A survey of regular solution parameters for the systems among the first transition metals
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TRANSACTIONS A
~o= 2(H[(i + j ) / 2 ] -
1
~H{d
{1]
H~]},
w h e r e H[i] and H~] are the enthalpies of vaporization of element i and j, respectively, and H[(i + j)12] is the enthalpy of vaporization of a real or imaginary element whose group number is the a v e r a g e of those for elements i and j. For practical p u r p o s e of eo estimation, the adjusted group a v e r a g e of enthalpy of vaporization, i.e., ~[i] function shown in Fig. 1, are used in o r d e r t o obtain favorable numerical values for all the systems involving the l a t e r transition elements. Thus, the eo can be evaluated from the equation, 1
1
eo : 2{~[(~ + j ) 1 2 ] - ~ +~[~1- ~ +~[j]}.
[2]
This cannot be applied to the f i r s t transition elements, because the m e a s u r e d enthalpy change of the f i r s t transition metals with group n u m b e r is quite different from that function, as shown in Fig. 1. Factors ep, e, and e2 are readily calculated by the data of measured enthalpy of vaporization, m o l a r volume and the enthalpy of liquid t o bcc solid t r a n s formation in each pure element. In this s t u d y , the factor eo is obtained by subtraction of ep, ez and e2 from the measured RSP for bcc phase. The measured RSP might mainly reflect the n a t u r e of eo, s i n c e the calculated factors ep, e~ and e2 are not so l a r g e . T a b l e I summarizes the reported RSPs mainly for bcc phase of the f i r s t transition m e t a l binary systems which are taken from various sources including those obtained by the authors. Some of them are not g i v e n by constants, but by functions of temperature a n d / o r composition. After c r u d e inspection on the table, one could easily find out some tendencies, i) For the alloy systems that span Cr (GN = 6) on the periodic table, i.e., T i - F e , Ti-Co, TiiNi, Ti-Mn, V - F e , V - C o , V-Ni and V-Mn, RSP shows a l a r g e negative value. if) For alloy systems coupled with Cu (GN = 1), i.e., Cu-Co, C u - F e and Cu-Cr, RSP shows a l a r g e positive value, iii) For alloy systems from a m o n g the elements from Mn (GN = 7) t o Ni (GN = 10) on the periodic
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