Prediction of Stable Composition for High-Entropy Refractory Alloys
The common approach for evaluation of stability of multicomponent substitutional solid solutions using thermodynamic, mechanical, and topological parameters of the constituent elements is developed. The high-temperature systems based on refractory elements (W, Ta, Mo, Nb, V, Ti, Zr, Hf, Cr) are inve...
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Інститут металофізики ім. Г.В. Курдюмова НАН України
2016
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irk-123456789-1126222017-01-25T03:02:23Z Prediction of Stable Composition for High-Entropy Refractory Alloys Melnick, A.B. Soolshenko, V.K. Фазовые превращения The common approach for evaluation of stability of multicomponent substitutional solid solutions using thermodynamic, mechanical, and topological parameters of the constituent elements is developed. The high-temperature systems based on refractory elements (W, Ta, Mo, Nb, V, Ti, Zr, Hf, Cr) are investigated using this approach. Optimal compositions for high-entropy alloys are obtained, and influence of various factors in the formation of stable alloys is described. As shown, the most resistant alloys have non-equiatomic element-contents’ ratios. The agreement between element distribution in experimental alloys and predicted stable compositions are obtained for the W— Ta—Mo—Nb and W—Ta—Mo—Nb—V systems. Розроблено загальний підхід для оцінки стабільности багатокомпонентних твердих розчинів заміщення з використанням термодинамічних, механічних і топологічних параметрів елементів, що їх складають. Високотемпературні системи, що містять тяжкотопкі елементи (W, Ta, Mo, Nb, V, Ti, Zr, Hf, Cr), були досліджені за допомогою цього підходу. Одержано оптимальні склади для високоентропійних стопів і описано вплив різних чинників у формуванні стабільних стопів. Показано, що найбільш стійкі стопи мають нееквіатомне співвідношення складів елементів. Для систем W—Ta—Mo—Nb і W—Ta—Mo—Nb—V було одержано узгодженість між розподілами елементів в експериментальних стопах і прогнозованих стабільних композиціях. Разработан общий подход для оценки стабильности многокомпонентных твёрдых растворов замещения с использованием термодинамических, механических и топологических параметров составляющих их элементов. Высокотемпературные системы, состоящие из тугоплавких элементов (W, Ta, Mo, Nb, V, Ti, Zr, Hf, Cr), были исследованы с использованием этого подхода. Получены оптимальные составы для высокоэнтропийных сплавов и описано влияние различных факторов при формировании стабильных сплавов. Показано, что наиболее стабильные сплавы характеризуются неэквиатомным отношением составов элементов. Для систем W— Ta—Mo—Nb и W—Ta—Mo—Nb—V было получено согласие между распределениями элементов в экспериментальных сплавах и предсказанных стабильных композициях. 2016 Article Prediction of Stable Composition for High-Entropy Refractory Alloys / A.B. Melnick, V.K. Soolshenko // Металлофизика и новейшие технологии. — 2016. — Т. 38, № 10. — С. 1395-1405. — Бібліогр.: 25 назв. — англ. 1024-1809 DOI: 10.15407/mfint.38.10.1395 PACS: 05.10.Ln, 05.70.Ce, 64.10.+h, 65.40.gd, 81.05.Zx, 81.30.Bx, 81.30.Fb, 82.60.Lf http://dspace.nbuv.gov.ua/handle/123456789/112622 en Металлофизика и новейшие технологии Інститут металофізики ім. Г.В. Курдюмова НАН України |
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Фазовые превращения Фазовые превращения |
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Фазовые превращения Фазовые превращения Melnick, A.B. Soolshenko, V.K. Prediction of Stable Composition for High-Entropy Refractory Alloys Металлофизика и новейшие технологии |
| description |
The common approach for evaluation of stability of multicomponent substitutional solid solutions using thermodynamic, mechanical, and topological parameters of the constituent elements is developed. The high-temperature systems based on refractory elements (W, Ta, Mo, Nb, V, Ti, Zr, Hf, Cr) are investigated using this approach. Optimal compositions for high-entropy alloys are obtained, and influence of various factors in the formation of stable alloys is described. As shown, the most resistant alloys have non-equiatomic element-contents’ ratios. The agreement between element distribution in experimental alloys and predicted stable compositions are obtained for the W— Ta—Mo—Nb and W—Ta—Mo—Nb—V systems. |
| format |
Article |
| author |
Melnick, A.B. Soolshenko, V.K. |
| author_facet |
Melnick, A.B. Soolshenko, V.K. |
| author_sort |
Melnick, A.B. |
| title |
Prediction of Stable Composition for High-Entropy Refractory Alloys |
| title_short |
Prediction of Stable Composition for High-Entropy Refractory Alloys |
| title_full |
Prediction of Stable Composition for High-Entropy Refractory Alloys |
| title_fullStr |
Prediction of Stable Composition for High-Entropy Refractory Alloys |
| title_full_unstemmed |
Prediction of Stable Composition for High-Entropy Refractory Alloys |
| title_sort |
prediction of stable composition for high-entropy refractory alloys |
| publisher |
Інститут металофізики ім. Г.В. Курдюмова НАН України |
| publishDate |
2016 |
| topic_facet |
Фазовые превращения |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/112622 |
| citation_txt |
Prediction of Stable Composition for High-Entropy Refractory Alloys / A.B. Melnick, V.K. Soolshenko // Металлофизика и новейшие технологии. — 2016. — Т. 38, № 10. — С. 1395-1405. — Бібліогр.: 25 назв. — англ. |
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Металлофизика и новейшие технологии |
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2025-07-08T04:18:28Z |
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2025-07-08T04:18:28Z |
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| fulltext |
1395
ФАЗОВЫЕ ПРЕВРАЩЕНИЯ
PACS numbers:05.10.Ln, 05.70.Ce,64.10.+h,65.40.gd,81.05.Zx,81.30.Bx,81.30.Fb, 82.60.Lf
Prediction of Stable Composition for High-Entropy Refractory
Alloys
A. B. Melnick and V. K. Soolshenko
G. V. Kurdyumov Institute for Metal Physics, N.A.S. of Ukraine,
36 Academician Vernadsky Blvd.,
UA-03142 Kyiv, Ukraine
The common approach for evaluation of stability of multicomponent substi-
tutional solid solutions using thermodynamic, mechanical, and topological
parameters of the constituent elements is developed. The high-temperature
systems based on refractory elements (W, Ta, Mo, Nb, V, Ti, Zr, Hf, Cr) are
investigated using this approach. Optimal compositions for high-entropy al-
loys are obtained, and influence of various factors in the formation of stable
alloys is described. As shown, the most resistant alloys have non-equiatomic
element-contents’ ratios. The agreement between element distribution in ex-
perimental alloys and predicted stable compositions are obtained for the W—
Ta—Mo—Nb and W—Ta—Mo—Nb—V systems.
Key words: high-entropy alloys, refractory alloys, solid solution, thermody-
namics.
Розроблено загальний підхід для оцінки стабільности багатокомпонент-
них твердих розчинів заміщення з використанням термодинамічних, ме-
ханічних і топологічних параметрів елементів, що їх складають. Високо-
температурні системи, що містять тяжкотопкі елементи (W, Ta, Mo, Nb,
V, Ti, Zr, Hf, Cr), були досліджені за допомогою цього підходу. Одержано
оптимальні склади для високоентропійних стопів і описано вплив різних
чинників у формуванні стабільних стопів. Показано, що найбільш стійкі
стопи мають нееквіатомне співвідношення складів елементів. Для систем
W—Ta—Mo—Nb і W—Ta—Mo—Nb—V було одержано узгодженість між розпо-
ділами елементів в експериментальних стопах і прогнозованих стабіль-
Corresponding author: Aleksey Bronislavovich Melnick
E-mail: mel@imp.kiev.ua
Please cite this article as: A. B. Melnick and V. K. Soolshenko, Prediction of Stable
Composition for High-Entropy Refractory Alloys, Metallofiz. Noveishie Tekhnol., 38,
No. 10: 1395—1405 (2016), DOI: 10.15407/mfint.38.10.1395.
Металлофиз. новейшие технол. / Metallofiz. Noveishie Tekhnol.
2016, т. 38, № 10, сс. 1395—1405 / DOI: 10.15407/mfint.38.10.1395
Оттиски доступны непосредственно от издателя
Фотокопирование разрешено только
в соответствии с лицензией
2016 ИМФ (Институт металлофизики
им. Г. В. Курдюмова НАН Украины)
Напечатано в Украине.
1396 A. B. MELNICK and V. K. SOOLSHENKO
них композиціях.
Ключові слова: високоентропійні стопи, тяжкотопкі стопи, твердий роз-
чин, термодинаміка.
Разработан общий подход для оценки стабильности многокомпонентных
твёрдых растворов замещения с использованием термодинамических,
механических и топологических параметров составляющих их элемен-
тов. Высокотемпературные системы, состоящие из тугоплавких элемен-
тов (W, Ta, Mo, Nb, V, Ti, Zr, Hf, Cr), были исследованы с использованием
этого подхода. Получены оптимальные составы для высокоэнтропийных
сплавов и описано влияние различных факторов при формировании ста-
бильных сплавов. Показано, что наиболее стабильные сплавы характери-
зуются неэквиатомным отношением составов элементов. Для систем W—
Ta—Mo—Nb и W—Ta—Mo—Nb—V было получено согласие между распреде-
лениями элементов в экспериментальных сплавах и предсказанных ста-
бильных композициях.
Ключевые слова: высокоэнтропийные сплавы, тугоплавкие сплавы,
твёрдый раствор, термодинамика.
(Received July 5, 2016)
1. INTRODUCTION
Currently, multicomponent high-entropy metallic alloys (HEAs) were
given special attention, as materials exhibiting a unique set of physical
and chemical properties [1—10]. In particular, they are considered as
promising high temperature cast alloys, which have high hardness and
strength, high corrosion and wear resistance [1, 4—10]. Usually, as a
HEA, multicomponent alloys, which have at least five principal ele-
ments with close-to-equiatomic ratios, are considered [2]. Each princi-
pal element should have a concentration between 5 and 35 at.% [1].
HEAs are in the forms of solid solutions rather than intermetallic
compounds or metallic glasses [1, 3, 4]. Thermodynamic and topologi-
cal parameters of the constituent elements were used for prediction of
high-entropy phase formation and design alloys [1, 3—6]. It should be
noted that topological and thermodynamic parameters are not used in
one approach. In this paper, we try to develop a general approach for
the prediction of compositions of HEA solid solutions.
Multicomponent alloys can have a simple structure of single-phase
solid solution with the energy lower than the energies of corresponding
multiphase heterogeneous structures. This can be achieved by increas-
ing entropy of mixing of the alloy by involving a large number of ele-
ments. This way decreases the Gibbs free energy, which characterizes
the thermodynamic stability of the system. Consider the question in
detail. Gibbs free energy G is expressed as follows:
PREDICTION OF STABLE COMPOSITION FOR HIGH-ENTROPY ALLOYS 1397
G H TS,
where H–enthalpy, T–the absolute temperature, S–entropy.
We consider HEAs production as the transition from liquid state to
crystalline. Any transition has to reduce the Gibbs free energy,
G G2 G1 H TS 0,
where G1 and G2 are free energies of the initial and final states of the
system.
According to the Boltzmann hypothesis, the entropy of mixing n el-
ements in a regular solution can be expressed as follows:
mix
1
ln ,
n
i i
i
S k c c
(1)
where ci is the atomic fraction of i-th element, k–Boltzmann constant.
According to Eq. (1), multicomponent alloys with equiatomic com-
position would have greatest entropy of mixing. HEAs are the substi-
tutional solid solutions with distorted lattice as atoms, which form
them, have different sizes. Elastic distortions arising from size mis-
match can affect the free energy of the alloy as well. Consideration of
various factors, which form the Gibbs free energy, is important to de-
termine the elemental composition and concentrations of HEA, includ-
ing elastic energy Hel and enthalpy of mixing in the liquid state
Hmix:
H Hmix Hel. (2)
The composition of the most stable HEA may be different from the
equiatomic one due to the contribution of factors additional to the en-
tropy. To find the compositions of the most stable solid solutions based
on the refractory elements (W, Ta, Mo, Nb, V, Ti, Zr, Hf, Cr), we will
estimate Gibbs free energies of these alloys. Many HEAs based on these
refractory elements have been in the focus of experimental studies
[11—19]. According to literature data, refractory HEAs exhibit high
specific yield strengths, while their plastic strains are in the range 5—
50% in compression loading conditions. Prediction resistant homoge-
neous high temperature composition is an actual problem.
2. METHOD
Substitutional solid solutions were considered within of the regular
solution approximation. The mixing enthalpy of multicomponent alloy
consisting of n elements is as follows [20]:
1398 A. B. MELNICK and V. K. SOOLSHENKO
mix
, 1,
,
n
i j ij
i j i j
H c c
(3)
where ij–parameter characterizing the interaction between i and j
elements of the regular solution, ij 4Hij
mix, ci–atomic fraction of i-
th component, Hij
mix–mixing enthalpy for binary liquid equiatomic
alloy. The values Hij
mix were taken from [21]. They have been tabulat-
ed by means of the semi-empirical Miedema’s model [22].
The local atomic volumes and bulk modules for solid solutions were
considered equal to values for one-component systems.
Mechanical equilibrium condition for solid solution lattice can be
written as
1
( ) ( )
0,
( )
n
i
i i
i
V T V T
c B
V T
(4)
where V(T)–the average volume of atom of the alloy, Vi(T)–atomic
volume, and Bi–bulk modulus of i-th element;
Vi(T) V0i(1 i(T T0))
3,
where i–linear expansion coefficient for the i-th component, T0 293
K–room temperature.
The expression for V(T) can be determined from Eq. (4):
1
1
( )
( ) .
n
i i i
i
n
i i
i
c B V T
V T
c B
(5)
Then, the elastic distortion energy of the solid solution, Hel, is as
follows:
2
el
1
( ( ) ( ))
.
2 ( )
n
i
i i
i i
V T V T
H c B
V T
(6)
Solid solution is considered at the effective melting temperature Tm
that was estimated as:
m m
1
,
n
i
i
i
Т cT
(7)
where m
iT –melting temperature of the i-th element.
We can obtain an expression for the concentration dependence of the
Gibbs free energy change for multicomponent alloy upon crystalliza-
tion from a liquid state to a substitutional solid solution:
PREDICTION OF STABLE COMPOSITION FOR HIGH-ENTROPY ALLOYS 1399
2
1 m
, 1 1 1
( ( ) ( ))
( ,..., ) ln .
2 ( )
n n n
i
n i j ij i i i i
i j i ii
i j
V T V T
G c c c c c B kT c c
V T
(8)
The minimum of expression (8) corresponds to the composition of sta-
ble alloy.
3. CALCULATION
As a first attempt, let us calculate the parameters G, Hmix, Hel, ,
Smix, Tm for the equimolar alloys of these elements. They are given in
Table 1. The parameter is expressed as follows:
2
1
1 ,
n
i
i
i
r
c
r
where ri (V0i)
1/3, V0i, ci are the atomic volume and percentage of the i-
th component,
1
n
i i
i
r c r
. Parameter describes the comprehensive
effect of the atomic size difference in n-element alloy [2].
The data in Table 1 show that the addition of elements to the equimo-
lar alloy increases the entropy of mixing. Other parameters do not be-
TABLE 1. Calculated parameters (G, Hmix, Hel, , Smix, Tm) for equiatomic
alloys.
No. Alloys
G,
kJ/mol
Hmix,
kJ/mol
Hel,
kJ/mol
,
%
Smix,
J/(molK)
Tm,
K
1 WTaMo 29.822 5.333 5.596 2.149 9.135 3294
2 WTaNb 29.845 6.667 6.463 1.964 9.135 3245
3 TaMoNb 25.634 4.888 6.462 2.232 9.135 2979
4 WTaMoNb 36.217 6.500 6.681 2.251 11.527 3158
5 WTaMoNbV 35.800 4.640 8.487 3.218 13.382 2963
6 WTaMoNbTi 38.249 5.280 6.031 2.111 13.382 2914
7 WTaMoNbHf 30.388 4.960 15.084 4.349 13.382 3027
8 WTaMoNbZr 31.313 5.440 13.627 4.885 13.382 2952
9 WTaMoNbCr 25.790 6.240 20.090 4.816 13.382 2962
10 WTaMoNbVTi 37.704 4.222 8.120 3.116 14.898 2793
11 WTaMoNbVTiHf 33.521 3.673 14.672 4.658 16.180 2751
12 WTaMoNbVTiHfZr 31.837 3.563 17.952 5.516 17.290 2674
13 WTaMoNbVTiHfZrCr 26.3684 4.938 26.413 6.608 18.269 2619
1400 A. B. MELNICK and V. K. SOOLSHENKO
have monotonically with the addition of elements in the alloy. The re-
sulting value G can decrease or increase with increasing number of
components in the system.
Therefore, it is necessary to find the compositions different from
equimolar that have the minimal G value.
The minimization procedure was carried out for this goal:
minG(c1,…, cn) ci (i 1,… n). (9)
The values of the constants i, V0i, Bi, m
iT in expressions (3)—(8) were
taken from tables [23], and the values of mixing enthalpies for the al-
loy elements Hij
mix were taken from Ref. [21].
Minimum (9) was found using the Monte Carlo method. It was per-
formed according to the following cycle algorithm.
1. The alloy concentrations c0i (i 1,…, n) were taken as current
composition.
2. G(с0i) was calculated according to Eq. (8).
3. Then the concentrations of the alloy were varied randomly c0i
c1i with steps of 0.001.
4. G(с1i) was determined.
5. At G(с1i) G(с0i), the current concentration value was taken as
с1i; at G(с1i) G(с0i), the current concentration was stayed as с0i.
6. Then transition was performed on second stage and so on.
In this way, the local minimum G on concentrations was determined.
The different concentrations have been chosen as the initials. How-
ever, in all cases, the same final concentrations of alloys were obtained
that correspond to the minimum Gibbs free energy. This indicates on
the absence of local energy minima in the systems studied.
Thus, we have the optimal compositions with minimal G to investi-
gated systems. They are given in Table 2.
4. RESULTS AND DISCUSSION
If we compare the compositions shown in Tables 1 and 2, it can be seen
that the alloys of Table 2 have less Gibbs free energy than similar
equimolar alloys. The calculated Gibbs free energy of solid solutions
for ternary and quasi-ternary alloy systems are presented in the form
of energy—composition diagrams in Figs. 1, 2.
It should be noted that the minimum energy compositions on the di-
agrams do not correspond to equiatomic concentrations. Therefore, it
is desirable to analyse all factors that determine their stability.
It can be seen that the free energy of the solution can be reduced by
both entropic part and reduction of the lattice deformation. Therefore,
an increase of number of components in solid solution opens the possi-
bility to obtain more equilibrium state with less elastic distortions.
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2
PREDICTION OF STABLE COMPOSITION FOR HIGH-ENTROPY ALLOYS 1401
1402 A. B. MELNICK and V. K. SOOLSHENKO
The alloys from Table 2 have usually less elastic distortions than
similar equiatomic alloys. This is evidenced by the values of Hel and
parameters.
According to [3], Hmix, parameters play a special role in the for-
mation of solid solutions. A solid solution is crystallized when 6%
and Hmix 10 kJ/mol. Therefore, the compositions of Table 2 are
formed from substitutional solid solutions.
Alloys of W—Ta—Mo—Nb—V (1) and W—Ta—Mo—Nb (2) systems with
compositions close to equiatomic (see Tables 3, 4) were produced by
vacuum arc melting in [11]. All components of these alloys have a b.c.c.
lattice, and so formation of b.c.c. substitutional solutions is most
probable. This was confirmed by diffraction analysis of these alloys
[11]. Moreover, the law of mixture describes density of experimental
Fig. 1. The calculated Gibbs free energy of solid solutions (G) for ternary al-
loy systems: W—Ta—Mo (a), W—Ta—Nb (b), Ta—Mo—Nb (c).
PREDICTION OF STABLE COMPOSITION FOR HIGH-ENTROPY ALLOYS 1403
alloys and their lattice parameters. Elemental analysis of real alloys
shows the heterogeneous distribution of elements [11] (see Tables 3, 4).
We investigated peculiarities of this distribution in alloys (1 and 2)
and corresponding data are presented in Tables 3 and 4. Here, cea–
average concentrations of the experimental alloys. The distribution of
elements in the samples is heterogeneous with the maximal–cemax and
minimal–cemin concentrations, according to [11]. Magnitude (cemax
cemin)/2 describing the amplitude of deviation of element concentra-
tions is given in Tables 3, 4.
Using modelling, we have found that the concentrations of the most
energetically favourable solid solutions (cm) are different from the
equiatomic concentrations. It is interesting to analyse the correlation
Fig. 2. The calculated Gibbs free energy of solid solutions (G) for quasi-
ternary alloy systems: W32.8Ta20.6(MoNbTi) (a), W34.1Ta20.6(MoNbV) (b),
W32.7Ta18.5Mo17.9(NbVTi) (c).
1404 A. B. MELNICK and V. K. SOOLSHENKO
between values of cm cea and (cemax cemin)/2. In the system 1, the
concentrations of W and V have the largest deviation from equiatomic
concentration. It was observed for both the model and real alloys (Table
3). For both the model and experimental alloys of system 2, the largest
deviation has W and the smallest deviation has Ta (Table 4).
Deviations from the equiatomic composition predicted by the model-
ling were observed experimentally [11]. Atomic simulation of the sys-
tem also showed a low content of vanadium in the solid solution [24,
25].
5. CONCLUSIONS
1. Method was proposed for determining Gibbs free energy of multi-
component substitutional solid solutions in the approximation of regu-
lar solution model.
2. It was obtained the most stable compositions for alloys based on the
refractory elements (W, Ta, Mo, Nb, V, Ti, Zr, Hf, Cr).
3. It was determined that the thermodynamic optimal compositions do
not coincide with equiatomic compositions having the largest mixing
entropy.
TABLE 3. cm1–modelled alloy concentration in the W—Ta—Mo—Nb—V system,
cа1–average concentration of experiment alloy [11], ce1max–maximal concen-
tration of the element in the experimental alloy [11], ce1min–minimal concen-
tration of the element in the experimental alloy [11].
Concentration W, at.% Ta, at.% Mo, at.% Nb, at.% V, at.%
cm1 34,1 20.6 20.0 17.7 7.6
cea1 22.1 18.0 19.1 20.9 20.0
(ce1max ce1min)/2 11.6 4.0 2.2 4.4 12.3
cm1 cea1 12.0 2.6 0.9 3.2 12.4
TABLE 4. cm2–modelled alloy concentration in the W—Ta—Mo—Nb system,
cа2–average concentration of experimental alloy [11], ce2max–maximal con-
centration of the element in the experimental alloy [11], ce2min–minimal con-
centration of the element in the experimental alloy [11].
Concentration W, at.% Ta, at.% Mo, at.% Nb, at.%
cm2 34,6 23.5 21.2 20.7
cea2 26.4 24.8 24.0 24.8
(ce2max ce2min)/2 6.8 1.2 3.0 5.0
cm2 cea2 8.2 1.3 2.8 4.1
PREDICTION OF STABLE COMPOSITION FOR HIGH-ENTROPY ALLOYS 1405
4. The predicted compositions of the most resistant alloys for the W—
Ta—Mo—Nb—V and W—Ta—Mo—Nb systems correlated with element dis-
tribution in experimental alloys.
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/UKR <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>
/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|