PS 9 2016 WWW.pdf


65PRZEGLĄD  SPAWALNICTWA       Vol. 88  9/2016

Calculation of Thermodynamically Optimized 
Temperature-/Time-Cycles 
in Nickel-Based Brazing Joints

Optymalizacja temperatury/cykli czasowych 
w lutowaniu twardym poprzez obliczenia termodynamiczne

Prof. Wolfgang H. Müller; Dipl.-Ing. Benjamin Schmorl – TU Berlin, Fachgebiet Kontinuumsmechanik und Materialtheorie, 
Institut für Mechanik;
Prof. Johannes Wilden; Oliver Stahn, M.Sc.– Hochschule Niederrhein, Krefeld.
Autor korespondencyjny/Corresponding author: oliver.stahn@hs-niederrhein.de

Streszczenie

Lutowanie materiałów z wykorzystaniem lutów na osno-
wie niklu jest już procesem znanym i opanowanym. W tym 
kontekście tworzenie się w złączu kruchych faz jest istot-
nym problemem. Wzrastająca ilość tych faz wpływa nega-
tywnie na własności mechaniczne połączenia. Efekt ten 
zwiększa się jeżeli lut produkuje się w postaci taśmy i ilość 
kruchych faz jest wyraźnie większa. Uniknięcie formowania 
się kruchych faz zmusza do stosowania małych szczelin 
lutowniczych. Stosowana dodatkowo obróbka cieplna rów-
nież częściowo redukuje ilość kruchych faz. W przedstawia-
nej pracy zastosowano symulację termodynamiczną w celu 
określenia przemian fazowych i procesu dyfuzji w złączu lu-
towanym. Symulacje wykonano przy pomocy Thermo-Calc 
i TC Dictra oraz modelu analitycznego. Sprawdzano różne 
cykle temperatura/czas aby ustalić ich wpływ na tworzenie 
kruchych faz. Wykonano dodatkowo wybrane badania doty-
czące interesujących nas materiałów. Zastosowano metodę 
pomiaru nanowgłębienia do określenia lokalnego modułu 
Younga oraz pomiaru twardości. Badanie wytrzymałości na 
rozciąganie wykonano na próbkach miniaturowych. Wyniki 
pozwoliły ustalić wpływ ilości kruchych faz w złączu na wła-
sności mechaniczne całego połączenia.

Słowa kluczowe: lutowanie twarde; luty na osnowie niklu; 
kruche fazy; obróbka cieplna; obliczenia i symulacje teore-
tyczne; badania własności połączeń

Abstract

Brazing with nickel-based filler materials is an estab-
lished joining process. In this context the formation of brit-
tle phases in the joint is a significant difficulty. An increased 
proportion of these phases influences the mechanical prop-
erties of the joints negatively. This effect gains strong influ-
ence if a continuous band of brittle phases is formed. In or-
der to avoid formation of brittle phases, small brazing gaps 
are necessary. Subsequent heat treatment is partially able  
to reduce the proportion of brittle phases. In this paper 
thermodynamic simulations are applied in order to calcu-
late phase transformations and diffusion processes dur-
ing brazing of commonly used materials. The simulations 
are performed by using Thermo-Calc and TC Dictra, as well 
as an analytical model. Different temperature-/time-cycles 
are examined in order to characterize their influence on  
the formation of brittle phases. Additionally, experiments 
were executed with the materials of interest. Nanoindenta-
tion is used to determine local values of YOUNG’s modulus 
and indentation hardness. Miniature tensile tests are ap-
plied to examine the tensile strength. The evaluated data  
is used to specify correlations between the properties  
of brittle phases in the joint and of its global mechanical 
properties.

Keywords: brazing; nickel-based filler materials; brittle phas-
es; heat treatment; calculations and theoretical simulations; 
investigations of joints properties

Introduction

High temperature brazing with nickel-based filler mate-
rials is widely applied in various sectors, e.g., aviation and 
aerospace engineering, medical technology and refrigera-
tion industry. Tensile strengths of more than 500 MPa are 
achievable. The brazing process is performed in vacuum 

and inert gas furnaces at temperatures above 900 °C. High 
temperature brazing has been subject of scientific investi-
gation since the 1970’s [1÷7]. The most significant obstacle 
is the occurrence of brittle phases in the brazing gap, which 
can influence the mechanical properties of the joint nega-

Wolfgang H. Müller, Johannes Wilden, Benjamin Schmorl, Oliver Stahn przeglad
Welding Technology Review



66 PRZEGLĄD  SPAWALNICTWA       Vol. 88  9/2016

tively. This effect is reinforced in case of continuous, band-
shaped brittle phases, cf. Fig. 1., i.e., the tensile strength can 
be reduced to values less than 50 MPa. In order to avoid 
the formation of brittle phases, the width of the brazing gap 
must not exceed a critical value. This requires a precise and 
therefore cost-intensive manufacturing of the components 
to be brazed. It is the objective of this work to propose tem-
perature/time-cycles which avoid the formation of brittle 
phases in larger brazing gaps. This is obtained by thermody-
namic simulations. Therefore the diffusion processes dur-
ing brazing can be analysed for commonly used filler materi-
als, namely Ni 620, Ni 650 and B-Ni60CrPSi-980/1020. Base 
materials are usual steels. At first, the commercial software 
packages Thermo-Calc and TC Dictra are examined for simu-
lation capability. Here, many difficulties occur due to limita-
tions of the available databases. Their applicability to the 
required simulation processes is currently unfortunately 
strongly restricted. Therefore, another simulation approach 
is used, which is based on an analytical solution of FICK’s 
diffusion equation. Diffusion coefficients are obtained from 
EDX-linescans and ARRHENIUS’ equation is used to take tem-
perature dependence into account. For examination of the 
mechanical properties of the joints, miniature tensile tests 
and nanoindentation tests are performed.

Fig. 1. Brazed joint, brazing gap 100 µm, base material: X5CrNi18-10 
(1.4301), filler: Ni 620, 90 min, 1050 °C
Rys. 1. Połączenie lutowane, szczelina 100 µm, materiał rodzimy 
– X5CrNi18-10 (1.4301), lut – Ni620, 90 min, 1050 °C

Thermo-Calc and TC Dictra

Thermo-Calc and TC Dictra are software packages  
for thermodynamic and diffusion calculations, respectively. 
Among other things Thermo-Calc can be used to calculate 
phase and so-called property diagrams for complex alloys. 
Figure 2 shows a property diagram for the filler material  
Ni 650 calculated by Thermo-Calc. The calculations are 
based on experimental data available in a number of databas-
es designed for a specific purpose, e.g., nickel superalloys  
or steels. Unfortunately there is no database specifically 
designed for brazing or usual brazing filler materials. There-
fore one has to use a database dealing with a similar kind  
of material. In case of nickel-based filler materials, one can 
use the database for nickel superalloys with some limita-
tions. These limitations concern the restricted amount  
of chemical elements that are available. Furthermore one 
need to pay close attention to the results of the calcula-
tions, if the application is outside of the originally planned 
range of use of the database. It is possible that the cal-
culations include some phases which are not found in ex-
periments and are therefore not to be expected to occur  
in the calculations either. In order to deal with this problem, 
one has to suspend manually the phases in question to get 
a more realistic result. In addition, some elements, such as 
boron or phosphorus, can be a reason for unrealistic results. 
If an element is not represented in the used database it is 
impossible to include it in the calculation. This leads to  

a change of alloy composition and therefore the result can-
not give insight into the real problem. Another point one 
has to take into account is the amount of the single ele-
ments in the composition. Especially the boron content  
in nickel-based filler materials is critical. If one considers 
these limitations of the software one obtains diagrams 
containing important properties of the filler material, i.e., 
solidus and liquidus temperature. On the other hand TC Dic-
tra offers insight into the dynamics of the brazing process.  
With the help of this software, one can perform diffusion 
calculations using experimental thermodynamic and mobil-
ity data in specific TC Dictra databases. Nonetheless some 
databases are shared between Thermo-Calc and TC Dictra. 
Therefore some of the crucial points mentioned above have 
to be considered in TC Dictra calculations as well. Further-
more another conflict arises concerning the combination  
of base and filler materials studied in this paper. Since all 
base materials of interest are steels which are brazed using 
nickel-based filler materials one has to decide which data-
base fits best. In contrast to the calculations with Thermo-
Calc one should use the steel database in TC Dictra so that 
the process of diffusion in the steel is represented as best 
as possible in the calculation. As a result of TC Dictra calcu-
lations one obtains the composition in the joint as a func-
tion of space and time, cf. Fig. 3. This data can be analysed 
and used as new input data for Thermo-Calc allowing for the 
possibility to calculate which phases are present in every 
point in space and time. With this information one is able 
to determine which temperature and holding time is needed 
during the brazing process in order to avoid brittle phases 
in the joint. These temperatures and holding times are the 
base for new temperature-/time-cycles. However, even if 
one considers all of the points mentioned above there are 
some obstacles which are unsolvable using Thermo-Calc 
and TC Dictra. Most notably it is not possible to calculate 
any type of phase or property diagram for the filler material 
B-Ni60CrPSi-980/1020 due to the high phosphorus content. 
Phosphorus is not available in the nickel databases of Ther-
mo-Calc and TC Dictra. One could use the steel database 
since it allows the usage of phosphorus which is recom-
mended to be in the order of magnitude of parts per million. 
Since the filler material contains about 6 wt.-% of phospho-
rus it is impossible to obtain any realistic results from Ther-
mo-Calc or TC Dictra if this material is involved. Addition-
ally the filler material Ni 620 needs further analysis. Some 
of the phases calculated by Thermo-Calc are not found in 
experiments. This results in solidus and liquidus tempera-
tures that are higher than expected for this material. If one 

Fig. 2. Property diagram of Ni 650
Rys. 2. Wykres własności Ni650 

brittle phase



67PRZEGLĄD  SPAWALNICTWA       Vol. 88  9/2016

excludes these phases from the calculation, the solidus and 
liquidus temperatures are lower but still differ from the ex-
pected value by about 100 °C. Due to this fact the results 
need to be interpreted carefully. In order to do research on 
these materials we needed to find a way of calculation with-
out using Thermo-Calc and TC Dictra. Therefore we started 
to use an experimental method based on energy dispersive 
x-ray analysis (EDX) and FICK’s laws of Diffusion.

FICK’s laws of diffusion

FICK’s first law of diffusion is an empirical equation cor-
relating the flux j and the concentration gradient. The sec-
ond law, the continuity equation, is a balance equation for 
the concentration. By combining FICK’s first and second law, 
one gets the diffusion equation under the assumption that  
D= const.

where D and c are the diffusivity and the concentration, re-
spectively. In order to use Equation (1) in brazing we have 
to formulate a proper mathematical problem. Since we are 
only interested in joints where the base material is the same 
on both sides, there is a symmetry to be used in the formula-
tion, cf. Fig. 4.

Fig. 3. Fraction of nickel mixed crystal in 16Mo3/Ni650 at 800 °C, 
20 µm distance from the middle of the brazing gap
Rys.  3. Frakcja wymieszanych kryształów dla 16Mo3/Ni650 
w 800 °C, odległość od środka szczeliny lutowniczej - 20 µm

2

2
∂ ∂
∂ ∂
c c
= D

t x
(1)

Fig. 4. Geometric model with and without using symmetry
Rys. 4. Symetryczny i asymetryczny model geometryczny

By considering the differential equation, i.e., FICK’s sec-
ond law, as well as proper initial and boundary conditions 
a well posed mathematical formulation of the problem can 
be derived

(2)

Due to the fact that in typical brazing processes l<<L, one 
need to be careful when solving the boundary value prob-
lem stated in (2). In order to avoid mistakes due to the large 
scale variation a dimensionless problem statement is pro-
posed. In order to do so we solve the dimensionless problem 
and transform the solution back to its dimension containing 
form. By applying the separation method the following solu-
tion can be derived

(3)
( )-1 2 21

1 2
2

2
n=1

sin nð nð nð
( ) 2 exp cos

nð
( )

( )
lLlc c

c x,t + c c t x
L LL

+ L-l D
-

∞

= −∑ .
sin π

nπ
n2π2 nπ

Note that neither the geometric l and L nor the physi-
cal parameters c1, c2 and D are known in this point. In order 
to calculate D, one has to make estimates for the other pa-
rameters.

Calculation of diffusivities

Due to the fact that diffusivities are usually not available 
for complex materials like steels or filler materials in braz-
ing, we aim to calculate diffusivities for our materials of in-
terest. In order to do so, we use data by an energy dispersive  
x-ray analysis unit (EDX) which gives us the local com-
position of a specimen. We used actual brazing joints for  
the sake of calculating diffusivities under the real conditions 
in the joint. This enables us to calculate the timely change 
in composition for all material combinations of interest.  
The calculation needs to be done numerically, since  
the diffusivity should ensure that the resulting concentration 
curve fits the measured data points in an optimal manner. 
We developed a corresponding algorithm which is illustrat-
ed in Fig. 5. The process of calculation starts by importing 
the data from the linescan into mathematical software and 
make estimates for all uncertain (geometric and physical) 
parameters but not for the diffusivity itself. In order to find 
these estimates one should read out the initial concentra-
tions and the geometric parameters from the EDX data. 
These estimates are combined with the solution of FICK’s 
second law. The remaining free parameter, the diffusivity,  
is now calculated using a numerical optimization tech-
nique to ensure that the data is fitted as good as possible.  
If the data is not fitted well enough, new estimates have to 
be made, the afore-mentioned steps have to be repeated.  
In case that the data is fitted well enough, one can de-
rive the temperature dependency of the diffusivity based  
on ARRHENIUS’ equation,

0 exp( ) .D T T
D

Q
R

−= (4)

However, to apply this equation one would need speci-
mens which were brazed using two different temperatures 
in the brazing process since there are two unknown param-
eters to be determined, i.e., activation energy and frequency 
factor. It can be shown, that Eq. (4) can be approximated by 

(5)
1

1( ) T
T

DD T ≈

where D1 is a known diffusivity at a temperature T1. This ap-
proximation is valid if the chosen temperature T differs not to 



68 PRZEGLĄD  SPAWALNICTWA       Vol. 88  9/2016

Fig. 5. Flow chart of the algorithm for calculation of diffusivities
Rys. 5. Schemat blokowy algorytmu do obliczania dyfuzyjności

much from T1. With the presented method one is able to calcu-
late all parameters needed in FICK’s second law to predict the 
composition of the materials in the joint as a function of time. 
Furthermore, one is not restricted to the temperature which 
was used brazing the specimen from which the diffusivity 
was calculated due to the shown approximation of ARRHENIUS’ 
equation. This is the foundation for the derivation of tempera-
ture-/time-cycles for joints with similar as well as dissimilar 
materials by changing the geometrical model shown in Fig. 4.

Derivation of temperature-/time-cycles

With the knowledge of the change of composition in time 
one is able to suggest new temperature-/time-cycles by 
evaluating phase diagrams. The phase diagrams can be tak-
en from the literature or can be calculated by using Thermo-
Calc. Especially good results are obtained from Thermo-Calc 
if binary phase diagrams are needed. These can be used to 
determine the possibly occurring brittle phases. If the over-
all amount for a critical element in the joint is less than 
needed for the formation of a brittle phase, one can be sure 
that this phase will not be found in the joint. Fig. 6 shows 
the evolution of the composition in the middle of the brazing 
gap in the joint B-Ni60CrPSi-980/1020 – 1.4301. The com-
position in the joint is evaluated in the middle of the brazing 
gap since this is the most critical point in the connection.

It is obvious that chromium and silicon reach their satu-

Fig. 6. Evolution of the composition in the middle of the brazing gap, 
steel: 1.4301, filler material: B-Ni60CrPSi-980/1020, brazing gap:  
50 µm, brazing temperature: 1195 °C
Rys. 6. Zmiana składu w środku szczeliny lutowniczej, stal: 1.4301, 
lut: B-Ni60CrPSi-980/1020 szczelina: 50 µm, temperatura lutowa-
nia: 1195 °C

ration concentration quickly. This is because of the similar 
amounts in base and filler materials. The change in concen-
tration of phosphorus is nearly completed after five hours. 
Merely the concentrations of iron and nickel are changing af-
ter this point. Since iron and nickel are completely miscible 
at the brazing temperature, one cannot expect any change 
in the occurring phases due to the interchange of iron  
and nickel.
Table I. Proposed temperature-/time-cycles, *calculated only using 
Thermo-Calc and Dictra
Tablica  I.  Zaproponowane cykle temperatura/czas, *wg obliczeń 
z Thermo-Calc I Dictra

filler 
material

base 
material

brazing 
temp. 
(°C)

holding 
time 
(min)

brazing 
gap  
(µm)

Ni 620

1.2343 1075 60 50

1.4301 1075 60 50

1.4404 1075 60 50

B-Ni60
CrPSi
-980

/1020

1.4301

1195 300 50

1220 180 50

1220 150 50

1.4404

1195 150 50

1220 120 50

1220 105 50

Ni 650
1.4301* 1220 360 50

16Mo3 1220 270 50

Therefore one should choose the brazing temperature to be 
1195 °C with a holding time of five hours if the brazing gap 
is 50 μm wide. This temperature-/time-cycle ensures the best 
chances to avoid brittle phases in the brazing gap for this 
combination of base and filler material. This procedure can 
be carried out in a similar manner for other combinations in 
order to derive new temperature-/time-cycles for these combi-
nations. By applying this method we calculated new tempera-
ture-/time-cycles for a wide variety of material combinations 
using a brazing gap of 50 µm. The results are shown in Tab. 1.

Results 
of proposed temperature-/time-cycles

Several specimen were produced using the proposed tem-
perature-/time-cycles. Table II shows the mechanical proper-
ties of some specimen brazed with B-Ni60CrPSi-980/1020. 
The resulting specimen are shown in Fig. 8. The tensile 
strengths were measured using miniature tensile tests and 
the indentation hardness was determined by nanoindenta-
tion tests with a BERKOVIC pyramid shaped indenter. Note that 
the columns with temperature 1220 °C show the measure-
ments of two proposed temperature-/time-cycles and the 
other are used for comparison. Specimen produced using 
the new cycles achieve considerably higher tensile strengths 
than the traditional joints. Furthermore the mechanical prop-
erties, i.e., YOUNG’s modulus and indentation hardness are 
homogenized across base material, mixed crystal and brittle 
phase. This yields the higher tensile strengths due to the dis-
solution of the mismatch in mechanical properties. The more 
homogenized material properties result in lesser stresses at 
the boundary layers between the different areas of the joint, 



69PRZEGLĄD  SPAWALNICTWA       Vol. 88  9/2016

i.e., base material, mixed crystal and brittle phase. In case of 
these joints it is not possible to get rid of the brittle phases 
in general since iron and phosphorus always form the brittle 
intermetallic Fe3P. This phase cannot be avoided, cf. Fig. 7.

Fig. 7. Fe-P phase diagram
Rys. 7. Wykres fazowy Fe-P

base 1.4301 1.4404

holding time 
(min)

20 90 180 20 90 120

temperature 
(°C)

1090 1090 1220 1090 1090 1220

tensile 
strength  
(N/mm2)

229 246 >320 199 232 261

Young’s 
modulus  

(103 N/mm2)

base 190±13 188±13 241±20 193±7 194±10 249±25

m.c. 195±9 189±17 249±20 197±7 197±7 249±25

b.p. 211±9 220±25 270±24 225±12 217±7 247±30

indentation 
hardness  

(103 N/mm2)

base 3.2±0.4 3.1±0.5 5±0.46 3.0±0.1 3.2±0.3 4.9±0.47

m.c. 3.6±0.3 3.6±0.3 4.8±0.4 3.6±0.3 3.3±0.2 4.9±0.5

b.p. 8.7±0.9 6.8±1.9 7.4±0.6 8.4±0.9 7.6±1.4 6.7±1.3

Table II. Mechanical properties of different brazing joints produced using the filler material B Ni60CrPSi-980/1020. Abbreviations m.c. 
– mixed crystal, b.p. – brittle phase. Tensile strength was measured by miniature tensile tests.
Tablica II. Własności mechaniczne różnych połączeń lutowanych przy użyciu lutu B Ni60CrPSi-980/1020. Skróty m.c. – wymieszany krysz-
tał, b.p. – faza krucha; Wytrzymałość na rozciąganie była mierzona na próbkach miniaturowych

In case of other filler materials brittle phases can be 
avoided completely by the temperature-/time-cycles pre-
sented in this work. Three joints Ni 620 – 1.2343, Ni 620 – 
1.4301 and Ni 620 – 1.4404 are depicted in Fig. 9. It can 
be observed that there are no brittle phases visible in the 
joint. All three joints were brazed at a brazing temperature of 
1075 °C with a holding time of 60 minutes. The microscopic 
images in Fig. 10 show the joint Ni 650 – 16Mo3, 1220 °C, 
270 minutes. The figure depicts both a non-normalised and 
a normalised specimen. It is clearly observable that without 
the process of normalisation there is a very coarse grain 
structure in the base material. In case of the normalised 
specimen refined grain structure is achieved due to the heat 
treatment. Note that in both cases the joint is free of brittle 
phases and is not affected by the heat treatment.

Fig. 8. Microscopic images of two joints brazed with the filler materi-
al B-Ni60CrPSi-980/1020 (a) 1.4301, 1220 °C, 180 min, gap > 100 µm,  
(b) 1.4404, 1220 °C, 120 min, gap 50 µm
Rys.  8. Mikrostruktura dwóch połączeń lutowanych – lut 
B-Ni60CrPSi-980/1020 (a) 1.4301, 1220 °C, 180 min, szczelina > 100 µm,  
(b) 1.4404, 1220 °C, 120 min, szczelina 50 µm

a)

b)



70 PRZEGLĄD  SPAWALNICTWA       Vol. 88  9/2016

Fig.  9. Microscopic im-
ages of three different 
joints using the filler ma-
terial Ni 620 and a brazing 
gap of 50 µm. The base 
materials are (a) 1.2343, 
(b) 1.4301 and (c) 1.4404
Rys.  9. Mikrostruktura 
trzech połączeń lutowa-
nych – lut Ni 620, szcze-
lina 50 µm. Materiał rodzi-
my (a) 1.2343, (b) 1.4301 
and (c) 1.4404

Fig.  10. Microscopic images of etched specimens. Base: 16Mo3, filler: Ni 650. (a) without normalising, (b) with normalising, 930 °C, 
30 minutes
Rys. 10. Mikrostruktura próbki trawionej. Materiał rodzimy – 16Mo3, lut Ni 650, a) bez normalizowania, b) po normalizowaniu 930 °C, 30 min

a) b) c)

b)a)

Summary and outlook
The main objective of this work was the development of new temperature-/time-cycles for brazing with nickel-based 

filler materials, Ni 620, Ni 650 and B-Ni60CrPSi-980/1020 in order to reduce brittle phases in the brazing gap. By applying 
the presented method, we were able to propose temperature-/time-cycles for a large variety of material combinations. Fur-
thermore the experimental evaluation of the new cycles showed that it is possible to produce brazing joints using Ni 620  
and Ni 650 without any brittle phases. In case of the filler material B-Ni60CrPSi-980/1020 the brittle phase Fe3P is unavoid-
able. Nevertheless the proposed cycles produced joints with better mechanical properties than the original brazing process. 
The presented method proposes the foundation of derivation of temperature-/time-cycles in case of joints using dissimilar 
materials, i.e., joints with different base materials on both sides of the gap.

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