Solid solution copper valence

It is important that the copper is in the monovalent state and incorporated into the silver hahde crystals as an impurity. Because the Cu+ has the same valence as the Ag+, some Cu+ will replace Ag+ in the AgX crystal, to form a dilute solid solution Cu Agi- X (Fig. 2.6d). The defects in this material are substitutional CuAg point defects and cation Frenkel defects. These crystallites are precipitated in the complete absence of light, after which a finished glass blank will look clear because the silver hahde grains are so small that they do not scatter light. 

In interstitial compounds, however, the nonmetal is conveniently regarded as neutral atoms inserted into the interstices of the expanded lattice of the elemental metal. Obviously, this is an oversimplification, as the electrons of the nonmetal atoms must interact with the modified valence and conduction bands of the metal host, but this crude picture is adequate for our purposes. On this basis, Hagg made the empirical observation that insertion is possible when the atomic radius of the nonmetal is not greater than 0.59 times the atomic radius of the host metal—there is no simple geometrical justification for this, however, as the metal lattice is concomitantly expanded by an unknown amount. These interstitial compounds are sometimes called Hagg compounds.9,10 They are, in effect, interstitial solid solutions of the nonmetal in the metal (as distinct from substitutional solid solutions, in which actual lattice atoms are replaced, as in the case of gold-copper and other alloys Section 4.3). 

The mutual solubilities of metals are not reciprocal. A metal of low valency is more likely to dissolve one of higher valency than vice versa. For example, in the solid solutions of copper and silicon, a silicon atom may replace four copper atoms in the copper lattice, but a copper atom, with only a single valency electron, cannot replace a silicon atom which is linked tetrahedrally with four other silicon atoms. Hence the solubility of silicon in copper is 14 per cent but that of copper in silicon only 2 per cent. In a similar way tin dissolves only I per cent of silver whereas silver can dissolve up to I2 2 per cent of tin. 

The range of solid solution in the y phases throws further light on the same problem. In the majority of these the limit of solid solution on the side of the component of higher valency occurs at an electron atom ratio of 170 (corresponding to 88 electrons in the Brillouin zone) and beyond this point a new phase develops. There are, however, some y phases, such as those of copper-aluminium or copper-gallium, in which this ratio is appreciably exceeded, and it is found in these cases that the phase has a defect structure in which some of the 52 sites normally occupied are vacant. This defect structure begins to develop when the electron atom ratio reaches the value of 170, and thereafter atoms drop out of the unit cell in such a way that the total number of electrons per cell remains constant at 88 in the copper-gallium system as many as five... 

Effect of Increasing Valency of Solute. It has been found that when size-factors are favourable extended solid solutions are most lilcely to be formed when the metals concerned have atoms with the same number of outer-layer electrons, i.e. when they have the sa ne valency. When size-factors arc favourable and valencies unequal tin4 extent of solid solubility will decrease as the difference between the respective valencies increases. To examine the effect of the valency-factor we may consider the extent of the solid solubility in copper ((1u).of the favourable size-factor but increasing valency metals, zinc (Zn), gallium (Ga), germanium (Ge) and arsenic (As), and in silver (Ag) of the corresponding favourable size-factor metals, cadmium (Cd), indium (In), tin (Sn) and antimony (8b). The necessary atomic diameters and valency data (vide p. bl), and the results of experimental work on these1 alloys, as far as the primary solid solutions are concerned, an1 summarised in Fables IX (a) and (h). 

Effects of reducing Electron Concentration. The1 restricted solid solubility of a solute of lower valency is not te>o difficult to explain if, first, we1 deal with an extreme case, e.g. the mutual solid solubilities e>f silicon and copper. The size-factors are be>th favourable (Cu, atomic diameter, 2-5oA Si, atomic diameter, 2-doA), and from our previous work we1 should oxpe ed copper to be1 able1 to take into solid solution about as mam atoms per rent, of quadri alrnt silicon as it docs of quadri alont tin, i.e. about 10 atomic per cent. Tim actual figure for the maximum solid solubility of silicon in copper is... 

The data seem to confirm the idea that atoms of identical size and valency can be substituted for one another with much less disturbance1 than occurs when either the atomic diameters or the valencies are different. The most favourable condition for wide solid solution is. therefore, that the atoms should be of nearly the same size and that they should have the same number of outer-layer or valency electrons. It must, however, be noted that the satisfaction of the latter condition does not, of necessity, mean that the metals concerned must belong to the same periodic table group. In fact, continuous solid solubility docs occur in manv hinar alloys of the transitional elements with one another and with tin1 elements of (Jroup 111 copper, silver and gold—provided, of course, that the size-factors are... 

When we compare, for example, the ordinary per cent, by weight equilibrium diagrams of the alloys of monovalent copper with, first, divalent zinc, second, trivalent aluminium, and, third, tetravalent tin, we find that each system is characterised by similar a, a + / , /3, /3 + y, y, etc., phase areas. We have already noted that the range of a-solid solution decreases with increasing valency of solute, and that the maximum solid solubility, in each case, occurs at an electron concentration of 1 4 (p. 69). 

Look at the table of valencies and symbols of ions (page 464). This shows that copper(II) ions are symbolized Cu " and that sulfate ions are symbolized SO . In solution, copper(II) sulfate consists of separate copper(II) and sulfate ions. In all ionic equations, solids (whether metals or insoluble compounds) are represented by their chemical formulae. Here, we represent the zinc metal as Zn(s). The left-hand side of the chemical equation may now be written as... 

This model was checked by alloying small amounts of other nontransition elements Y, or transition elements Z, with nickel-copper alloys and noting the specific compositions at which icnticai and ipasive merged or at which Flade potentials disappeared. Non-transition-metal additions of valence >1 should shift the critical composition for passivity to higher percentages of nickel, whereas transition-metal additions should have the opposite effect. For example, one zinc atom of valence 2 or one aluminum atom of valence 3 should be equivalent in the solid solution alloy to two or three copper atoms, respectively. This has been confirmed experimentally [47]. The relevant equations become... 

An example of a substitutional solid solution is found for copper and nickel. These two elements are completely soluble in one another at all proportions. With regard to the aforementioned rules that govern degree of solubility, the atomic radii for copper and nickel are 0.128 and 0.125 nm, respectively both have the FCC crystal structure and their electronegativities are 1.9 and 1.8 (Figure 2.9). Finally, the most common valences are -l-l for copper (although it sometimes can be +2) and +2 for nickel. 

The liquid L is a homogeneous liquid solution composed of both copper and nickel. The a phase is a substitutional solid solution consisting of both Cu and Ni atoms and has an FCC crystal structure. At temperatures below about 1080°C, copper and nickel are mutually soluble in each other in the solid state for all compositions. This complete solubility is explained by the fact that both Cu and Ni have the same crystal structure (FCC), nearly identical atomic radii and electronegativities, and similar valences, as discussed in Section 4.3. The copper-nickel system is termed isomorphous because of this complete liquid and solid solubility of the two components. 

Martin BE and Petrie A. Electrical properties of copper-manganese spinal solutions and their cation valence and cation distribution. J. Phys. Chem. Solids 2007 68 2262-2270. 

This review of mixed valence copper(I)/(II) systems has clearly established the predominance of the class I Robin and Day behaviour (Table 17), 360-362 but equally has shown how few copper class II or III systems have been well defined. This particularly applies to the class II systems, which can still be considered well-defined coordination complexes, with the electronic properties of these systems in the solid state and in solution. This suggests a fruitful area of research in these copper(I)/(II) mixed valence systems, especially of class II behaviour. 

Modifications. It should be noted that both of the solvent elements, copper and silver, are monovalent, i.e. they both have atoms in which there is only one outer-layer or valency electron, while the solute elements, zinc, magnesium, cadmium and berylium, are all divalent, i.e. they all have atoms with two outer-layer or valency electrons. We shall soon be in a position to show how important in alloy structures these valency electrons can be we must content ourselves for the moment, however, by stating that Hume-Bothery has examined the solid solubility of various metals in the divalent solvent magnesium, and has shown that the favourable size-factor principle may be equally well applied to magnesium alloys, typical of... 

The data show that increasing valency of solute has a marked effect in restricting solid solubility, and bring out the remarkable fact that the maximum solid solubilities of the divalent metals zinc and cadmium in copper and silver respectively are both about 40 atomic per cent., those of the trivalent metals gallium and indium art4 both about 20 atomic per cent., and those of the tetravalent metals germanium and tin art1 both about 12 atomic pm cent. 

Table IX a).—Data for Solid Solubility of Solutes of Increasing Valency in Copper and Silver...

Table IX (6).—Solid Solubilities in Copper and Silver of Solutes of Favourable Size-Factor and Increasing Valency...

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