589.6 * x;           % your equation
ax1 = axes;
plot(ax1, x, y);
ax1.Box = 'off';                % update: turn off extra ticks

% create a second axis
ax2 = axes('Position', ax1.Position, 'Color', 'none', 'YTick', [], 'XAxisLocation', 'top', 'YTick', [], ...
    'XDir', 'reverse', 'XLim', 1000./flip(ax1.XLim)-273);
TC = (-20:20:120);               % ticks at T deg C
xTC = 1000./(TC + 273);          % Corresponding x
% map xTc onto TC
xTCmap = (xTC - ax1.XLim(1))*(-diff(ax2.XLim)/diff(ax1.XLim)) + ax2.XLim(2)

xTCmap = 1×8

-18.2569 10.6996 35.7031 57.5112 76.6997 93.7139 108.9035 122.5471

ax2.XTick = xTCmap;
ax2.XTickLabel = TC;

ax2.YAxisLocation = 'right';    % Update: move yaxis of ax2 to right
ax2.YTick = [];

xlabel(ax1, "1000/T (K^{-1})")
xlabel(ax2, "Temperature (^\circ C)");

ax1.Position(4) = ax1.Position(4) - 0.1;   % Update: make space on top 
ax2.Position(4) = ax2.Position(4) - 0.1;

[ASC]

This is great. Thanks you very much Chunru!

When I run the code on my data I have two probelms.

x = 1000./(T(1:end)+273.15);       % my data
y = log(V(1:end));           % my data
ax1 = axes;
plot(ax1, x, y);
% create a second axis
ax2 = axes('Position', ax1.Position, 'Color', 'none', 'YTick', [], 'XAxisLocation', 'top', 'YTick', [], ...
    'XDir', 'reverse', 'XLim', 1000./flip(ax1.XLim)-273);
TC = (0:100:500);               % ticks at T deg C
xTC = 1000./(TC + 273);          % Corresponding x
% map xTc onto TC
xTCmap = (xTC - ax1.XLim(1))*(-diff(ax2.XLim)/diff(ax1.XLim)) + ax2.XLim(2);
% xTCmap = 1×8
%   -18.2569   10.6996   35.7031   57.5112   76.6997   93.7139  108.9035  122.5471
ax2.XTick = xTCmap;
ax2.XTickLabel = TC;
xlabel(ax1, "1000/T (K^{-1})")
xlabel(ax2, "Temperature (^\circ C)");

One problem is that there are extra ticks on the upper x-axis (see plot).

The other probelm is that the upper axis label is cutoff.

Can you make suggestions for these two problems? Thanks so much.

[Chunru]

See the update above for solving these two problems.

[ASC]

Thanks again for your help.

This solved the space-up-top-problem. But I still have the problem of there being extra ticks on the top y-axis. Any thoughts? Am I missing something. My Current code is:

figure
ax1 = axes;
plot(ax1, x, y);
% create a second axis
ax2 = axes('Position', ax1.Position, 'Color', 'none', 'YTick', [], 'XAxisLocation', 'top', 'YTick', [], ...
    'XDir', 'reverse', 'XLim', 1000./flip(ax1.XLim)-273.15);
TC = (0:100:500);               % ticks at T deg C
xTC = 1000./(TC + 273.15);          % Corresponding x
% map xTc onto TC
xTCmap = (xTC - ax1.XLim(1))*(-diff(ax2.XLim)/diff(ax1.XLim)) + ax2.XLim(2);
ax2.XTick = xTCmap;
ax2.XTickLabel = TC;

% ax2.YAxisLocation = 'right';    % Update: move yaxis of ax2 to right
% ax2.YTick = [];

xlabel(ax1, "1000/T (K^{-1})")
xlabel(ax2, "Temperature (\circ C)");
ylabel('ln(V)')

ax1.Position(4) = ax1.Position(4) - 0.1;   % Update: make space on top 
ax2.Position(4) = ax2.Position(4) - 0.1;

The code:

ax2.YAxisLocation = 'right';    % Update: move yaxis of ax2 to right
ax2.YTick = [];

Moved the y-axis labe to the right side of the plot.

[Chunru]

Can you post your code and make it executable so that I can run here and see what is problem?

You need the following to turn off the extra ticks. When box is on, the x-axis ticks will show up on both bottom and top.

ax1.Box = 'off';                % update: turn off extra ticks

[Walter Roberson]

Dustin Mangus comments to @Chunru about the Answer:

The right side of the upper x-axis is on a moving scale based on the TC array that you define. It is adjustable and seem to only be accurate at the y-axis. This means that for all higher temperatures (further to the left) are inaccurate unless TC is adjusted precisely. I give this code a 3/10.

Answer 2

[ASC]

I missed this addtional line in your code. Adding

ax1.Box = 'off';                % update: turn off extra ticks

solved the problem. Thank you very much for you help.