the present disclosure sets forth an unexpected discovery regarding the effect of rare earth elements on the yield strength of tin - indium alloys . that is , present disclosure describes how a doping of rare earth elements , such as , for example , cerium ( ce ), neodymium ( nd ), and lanthanum ( la ), of up to 2 wt . % to tin - indium alloys results in a significant reduction of the yield strength of the tin - indium alloys . referring to fig1 , there is shown a graph revealing the effect of rare earth doping on the yield strength of tin - indium ( sn — in ) alloys in accordance with an embodiment of the present disclosure . in the graph of fig1 , average yield strength data was obtained from at least 5 dumbbell specimens using tensile test equipment . the strain rate of the tensile testing was measured to be 0 . 0017 / sec . fig1 shows selected tin - indium alloys exhibiting yield strengths of between about 2200 and about 6100 psi . referring to fig2 , there is shown a table listing the yield strengths of a tin - indium ( sn — in ) alloy and rare earth element doped tin - indium ( sn — in ) alloys in accordance with an embodiment of the present disclosure . the rare earth element doped tin - indium ( sn — in ) alloys listed in the table of fig2 were doped with the rare earth elements cerium ( ce ), neodymium ( nd ), and lanthanum ( la ). the graph of fig1 and the table of fig2 clearly indicate the effect of rare earth element doping in reducing yield strength in tin - indium ( sn — in ) alloys . in the case of cerium ( ce ) doping , the effect became more significant when the concentration of in was approximately or greater than 5 %, and became less effective when the concentration of in was approximately or greater than 28 %. in the cases of neodymium ( nd ) and lanthanum ( la ) doping , good results were achieved at the same range of tin - indium ( sn — in ) alloy compositions . in order to further understand the mechanism that results in the unexpected decrease of yield strength by doping rare earth elements to tin - indium ( sn — in ) alloys , microstructural analysis using scanning electron microscopy ( sem ) and energy dispersive spectroscopy ( eds ) may be employed . for example , referring to fig3 , there is shown a micrograph of a sn - 13in - 0 . 16ce solder alloy having tin - cerium ( sn — ce ) particles in a matrix of γ intermediate phase in accordance with an embodiment of the present disclosure . more specifically , fig3 shows a microstructure of a sn - 13in - 0 . 16ce solder alloy having a tin - indium ( sn — in ) matrix with cesn 3 particles . in this micrograph , the sn - 13in - 0 . 16ce solder was soldered to a pure nickel substrate . the tin - cerium ( sn — ce ) particle shown in the micrograph of fig3 , which was obtained using scanning electron microscopy ( sem ), was identified to be a cesn 3 particle in a tin - indium ( sn — in ) matrix , which was identified to be a γ intermediate phase using energy dispersive spectroscopy ( eds ). in a phase diagram of tin - indium ( sn — in ), the γ intermediate phase is an ordered structure with an indium ( in ) concentration of 12 - 28 wt . % at room temperature ( see charles e . t . white and hioaki okamoto , “ phase diagrams of indium alloys ”, asm international , 1992 , p . 255 ). generally speaking , an ordered structure possesses greater yield strength than that of a disordered structure of the same composition due to a strong electronegativity and valency ( see david a . porter and kenneth e . easterling , “ phase transformation in metals and alloys ”, van nostrand reinhold ( uk ) co . ltd ., 1984 , p . 24 - 28 ). it may be speculated that the yield strength of a γ intermediate phase may be reduced due to a disordering of an ordered γ intermediate phase , resulting in a structure with lower strength . in light of the above - cited mechanism , in addition to cerium ( ce ), other rare earth elements may act in the same fashion to result in a reduction of yield strength and increasing compliance . referring to fig4 , there is shown a graph of an energy dispersive spectroscopy ( eds ) that was used to identify the tin - cerium ( sn — ce ) particle shown in the micrograph of fig3 as a cesn 3 particle in accordance with an embodiment of the present disclosure . in addition to low yield strength , ductility of tin - indium ( sn — in ) alloys is important for the reliability of electronic devices . for example , a ductile flip chip interconnect could accommodate a greater coefficient of thermal expansion ( cte ) mismatch of a silicon chip and an organic substrate by plastic deformation . furthermore , ductile solders could absorb more impact energy and increase the service life of an electronic device . in this respect , doping of cerium ( ce ), neodymium ( nd ), and lanthanum ( la ) to tin - indium ( sn — in ) alloys results in alloys with superior ductility to that of un - doped tin - indium ( sn — in ) alloys . referring to fig5 , there is shown a table revealing that the ductility of tin - indium ( sn — in ) alloys doped with cerium ( ce ), neodymium ( nd ), and lanthanum ( la ) in accordance with an embodiment of the present disclosure is superior to the ductility of un - doped tin - indium ( sn — in ) alloys . in the table of fig5 , pb95sn5 is a control alloy . the following examples present illustrative , but non - limiting , embodiments of the present disclosure . referring to fig6 , there is shown a table listing the yield strengths of a tin - indium alloy ( sn - 13in ) and cerium ( ce ) doped tin - indium ( sn — in ) alloys in accordance with an embodiment of the present disclosure . as shown in the table of fig6 , the effect in reducing the yield strength of the tin - indium alloy ( sn - 13in ) becomes significant when a concentration of cerium ( ce ) is 0 . 4 - 0 . 04 wt . %. compositions that deviate from this range result in a less effective yield strength reduction of the tin - indium alloy ( sn - 13in ). referring to fig7 , there is shown a table listing the yield strengths of a tin - indium alloy ( sn - 14 . 7in ) and neodymium ( nd ) doped tin - indium ( sn — in ) alloys in accordance with an embodiment of the present disclosure . as shown in the table of fig7 , the most effective concentration range of neodymium ( nd ) in doping the tin - indium alloy ( sn - 14 . 7in ) was found to be 0 . 01 wt . %, and deviation from 0 . 01 wt . % results in less reduction of yield strength . referring to fig8 , there is shown a table listing the yield strengths of a tin - indium alloy ( sn - 13in ) and neodymium ( nd ) doped tin - indium ( sn — in ) alloys in accordance with an embodiment of the present disclosure . as shown in the table of fig8 , with only 0 . 01 wt . % doping of neodymium ( nd ), the yield strength of the tin - indium alloy ( sn - 13in ) is reduced by more than 35 %. referring to fig9 , there is shown a table listing the yield strengths of a tin - indium alloy ( sn - 14 . 7in ) and lanthanum ( la ) doped tin - indium ( sn — in ) alloys in accordance with an embodiment of the present disclosure . as shown in the table of fig9 , the most effective doping concentration of lanthanum ( la ) was found to be at approximately 0 . 1 wt . % for the tin - indium alloy ( sn - 14 . 7in ). deviation from this concentration results in only limited reduction or even a slight increase of yield strength . referring to fig1 , there is shown a table listing the yield strengths of a tin - indium alloy ( sn - 20in ) and both cerium ( ce ) and neodymium ( nd ) doped tin - indium ( sn — in ) alloys in accordance with an embodiment of the present disclosure . as shown in the table of fig1 , with either cerium ( ce ) or neodymium ( nd ) doping , the yield strength of the tin - indium alloy ( sn - 20in ) is significantly reduced . referring to fig1 , there is shown a table listing the yield strengths of a tin - indium alloy ( sn - 13in ) and cobalt ( co ) doped tin - indium ( sn — in ) alloys in accordance with an embodiment of the present disclosure . since dopants such as cobalt ( co ) and iron ( fe ) are known to refine the microstructure of an interfacial intermetallic compound ( see i . e . anderson , b . a . cook , and r . l . terpstra , “ microstructural modifications and properties of sn — ag — cu solder joints induced by alloying ”, journal of electronic materials , vol . 31 , no . 11 , 2002 , p . 1168 - 1174 ) so as to prevent interfacial brittleness between a solder and an under bump metallization ( ubm ) of a silicon chip , further modification of compositions of rare earth element doped tin - indium ( sn — in ) alloys with cobalt ( co ) and iron ( fe ) may be employed . as shown in the table of fig1 , doping of cobalt ( co ) to un - doped and rare earth element doped tin - indium ( sn — in ) alloys has results in compositions with desirable low yield strength . referring to fig1 , there is shown a table listing the yield strengths of cerium ( ce ) doped tin - indium ( sn — in ) alloys in accordance with an embodiment of the present disclosure . as shown in the table of fig1 , the ductility of the 0 . 06 - 0 . 16 wt . % cerium ( ce ) doped tin - indium ( sn — in ) alloys with varying indium concentration was found to be comparable to that of pb95sn5 solder , which has a ductility of 16 . 1 %. referring to fig1 , there is shown a table listing the yield strengths of a tin - indium alloy ( sn - 14 . 7in ) and neodymium ( nd ) doped tin - indium ( sn — in ) alloys in accordance with an embodiment of the present disclosure . as shown in the table of fig1 , doping approximately 0 . 002 - 0 . 01 wt . % of neodymium ( nd ) to the tin - indium alloy ( sn - 14 . 7in ) results in a significant increase of the ductility of the tin - indium alloy ( sn - 14 . 7in ). referring to fig1 , there is shown a table listing the yield strengths of a tin - indium alloy ( sn - 14 . 7in ) and lanthanum ( la ) doped tin - indium ( sn — in ) alloys in accordance with an embodiment of the present disclosure . as shown in the table of fig1 , doping 0 . 1 wt . % lanthanum ( la ) to the tin - indium alloy ( sn - 14 . 7in ) results in a significant increase of the ductility of the tin - indium alloy ( sn - 14 . 7in ). deviation from this composition results in a lowering of the ductility . the present disclosure is not to be limited in scope by the specific embodiments described herein . indeed , other various embodiments of and modifications to the present disclosure , in addition to those described herein , will be apparent to those of ordinary skill in the art from the foregoing description and accompanying drawings . thus , such other embodiments and modifications are intended to fall within the scope of the present disclosure . further , although the present disclosure has been described herein in the context of a particular implementation in a particular environment for a particular purpose , those of ordinary skill in the art will recognize that its usefulness is not limited thereto and that the present disclosure may be beneficially implemented in any number of environments for any number of purposes . accordingly , the claims set forth below should be construed in view of the full breadth and spirit of the present disclosure as described herein .