Grain Boundaries
Grain boundaries are formed initially during solidification of molten metal, and they can change in number and location during later processes such as rolling, drawing or annealing. When molten metal starts to cool solidification is not uniform throughout the whole volume. The temperature will not be uniform, but apart from this the level of impurities also varies, and the melting point is generally lower in regions of high impurity. The result is that regions of higher purity solidify first to form a regular crystal structure. Those regions aligned with the direction of maximum temperature gradient grow the fastest, and so the final grain orientation is not random. The grains are separated by regions of lower purity. Most copper rod is now made by a process called 'continuous casting', and the temperature gradient in this process commonly produces grains aligned in a 'chevron' pattern, the exact shape and size depending on the casting speed (Ref.1). This initial structure will of course be changed by further processing such as annealing or drawing into a fine wire.
The effect of impurities is complex, there being considerable interaction between different elements. An example is investigated in detail in Ref.2 where it is found that sulphur tends to segregate into the grain boundaries forming copper sulphide precipitates, even in ultra high purity copper, but if phosphorus or silver are also present these appear to compete for the available grain boundary locations and reduce the size of copper sulphide precipitates, leaving more sulphur in solid solution in the copper grains. All three elements have a tendency to attach to lattice vacancies, and they also compete for these. A sulphur-vacancy pair has high mobility and so in segregating to the grain boundary a sulphur atom brings a vacancy with it, so increasing vacancy concentration at the grain boundary.
The study of grain boundaries is of great importance for many applications, ranging from containers for nuclear waste to superconducting films. A vast amount of research information is available, and anyone interested can find many websites dealing with this subject. For audio cable aplications there are arguments for and against grain boundaries and various impurities. Oxygen is introduced intentionally in the manufacture of ETP copper and this improves conduction by combining with other impurities to form precipitates, which have little effect on conduction compared to impurities in solution. Low oxygen copper needs a higher level of purity to achieve similar conductivity to ETP copper, and only with far higher purity is there actually an improvement. The reduction in the number of grain boundaries sometimes thought to be beneficial also can have the effect that when impurities are segregated in the boundaries the impurity concentration per boundary is higher because fewer boundaries are available.
Grain boundary scattering is generally small compared to thermal scattering, but not always. In thin films each boundary can be large compared to the film thickness, and random variations in both impurity levels and misorientation of crystal lattice between adjacent grains mean that there can be significant impedance to current flow, and few alternative lower impedance routes. It has been found that a small grain size may actually improve current flow in superconducting thin films because there are more possible current paths, and any high impedance boundaries can just be bypassed. Large grain size has a far more variable effect (Ref.3). This selection of current routes is described by 'percolation current theory'. In copper cables this effect is unlikely to have similar importance, and boundaries will not have such a wide range of effect. A greater misalignment angle will just increase the scattering probability rather than prevent current flow, but it seems likely that something similar to the percolation effect will occur, with current tending to follow the path of least resistance.
Percolation theory suggests that there may be some advantage in increasing the number of possible current paths to ensure that there are always low impedance routes available irrespective of the grain size and condition. One way to do this is to use a large number of very fine parallel wires in good electrical contact along their length rather than a single conductor. Measurements by D.Self (Electronics World March 1996 p253) suggest that in any 'normal' multistrand copper cable there is good contact between strands along the entire length. (Some cables are not entirely 'normal', and some wires with transparent insulation have been seen to gradually turn green, possibly as a result of chemicals in the insulation combining with the copper. These cables should certainly be avoided.) What matters is that if one strand has a particularly bad grain boundary at one location it is unlikely that all adjacent strands have similar problems in the same place, and so there will be alternative nearby routes for the current.
This argument in favour of multistrand cable is speculative, but seems plausible. Measurements of distortion invariably fail to find any in any speaker cable at audio frequencies, but of course every individual cable has not been tested, and so the multistrand option may be worthwhile to guarantee that a particularly bad grain structure in one location in an individual cable will have no significant effect because of the many alternative current paths. It is the guaranteed consistency which may be of value. Cables with 100 or more strands of high purity copper are readily available for as little as 36p (UK) per metre, as mentioned elsewhere. Occasional claims that multistrand cables have problems caused by current 'jumping' from strand to strand, somehow caused by the skin depth effect, appear to be just another marketing ploy with no real effect ever having been found to support the claims. Measurements have been carried out which reveal that multistrand, compared to single strand with the same copper cross-section area, has a lower attenuation at high frequency corresponding to a lower skin depth effect (Ref.4), but their suggestion that it behaves like litz wire with insulated strands because the strands are insulated by oxidation etc. are not supported by any measurements, unlike the opposite conclusion from the D.Self measurements mentioned earlier.
Ref.1 '3D Modelling of Grain Structure Formation During Solidification' by Gandin et al, EPFL-SCR No.8 Nov 96.
Ref.2 'Theoretical Investigation of the Defect Interactions in Dilute Copper Alloys Intended For Nuclear Waste Containers', by P.A.Korzhavyi et al, Condensed Matter Theory Group, Uppsala University, Sweden.
Ref.3 'Percolation modelling for highly aligned polycrystalline superconducting tapes' by Rutter et al, Supercond. Sci. 13 (2000) L25-L30
Ref.4 Audioholics, Cable Face-Off part 2.
