９-1 － 1

2. 1.3 GHz SRF Cavities

refrigeration cost, BCS losses and Carnot

There are currently two main types of 1.3

efficiency.

GHz SRF cavities that are in large scale use foraccelerators:
2.1. Tesla cavities

The Tesla cavity is 9-cell standing wave
structure of about 1 m length whose lowest TM
mode resonates at 1300 MHz, as seen in Fig. 2.
The shape of the cavity is influenced by manyfactors like to lower peak electric field the irisneeds to be rounded, and peak magnetic field
considerations requires rounding of the equator
region (larger diameter of cell), where themagnetic field is the strongest and needs to be

weakened significantly. Multipacting is also a
key factor that governs the overall rounded
contour of the cavity profile. If the shape is notrounded, one-surface multipacting will severely
limit

the

cavityperformance.

Moreover,elliptical arc segments of cell increase thestrength of the cavity against atmospheric load
and also provide a slope for efficient draining
and rinsing of liquids during surface etching
and cleaning in vertical orientation [3].

Fig. 3 1.3 GHz 9-Cell Niobium Superconducting
Tesla cavity assembly (Rey.hori©)
The largest accelerator using the cavities
with this design is the European Free Electron
Laser(Eu-XFEL).

It

is

a

2.1

superconducting Linac to accelerate electron to

17 GeV by using 808 1.3 GHz 9-Cell SRF
cavities. The cavity design performance for the
Eu-XFEL required an average Eacc ≥ 23.6 MV/m
at a Q0 ≥ 1 × 10^10 [4]. Design of the Eu-XFEL’s
1.3 GHz Tesla cavity assembly is shown in theFig. 4.

Fig. 2 1.3 GHz 9-Cell Niobium Superconducting
Tesla cavity [2]The cavity is equipped with its own Titanium
tank or jacket, a tuning system driven by astepper motor, a coaxial rf power coupler
capable of transmitting more than 200 kW, apickup antenna and two higher order mode
couplers, as seen in Fig. 3 and 4 [4]. It is cooledwith 2.0 K superfluid helium (He II) which isanother phase of liquid helium when cooled
below 2.17 K. This is considered as an optimal
temperature
range
consideringthekmFig. 4 Tesla cavity assemble at Eu-XFEL DESY
(top) and its cut view (below) [4]

９-1 － 2

3. Materials for SRF Cavity Assembly

2.2. Tesla-like cavities

There

were

some

modifications

andoptimizations made at KEK in the design ofTesla cavities and was named as Tesla-likecavity. The modifications are listed below andare shown in Fig. 5 [5]:• Improved support stiffness: Thick Ti end
plates improved the stiffness of the cavity
support structure. This is to suppress cell

shrinkage in the axial direction due to theLorentz force in a pulsed operation.
• Enlarged

beams

pipe

diameter:To

compensate for the weakened input
coupling due to the thick end plates.
• Enlarged input port diameter: To enlarge
the RF window for improved power
capability.

3.1. Niobium (1.3 GHz SRF Cavity)

Niobium (Nb) has a body-centred cubic (bcc)
crystal structure and a melting point of
2,468 °C. Among others, its low density incomparison to other refractory metals, its
corrosion resistance, its superconductivity
properties and its capability for forming
dielectric oxide layers, have made niobium amaterial of choice in many different fields [6].

For these reasons, niobium-based alloys are
often

used

in

aerospaceandmedicalapplications. However, the vast majority of Nb

reduced from raw ores are used as an alloying
element for steels. Moreover, because of its
strengthening effect at elevated temperatures,its principal commercial use is as an additive in• Optimization of cell shape: To decrease thesteels and super alloys like carbon steels, newratio of the surface peak magnetic field to

X-series of alloys for pipeline construction etc.
[7]. Niobium-titanium and niobium-tin alloys• Installation of magnetic shield inside theare also used as superconducting materials. For

the accelerating gradient.
helium vessel.

particle
accelerators,
theNiobium’s
superconductivity at 9.2 K makes it ideallysuited for the construction of SRF cavities forhigh energy physics.
3.2. Mining of Niobium

Niobium and tantalum always occur inassociation with one another in nature. The
main mineral, pyrochlore, is mostly processedby primarily physical processing technology toobtain niobium oxide, with a concentration from
55% to about 60%. The most important reserves
are calcium niobate from Brazil (about 80%) andCanada (about 10%), and stibiotantalite from
Fig. 5 Comparison between cavities structures
Tesla cavity at DESY (top) and Tesla-like at KEK(below) [5]West Australia. The second most importantsource of Nb producing ore is niobite (columbite)When–tantalite[(Fe,Mn)(Nb,Ta)2O6].
tantalum significantly exceeds niobium byweight, it is tantalite; and when niobium

９-1 － 3

significantly exceeds tantalum by weight, it iscolumbite. As a mineral with a ratio of
Nb2O5:Ta2O5 from 10:1 to 13:1, columbite occurs
in Brazil, Nigeria, and Australia, as well asother countries of Central Africa. Usually,

niobium is recovered when the ores areprocessed for tantalum [8].
The world’s largest niobium deposit, locatedin Araxá, Brazil, is owned by Companhia
Brasileira de Metalurgia e Mineração (CBMM).
The reserves are enough to supply current
world demand for about 500 years, about 460

million tons. The weathered ore mine contents
are between 2.5 and 3.0% Nb2O5. The mining iscarried out by open-pit extraction. The ore iscrushedandmagnetiteismagneticallyseparated from the pyrochlore. By chemical
processes, the ore is concentrated with regard to
its Nb content (50–60% of Nb2O5) [8].
3.3. Purification of Niobium

The melting and purification of Niobium isconducted by an electron beam furnace. It is anefficient and reliable methodology conducted in

vacuum of < 3E-3 mbar for the first melt and <1E-6 mbar for last melt to obtain high purity Nb[8]. During the melting process the molten
globules drop into water cooled copper crucible
to form an ingot. The material is pressed to form
and the ingot to be fed vertically for remelting
for purification under vacuum, as shown in Fig
6. During the melting process the gases andimpurities with lower melting temperatures
than Nb evaporates. Most of the times theimpurities on top of the ingot are higher thanthe bottom of the Ingot and is non-homogenous.
Although, most of the impurities are present on
the skin of the ingot which can be machined
away for a purer ingot.

Fig. 6 Schematic of drip melting in an electron
beam melting furnace (top) [8]; Intermediate Nb
ingot ready for re-melting [9] (below)
At CBMM, there are two furnaces that areused to produce pure Nb (high RRR). A Leybold

furnace with 500 kW nominal power and 50,000
liter per second pumping capacity melts the
Niobium from 40 – 50 kg/hr, and another 1.8
MW nominal power and 150,000 liters per
second pumping capacity melts with 90 – 120
kg/hr and pressures < 1E-3 mbar [6]. There areseveral companies that can produce high purity
refractory metals in larger quantities: ATI Wah
Chang (USA), Cabot (USA), W.C. Heraeus(Germany), Tokyo Denkai (Japan), Ningxia(China), CBMM (Brazil), H.C. Starck (Germany,
USA). A picture of electron beam melting
furnace at ATI Wah Chang is shown in Fig. 7.
The main impurities that significantly effects
the properties of the Nb are O, N, C and H. The
level of O, N and C should be < 10 ppm and H <1 ppm to achieve high residual resistivity ratio(RRR) > 300.

９-1 － 4

hence degassing is preferable in surface
preparation [10].

Hydrogen degassing is basically a form ofhigh temperature treatment of Nb, where
Niobium is placed in an electric or induction

furnace under a vacuum pressure of < 10-3 Pa.
The electric furnace used for the high-temperature heat treatment of SRF cavities isanultra-high-vacuum
furnacewithmolybdenum hot-zones of molybdenum (ortungsten) resistive heating elements, and thecavities are heated by radiation from theheating elements. The ultra-high vacuum inside
the furnace is created with cryo-pumps, an
Fig. 7 Electron beam melting furnace at ATI Wah
Chang Company [9]3.4. Post-purification

The cavity processing techniques such as
high-pressure rinsing, chemical polishing andelectro-polishing can instill impurities such ashydrogen, hence further purification isrequired. The commonly used technique ishydrogen degassing by annealing the cavities athigh temperatures.

example of electric vacuum furnace at KEK isshown in Fig. 8.

In the case of ultra-high vacuum induction
furnace, the hot zone is made of Niobium andthe cavity is treated by black-body radiation. It
makes use of Cu induction coil to instill eddy

current in the Niobium, to produce heat fromthe electric resistance of the material, as shownin Fig 9.

In many facilities like KEK (Tesla-like), Eu-

XFEL, LCLS II etc. hydrogen degassing is
conducted at 800 °C for 2-3 hours. However, thisbeing a form of annealing does degrade the3.4.1. Hydrogen Degassing
Hydrogen can dissolve in the bulk material atroom temperature at a rate of several mm/hr.

mechanical properties of the Niobium, which
will be shown in later sections.

The concentration of hydrogen tends to behigher near the surfaces, interfaces and crystal
defects. Higher concentration of hydrogen has
been known to cause “Q-disease” in SRF cavities
where the Q0 of the cavity degrades
significantly. To avoid this there are two ways:
either cool the cavity rapidly in the cryostat
through 75 K < T < 150 K region to avoid
precipitation of ε-phase or degas the cavities athigher temperatures > 500 °C under vacuum
conditions. Fast cooling is not a permanent fix,

９-1 － 5

3.5. Various Grade of Niobium

The Niobium material in SRF community is
usually classified base on two categories: RRR
and the Grain size.
3.5.1. Residual Resistivity Ratio (RRR)
It is a common indicator to the level of purityof a material. It is defined as the ratio of theresistivity of a material at room temperature
293 K or 300 K to the resistivity of a material at
4.21 K. The resistivity of a general metals at low
temperatures can be defined as:

Fig. 8 Electric furnace at KEK for hydrogendegassing at KEK(2)

ρ = ρ!"# + ρ(T) + ρ$

Where first term is residual resistivity at T =0 𝐾𝐾 ,
caused mainly by electron impurity
scattering and scattering on lattice defects(𝜌𝜌%&' = 𝜌𝜌()* + 𝜌𝜌+&, ). Second term ρ(T) refers toelectron-phonon

scattering

and

𝜌𝜌)

is

responsible for increase in resistivity due tomagnetic field. For recrystallized Nb, the latticedefects are quite small and in the absence ofmagnetic field, consists only of electron–
impurity

scattering

andelectron–phonon

scattering contributions [8].
ρ(293 K)ρ(9.3 K)ρ(293 K)
RRR (normal conductors) =ρ(4.2 K)RRR for Nb =(1)

For SRF cavities high thermal conductive
wall (at least 10 W/m-K at 2.0 K) is necessary to

guide dissipated RF power to superfluid helium
coolant, hence high purity material is necessary.
Examples of thermal conductivity variation
with respect to RRR for Nb is shown in Fig. 10.

Fig. 9 Induction furnace at Jefferson lab forhydrogen degassing [11]９-1 － 6

which FG Nb is manufactured at Tokyo Denkai
Company is shown in the Fig. 11. The smaller

grain size was considered necessary to haveisotropic properties, good formability and to
avoid excessive rough surface of cavity (called asorange peel surface effect), which is due to non-uniform deformation of larger grains [12].
Research on SRF cavities manufactured with
FG Nb has been carried out extensively andFig. 10 Thermal conductivity of various grades of
Nb with respect to temperature [8]For pure Nb the RRR can be categorized inthree ranges: Low (< 100), Medium (100 to 300)

some of the renowned research on determining
the mechanical properties of FG Nb has been
conducted by G. R. Myneni et al., Nakai et al.
etc [13, 14].

and High (> 300). To meet the ILC specification
the SRF cavities usually must be in high RRR
range, hence our focus will be basically on thegrain size of the Niobium for SRF cavity.
3.5.2. Grain Size
The structure of material are formed byindividual crystalline structures known as‘Grains’ and grain boundary is the region
separating two grains in the same phase. The
size, structure, orientation of the grains in a
metal or metal alloys is dependent on theprocesses that are employed to manufacture themetal like forging, rolling, casting etc. For Nb,
the grain size is divided in two categories; Fine
Grain (< 50 µm) and Large grain (few mms to
cms).

Fig. 11 Fabrication of FG Nb sheets at Tokyo
Denkai Company [8]Large Grain Niobium (LG Nb)
Large Grain (LG) Nb was developed as a clean
and low-cost alternative, where the LG Nb Ingot
is directly sliced into disks, rather than cutting

Fine Grain Niobium (FG Nb)
After the Nb is extracted from mines, it ismelted by electron beam melting method undervacuum to remove interstitial impurities such
as H, C, O and N to form it in an ingot, which isin LG Nb form [1]. The fine grain (FG) Nb isthen manufactured by a series of forging,rolling, annealing and etching process reducing
the ingot in sheet forms, producing grains withsize < 50 µm [1]. The outline of the process without disks from Nb sheets. The omitted processes
in the case of LG Nb manufacturing procedureis shown in Fig. 12 [12]. The grain size of LG Nb
usually varies from a few mms to several cms,
as seen in Fig. 14, due to which it has
anisotropic mechanical properties causing its
0.2% Yield Strength (Y.S) and Tensile Strength(T.S) to sometimes fall short of the mechanicalproperty requirement set for 9-Cell 1.3 GHz
SRF cavities. W. Singer et al., Zhao et al., Enami

９-1 － 7

et al., Yamanaka et al., has conducted in depth
research on determining the mechanicalproperties of the LG Nb at various
temperatures and strain rate ranges [15-18].

Fig. 13 Frame format of multi-wire sawing (top);
Multi-wire sawing machine and Slicing of Ingot(down) [19]Fig. 12 Manufacturing step reduction in
fabrication of LG Nb sheets at Tokyo Denkai
Company [12]Fig. 14 Directly sliced LG Nb disks [9]3.6. Titanium

Direct Slicing of LG Nb
Direct-slicing or multi-wire sawing techniqueisawell-establishedtechniqueinThis is a material of choice for the helium
jacket of the SRF cavity. The main advantage ofthis material is its coefficient of thermal

semiconductor industry for silicon wafers. The

expansion, which is lower than the well-known
vessel materials like Stainless steel (SUS304

distance between them is decided by the grooves

and SUS316) and similar to Nb. Lower

wires are placed parallel to each other and theon the rollers. The wires move at high speed,
and an abrasive liquid compound iscontinuously sprayed on them, as seen in Fig .13[19]. This process is highly cost-effective andproduces clean surfaces that can applied forlarge scale production of LG Nb discs for ILC, if
necessary. The ingot is slowly lowered andpressed against the wires and the whole process
can take 2-3 days to complete.

coefficient of thermal expansion which issimilar to Nb, is necessary to suppress the highstress generated at the interface Nb SRF cavity
and the jacket welded section, to avoid failure ofwelds during cooldown from 300 K to 4.21 K. Ti
has also been known to retain its strength andductility at cryogenic temperatures. Also, thismaterial has sufficient mechanical strength tobe considered for the helium jacket for SRF
cavities. For Tesla-like cavity, two types ofcommercially available pure Ti can be used, JISclass 1 and class 2. Another well-known
application of this material is in aerospaceindustry. There it is used as a fuel tank material
to

store

conditions.

９-1 － 8liquidhydrogenatatmospheric3.7. NbTi AlloyTo

It is an alloy of Niobium and Titanium andmostly used as a type II superconductor for

NbTi’sinvolved in the cavity design at room andmechanicalin liquid helium temperatures. Moreover,the mechanical properties of welded joints

strength to Ti at high annealing temperature.

like Nb-Nb weld, Nb-Ti weld, Nb-NbTi, Ti-

For Tesla-like cavity assembly, instead of NbTi

NbTi welds and TI-Ti welds.

pure Ti is used for end plates.

• Stress and buckling analysis of the cavity
assembly using CAE software at maximum

Pressure Vessel Compliance for SRF
cavitiesAs

discussed

beforeSRF

for• Mechanical properties of the materials

properties are known to be on par or greater in4.

documentation• Description of the SRF cavity assembly.

manufacture conical discs for the end-group ofcavities.

thecertain steps have to be followed:

assembly for Eu-XFEL employs this material to
type

for

authorities of high-pressure gas safety basicallysuperconducting magnets. The Tesla cavity

Tesla

preparecavities

allowable working pressure and tuner
displacement.

are• Cavity fabrication information.

constructed of Niobium and are cooled to• Pressure test and examination reports.

temperatures of 4.21 K or below, to achieve high• Documentation to summarize above items

quality factor. To achieve these temperatures

to be submitted to the high-pressure gas

the cavities are bath cooled with liquid orsafety authority.

superfluid helium which is stored between the

Nb SRF cavity and its Titanium jacket, hence it
is considered as a pressure vessel, as seen in
Fig. 15 [20]. The materials such as Niobium,
Titanium and NbTi alloys are not approved forpressure vessel design due to the lack of code
data in high pressure gas safety codes
throughout the world, for room temperatureand cryogenic temperatures (at 4.21 K or
below). Hence, to operate the SRF cavity
assembly it is necessary to show certain level ofsafety which is greater than or at least equal toacceptable standards to the high pressureauthorities for cavity operation [20].
Niobium tends to be ductile at room
temperature, but the ductility decreases atliquid helium temperatures < 4.21 K. Hence,
one must be careful in determining the stresses
generated in SRF cavity during cavity operationand cooldown. Titanium has almost similar
ductility at room and cryogenic temperatures.

Fig. 15 Illustration of a 1.3 GHz Nb SRF cavity
assembly (Top) [20]; 1.3 GHz SRF cavity assemblyfor ILC [2]９-1 － 9

5.

Methodology to Evaluate Mechanical
Properties• Stress: It is the force acting on the unit
surface area. In this case of Fig. 16, thestress acting on its cross-sectional area is

5.1. Why mechanical properties are important?

𝐹𝐹/(𝐿𝐿 × 𝑊𝑊).

As discussed before, the SRF cavity is housed• Strain or Longitudinal strain (𝜀𝜀): It is thein a Titanium jacket and is considered as apressure

vesselaccordingJapanese

ratio of change in length to the actual

andlength of acompression.

worldwide high pressure gas safety authorities.

Hence, the mechanical properties for Nb, Ti,

NbTi and their respective welded joints has tobe determined at room and in liquid heliumtemperatures, to determine the robustness ofthe cavity assembly design.

materialε=intension∆LLor(5 − 1)

Here 𝐿𝐿 is the original length of the materialand ∆𝐿𝐿 is the change in the original length, as

in Fig.16. If the material is in compression force
the strain will be negative.

5.2. Methodology• Young’s modulus (E): It measures the

5.2.1. Terminology

stiffness of the material in tension and is

Tensile testing is a methodology where athe ratio of tensile stress and axial strainmaterial is subjected to uni-axial tension untilof a material in its elastic region (see Fig.

failure, as shown in Fig. 16, to obtain16).

mechanical properties, such as:

E=Stress(in Elastic Region)
Strain(5 − 2)• Poisson’s Ratio (𝜈𝜈): When a material is intension it extends in axial direction while
contracting in transverse direction called

as transverse strain. The absolute value ofthe ratio of longitudinal strain to thetransverse strain is called as Poisson’s
ratio, as in Fig 16.
ν=T

ΔL/L
Longitudinal strain
T=T
T
−ΔW/W
Transverse strain(5 − 3)• 0.2% Yield Strength (Y.S) or 0.2% Proof
Stress: This point indicates the limit of theelastic behavior of a material. It isdetermined by constructing a line parallelto the elastic region of the material by an
offset of 0.2% strain from the origin in a

Fig. 16 A rectangular bar under tensile orcompressive force (top); General stress-strain
curve for a metal under tension (below)

stress-strain curve. The intersection of the
0.2% offset line with the stress-strain curve

９-1 － 10

is the 0.2% Yield strength of the material,

adoptedas seen in Fig. 16.

throughout

countries.

• Tensile Strength (T.S) or Ultimate tensile
strength (UTS): It is the stress at thehighest point of the stress-strain curve of amaterial, as seen in Fig. 16. At this point
necking phenomenon starts happening for
ductilematerials

andinstantaneous

rupture for brittle materials. This point iscloser to Y.S for brittle materials.
• Elongation: It is a measure of the ductilityof a material. It is often defined as thepercent ratio of the difference of length of
the straight section of the tested material
at failure to the original length of thetested specimen. If L is the original lengthof the tested specimen and ∆L- is theextended length of the specimen after
tensile test, as in Fig. 16, the elongation is;Elongation (%) = 100 × ∆L- /L,

5.2.2. Tensile testing standards(5 − 4)The materials are usually tested according tostandards set throughout the world. Thesestandards lists the methodologies to be adopted
to conduct the tensile tests like the dimensions

by

most
the

of

world,

thecountries

around165

5.3. Instrumentation

5.3.1. Tensile testing machine
At KEK, Shimadzu’s Autograph AG-5000C

tensile test machine is utilized to conducttensile tests at room and cryogenic temperature(in liquid helium). This machine is rated toprovide maximum force of ±50 kN and amaximum stroke of 1.5 m. At KEK, the crosshead speed (pulling rate) is kept constant at 2

mm/min for all tests with a nominal strain rateof 4.4E-4 s-1.
5.3.2. Strain Gages and Extensometers
Strain Gages: It is a device whose resistancevaries with respect to applied force. It works on
the principle of change in electrical resistance ofa metal when it deforms. For example, if a
metallic wire is pulled, its cross-sections
reduces and its length increases causing theresistance of the metal to increase, as seen in
Fig. 17.

of the specimens, extensometers standards,
strain rates for tensile tests etc.
• ASTM (American Society for Testing andMaterials): ASTM E/E8M – 13a defines thestandard test methods for tensile testing of
metallic materials. It is mainly employedin USA.
• JIS (Japanese Industrial Standards): JIS Z
2241 outlines the method of tensile testingfor metallic materials at room temperature
and JIS Z 2277 for tests in liquid helium.

• ISO(International

Organization

forStandards): ISO 6892-1 defines the method

Fig. 17 Strain gage operating principle [21]The strain gage transforms the strain applied
into proportional change in the resistance, andthe relationship between applied strain ε =∆L/L and the relative change in resistance of astrain gage is described by,of tensile testing at room temperature. It is

９-1 － 11∆L∆R=k= k. ε,LR.

(5 − 5)Here k is the gage factor of the strain gage. It

and is available for wide range of gage length

expresses the gage sensitivity. Most of thegeneral-purpose strain gages uses copper-nickel(10 – 200 mm).

or nickel-chromium alloys for the resistive
elements.
Strain gages are manufactured with various
resistances, the value 120 Ω is the most widelyused and proven one. For measurements atroom

temperature

and

in

liquidheliumtemperatures at KEK, mostly foil strain gage
type are employed, as seen in Fig. 18. These arebonded on the specimens and the coefficient ofthermal expansion of the strain gage andadhesive should be closer to the material being
tested, when there is large variation intemperature.

Fig. 19 Clip-on type extensometer for room
temperature tensile testing
5.3.3. Bridge box
It is a device that forms a Wheatstone bridge
for the strain gages that are attached on thetensile testing specimens. The device shown in

Fig. 18 Thin foil type strain gage [22]Extensometers: It accurately measures theaverage strain in the gage section (straightsection) of a tensile test specimen, as seen in
Fig. 27. Clip-on extensometers are widely used

Fig. 20 is a bridgebox from Kyowa®, it consistsof 120 Ω resistors that can form a Wheatstonebridge.

and doesn’t require any kind of independent
mounting device. They are used for testing
metals, plastics etc. over a wide range oftemperatures and can also be used in cryogenic
temperatures. Clip-on extensometer use a pairof knife edges located on the specimen to define
the gage length, held with spring loading or
clipping mechanism, as seen in Fig. 19. At thegage length the circuit is balanced and there is
not output voltage, and when the material is put
under tension the knife edge moves with thegage length to produce output voltage. This typeof extensometer can measure strains upto 100%

Fig. 20 Kyowa® DB-120A bridgebox [23]Wheatstone Bridge: Wheatstone bridge is acircuit that measures the unknown resistancecompared to known resistance values in anelectric circuit, allowing measurement of very

９-1 － 12

low resistances down to milli-ohms range. It has
4 resistors connected in a series-parallel
arrangement as seen in Fig. 21, two diagonally
opposite terminals are used to supply excitation
voltage to the circuit and the other two are used
to measure the output voltage of a circuit. The
output is usually expressed in millivolts per
input voltage, as seen in Equation 5-6.

and 𝑅𝑅2 = 𝑅𝑅3 = 𝑅𝑅2 , and if the resistance to vary,

the bridge will be detuned and an output
voltage will appear.

With the assumption that the variation inresistance ∆𝑅𝑅( is much smaller than theoriginal resistance 𝑅𝑅( , which is always true formetal strain gages, second order effects can bediscarded. We get the relationship [22],V/ 1 ∆R0 ∆R 1 ∆R 2 ∆R 3
= `
−
+
−
a,
V# 4 R0R1
R2
R3(5 − 8)V/ k= [ε − ε1 + ε2 − ε3 ],V# 4 0(5 − 9)Substituting eqn. 5-5 in 5-8, we get the relation
between voltages and the strain developed,

Different Configuration of Strain Measurement

The strain gages can be attached in various
arrangements

according

to

the

type

of

measurement. The most commonly used ones
are listed below• Quarter

Fig. 21 Representation of Wheatstone bridge
circuit
V/
R0
R2
=
−
,
V# R0 + R 1 R 2 + R 3

thisother 3 branches are fixed resistors of samevalues (usually 120 Ω), as shown in Fig. 22.
is widely used for stress-strainItmeasurement.

of same value the circuit is balanced and theoutput is 0 V, and we get a relation between

Although,

if

there

is

temperature change and/or bending strain
expected during measurement, it cannot be

resistances of the circuit:negated. The output voltage with thisR0 R 2=,
R1 R3

circuit will be,(5 − 7)

In cases where strain gages are used, theinstruments measuring the output ofareIn

attached to a branch of the bridge while the(5 − 6)the output voltage. When all the resistance arebridgessystem:configuration, upto 4 strain gages are

Where 𝑉𝑉' is is the supply voltage and 𝑉𝑉4 is

Wheatstonebridgeequippedwithbalancing elements, to allow to show theindication to be set to zero for the initial statekV/ = V# (ε. )4Here S.G1 produces strain 𝜀𝜀. .

[22].
For strain measurements the resistances in
the opposite arms must be equal 𝑅𝑅0 = 𝑅𝑅1 = 𝑅𝑅0

９-1 － 13(5 − 10)out), when strain gages are bonded on front andrear of a tensile test specimen.

Fig. 22 Quarter bridge system with one strain gage
(S.G 1) attached to a branch• Half bridge system: In this configuration, 2
branches are connected with a strain gageand the other 2 branches are fixedresistors. There are two systems that canbe configured with this configuration:
active-dummy and active-active. In thecase of active-dummy configuration, one
strain gage serves as a dummy gage toeliminate the effect of temperature
variation, as seen in Fig. 23a. Active gageis attached to the specimen which will be
under tension and the dummy gage is
attached to a dummy specimen made of thesame material. When both specimens are
subjected to large temperature variation(like cooling a specimen from 300 K to 4.21K), the specimens will undergo equal
contraction or expansion, hence the strain

Fig. 23 Half bridge configuration: (a) Activedummy configuration (S.G 1 is active and S.G 2 isdummy); (b) active-active configuration (bothgages are active).
• Full bridge system: In this configuration, 4
strain gages are connected, one to eachbranch of the Wheatstone bridge. Thisconfiguration allows for both temperature

instilled from expansion/contraction will be
negated. The output voltage with thiscompensation and elimination of othercircuit will be,kV/ = V# (ε. )4strain like bending strain, simultaneously.
The output voltage with this circuit will be,(5 − 11)Here, for the case in Fig 23a, S.G1 produces
strain 𝜀𝜀. and S.G2 produces no strain during

tensile testing. In the case of active-active
setup, in Fig. 23b, the output voltage is doubled,
and the bending strain is negated (or averagedk
V/ = V# (ε. )2(5 − 12)Here, S.G1 and S.G2 produces strain 𝜀𝜀. andS.G3 and S.G4 produces no strain during tensile

testing, and the output voltage is doubled, as
seen in Fig. 24.

９-1 － 14

Fig. 25 Bock diagram of basic elements of strain
gage instrumentation system [24].
At KEK, usually Kyowa® strain amplifiers
are used to supply bridge voltage andamplification of the bridge output voltage, anFig. 24 Full bridge configuration: (a) Activedummy configuration (S.G1 and S.G2 are active
and S.G3 and S.G4 are dummy)

example of it is Kyowa® DPM-911B, as seen in
Fig. 26. They usually have high resistanceagainst external noise. These have a gage factor

5.3.4. Strain Amplifierof 2 and can provide bridge excitation voltage of

The output voltage from a Wheatstone bridge
circuit is usually very small, especially in elastic

2 V and 0.5 V. They are compatible to bridge
resistance of 60 to 1000 Ω. It can output

regions of a metal. Hence, some sort of electricalmaximum voltage of 10 V with maximum strain

an acceptable level for measurement andinstrument, the internal gain can be set from

amplification is required to bring the signal torecording, as shown in block diagram in Fig 25.
The individual components should be fixedof 9999 micro-strains, i.e 1% strain. In this
200x to 2000x.

according to the nature of the strain being
measured, type of information and mutualcompatibility of the systems. Consideration
should be given to the required frequency
response, the input and output impedances of
the units in the system, the signal amplitudes
being

dealt

with,

and

the

accuracyofmeasurement desired [24]. Most commerciallyavailable strain amplifiers combine most if not
all the components shown in Fig. 25 in a single
unit.

Fig. 26 Kyowa® DPM- 911B strain amplifier

９-1 － 15

5.4. Tensile testing

5.4.1. At room temperature
Tensile testing at room temperature isnecessary as the cavity is fabricated at room
temperature conditions. The materials shouldhaverequisite

strengthtohandletheprocedures involved in cavity fabrication, suchas press forming, trimming, welding etc.
Moreover, once the cavity is assembled with its
Ti tank, it should be able to handle theconditions set by Japanese high-pressure gas
safety authority for high pressure vessel. The
materials for cavity assembly such Nb, Ti and
NbTi are known to be weakest at room
temperature conditions.
The setup for room temperature tests consistsof tensile test machine, strain amplifier, dataacquisition system, tensile test specimens withstrain gages bonded on it or tensile test
specimen with extensometer attached to it, asseen in Fig. 27 and 28.

Fig. 28 Illustration of room temperature tensile test
setup (top) and a pic of tensile test setup at KEK(below)
5.4.2. At cryogenic temperatures
Tensile testing in liquid helium is necessary
as the SRF cavity assembly materials such as
Nb, Ti and NbTi operational temperature is 2.0
K. Moreover, the mechanical properties ofmetals changes drastically from room
temperature conditions (300 K) to cryogenic
temperatures such as 77 K (liquid nitrogen) and4.21 K (liquid helium). For testing in liquid
helium, a custom-built cryostat, as shown in
Fig. 29 is used where tensile test specimen are
dipped in liquid helium during the tensile test.
The cryostat is vacuum jacketed in which three
specimens can be tested for one cycle ofcooldown, with one dummy specimen. The
fixtures for the specimens are made of Tungsten
and connected by a GFRP (Glass fiber) rod toFig. 27 Tensile test specimens used for tensile
testing at KEK: for testing in liquid helium (top)and room temperature testing and a pic of tensile
test specimen with bonded strain gage (below)

the top of the cryostat. This GFRP rod can beconnected to the load cell of the tensile testingmachine to provide tensile force on thespecimens to be tested which are fixed on thebottom tungsten plate of the cryostat. The

９-1 － 16

cryostat is filled with liquid helium before
placing it on the tensile testing machine.

6.

Mechanical Properties

6.1. Niobium

The mechanical properties of various gradesof Niobium from room temperature to liquid
helium temperatures are discussed in thefollowing sub-sections. The required properties
includes yield strength (Y.S), tensile strength(T.S), Young’s modulus (E) and elongation.
6.1.1. Fine Grain (FG) NiobiumThis material has an isotropic property withadequate Y.S and T.S to clear the high-pressure
regulations set throughout the world for SRF

cavities (crab cavities to high frequency RF
cavities). It’s mainly, as explained before due tosmaller and randomly oriented grains. The

mechanical property of FG Nb from 300 K to
4.21 K was studied in detail by H. Nakai et al.
at KEK (Japan). They annealed the Nb
specimens to 750 °C before testing [14].
At liquid helium temperatures, an interesting
phenomenon occurs during tensile test of ametal is the serrated yielding. Serrated yielding
is usually seen in high purity material in liquid
helium temperatures, an example shown in Fig.
31. They are noticeable in terms of sudden load
drop accompanied with large increase in strainof a material. This phenomenon has been
known to occur due to thermal instabilities

during plastic deformation [25]. This makes thedetermination of 0.2% Y.S in liquid helium quitedifficult, as the serrations can be as large as±100 MPa, as seen in Fig. 31.

Fig. 29 Schematic view of cryostat with tensile
testing machine for liquid helium testing (top) [17];Cryostat with tensile testing machine for liquid
helium dipped tensile testing at KEK (below)

９-1 － 17

Fig. 30 Examples of Stress-strain curves for FG Nb
at room temperature [5]Fig. 32 Tensile strength of Niobium measured withdifferent type of test pieces [14]Fig. 33 Yield strength of Niobium at various
temperatures [14]Fig. 31 An example of stress-stroke curve for FG
Nb in liquid helium
From literature survey, at room temperature
the FG Nb is known to have T.S ~ 150 MPa, andin liquid helium (at 4.21 K) the T.S is known to
be in the range of 800 to 900 MPa, as seen in
Fig. 32. The Y.S of the material is usuallyaround 50 MPa at room temperature andapproximately 400 to 600 MPa in liquid helium,
as seen in Fig 33. The elongation of the material
at room temperatures is > 30% and < 10% in
liquid helium, which is expected as thematerial’s

ductility

reducesinFig. 34 Young’s modulus of Niobium with respect
to temperature [14]coldertemperatures, as seen in Fig. 35. The elongationof > 30% in room temperature is necessary topress form the disks into half cells.

９-1 － 18

6.1.2. Large Grain (LG) NiobiumThis material was developed as a clean andcost effective alternative to FG Nb but is known
to have anisotropic properties. It’s mainly
because of larger grain size (in few mms to cms).
Anisotropy itself is not a major issue but
sometimes the material has inadequate Y.S and
T.S to clear the high pressure regulations set
throughout the world for SRF cavities. The
mechanical property of LG Nb at room
temperature has been studied in detail by W.

Fig. 35 Elongation of Niobium with respect totemperature [14]G.R. Myneni et al. also determined themechanical properties of FG Nb from 4.21 K to300 K range [13], and at different annealing
temperatures, as shown in Fig. 36. As expected,

the material properties at room temperature

deteriorate at higher annealing temperaturesfrom 600 °C to 800 °C for 6 hours. The least
deterioration in mechanical properties wasfound to be at 600 °C without any loss inhydrogen degassing performance [25]. However,the standard for cavity heat treatment orhydrogen degassing is at 800 °C for 2-3 hours inmost of the laboratories dealing with SRF
cavities, as it is beneficial with flux expulsion.

Singer et al. and Zhao et al. [15, 16]. At KEK, in
depth studies on LG Nb were conducted by
Enami et al. and Yamanaka et al. at room andin liquid helium temperatures [17, 18].
Results summarized by Zhao et al. showed
the properties of LG Nb had a large variation inmechanical properties, as seen in Fig. 37. The
Y.S varied from 66 to 124 MPa and T.S varied
from 84 to 136 MPa. Moreover, the Young’s

modulus also fluctuated from 59 to 127 GPa. At
4.21 K temperature, Yamanaka et al. showedthat the average tensile strength of LG Nb wasapproximately

611

MPa

with

standard

deviation of 133 MPa [18]. The advantage thismaterial has is with its elongation which wasalways larger than 30% and sometimes as large
as 92%, at room temperature.

Fig. 36 Behavior of FG Nb at various annealing
conditions [25]９-1 － 19

Table 1 Mechanical properties of FG and LG Nb atroom temperature
Material

Y.S
[MPa]

T.S
[MPa]

Elongation
[%]

FG Nb
~50
~150
~40
LG Nb
66-12484-136> 30---------------------------------------------------------------Tesla-like
> 39
> 120
> 30
Eu-XFEL
> 50
> 140
> 30

Table 2 Mechanical properties of FG and LG Nb inliquid helium

Fig. 37 Stress-strain curves for some specimen
tested by Zhao et al. [16]Material

6.1.3. Comparison of FG and LG Nb with SRF
cavity strength requirement
The mechanical properties of both FG and LG
Nb were shown in previous two sections.
Basically, the mechanical properties of FG Nb
are isotropic and for LG Nb they are anisotropic
due to the grain size. FG Nb is the standard
material that designers have used to carry out
structure analysis of the SRF cavity design andis approved worldwide for SRF cavity operation.
Hence,

any

newmaterial’s

mechanicalproperties should be comparable or better than
FG Nb. The data summarized in Table 1 and 2
are for comparison between FG and LG Nb atroom temperature properties. At 4.21 K, thedata presented here is from the internal testing
conducted at KEK on FG and LG Nb [18]. The
requirementofTesla-likeandEu-XFELmechanical strength criteria is also presented
in the tables. As Nb is weakest at room
temperature, most of the facilities focus on the
Nb’s
mechanicalproperties
temperature as a requirement.

at

Y.S
[MPa]

T.S
[MPa]

Elongation
[%]

FG Nb
~ 500
800 - 900
~7LG Nb
400 - 800~6---------------------------------------------------------------Tesla-like> 300

6.2. Titanium

Research on the mechanical properties ofpure Ti has been conducted in detail in the past.
At

KEK,

Nakai

et

al.

determinedthemechanical properties of pure Titanium JIS
class 1 and class 2 from 300 K to 4.21 K
temperature, as shown in Fig. 38 to 41. At room
temperature,thismaterial

has

highermechanical strength compared to Nb. The
elongation of this material, as described before
in section 4.1, remains uniform throughout theoperational temperature range and can be seenin Fig. 41. They also determined properties ofwelded joints like Nb-Nb, Nb-Ti, Ti-Ti, NbTi-Ti
and NbTi-Nb which can be seen in Ref. 14.

room

９-1 － 20

Fig. 38 Tensile strength of Titanium with respect totemperature [14]Fig. 41 Elongation of Titanium with respect totemperature [14]K. Mukugi et al. also determined theproperties of pure Ti and electron beam welded
Ti-Ti joints and TiG joints for thesuperconducting proton Linac at JAESRI, as
shown in Fig. 42 and 43. The material wascommercially available JIS class 1 and class 2
pure Ti [26]. The mechanical properties of pure
Ti were comparable with the data summarized

Fig. 39 Yield Strength of Titanium with respect totemperature [14]by Nakai et al. The mechanical strength of the
Ti-Ti TIG welds is comparable to pure Ti, as
seen in Fig. 42, and there is a tolerable level ofdegradation in mechanical properties for Ti-Ti

EBW weld, approximately < 15% at 4.21 K, canbe seen in Fig. 43.

Fig. 40 Young’s modulus of Titanium with respect
to temperature [14]Fig. 42 Tensile strength and Yield strength ofTitanium with respect to temperature [26]９-1 － 21

Fig. 43 Yield strength of Titanium base metals andwelded joints with respect to temperature [26]Fig. 45 Yield strength of NbTi alloy at room
temperature [14]6.3. Nb-Ti Alloy

H. Nakai et al. also determined the properties
of NbTi alloys which are used to manufacture
end plates of Tesla shaped cavities and end

flanges for Tesla-like cavity, as shown in Fig. 44- 47. It being an alloy has better mechanicalproperties than Nb and Ti, hence is acceptablefor fabrication of endplates of Nb cavities.

Fig. 46 Young’s Modulus of NbTi alloy at various
temperatures [14]Fig. 44 Tensile strength of NbTi alloy at various
temperatures [14]Fig. 47 Elongation of NbTi alloy at various
temperatures [14]９-1 － 22

7.

Recent Developments in Niobium
Material Technology
Recently, a new material has been developedand introduced to SRF community called as
Medium Grain (MG) Niobium. Its grain size is

200 to 300 µm, with occasionally 1-2 mms
grains. This material is manufactured byforging and annealing of LG Nb ingot and thendirectly slicing the forged Ingot to produce MG
Nb disks. This methodology has the potential tosubstantially reduce the cost of the Nb, andmoreover direct-slicing produces clean surfaces,

hence it is cost-effective and a clean technology.
This material is expected to have isotropic

mechanical properties closer to FG Nb and isbeing determined at KEK. The initial results
looks promising, as mechanical properties arecloser to FG Nb at room temperature [27].
Moreover, T. Dohmae et al. fabricated a single
cell cavity and has been able to achieve theaccelerating gradient of 38 MV/m at quality
factor of 1.5 × 100. [28].

REFERENCES[1] A. Yamamoto et al., “Ingot Nb based SRF
technology for the International Linear Collider”,
AIP Conference Proceedings 1687, 030005 (2015);
doi:10.1063/1.4935326[2] The International Linear Collider: A Global Project,
arXiv:1903.01629 [hep-ex][3] Hasan Padamsee 2001 Supercond. Sci. Technol. 14
R28[4] B. Aune et al., “Superconducting TESLA Cavities”,
Phys. Rev.ST Accel. Beams 3, 092001 (2000)[5] E. Kako et al., “Cryomodule tests of four Tesla-likecavities in the superconducting RF test facility at
KEK”, Phys. Rev. ST Accel. Beams Vol. 13, 041002(2010); doi: 10.1103/PhysRevSTAB.13.041002[6] Lourenço de Moura et al., “Production of high purity
Niobium ingot at CBMM”, AIP Conference
Proceedings1352,
69(2011);
https://doi.org/10.1063/1.3579225[7] Ricker, R. and Myneni, G. (2010), Evaluation of thePropensity of Niobium to Absorb Hydrogen During
Fabrication of Superconducting Radio Frequency
Cavities for Particle Accelerators, Journal of
Research (NIST JRES), National Institute ofStandards and Technology, Gaithersburg, MD,[online],https://doi.org/10.6028/jres.115.025(Accessed August 2, 2021)[8] W. Singer, “SRF Cavity Fabrication and Materials”,
arXiv:1501.07142[physics.acc-ph];doi:10.5170/CERN-2014-005.171[9] R.A. Graham, “RRR Niobium manufacturingexperience”, AIP Conference Proceedings 927, 191(2007); https://doi.org/10.1063/1.2770692[10] G.R. Myneni et al., “Elasto‐Plastic Behaviour ofHigh RRR Niobium: Effects of Crystallographic
Texture,MicrostructureandHydrogen
Concentration”, AIP Conference Proceedings 671,
227 (2003); https://doi.org/10.1063/1.1597371[11] P. Dhakal et al., “Design and performance of a new
induction furnace for heat treatment ofsuperconducting radiofrequency niobium cavities”,
Review of Scientific Instruments 83, 065105 (2012);
https://doi.org/10.1063/1.4725589[12] P. Kneisel et al., “Review of ingot niobium as amaterial for superconducting radiofrequency
accelerating cavities”, Nuclear Instruments andMethods in Physics Research A 774 (2015) 133–150;
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[14] H. Nakai et al., “Tensile test of materials at low
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Soc. Japan) Vol. 48 No. 8 (2013)[15] W. Singer et. al., “Development of Large Grain
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in liquid helium”, Teion Kogaku (2021), undersubmission.
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GbbH, Darmstadt

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[23] https://www.kyowaei.com/eng/product/category/bridge/db120a/index.html[24] Allen G. Piersol et al., Harris' Shock and Vibration
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