MTEX Workshop 26.02.2016
Characterisation of texture of
strontium hexaferrite with EBSD
and XRD
Timmy Reimann, Arne Bochmann, Jörg Töpfer
Timmy Reimann
0. Outline
1. Introduction
2. EBSD results
3. XRD results
4. Evaluation with MTEX
5. Summary
6. Outlook
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1. Introduction – field of interest
Functional ceramics
 Soft ferrites
o Mn-Zn ferrites for multilayer inductors
o M-, Y-, Z-type hexaferrites
H. Bartsch
 Hard ferrites
o Sr hexaferrites for permanent magnets
 Dia- and Piezoelectrics
o CaCu3Ti4O12
o PZT (PbZrO3)
o Pb free BNBT (Bi0.5Na0.5)TiO3 – BaTiO3
and KNN (K0.5Na0.5NbO3)
multi layer round coil
 Thermoelectrics
o CCO (Ca3Co4O9); CaMnO3
 Low temperature ceramic cofiring (LTCC)
devices sintered at 900°C
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multi layer capacitor
1. Introduction - Hexaferrite
3+ 2−
𝑆𝑟 2+ 𝐹𝑒12
𝑂19
M-Type hexagonal ferrites (Ba/Sr)Fe12O19:
most important material group for permant
magnets
market share:
Sinter Ferrite (47%)
S-Block
Compound-Ferrite (21%)
Sinter-NdFeB (19%)
R-Block
Compound-NdFeB (6%)
Sinter-SECo (6%)
Compound-SECo (1%)
SG: 6/mmm
a = b = 5.8836 Å
c = 23.0376 Å
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1. Introduction - Tridelta Maniperm® 882
Data sheet
Maniperm 882 :
1,0
flux density B
remanence:
magnetic field H
coercivity:
HCB = 270-240 kA/m
energy product:
(BH)max = 32 kJ/m2
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0,5
B (T)
BR = 405-415 mT
Tridelta Maniperm 882
EAH Jena Permagraph
sample 70A
0,0
-0,5
𝐵 = 𝐽 + 𝜇0 𝐻
𝐽 … 𝑚𝑎𝑔𝑛𝑒𝑡𝑐 𝑝𝑜𝑙𝑎𝑟𝑖𝑠𝑎𝑡𝑖𝑜𝑛
𝜇0 … 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑓𝑖𝑒𝑙𝑑 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
-1,0
-600
-400
-200
0
H (kA/m)
200
400
600
1. Introduction – sample preparation
uniaxial pressing with
applied magnetic field
𝐻=𝐼
𝑁
𝑙2 + 𝐷2
𝐼 … 𝑐𝑢𝑟𝑟𝑒𝑛𝑡
𝑁 … 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑖𝑛𝑑𝑖𝑛𝑔𝑠
𝑙 … 𝑙𝑒𝑛𝑔𝑡ℎ
𝐷 … 𝑐𝑜𝑖𝑙 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟
sample
current variation:
0 A; 20 A; 40 A; 60 A; 70 A
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1. Introduction - sample preparation
uniaxial pressing with
applied magnetic field
H field in z direction
orientation of c axis in powder
particles of slurry in z direction
due to uniaxial magnetocrystalline anistropy of
SrFe12O19
goal:
increase of remanence in z
direction
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1. Introduction – magnetic properties
2. quadrant of H – J plot
increase of remanence
with increasing H field in
pressing process
observed
0,40
0,32
task:
characterisation of
texture
J (T)
0,24
0,16
70 A
20 A
0A
0,08
0,00
-350
-300
-250
-200
-150
-100
-50
H (kA/m)
𝐵 = 𝐽 + 𝜇0 𝐻
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0
1. Introduction – goals
Characterisation of texture
 measurement of texture with EBSD and XRD and evaluation of both data sets
with same procedure
 computing ODF
 tetermine vector of main orientation
 calculating amount of fibre texture
 derivation around main orientation and calculating Br according to the ODF
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2. EBSD results – 0 A sample
IPFX Map
112 x 84 µm
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2. EBSD results – 0 A sample
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2. EBSD results – 20 A sample
IPFX Map
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2. EBSD results – 20 A sample
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2. EBSD results – 70 A sample
IPFX Map
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2. EBSD results – 70 A sample
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2. EBSD results – ODF (MTEX)
To calculate the ODFs given in the pole figures below a kernel function with a
halfwidth of 5 ° was used.
0A
70 A
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20 A
(10-10)
(10-11)
15,0
17,5
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20,0
22,5
25,0
27,5
2 (°)
30,0
32,5
35,0
(11-26)
(20-23)
(11-24)
(10-17)
SrFe12O19
(20-20)
(20-21)
(10-18)
(20-22)
(0008)
(11-22)
(11-20)
Hexaferrit 60 A pellet
c-axis in x direction
(10-16)
(10-15)
(0006)
(10-13)
(10-12)
(0004)
intensity (a. u.)
3. XRD results
37,5
3. XRD results – Bruker Multex
Polfigures
(1010)
Calculated polfigure for fibre texture
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(1017)
(1124)
3. XRD results – Bruker Multex
phases
rotation axis f
rotation axis
halfwidth: 30°
f.polar = 82,32°
f.azimuth = 177,49°
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4. Evaluation with MTEX
Polfigures plotted with MTEX (halfwidth = 5°)
Calculation of ODF
Plot of polfigures
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4. Evaluation with MTEX
polefigure of ODF
Multex Fit
fibre: 72 % , halfwidth: 30 %
MTEX Fit
ODF_mea = x*ODF_Fibe + (1-x)*ODF_Uni*
fibre:69 %, halfwidth: 17 %
uniform: 31%
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*matlab script at the end
4. Evaluation with MTEX
Anteilfibre = [];
i = 1;
for theta = 5 : 5 : 90
theta_array(i) = theta;
Anteilfibre(i) = fibreVolume(odf_measured, Miller(0,0,1,cs), o_min_vector,…
theta*degree) * 100;
i = i+1;
end
16
60 A
14
80
volume fraction (%)
cumulative sum
fibre amount (vol.%)
100
60
40
20
12
10
8
6
4
2
0
0
0
20
40
halfwidth (°)
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60
80
20
40
60
halfwidth (°)
80
4. Evaluation with MTEX
Br (theo.) = 0.437 T
in c direction
𝐵𝑅𝑖 = 𝐵𝑅𝑡ℎ𝑒𝑜 cos 𝜑𝑖
𝑁90°
𝐵𝑅𝑔𝑒𝑠 =
𝐵𝑅𝑡ℎ𝑒𝑜 cos(Δ𝜑 ∗ 𝑖)
𝑖
𝐵𝑅𝑔𝑒𝑠 = 0.413 𝑇;
𝐵𝑅𝑔𝑒𝑠
𝐵𝑅𝑡ℎ𝑒𝑜
0,07
0,40
0,06
0,35
60 A
0,05
0,30
0,25
0,04
0,20
0,03
0,15
0,02
0,10
0,01
0,05
0,00
0,00
0
20
40
60
halfwidth (°)
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80
cmulative sum Brges (T)
Anteil an Brges - Bri (T)
𝜑
100 = 95 %
5. Summary – 60 A sample
EBSD polefigure of ODF
XRD polefigure of ODF
MTEX Fit
fibre: 75 %, halfwidth = 20,5°
uniform: 25 %
fibre:69 %, halfwidth: 17°
uniform: 31%
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5. Summary – 60 A sample
17,5
100
Hexaferrit 60 A
XRD
EBSD
volume fraction (%)
cumulative sum
fibre (vol.%)
80
Hexaferrit 60 A
XRD
EBSD
15,0
60
40
20
12,5
10,0
7,5
5,0
2,5
0
0
10
20
30
40
50
60
70
80
90
0,0
0
halfwidth (°)
20
40
60
halfwidth (°)
cumulative sum Br (T)
0,4
Br (XRD) = 0.413 T
Br (EBSD) = 0.416 T
0,3
Measured Br:
Br (Robograph) = 0.405 T
0,2
Hexaferrit 60 A
XRD
EBSD
0,1
0,0
0
10
20
30
40
50
halfwidth (°)
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60
70
80
90
80
6. outlook
XRD Pole figures of 70 A sample
 measuring of a sample with c in z direction with XRD and EBSD
 use of Co-radiation instead of Cu-radiation
 preparation of an isotrop SrFe12O19 sample for calibration of XRD polefigures
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6. outlook
 Characterisation of screen printed thick
film hexaferrites for circulators
 Characterisation of KNN piezoelectics
15 mm
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Thanks!
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Script for MTEX Fit
%% Fitten Fibre
Miller_c_Achse = Miller (0 ,0 , 1 ,cs);
fibrevector = odf_max_orientation*Miller_c_Achse;
odf_fibre = fibreODF(Miller(0,0,1,cs),fibrevector,'halfwidth',20*degree);
% definition Anfangsvektor, x(1): Amplituden; x(2), x(3), x(4): Eulerwinkel (°), x(5): Halfwidth unimodale ODF
[h1, h2, h3] = Euler(odf_max_orientation,'Bunge');
x0 = [0 h1/degree h2/degree h3/degree 10];
% Definition Nebenbedingungen: 0<= x(1) <= 1; 0<= x(5) <= 45;
A = [-1 0 0 0 0; ...
1 0 0 0 0; ...
0 0 0 0 -1; ...
0 0 0 0 1];
b = [0;1;0;45];
min_func = @(x)calc_ODF_Error(x,odf_measured, ss,cs);
[x,fval,exitflag,output] = fmincon(min_func,x0,A,b,[],[],[],[],[],optimset('Algorithm','interior-point','Display','iterdetailed'));
o_min = orientation('Euler',x(2)*degree,x(3)*degree,x(4)*degree,cs,ss);
o_min_vector = o_min*Miller_c_Achse;
ampl_min = x(1);
halfwidth_min = x(5);
odf_min = ampl_min*fibreODF(Miller(0,0,1,cs), o_min_vector,'halfwidth',halfwidth_min*degree) + (1ampl_min)*uniformODF(cs,ss);
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