1. Metals

1.1. Bismuth

Bismuth has characteristics which are uncommon in the majority of the metals. As with gallium, it expands when solidified, approximately 3.32%. Its electrical resistance is higher in the solid state than in the liquid (in a half proportion). The thermal conductivity is low, only bigger than the mercury one (just considering pure metals). It is fragile, highly diamagnetic (higher value of metals) with magnetic susceptibility of -1,68x10⁻⁵mks. Bismuth is used as catalyst in the production of plastics and cosmetics, as additives in steel alloys, aluminum and in electronics. It has a rhombohedral (Biα) structure, with an atomic radius of 1.54 Å, electronegativity of 1.83, and valence of +3 and +5. ^{[1] [2] [3] [4] [5] [6]}

1.2. Indium

Indium is a metal softer than lead (hardness of 0.9 HB), permitting it to be scratched by a nail. It is also malleable, ductile and has a thermal conductivity value of 0.78 W/m°C (85 °C). It also has the capacity of wetting glass, quartz and other ceramic materials. It maintains the plasticity and ductility when exposed to cryogenic environments and has a big gap between the melting point and the boiling point (156.6 °C and 2080 °C respectively). Under compression, it has high plasticity that allows almost unlimited deformation (2.14 MPa of compression resistance) and under tensile it has low elongation (4 MPa of tensile resistance). Indium is used in dental alloys, semiconductor components, nuclear reactor panels, sodium lamps, strengthening factor in lead-based welds and low melting temperature welds. The metal has a body centered tetragonal structure, atomic radius of 1.63 Å, electronegativity of 1.81 and valence of +3 or +5, being the trivalent the more common.^{[1][2][3][4][5][6]}

2. Common Compositions of Alloys

The most common application of this alloy is as a solder, with the composition of 95wt% of In and 5wt% of Bi. The liquidus line of this composition occurs at 423K (150 °C; 302 °F), and the solidus line at 398K (125 °C; 257 °F), being the first solid phase to be formed during the cooling process In, with Bi as a substitutional solid solution.^[1][4]

With a smaller application area, due to difficulties on the process of synthesizing, is the alloy composed by 33 wt% of In and 67wt% of Bi. This alloy presents a eutectic temperature of 382K (109 °C; 228.2 °F). The resistance to thermal fatigue of this material is higher, but the quantity of slag when compared to the alloy between tin and lead.

There is, on the market a solder composed by 49 wt% of Bi, 21 wt% of In, 18 wt% of Pb, and 12 wt% of Sn, called commercially solder 136. This alloy presents a density of 8.58g/cm³, tensile strength of 43 MPa, toughness of 14HB, eutectic temperature of 331k (58 °C; 136.4 °F), thermic coefficient of expansion of 12,8 10⁻⁶/K. It is used to parts where precision is necessary, as in inspections, and fusible cores to wax patterns compounds.^[1]

Another alloy also on the market is the solder 117, composted by 44.7 wt% of Bi, 22.60 wt% of Pb, 19 wt% of In, 8.30 wt% of Sn, and 5.30 wt% of Cd. The density of this alloy is 8.86g/cm₃, tensile strength of 37 MPa, toughness of 12HB, eutectic temperature of 320K (47 °C; 116.6 °F). It is also used to parts on inspection equipment, spindles for machining (polishing), molds for development of prosthesis and dental molds.^[1][4]

Other compositions founded on the market:

- Solder 174: 26 wt% of In, 17 wt% of Sn, and 57 wt% of Bi, presenting a eutectic temperature of 352K (79 °C; 174.2 °F).

- 32.5 wt% of Bi, 16.5 wt% of Sn, and 51 wt% of In, presenting a eutectic temperature of 333K (60 °C; 140 °F).

- 48 wt% of Bi, 25.63 wt% of Pb, 12.77 wt% of Sn, 9.6 wt% of Cd and 4 wt% of In, present a liquids temperature of 338K (65 °C; 149 °F), and a solidus temperature of 334K (61 °C; 141.8 °F).

The influence of each element

Antimony: is added to increase the strength, but not changing the wettability.

Bismuth: it significantly improves the wettability of the solder. When the composition is more than 47% Bi, it will expand upon cooling.

Cadmium: It oxidizes fast, causes tarnishes, and slow pace of solder. It improves the mechanical properties of the alloys.

Indium: Each 1 wt% of In added on the alloy of the melting point reduces 1.45 °C. It easily oxidizes, has a very high cost, enables soldering for cryogenic applications, and allows soldering between nonmetals. It makes easier the fabrication process if compared with Bi.

Lead: With presence of In it forms a compound that have a phase change at 387K (114 °C; 237.20 °F).

3. Phase Equilibrium Diagram

The phase diagram of the alloy between Bi and In, in room temperature can form three intermetallic, being them: Bi(α), BiIn; Bi₃In₅; BiIn₂. Above the room temperature there is another phase named ε.

Solubility of the elements

The solubility of the basic elements is not too high, being de 0 - 0,005 wt% of In, on the Bi structure; and ~0 -14 wt% of Bi, on the In structure. This percentage of solubility can be explained by the Hume-Rothery rules, where the crystalline structure must to be the same, the atomic radius must differ 15% or less, the valency must to be the same and the electronegativity of the two components must to be similar.

Main points on the equilibrium diagram.^[3]

When the two elements are mixed together, the alloy between Bi an In presents three eutectic points, being:

When cooled from the melt, it will form a lamellar structure.

There is one eutectoid point on the diagram, at 83 wt% of In. The eutectoid temperature is 322K (49 °C; 120.20 °F). In the cooling process the phase ε will form BiIn₂ and In.

In the Peritectic point, with the composition of 86 wt% of In, the liquid and the already formed In_(s) will result in the phase ε.

There are three intermetallic formed in the equilibrium, being:

- BiIn (from 0,005 to 35.4 wt% of In), presenting a structure tetragonal, with 2 atoms per unit cell.

- Bi₃In₅ (from 47.5 to 97.97 wt% of In), with a tetragonal structure and 4 atoms per unit cell.

- Bi In₂ (from 52.5 to 53.5 wt% of In), having a hexagonal structure, with 2 atoms per unit cell.

There is regions on the diagram with were determinate thermodynamically due the process of formation take too much time or difficulties on the visualization of the phase.^[4][6]

The lowest fusion value found for the alloy is at 345.7K (72,7 °C; 162.86 °F), on the composition of 66,7 wt% of In. In a cooling process the phases that will be formed is the Bi In₂ and ε.

This alloy also present a metastable phases BiIn₃, occurring at 62 wt% of In.

4. General Considerations

Fusible alloys present a precipitation hardening (aging), so the mechanic properties will be dependent of the melting conditions, solidification rate, time since the melting, and the conditions in which the alloy will be used.

We can attribute advantages of the Bi In alloy, when compared to the traditional ones (Sn Pb), as bigger thermal fatigue resistance, and lower melting point. Some of the disadvantages are that they are less ductile and they will produce more slag.