Introduction to the Metal Foil Resistors.
A study of Elias Eduardo Ghershman, that compiles the work of many researchers over many years.
Historical
summary of the development of Metal Foil Resistors.
The
following sequences are scientific and technological developments led
to the
creation of the idea of metal foil resistor, it is organized
temporarily.
1826
Measurement
of
Current.
Although
the 1820s was a
time of great
discoveries concerning the production of current electricity, it was
also a
time of widespread confusion about proper definitions fur such
fundamental
terms as tension, intensity, and
quantity.
Ampere had provided an electromagnetic definition of the intensity of a
current, and had clearly drawn a distinction between electrical tension
and
electricity, but scientists still lacked a means of relating the
tension of a
voltaic pile to the intensity of the current it produces and to the
properties
of the conductor carrying this current. A complete theory of voltaic
circuits,
which takes into account the driving power of the battery, was first
provided
in1826 by the German physicist Georg Simon Ohm (1789-1854). In 1825,
Ohm
resolved to dedicate himself to research in electricity. In his
research was
inspired by the work on heat of Joseph Fourier (1768-1830), who pointed
out in
1822 that the flow of heat between any two points depends on the
temperature
difference and the conductivity between them. Applying this insight to
the case
of electricity, Ohm reasoned in a general way that the flow of current
is
proportional to the voltage (the electromotive force) and inversely
proportional to the resistance.
Ohm
first
determined the lengths of wires, made from different metals, which gave
the
same current. He called these various lengths "equivalent lengths."
Ohm then showed that the resistance was proportional to the to its
length and
inversely proportional cross-sectional area of the wire. Ohm performed
this
first series of experiments, replacing the voltaic pile with a
thermocouple,
recently discovered in 1821 , see in the following figure by Thomas
Johann
Seebeck (1770-1831). The thermocouple had the advantage over of the
voltaic
pile of not being prone to fluctuations in voltage. After trying the
experiment
with different metals and temperatures, Ohm was able to publish the law
that
bears his name.
1833
In
1843 Wheatstone communicated an important paper to the Royal Society,
entitled
'An Account of Several New Processes for Determining the Constants of a
Voltaic
Circuit.' [20]
It contained an exposition of the well
known balance for measuring the electrical
resistance of a conductor, which still goes by the name of
Wheatstone's Bridge or
balance, although it was first devised by Mr. S. W.
Christie, of the Royal Military Academy, Woolwich, who published it in
the Philosophocal
Transactions for 1833. The method was
neglected until Wheatstone brought it into notice. His paper abounds
with
simple and practical formula: for the calculation of currents and
resistances
by the law of Ohm. He introduced a unit of resistance, namely, a foot
of copper
wire weighing one hundred grains (6.5 g), and showed how it might be
applied to
measure the length of wire by its resistance.[21]
Although
this document
and does not establish the mathematical relationships of the bridge
that bears
his name and that an important component in measuring resistances,
demonstrates
the sensitivity of the system, from the page 323, “The Differential
Resistance
Measurer”, of such document, extract the following description
: The drawing, Fig. 5 represents a board on which are
placed four copper
wires, Z b, Z a, C a,
C b, the extremities of which
are fixed to brass binding screws. The binding screws Z, C
are for the purpose of receiving wires proceeding from the
two poles of
a rheomotor, to denote
any apparatus which
originates, an electric current, whether it be a voltaic element or a voltic battery, a
thermo-electric element or a thermo-electric
battery, in words of Wheatstone and those marked a, b are for holding
the ends
of the wire of a galvanometer. By this arrangement a wire from each
pole of the
rheomotor proceeds to
each end of the galvanometer
wire, and if the four wires be of equal length and thickness, and of
the same
material, perfect equilibrium is established, so that a rheomotor
however powerful will not produce the least deviation of the needle of
the
galvanometer from zero, in this
last paragraph and see
the phenomenon of the bridge .
The
circuits Z b a
C Z, and Z a b C Z, are in this case
precisely equal, but as both
currents tend to pass in opposite directions through the galvanometer,
which is
a common part of both circuits, no effect is produced on the needle. Currents
are however established in Z b CZ, and Z
a C Z,
which would exist were the galvanometer entirely removed.
But if a resistance be interposed in either of the four wires, the equilibrium of the galvanometer will be disturbed ; if the resistance be interposed in Z b or C a, the current Z a b C Z will acquire a preponderance ; if it be inserted either in Z a or C b, the opposite current, Z b a C Z, will become the most energetic.
If the resistance interposed in the wire be infinite, or which is the same thing, if the wire (which we will suppose to be C b) be removed, the energy of the current passing through the galvanometer will be that of a partial current Z b a passing through one of the wires plus the galvanometer wire.
In the
following
paragraph we see that Wheatstone anticipates that the phenomenon
undergoing
mechanical stress to the wire is a resistance change, slight
differences in the
lengths, and even in the tensions of the wires, are
sufficient to disturb
the equilibrium ;
it is therefore necessary to have an adjustment, by means of which,
when two
exactly equal wires are placed in C a and Z a, the equilibrium may be
perfectly
established.
1833
In 1833, Lenz revealed details of his research. A pair of identical spirals were built for each metal under investigation and connected in series into a single circuit whose free ends were joined by cooper lead wires to a galvanometer very similar to that invented by Nobili. By using a circuit with an electromotive force which was free of the uncertainty implied by the internal resistance of the battery, Lenz was able to find the electric conductivity of each one of the studied metals at different temperatures and found with considerable degree of accuracy the magnitude of their respective changes with this variable. determine values at between six and twelve different temperatures for, silver, copper, brass, iron and platinum , and sometime later, gold, lead and tin too. The relation he found for this specific case was, using his own notation :
The resistivity
of metals increases
with increased temperature, positive resistance-temperature
coefficient,
although there may be metals with negative
resistance-temperature coefficient ;
within narrow ranges of temperature where
the resistance-temperature coefficient may be considered constant, the
resistance of a conductor at the temperature
t is :
It was Lord
Kelvin [1]
from his investigations into the electrodynamics properties
of metals who first reported in 1856 that metallic conductors subjected
to
mechanical strain exhibit a change in their electrical
resistance, although this is not exactly true, see above Wheatstone
work. He used a Wheatstone bridge circuit
with a galvanometer as the indicator, adopts the system of Wheatstone
to be very sensitive.
Lord Kelvin
showed
that metallic conductors subjected to mechanical elongation (strain)
exhibited
a change in resistance, compressional strains producing a decrease. The
resistance of a wire is defined by
Telegraph wire signal propagation changes and time-related conductivity changes, nuisances to telegraph companies, motivated further observations of conductivity under strain. In his classic Bakerian lecture to the Royal Society of London, Kelvin reported an elegant experiment where joined, parallel lengths of copper and iron wires were stretched with a weight and the difference in their resistance change was measured with a modified Wheatstone bridge. Kelvin determined that, since the elongation was the same for both wires, “the effect observed depends truly on variations in their conductivities.” Observation of these differences was remarkable, given the precision of available instrumentation.
Furthermore,
he
observed that the iron wire showed a greater increase in resistance
than the
copper wire when they were both subjected to the same strain. Lord Kelvin
also employed the Wheatstone bridge technique to measure the
resistance change. In that classical experiment, he established three
very
important facts which helped further development of electrical
resistance
strain gages; 1. The
resistance of the wire changes as a
function of strain. 2 Different materials have different sensitivities.
3
Wheatstone bridge can be employed to accurately measure these
resistance
changes.
1905
Nichrome. [6]
In 1905,
after several years of joint experimentation, Albert L. Marsh [7] , a Michigan metallurgist and
William Hoskins an Illinois inventor/entrepreneur patented a tough new
alloy of
nickel and chromium, to which they gave the trade name “Nichrome”.
Containing only a small amount of iron and being carbon free, Nichrome was much stronger and more long
lived than earlier thermal wire. Hoskins Manufacturing Company was former to produce high
temperature electric laboratory
furnaces using the wire and is credited by some with manufacturing the
first
commercially successful electric bread toster
in 1907
derived from these furnaces.
Hoskins
eventually
sold the Nichrome
patent to General Electric who had
tried unsuccessfully for years to create its own thermal wire. Until
the Marsh
patent ran out in the mid-1920s, GE
charged all other
manufacturers twenty-five cents per appliance for the right to use it.
Early “Nichrome” was a major
improvement over iron alloy wire in
both electrical efficiency and physical strength.
1930
America 1930, Titanium and Aluminium added to the classic heating element alloy nichrome (Ni-20Cr), resulted in significant increase in creep resistance.
Designers have long had a need for stronger, more corrosion-resistant materials for high-temperature applications. The stainless steels, developed and applied in the second and third decades of the 20th century,
served as a starting point for the satisfaction of high-temperature engineering requirements. They soon were found to be limited in their strength capabilities. The metallurgical community responded to increased needs
by making what might be termed ‘‘super-alloys’’ of stainless varieties. Of course, it was not long before the hyphen was dropped and the improved iron-base materials became known as superalloys. Concurrently, with the advent of World War II, the gas turbine became a high driver for alloy invention or adaptation. Although patents for aluminum and titanium additions to Nichrome-type alloys were issued in the 1920s, the superalloy industry emerged with the adaption of a cobalt alloy (Vitallium, also known as Haynes Stellite 31) used in dentistry to satisfy high-temperature strength requirements of aircraft en engines.
Some nickel-chromium alloys (the Inconels and Nimonics), based more or less, one might say, on toaster wire (Nichrome, a nickel-chromium alloy developed in the first decade of the 20th century) were also available.
So, the race was on to make superior metal alloys available for the insatiable thirst of the designer for more high-temperature strength capability. [ 16 ].
1938
Alloys for electrical resistance. [2]
Chromium
nickel alloys are characterized by having
a large electrical resistance (about 58 times that of copper), a small
temperature coefficient and high resistance to oxidation. Examples are Chromel A and Nichrome V, whose
typical composition is 80 Ni and 20 Cr, with its melting point to 1420
° C.
When you add a small amount of iron to nickel-chromium alloy, are becoming more ductile. The Nichrome and Chromel C are examples of an alloy containing iron. The commposicion typical of Nichrome is 60 Ni, 12 Cr, 26 Fe, 2 Mn and Chromel C, 64 Ni, 11 Cr, Fe 25. The melting temperature of these alloys are 1350 ° and 1390 ° C, respectively. In the figure are variations of resistance with temperature of these alloys.
Temperature coefficient of resistance (TCR).
If you look at this chart the variation of resistance with temperature and especially for the Nichrome V, we observed several areas in rough form, the zones A and E have an increase in resistance with temperature (TCR positive), in zones B and D it comes to points of zero or very small variation (TCR null), the C zone is characterized by a reduction in resistance with temperature(TCR Negative) .
1938
Rugeof of M.I.T. conceived the idea of making a preassembly by mounting wire between thin pieces of paper
1939
RESISTANCE FOIL
STRAIN GAGES
In 1856 Lord Kelvin [1] reported that the electrical resistance of copper and iron wires increased when subjected to tensile stresses. This observation ultimately led to the development of the modern "strain gage" independently at California Institute of Technology and Massachusetts Institute of Technology in 1939. The underlying concept of the strain gage is very simple. In essence, an electrically-conductive wire or foil (i.e. the strain gage) is bonded to the structure of interest and the resistance of the wire or foil is measured before and after the structure is loaded. Since the strain gage is firmly bonded to the structure, any strain induced in the structure by the loading is also induced in the strain gage. This causes a change in the strain gage resistance thus serving as an indirect measure of the strain induced in the structure.
1940
Superalloys
The material and casting technique improvements that have taken place during the last 50 years have enabled superalloys to be used first as equiaxed castings in the 1940s, then as directionally solidified (DS) materials during the 1960s, and finally as single crystals (SC) in the 1970s. Each casting technique advancement has resulted in higher use temperatures.
1946
Metal Foil Type Strain Gauge, Metal Foil Type Strain Gauge and Method of Making Same, William D. Van Dyke [3]
950
During the
1950s the foil-type
gage replaced the wire gage.
1954
In 1954 a
company Wilbur B. Drive Co.
starts
selling a Nickel-chromium-aluminium-copper alloy film of the order of
fraction
of a micron thick, called Evanohm.
1959
The
resistance-temperature
coefficient of all metals depends to a large extent upon their purity
and the
thermal treatment. Pure metals have relatively high coefficients; the
coefficients of alloys are usually smaller and can even be negative in
certain
ranges of temperature (manganin).
Change of the
physical character of the metal (annealing, recrystallization) can
cause a
change of the temperature coefficient which in some cases, e.g., at the
curie point, can be
discontinuous. [8]
Instrumentation in Scientific Research, Kurt S. Lion, 1959.
1960
In 1960, James E. Starr patent [4] a resistance made of a metal foil, as shown in the figure below,
The resistor
formed of metal foil, the idea is
similar to of invention of William D. Van Dyke [3],
the
ease in which the resistance value can be varied by thinning or
narrowing the
element of the pattern, either chemical etching or mechanical reduction
of the
with or thickness to increase the resistance. A resistor foil pattern
or grid
is formed, as by a photographic printing and chemical etching process
and
adhesively bonded to a thin insulating layer, epoxy or glass, .
1965
In 1960,
Felix Zandman
patent the precision resistor of great stability [5],
the invention has the following properties, controlled temperature
coefficient
of resistance, the idea is similar to of invention of Starr
[4]
, a thin film of a selected metal alloy upon a substrate,
many times thicker than the metal film, the bulk metal film is a
resistive
alloy such as one of the Nichome,
wherein nickel nickel
and chromium are the principal metals,
as indicated by John Strong [2],
the
film may be of the order of 0.04 inch,
the substrate may be made of glass, the metallic film is photo-etched
to
pattern of the resistor, the two
pictures are similar.
The
structure of the system has a
substrate made of glass having a temperature coefficient of expansion
of the
order of 3 parts per million per degree F, the thickness of the
substrate is
0.04 inch and bulk metal film may be made from resistive alloy as one
of the Nichrome alloy,
wherein nickel and chromium are the
principal metals, Ni75%Cr20%Cu2.5%Al2.5% [12],
this film
may be of the order of 0.0001 inch thick.
Zandman's contribution to the development of metal foil resistors is as follows. The resistive alloy film, etched in its predetermined pattern and bonded to the glass substrate, being of the order of one hundredth to one thousandth the thickness of the glass, exerts minimal influence upon the glass or ceramic substrate,
the response of the unit, i.e. the variation of the electrical resistance to changes in temperature and humidity is minimal, due to the construction of the component
The changes of resistance in the path ultimately
determined in
the patterned film between the junctions 16 and 17 is influenced by the
following
factors: (a) The temperature coefficient of resistivity of the alloy of
which
the patterned metal film is comprised; (b) The elongation and narrowing
and
consequent increase of resistance of the alloy film caused by the
expansion of
the symmetrically coated substrate
with increase of
temperature (and conversely, the compression and broadening of the
alloy film
when the symmetrically coated substrate
contracts with
decreasing
temperature); (c) The variation of resistance as a
function of the stress
produced in the alloy film when the symmetrically
coated substrate expands or contracts with changes of temperature.
As will be readily apparent, the factors b and c above represent the resultant effect of the forces produced in the substrate and the forces produced in the coatings thereon. By the selection of a nickel chromium alloy with such minor alloy components as to provide a desired curve of resistivity versus temperature and a desired temperature coefficient of expansion, the resistor may be made to have a reliable temperature coefficient of resistivity as low as 1 part per million per degree C. in the vicinity of a desired design temperature such as 25° C. and to have an extremely low overall temperature coefficient of resistivity throughout a range from - 55 ° C. to +175 ° C. In general, the alloy consisting primarily of nickel and chromium will have a greater temperature coefficient of expansion than the glass substrate. Hence, with increasing temperature, as the glass substrate elongates and carries with it the alloy film layer, the alloy film is subjected to compressive stress, in that paragraph shows an application of the discovery of Kelvin [1].
Conversely, as the glass substrate contracts with decreasing temperature and the alloy layer tends to undergo greater contraction, the resistive metallic film which is bonded to the glass and constrained to duplicate the contraction of the glass is subjected to tensile stress. Provided that the net sum effect of the resistance change component due to changing stress in the alloy film and the resistance change component due to expansion or con- traction of the film is substantially equal to the temperature coefficient of resistivity of the alloy under stress free conditions, and of opposite sign, the overall temperature coefficient of resistivity of the device is substantially zero. Since the last named factor is not linear, the device will have a predictable variation of its temperature coefficient of resistivity throughout the design temperature range.1976
In 1976, Paul
Rene
Simon, patent a
process for etching a thin film or foil of an electrically
conductive resistive material, preferably an alloy predominantly
comprising
nickel and chromium, by electrolytic etching under conditions of
electrochemical machining above Jacquet's
plateau on the I.V. characteristic curve, process called electropolishing. The process
is particularly suitable for
manufacturing a planar electrical resistor having a high stability, a
low
temperature coefficient, and a high ohmic
value
despite the relatively low resistivity of the film or foil. The anode
surface
polarization is maintained substantially constant over the surface of
the foil
or film by removing the by-products of the etching process, i.e.,
gases,
viscous layers and other impurities, by mechanical effects such as an
electrolytic flow or mechanical vibration, or both together. These
mechanical
effects are carefully balanced against the applied potential values
such that
the rate of formation of the layers and gases at the anode is equal to
their
rate of removal. Moreover, the anode electrical resistance is kept at a
negligible value independent of the progress of the attack, by securing
the
film or foil to a thick layer of a conductor such as copper, whereby
the
evolution of potential drop across the foil, due to the electrical
current
flow, is kept at a negligibly small level. Under these conditions, a
quasi-uniform etching is obtained all over the foil or film surface.
The
operating parameters of the process are also described as well as the
advantages of the resistor produced according to the process of the
invention.
1980-1990
Between 1980 and 1990, Mark Robinson presents a publication Strain Gage Materials and Processing, Metallurgy and Manufacture, using evanohm alloy, among other. [15]
Technology
Principles of Metal Foil Resistors.
These resistors comprise an insulating
substrate, usually ceramic material,
of thickness about 0.5 mm, a thin metallic foil bonded to the
substrate, the
foil having a circuit path formed by photographic techniques
denominated etched-pattern
resistor layer of bulk metal film ,the foil is a resistive Ni-Cr,or similar alloy like Karma o
Evanohm
[9],
with a thikness of 2-8 mm
(78.74 min-314.96 min)
, the foil initially is heat
treated to adjust
its temperature coefficient of
resistance (TCR) [10].
A
photosensitive resin
is then deposited on the foil using microelectronic processes, similar
to
integrated circuit process technology. The photosensitive resin is
exposed
(photolithography) through a photographic mask representing the design
of
resistance circuit, which resembles a series of looping filaments. The nonexposed areas are washed off,
leaving the exposed areas
intact, forming a meander pattern (photoresist mask) on top of the
foil. The
foil areas not protected by the photoresist mask are then etched by
means of electrolytic
or chemical processes, reproducing the
design of the mask. This step creates hundreds of resistive filaments
in series
or parallel such that the resistance of the circuit reaches the desired
value.
Such resistance elements are usually produced in an array of several
hundred on
a wafer. The next process step is to singulate
resistor chips from the wafer.
Resistor Theory and
Technology. Felix Zandman,
Paul Rene Simon, Joseph Szwarc.
Pag. 156
[10].
The
following step is to cut the ceramic
formed by many resistors to obtain them
individually, next connector leads attached to the thin foil at each
end of the
circuit path and a protective coating surrounding the entire structure.
The
metal foil may be made from a resistive
alloy initially developed
for precision resistor application in the 1950’s is also widely used
known as
Karma or Evanohm. [9] , [11]
The Karma is compound one of alloy of Ni 74%, Cr 20%, Al 3%, Fe 3% and used to make grids of electrical resistance strain gages for applications at both cryogenic and elevated temperatures. It also possesses good fatigue characteristics. Karma alloy has similar overall properties to Constantan.
A high-precision
resistor is constructed by supporting a metal film of Evanohm
(Ni75%Cr20%Cu2.5%Al2.5%) alloy [12],
for example, upon a
substrate having know
physical properties , the substrate
being many times
thicker than the
metallic film, in the order of 100 to 1,000 times thicker. The metallic
film is
caused to have a predetermined pattern, including a great number of
parallel
narrow linear path portions in a planar array.[7]
A low temperature coefficient of resistance (TCR), is generally accomplished by making use of a foil resistive element wherein the foil's resistivity changes with temperature are capable of compensating for the strain induced resistance changes which are developed as a result of mismatch of the coefficients of thermal expansion of the resistive foil and of the substrate to which it is applied.
Strain (e) is capable of being expressed as a function of temperature and as a function of resistance, in accordance with the following equations: (the following analysis was studied from a document of doctor Zandman, Swarc [13] )
[1]
On the Electro-Dynamic Qualities of
Metals:--Effects of Magnetization on the Electric Conductivity of
Nickel and of
Iron (January 1, 1856), Proceedings of the Royal Society of London,
546–550.
[2]
Procedures in Experimental Physics, John
Strong, pag. 546.
[3]
METAL FOIL TYPE STRAIN
GAUGE AND METHOD OF MAKING SAME William D. Van Dyke, Patent
number: 2457616
[4]
ADJUSTABLE RESISTORS
AND METHOD OF MAKING THE SAME James E. Starr, Patent
number: 3071749
[5]
Precision Resistor of Great Stability,
Felix Zandman,
Patent number: 3517436
[6]
Antique
Electric Waffle Irons 1900-1960, A History of the Appliance Industry , By William George
[7] ELECTRIC RESISTANCE ELEMENT ALBEET L. MARSH, Patent number: 811859
[8]
Instrumentation
in
Scientific Research, Kurt S. Lion, 1959, page 156.
[9]
Zero
TCR Foil Resistor Ten Fold Improvement in Temperature Coefficient.
Reuven Goldstein .
[10] Resistor
Theory and Technology. Felix Zandman,
Paul Rene
Simon, Joseph Szwarc.
Pag.
158
[11]
http://www.vishay.com/brands/measurements_group/guide/glossary/karalloy.htm
[12] Experimental
study of Evanohm thin
film resistors at subkelvin
temperatures. A
F Satrapinski,
A M Savin, S Novikov and O Hahtela, Measurement Science and
Technology, Volume 19
Number 5.
Thin
film resistors, based on the Evanohm
(Ni75%Cr20%Cu2.5%Al2.5%) alloy, have been investigated at cryogenic
temperatures. The objective of the study is the development of the high
value
resistor for precision electrical measurements at low temperature and
particularly for metrological triangle experiments. Thin film resistors
of
different configurations have been designed and fabricated by the
thermal
evaporation process. The resistivity of investigated resistors is 110 ×
10−8
Ω m; the resistance exhibits a Kondo minimum at a temperature near 30 K
and increases with further reduction of temperature. In the temperature
range
50–65 mK,
the temperature
coefficient reaches −20 × 10−3 K−1. Power dependence
measurements at subkelvin
temperatures demonstrate
that noticeable electron overheating takes place only at the power
level above
10 pW for a 500 kΩ
resistor. The electron–phonon coupling constant for the fabricated Evanohm thin films has been
derived from experimental
results.
[13]
Felix Zandman,
Joseph Swarc ( USP
4,677,413), 1987, Patent number: 4677413
[14] Kazuo
Horii, Kazuo Horii, An improved
thin-film resistor, Patent number: 3824521
An
improved thin-film resistor low in the resistance
temperature coefficient is provided. A metal film or foil is bonded
with a
thermosetting resin onto an insulating base plate having a lower linear
expansion coefficient than the metal and is etching-processed so as to
be of a
desired resistance pattern. The difference in the linear expansion
coefficient
between the metal and the insulating base is selected to be 26
to 66 .times. 10.sup.-.sup.7
/.degree.C. The metal
and base are covered with a resin so as
to be a molded
assembly, together with lead wires
connected to both ends of the metal.
[15] Strain
Gage Materials Processing, Metallurgy and Manufacture, Mark
Robinson,
Hamilton Precision Metals.
TCR
Manipulation in Gage Materials.
Adjustment
of the TCR to compensate for thermal effects is carried out by heat
treating
the cold rolled gage resistor foil. Both Constantan and Evanohm
can be adjusted over the range of interest, but the heat treating
response of
the two alloy is
different.
Cold
rolled Evanohm
foil can have its TCR adjusted over the range of about + 10 to – 40
ppm/°C by
heat treating in the 400°C to 600°C(750°F to 1100°F) temperature range.
A curve
showing the TCR resulting from a 4 hour heat treatment is shown in
Figure 8.
The TCR response is parabolic in shape, going through a minimum of
about – 40
ppm/°C near 500°C(925°F)
and crossing the zero TCR
axis twice.
Different
heats of Evanohm, which
exhib
slight differences in composition, all show similar behavior.
The parabolic curve shifts slightly from heat to heat, but remains
generally
the same.
The
mechanism responsible for this change in TCR is not fully understood.
The TCR
response for Evanohm
was empirically determined and
has been used in both strain gage and precision resistor manufacturing
for some
time. The most likely cause of the TCR shift is a phenomenon called
short range
ordering which is known to occur in many nickel-chromium alloys heated
into
this temperature range. When short range ordering occurs in a metal
crystal,
the random first-neighbor
arrangement of alloying
atoms on the crystal lattice is replaced by a specific arrangement over
a few
atomic distances. Short range ordering is difficult to observe
directly, so its
presence is usually detected indirectly by observation of properties
affected
by ordering, such as electrical resistivity.
[16] Superalloy for High
Temperatures, a Primer.
[17] Heat
Treatment: Principles and Techniques By
T. V. Rajan, C. P.
Sharma, Ashok Sharma
[18] EVANOHM®
Alloy , Carpenter
[19]
Hamilton
Precision Metals.
[20] The Bakerian
Lecture: An Account of Several New Instruments and Processes for
Determining
the Constants of a Voltaic Circuit (January 1, 1843)
[21]
Wheatstone bridge
[22]
Metal Foil Reasistance
Strain Gage,
Nanjing
University of Aeronautics and Astronautics,
[23]
Study of precision
alloys for the production of foil resistors G. A. Frank, V. V. Marakanov, Izmeritel'naya Tekhnika, No. 12, pp. 27–29,
December, 1984.
[24]
Experimental Stress Analysis:
Principles and Methods By
G. S. Holister
[25]
Theory of
Elasticity, S. Timoshenko, J. N. Goodier,
1951
[26]
Metal
and Alloy Bonding:
An Experimental Analysis, R. Saravanan
, M. Prema Rani
[27]
Deviations
from Matthiessen’s Rule
for the Electrical Resistivity of
Imperfect Metals, Robert J. Berry, 1972
[28]
Intorduction
to Solid State Physics, Charles Kitel,
seventh
edition, John Wiley, 1996.
[29]
Benjamin Solow, Metal foil resistor,
4,297,670
[31]
Method
for etching thin
foils by electrochemical machining to produce electrical resistance elements , Paul Rene Simon, 1976,
4,053,977
[32]
Method
for producing electrical resistance strain gages by electropolishing,
Post Daniel, 1961, 3,174,920
[33]
What
is Electropolishing?
[34]
AUTOMATED
ELECTROPOLISHING, V. Palmieri,
V. Rampazzo
[36] Vibration Proofing Metal Foil Resistors for Reliable Performance in Aerospace and Data Logging Applications