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[[Image:Mtshabezi chemistry.png|thumb|right|200px|Piper diagram of water samples from the [[Mtshabezi River]], [[Zimbabwe]]. Data source:<ref>{{cite web|last=Love|first=D.|coauthors=Moyce, W., Ravengai, S.|year=2006|title=Livelihood challenges posed by water quality in the Mzingwane and Thuli river catchments, Zimbabwe|publisher=7th WaterNet/WARFSA/GWP-SA Symposium, Lilongwe, Malawi|url=http://www.bscw.ihe.nl/pub/bscw.cgi/d2607514/Love.pdf|format=[[Portable document format|PDF]]|accessdate=2008-06-20}}</ref>]]
A '''piper diagram''' is a graphical representation of the [[chemistry]] of a [[water]] [[Sample (material)|sample]] or samples.


The [[cation]]s and [[anion]]s are shown by separate [[ternary plot]]s. The apexes of the cation plot are [[calcium]], [[magnesium]] and [[sodium]] plus [[potassium]] cations. The apexes of the anion plot are [[sulfate]], [[chloride]] and [[carbonate]] plus [[hydrogen carbonate]] anions. The two ternary plots are then projected onto a diamond.<ref>{{cite book|author=Piper, A.M.|title=A Graphic Procedure in the Geochemical Interpretation of Water Analysis|publisher=[[United States Geological Survey]]|location=Washington D.C.|year=1953|isbn=ASIN: B0007HRZ36}}</ref>  The diamond is a [[Transformation matrix|matrix transformation]] of a graph of the anions ([[sulfate]] + [[chloride]]/ total anions) and cations ([[sodium]] + [[potassium]]/total cations).<ref>{{cite journal |title=MHPT.BAS: a computer program for modified Hill–Piper diagram for classification of ground water |doi=10.1016/S0098-3004(98)00083-1 |first=N. Srinivasa |last=Rao |journal=Computers & Geosciences |volume=24 |issue=10 |date=December 1998 |pages=991–1008 |bibcode = 1998CG.....24..991R }}</ref>


The required matrix transformation of the anion/cation graph is:
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:<math>
\begin{bmatrix} x' \\ y' \\ 1 \end{bmatrix} = \begin{bmatrix} \cos(\frac{\pi}{2}) & \sin(\frac{\pi}{2}) & 0 \\ -2\sin(\frac{\pi}{2}) & 2\cos(\frac{\pi}{2}) & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ 1 \end{bmatrix}
</math>
 
==Software==
* [http://www.rockware.com/product/overview.php?id=150 AqQA] Commercial software available from [http://www.rockware.com/index.php RockWare, Inc.]
* [http://www.rockware.com/product/overview.php?id=70 AquaChem] Commercial software from [http://www.swstechnology.com/ Schlumberger Water Services]
* [http://www.rockware.com/product/overview.php?id=74 ChemPoint Pro] Commercial software from [http://www.pointstar.com/Default.aspx Starpoint software, Inc.]
* [[The Geochemist's Workbench]] Commercial software from [http://www.gwb.com/ Aqueous Solutions LLC]
* [http://water.usgs.gov/nrp/gwsoftware/GW_Chart/GW_Chart.html GW Chart] Free software for creating piper diagrams from the [[United States Geological Survey]]
* [[Rockworks|RockWorks Utilities]] Commercial software from RockWare, Inc.
* [[HydroAnalysis|EnviroInsite]] Commercial software from HydroAnalysis, Inc.
* [[Origin (software)|Origin 9.1]] commercial software from [http://www.originlab.com/ Originlab] can [http://www.originlab.com/index.aspx?go=PRODUCTS/Origin/91/Piper create Piper diagrams] from spreadsheet data.
 
==References==
{{commonscat}}
<references/>
 
{{Commonscat|Ternary plots}}
 
[[Category:Diagrams]]
[[Category:Water chemistry]]
[[Category:Physical chemistry]]
 
{{chem-stub}}

Latest revision as of 19:59, 9 January 2015


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