## ISOGEOCHEM@LIST.UVM.EDU

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Re: delta conversion equation

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Thu, 12 Jun 2008 12:07:44 -0500

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 ```Dear Andy: Derivation of the equation: By definition Delta (sa-st)=(Rsa/Rst-1)*1000 (1) Delta (sa-ws)=(Rsa/Rws-1)*1000 (2) Delta (ws-st)=(Rws/Rst-1)*1000 (3) From equ. 2 and 3. (Delta (sa-ws)/1000)+1=(Rsa/Rws) (Delta (ws-st)/1000)+1=(Rws/Rst) If we multiply these terms, we get 1+ (Delta (sa-ws)/1000) +(Delta (ws-st)/1000)+ (Delta (sa-ws)/1000) (Delta (ws-st)/1000) =(Rsa/Rst) Simplifying above equation  Delta (sa-ws) +Delta (ws-st)+ (Delta (sa-ws)*Delta (ws-st))/1000 =(Rsa/Rst-)*1000=Delta (sa-st) If the product of delta values is very small than 1000, we leave the third term. It is generally true. Best wishes Mahendra -----Mensaje original----- De: Stable Isotope Geochemistry [mailto:[log in to unmask]] En nombre de Andrew Schauer Enviado el: Jueves, 12 de Junio de 2008 11:00 a.m. Para: [log in to unmask] Asunto: delta conversion equation Hi all, An equation for converting from a working standard scale to an international reference material scale is: d sa/st = d sa/ws + d ws/st + 10^-3(d sa/ws * d ws/st) where d is the delta, sa is a sample, st is the international reference material, ws is the working standard, and sa/ws is a sample relative to a working standard. This equation is found many places (e.g. W.A Brand's chapter 38 (p855) in Handbook of Stable Isotope Analytical Techniques (ed. P.A. de Groot)). My question is, what is the derivation of the final term: 10^-3(d sa/ws * d ws/st) The term clearly deals with those samples and standards that are very different from one another, as it is larger the more disparate samples and standards are. Searching the IsoGeoChem archives shows that many folks leave off this term. Thank you all for your help. andy  Andrew Schauer ISOLAB Department of Earth and Space Sciences University of Washington Seattle, WA 98195 206.543.6327 [log in to unmask] ```