© 2003 ASM International. All Rights Reserved. www.asminternational.org Brazing (#06955G) CHAPTER 2 Brazing Fundamentals BRAZING does not involve any melting or of the liquid in equilibrium with its saturated plastic state of the base metal. Brazing com- vapor, γ at the interface between the solid and sl γ prises a group of joining processes in which the liquid, and sv at the interface of the solid in coalescence is produced by heating to suitable equilibrium with the saturated vapor of the liq- temperatures above 450 °C (840 °F) and by uid. Hence: using a ferrous and/or nonferrous filler metal γ = γ cos θ + γ (Eq 1) that must have a liquidus temperature above 450 sv lv sl °C and below the solidus temperature(s) of the It is important to keep in mind that phases are base metal(s). The filler metal is distributed supposed to be mutually in equilibrium. The between the closely fitted surfaces of the joint γ designation sv is a reminder that the solid sur- by capillary attraction. Brazing is distinguished face near the liquid should have an equilibrium from soldering in that soldering employs a filler film of vapor due to the film pressure. Young’s metal having a liquidus below 450 °C. equation has been used extensively in literature, Brazing has four distinct characteristics: which reflects its general acceptance. However, Eq 1 has never been verified exper- • The coalescence, joining, or uniting of an imentally. The problem is that surface tensions assembly of two or more parts into one struc- of solids are not easy to measure due to the ture is achieved by heating the assembly or inevitable presence of the interfacial tension the region of the parts to be joined to a tem- between a solid and its liquid. More impor- perature of 450 °C or above. tantly, there is the difficulty that any tensile • Assembled parts and filler metal are heated to stresses existing in the surface of the solid a temperature high enough to melt the filler would prevent the system from being in equilib- metal but not the parts. rium. The surface tension at the solid-vapor • The molten filler metal spreads into the joint interface (γ ) has a relationship with surface and must wet the base-metal surfaces. sv tension of a solid in vacuum (γ ) as follows: • The parts are cooled to freeze the filler metal, s which is held in the joint by capillary attrac- γ γ π sv = s – e (Eq 2) tion and anchors the part together. π where e refers to the spreading pressure. Con- sequently, Young’s equation may be rewritten Adhesion, Wetting, Spreading, as: γ γ θ γ π and Capillary Attraction s = lv cos + sl + e (Eq 3) Because most of the solids have a negligible Metals π θ e, particularly when the contact angle ( ) is More than 195 years ago, Thomas Young greater than 10°, Young’s equation becomes: (Ref 1) proposed treating the contact angle (θ) γ = γ cos θ + γ (Eq 4) of a liquid as the result of the mechanical equi- s lv sl librium of a drop resting on a plain, solid surface A decrease of the contact angle causes an under the action of three surface tensions (Fig. increase of the liquid drop surface area and thus γ 2.1). The surface tensions are lv at the interface increases the total liquid surface free energy. © 2003 ASM International. All Rights Reserved. www.asminternational.org Brazing (#06955G) 8 / Brazing, Second Edition The total surface free energy of the solid between the phases to be bonded (as with con- decreases concurrently. A balance of these two taminated solid surfaces, such as absorbed car- forces results in a steady-state condition repre- bonaceous layers), γ is larger than γ and also γ sl sv sented by an acute contact angle. Mathemati- lv. Then, a large, obtuse contact angle forms cally, this balance is expressed as Young’s equa- and approaches 180° with decreasing attractive tion (Eq 1) acting at the periphery of the drop. forces, as indicated by the absence of reduction The driving force for wetting thus is (γ – of either the solid or liquid surface free energy γ sv sl). The balancing resisting force is represented and very weak adherence. An optimal 180° by the horizontal component of the surface ten- angle would indicate no attractive forces γ θ sion of the liquid ( lv cos ), as shown in Fig. between the two phases. 2.1. A balance of vertical forces also exists, but Technologically, a nonwetting liquid is vertical forces do not play a role in this problem. highly unfavorable with regard to the formation γ γ γ γ γ When sv < lv and sv < sl < lv (again, in the of an intimate interface, due to its lack of capa- absence of a reaction), a steady-state condition bility of penetration of surface and grain-bound- results with θ > 90°. With a decrease of the ary irregularities because of the lack of capillary obtuse contact angle, the liquid drop surface behavior. Also, the liquid does not distribute area (and thus the total liquid surface free itself uniformly. energy) also decreases. In either case of a starting acute or obtuse Young’s equation (Eq 1) represents a steady- contact angle, the characteristic of wetting can state condition for a solid-liquid interface in sta- be achieved and enhanced by a reaction at the ble or metastable thermodynamic equilibrium. interface at an elevated temperature. However, there is no definite indication of Young’s equation (Eq 1) can be modified to whether chemical or van der Waals bonding represent a spreading coefficient, S1 (Ref 2), or exists, other than that the contact angle is gener- a work of spreading, Ws, by taking the extreme ally smaller with chemical bonding versus van case of wetting when the contact angle γ θ der Waals bonding (because when sl is smaller, approaches 0 and cos approaches 1. The re- the driving force for wetting is greater). sisting force to the extension of the drop then is In either wetting (γ > γ ) or nonwetting (γ γ , as discussed earlier. Young’s equation can γ sv lv lv lv > sv), if an intimate interface does not form then be expressed as: γ γ γ Ws = sv – sl – lv (Eq 5) In order to have spreading occur, Ws has to be positive. Under these conditions, the driving γ γ γ force for wetting ( sv – sl) is greater than lv. If the Ws is negative, then the driving force for wetting is smaller, and spreading does not occur, but an acute angle forms. If a reaction occurs in which the substrate is an active partic- ipant, then the free energy of the reaction, ∆G /dAdt, contributes to the driving force for R γ wetting, which practically always exceeds lv. Spreading thus occurs. Young’s equation (Eq 1) for a nonreacting steady-state sessile drop can be modified to include the contribution of the free energy of reaction: γ + G γ sl R ≥γ sv –΂΃lv cos q (Eq 6) dAsdt Sessile drop configurations: (top) wetting, and (bot- Fig. 2.1 γ γ tom) nonwetting. sv and lv, surface tensions and The free energy required for the increase of the surface free energies of the solid-vapor and liquid-vapor, respec- γ surface area of the drop as the perimeter ex- tively; sl, interfacial energy of the solid-liquid; –dGR/dA · dt, free energy of reaction pands provides the only resisting force to the © 2003 ASM International. All Rights Reserved. www.asminternational.org Brazing (#06955G) Chapter 2: Brazing Fundamentals / 9 γ γ expansion. It can be shown thermodynamically ior corresponds to sv > lv, because, in a given that in the absence of a reaction, the driving system, the surface free energy of a liquid is less γ force for wetting does not exceed lv, resulting than that of a solid, due to its lack of long-range in a steady-state contact angle (Ref 3). The driv- order. The liquid thus has the opportunity to ing force with the contribution of the free rearrange its surface structure to a lower free- energy of reaction in most cases exceeds the energy state. However, when liquid C is placed γ θ resisting force represented by lv, because is on solid A, spreading occurs, because substrate 0° during spreading. A condition of an expand- A (as an active participant in the reaction) ing drop during a reaction is defined as spread- changes its surface composition toward B. The ing. It can be seen that the free energy of a reac- third equation in Fig. 2.1 applies in this case. tion in which the substrate is a passive Another example is that of liquid D on solid participant does not contribute to the driving B. Liquid D is not in equilibrium with B and dis- force for wetting; thus, spreading does not solves some of the substrate to change its com- occur. The contact angle, however, adjusts to position to C. Even though a reaction occurs, conform with the surface-energy changes of the there is no spreading, because B is a passive par- liquid caused by composition changes due to the ticipant with no change in composition, even reaction. though it is being dissolved. However, with liq- Example: Copper-Silver System. The uid D on solid A, spreading occurs, because equilibrium phase diagram for the copper-silver both are active participants as they change to binary system (Fig. 2.2) can be used to illustrate equilibrium compositions C and B, respec- examples of wetting and spreading (Ref 3).