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ALGEBRAIC METHODS FOR DETERMINING DIRECTIONS



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Canadian Mineralogist Yol 29 pp 687 692 1991 OF DIRECTIONS ALGEBRAICMETHODSFOR DETERMINING LINES UNIVARIANT LIOUIDUS ALONG ISOBARIC TEMPERATURE DECREASING DEAN C PRESNALL GeosciencesProgram The University of Texasat Dallas P O Box 830688 Richardson Texas 75083 U S A ABSTRACT Two featuresof temperature compositionslopesalong isobaric liquidus univariant boundary lines are of particular interest One is the direction of decreasing temperatureas theselines terminate at isobaric liquidus invariant points and the other is the existenceand location of temperaturemaxima and minima In systems of more than four components thesefeaturescannot be defined by conventional geometrical procedures Algebraic methods are necessary For an component system the form of the balancedequation involving the I phases in equilibrium at an isobaric liquidus invariant point allows a determination of the temperature compositionslopesof all the liquidus univariantlines terminating at the invariant point To determine the existenceand location of a temperature maximum or minimum along an isobaric liquidus boundary line balancedequationsare used that involve two liquids on the univariant line and the r I crystalline phasesin equilibrium wirh each of thesetwo liquids isobaresur le liquidus et d en d unecourbecotectique d utiliserdes il est n6cessaire trouverles coordonn6es impliquantdeuxliquidessur cette 6quationsbalanc6es courbeet lesn I phasesen 6quilibreavecchacunde ceux ci Keywords algebraicniethods multicomponentsystems temperature maximum temperature minimum liquidusboundarylines Souvatns Il y a deux aspectsd int6r6t a propos de la temp6rature et de la composition le long des courbes univariantes cotectiquessur le liquidus Premidrement quelle est la direction de diminution en temp6ratureli ott cescourbes atteignent un point isobariquement invariant sur le liquidus Deuxibmement y a t il des minima ou des maxima en temperature et oir se trouvent ils Dans tout systcmed plus de quatre composants ces



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