Electrical Resistivity of the Elements
This Table is a collection of the electrical resistivity values for the elements extracted from the sources listed below:
Sources
The following is a list of the documentation sources from which the above data has been selected.
HME: Handbook of Metal Etchants; Perrin Walker, William H. Tarn; CRC Press
MSHME: Mark's Standard Handbook for Mechanical Engineers; Theodore Baumeister; McGraw Hill
JPCR: Journal of Physical and Chemical Reference Data; Donald R. Burgess, Jr. & Allan H. Harvey; AIP Publishing
NIST: National Institute of Standards & Technology; US Department of Commerce
SMRB: Smithell's Metals Reference Book; E A Brandes & G A Brook; Elsevier
CRC: CRC Materials Science and Engineering Handbook;
W: Wikipedia.org;
MW: MatWeb.com;
CC: Chemicalaid.com;
comments: CalQlata believes (rightly or wrongly) data provided in 'published books' may be more reliable than website sources, simply because, CalQlata also believes that greater care is taken over data verification.
Caution
The empirical measurements provided in the above Table have been taken from numerous sources, all of which are claimed to be as a result of laboratory measurements, which are of course, subject to experimental error, such as;
1) Measurements taken using equipment that is not manufactured from the subject material.
2) Experiments not usually taken on a pure crystal of the subject material.
3) Experiments not necessarily carried out in an oxygen-free atmosphere; e.g. no consideration is given to the immediate oxidisation of the subject material (such as potassium, sodium, rubidium and lithium).
4) Most documented values vary with all other documented values except - such as those on internet sites - where such values are simply copied without verification.
5) Documented values such as 1E+07 μΩ.m, 2E+12 μΩ.m & 2E+21 μΩ.m, 10⁵ μΩ.m, 1.8E+16 μΩ.m, etc. are at best questionable.
6) Values for carbon, for example, are not always specified according to form; diamond, graphite, coke, etc.
7) The resistivity of metals such as mercury that have been measured @ 300K in liquid form, meaning that its volumetric state will have given unrepresentative values. The one solid value must have been carried out at less than 273K, and therefore incomparable.
8) The rare earth elements are of particular concern due to; a) the limited work performed on pure crystals of these elements due to the expense, and b) their variability.
For Example
As can be seen in Fig 1, even the most dedicated and capable experimentation⁽³⁾ is subject to significant variation;
1.8 < ρ < 9 (10⁻⁸ Ω.m) (δρ = 5.4E-08Ω.m ±67%).
Fig 1 is a graphical image of the electrical resistivity results from numerous well-respected experimenters on copper, and the variation achieved is more than twice that between the documented and calculated values.
Given that even greater variability can be found in numerous documents and websites, it becomes very evident that great care must be taken when relying on values based upon experimentation, and even greater care with values extracted from generally available documentation (especially website sources).
The following tungsten filament dimensions were extracted from a General Electric brochure by Dr. Lawrence Woolf⁽⁴⁾, which equates to an operational electrical resisitivity of 7.79E-07 Ω.m:
| Power (W) | Diameter (m) | Length (m) | ℓ/A (/m) | resistance (J.s/C²) | resistivity (J.s.m/C²) |
| 25 | 3.00E-05 | 0.56 | 7.92E+08 | 576 | 7.27E-07 |
| 40 | 3.30E-05 | 0.38 | 4.44E+08 | 360 | 8.10E-07 |
| 60 | 4.60E-05 | 0.53 | 3.19E+08 | 240 | 7.53E-07 |
| 75 | 5.30E-05 | 0.55 | 2.49E+08 | 192 | 7.70E-07 |
| 100 | 6.40E-05 | 0.58 | 1.80E+08 | 144 | 7.99E-07 |
| 200 | 1.02E-04 | 0.72 | 8.81E+07 | 72 | 8.17E-07 |
| GE Filament Dimensions & Calculated Resisitivity 120 Volts and operating temperature (≈2900K) Calculation Method: current: I = P/V; resistance: R = V/I; resistivity: ρ = R.A/ℓ | |||||
Moreover, Fig 2 is a compilation of various values for the resistivity of tungsten from the National Bureau of Standards⁽⁵⁾;
which shows the resistivity of tungsten at 2873K of 8.7E+07 Ω.m, and 1.286E+07 Ω.m at 300K.
Using the following atomic formulas
outermost electron orbital shell (Z/2):
number of electrons in shell (Z/2): N = 1 or 2
temperature in shell (Z/2): Ṯ = input {K}
potential energy: PEₛ = mₑ.Ṯ/X {J}
electron orbital velocity: v = √[Ṯ/X] {m/s}
atomic spacing (viscous): d = ³√[mₐ./ρ] {m}
voltage: V = N.PEₙ/e {J/C}
current: I = e.v/d = e/d . √[Ṯ/X] {C/s}
resistivity: ρ = V/I . d.ψ {J.s.m/C²}
the resistivity of tungsten is found to be;
2.2803E-07 Ω.m @ 300K
7.07E-07 Ω.m @ 2883.9K
Both of which are considerably closer to the values quoted by General Electric and the National Bureau of Standards than the documented values in the above Table (≈5.3E+08 Ω.m), which gives good reason to be very cautious when accepting any documented value for the electrical resistivity of elemental matter.
Notes
- unreliable data, as stated values at 273K are greater than (or equal to) others quoted at 293K
- comment 'unreliable' is applied to elements the values of which are too variable (according to CalQlata)
- National Institute of Standards and Technology; Centre for Information and Numerical Data Analysis and Synthesis; Purdue University, West Lafayette, Indiana 47906; R. A. Matula; Electrical Resistivity of Copper
- Seeing the Light: The Physics and Materials Science of the Incandescent Light Bulb; February 20, 2002; Dr. Lawrence D. Woolf, General Atomics, San Diego, CA 92121 (Larry.Woolf@gat.com)
- National Bureau of Standards Library (260-52) (US Department of commerce); Thermal Conductivity and Electrical Resistivity Standard Reference Materials: Tungsten SRM's 730 and 799 (from 4K 3000K); Page 23; Figure 14