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1 NAME IGNEOUS & METAMORPHIC PETROLOGY DENSITY & VISCOSITY OF MAGMAS I. Desity The desity (mass/vlume) f a magma is a imprtat parameter which plays a rle i a umber f aspects f magma behavir ad evluti. Fr example, durig fractial crystallizati the rate at which crystals settle (r rise) thrugh a magma is a fucti f the desity ctrast betwee the magma ad the crystals, the size f the crystals, ad the viscsity f the magma. Additially, the ctrast i magma desity is imprtat i gverig the rate f cvective vertur i a magma chamber ad magma mixig. Additially, the ctrast i desity betwee a magma clum ad the surrudig cutry rck will determie the height t which a magma clum will rise. The physical measuremet f magma desity is rather difficult. Hece, a variety f methds f have bee develped t estimate r determie magma desity withut havig t directly determie the desity f the liquid magma. Desity estimated frm average vlume icrease durig meltig. Frm bservati we kw that the vlume expasi meltig fr mst rcks is abut 10%. Hece, mst magmas have a desity abut 90% that f the equivalet slid rck. This is a relatively crude, but smetimes adequate, estimate. Desity determied frm queched glass at rm temperature. Because glass is a supercled liquid, the high-temperature desity ca be calculated frm the rm-temperature desity if the cefficiet f thermal expasi is kw. The desity f the liquid at temperature T ca be calculated as fllws ρ T ' ρ 1 [1 & α(t & T 1 )] where ρ T = the desity at temperature T, ρ 1 = the desity at rm temperature (r the temperature at which the glass desity was measured), α = the cefficiet f thermal expasi, T = the temperature at which the desity is calculated, ad T 1 = the temperature at which the desity is measured. 1. A sample f graite with desity 670 kg m is fused ad queched t a glass that has a desity f kg m at 5 C. The cefficiet f expasi, α, fr the glass is x 10 C. Calculate the desity f the magma at 105 C, ad cmpare this with the value btaied by simply takig 90% f the desity f the rck. -1-

2 Desity calculated frm mlar vlumes f cstituet xides. Bttiga ad Weill (1970) develped a mdel which eables e t calculate the magma desity frm the cmpsiti f the magma. Desity is writte as ρ ' M V where M = mass ad V = vlume. I Bttiga ad Weill s mdel ρ ' j ) j ) V T ' V 1 [1 % α(t & T 1 )] 3 6 where X i= the mle fracti f cmpet i, = the gram frmula weight f cmpet i, ad = the partial mlar vlume f cmpet i. The imprtat parameter is, measured i m /(mle x 10 ), which 3 varies as a fucti f temperature. Nte that what represets is the umber f m ccupied by 1 mle f a particular xide. Therefre, if we determie the fractial mass f each xide cmpet i the melt, ad the vlume that each xide ccupies, the summati fr all xides gives the desity f the magma. The table belw gives the partial mlar vlumes ad cefficiets f expasi fr cmm xide cmpets f silicate liquids at 1400 C. The partial mlar vlumes at temperatures ther tha 1400 C ca be calculated frm the relatiship where V T = the vlume at temperature T, V 1 = the vlume at 1400 C, α = the cefficiet f thermal expasi, T = the temperature at which the vlume is calculated, ad T 1 = 1400 C. Mlar Vlume Cefficiet f expasi Oxide V (m ml ) x α ( C ) x 10 i SiO TiO Al O Fe O FeO MgO CaO NaO KO The partial mlar vlume f water ca be calculated as fllws: --

3 V H O ' 4.7 % 7.0x10&3 (T & 900) & 1.5P % 8.4 x 10 & P & 1.4x10 &3 P 3 6 where V H O = m /(mle x 10 ), T = C, ad P = kilbars. Nte that the mdel f Bttiga ad Weill igres the effect f pressure all the xide cmpets except water. This is a reasable simplificati fr magmas which reside i the crust, but at matle depths pressure shuld be csidered.. Calculate the desities f the magmas Rhylite 1 (800 C), Rhylite (800 C), ad the Basalt at 1000 C ad 1100 C. The relevat data ad space fr the calculatis are fud i the table page Based the calculated desities, what geeral cclusis ca yu make abut the effect f cmpsiti, water ctet, ad temperature magma desity? -

4 Mlecular Mle Mlecular Mle Mlecular Mle Mlecular Oxide Rhylite 1 prprti fracti Rhylite prprti fracti Basalt prprti fracti weights SiO TiO Al O Fe O FeO MO MgO CaO NaO KO HO Rhylite 1: (T = 800 C) ρ ' j )/ j Rhylite : (T = 800 C) (P = 1kbar) ρ ' j )/ j V H O ' 4.7 % 7.0x10&3 (T & 900) & 1.5P % 8.4 x 10 & P & 1.4x10 &3 P 3 ' Basalt 1: (T = 1000 C) ρ ' j )/ j Basalt : (T = 1100 C) ρ ' j )/ j -4-

5 II. Viscsity Viscsity is a measure f the iteral resistace f a liquid bdy t flw. Viscsity plays a rle i determiig the style f magmatic emplacemet ad irrupti, the rate at which crystals r ther slids settle thrugh a melt, ad the rate f diffusi f is thrugh a melt. The cefficiet f viscsity is the rati f the applied shear stress t the time rate f shear strai. The viscsity is said t be Newtia if this cefficiet is idepedet f the magitude f the shear stress ad strai. The structure f a silicate melt (which is a fucti f its cmpsiti), temperature, ad pressure determie the viscsity f a melt. Ulike desity, it has prve very difficult t develp a mdel fr the calculati f magma viscsity. Hwever, it is pssible t determie the viscsity f melts (ce the desity is kw) by measurig the rate at which spheres f kw size ad desity settle thrugh the melt. The gverig priciple is Stke s Law v ' gδρr 9η -1 - where v = settlig velcity (m s ), g = accelerati due t gravity (9.8 m s ), Δρ = desity ctrast betwee the sphere ad the melt (kg m ), r = the radius f the sphere (m), ad η = dyamic viscsity (Pa s). Give the desity f the sphere, the magma, ad the radius f the sphere, we ca measure the settlig velcity f the sphere ad frm this velcity calculate the viscsity f the magma. 4. Usig Stke s Law, calculate the viscsities f the fur magmas csidered i questi 1. The radius f the sphere is 0.01 m ad its desity is 5000 kg m. Desity Settlig velcity Magma (kg m ) -1 (m s ) Viscsity (Pa s) Rhylite x 10-9 Rhylite 5.77 x Basalt (1000 C) 5.07 x 10-4 Basalt (1100 C) 5.05 x Based the calculated viscsities, what geeral cclusis ca yu make abut the effect f cmpsiti, water ctet, ad temperature the viscsity f magmas? -5-

6 III. Melt Plymerizati A silicate melt ca be viewed as a material that has a shrt-rage structural rder. The structure csists - f certai catis tetrahedrally crdiated with O is frmig tetrahedra that are the liked directly t ther tetrahedra r separated frm ther tetrahedra by etwrk mdifyig catis. The degree t which the silica tetrahedra are liked is referred t as plymerizati. Fr example, a melt frmed frm quartz wuld be highly plymerized with virtually all the tetrahedra itercected. A measure f the degree f plymerizati is the rati f tetrahedrally crdiated catis (T) t bridgig xyge is (NBO), i.e., xyge is that are directly bded t tetrahedrally crdiated catis. The larger this rati, the less plymerized is the melt. The NBO/T rati is calculated as fllws: 1. Cvert the chemical aalysis f the rck t atmic prprtis. Assig Si, Ti, ad P t T 3. Assig Al t T uless Al > Na + K + Ca + Mg. I this case, Al i T = Na + K + Ca + Mg Fe i T = (Na + K) - Al # Fe 5. Sum all T catis = T 6. NBO =O - 4T 7. Calculate NBO/T 6. Calculate the NBO/T rati fr Rhylite 1 ad Basalt. Nte that yu ca btai the atmic prprtis by multiplyig the mlecular prprtis by the umber f is i the xide frmula. Fr example, i the case f AlO 3, Al = x mlecular prprti AlO 3 ad O = 3 x mlecular prprti AlO 3. What is the relatiship betwee the degree f plymerizati ad the viscsity f the melts? -6-