('heroical Geology, 107 ( 1993 ) 19-27 19 Elsevier Science Publishers B.V., Amsterdam [NA] Partitioning and mass-balance relations in lherzolites John C. Ayers" Department of Geology, Rensselaer Polytechnic Institute, Troy, NY 12180- 3 5 90, USA ( Received November 25, 1991: revised and accepted January 20, 1993 ) A BST RACT The dependence of mineral composition on modal amounts in lherzolites is examined using mass-balance equations coupled with inter-phase partition coefficients. The composition of clinopyroxene changes dramatically as its modal abun- dance approaches zero because clinopyroxene strongly concentrates incompatible elements compared with orthopyroxene and olivine Compositional variables for clinopyroxene such as element concentrations (La), element ratios (La/Yb) and interpolated concentrations (Nb/Nb*) are not representative of bulk-rock composition when clinopyroxene weight frac- tion <0.2. In the absence of other minerals that concentrate incompatible elements, clinopyroxene always has higher La/ Yb and lower HFSE/HFSE* than the host lherzolite. Claims of bulk-rock REE enrichment or HFSE depletion in lherzo- lites based solely on clinopyroxene analyses may be in error. 1. Introduction A knowledge of element partitioning behav- ior in multi-phase assemblages is essential to the understanding of rock chemistry. Some in- vestigators infer bulk-rock composition in mantle rocks from the analysis of a single phase, usually clinopyroxene (e.g., Salters and Shimuzu, 1988). Although clinopyroxene (CPX) is present in low modal abundance in most mantle rocks, investigators frequently treat it is as representative of the composition of the bulk rock. This is because it concen- trates important trace elements such as the rare-earth elements (REE), which makes it easier to analyze. This paper demonstrates that when CPX is present in low modal abundance, the composition of CPX in equilibrium with olivine and orthopyroxene does not represent the bulk-rock composition. ~'Present address: Department of Geology, Vanderbilt University, Nashville, TN 37235, USA. 2. Mass-balance equations The derivations of mass-balance equations follow the approach of' Shaw (1970). State- ment of the conservation of mass for the ele- ment a in a closed system relates the element concentration in the constituent phases Ca' and in the bulk-rock CaT and the weight fractions of each phase X i as follows: =X C.+X C~+...+X C~ (1) Ca T c¢ oe , B fl n n where sum Xi= 1. Note, that the weight frac- tion of a phase is proportional to the product of the mode (volume fraction) of the phase and its density. In conventional least-squares analysis there is an equation equivalent to eq. 1 for each ele- ment. To solve the set of equations there must be at least as many equations as there are un- knowns. The unknowns can be the modal amounts, given element concentrations in each phase and in the rock. Alternatively, phase compositions can be calculated given the modes and the bulk-rock composition. Mass-balance calculations of phase compo- 0009-2541/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.