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COMUNICAÇÃO TÉCNICA ______________________________________________________________________________________________________________________________________________________________________________________________________
Nº 174932.1
Effects of forced convection on the micro and macrostructure of metallurgical grade ingots obtained by unidirectional solidification Denir Paganini Nascimento Marcelo de Aquino Martorano João Batista Ferreira Neto Moysés Leite de Lima Tiago Ramos Ribeiro
Apresentação no SEMINÁRIO DE ACIARIA, FUNDIÇÃO E METALURGIA DE NÃO-FERROSOS, 48., 2017, São Paulo. Palestra... 24 slides. ABM WEEK 2017, Rio de Janeiro
A série “Comunicação Técnica” compreende trabalhos elaborados por técnicos do IPT, apresentados em eventos, publicados em revistas especializadas ou quando seu conteúdo apresentar relevância pública. ___________________________________________________________________________________________________
Instituto de Pesquisas Tecnológicas do Estado de São Paulo S/A - IPT
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São Paulo | SP | Brasil | CEP 05508-901 Tel 11 3767 4374/4000 | Fax 11 3767-4099
www.ipt.br
EFFECTS OF FORCED CONVECTION ON THE MICRO AND MACROSTRUCTURE OF METALLURGICAL GRADE SILICON INGOTS OBTAINED BY UNIDIRECTIONAL SOLIDIFICATION
Denir Paganini Nascimento - Universidade de São Paulo Marcelo de Aquino Martorano - Universidade de São Paulo João Batista Ferreira Neto - IPT Moysés Leite de Lima - IPT Tiago Ramos Ribeiro - IPT
05/10/2017
o Objective
Study the effect of the forced convection during the controlled solidification of
metallurgical grade silicon.
Introduction
o Refining of silicon through metallurgical route:
Controlled unidirectional solidification to segregate the metallic impurities to the last
solidified part of the ingot (macrossegregation).
Solute partition coefficient 𝒌𝒌𝟎𝟎 = 𝑪𝑪𝑺𝑺𝑪𝑪𝑳𝑳
For silicon, most of metallic impurities have 𝒌𝒌𝟎𝟎 ≪ 𝟏𝟏
o Forced convection:
Homogenize the impurities at the bulk liquid.
Transport the rejected impurities by the interface far away.
Introduction
o Constitutional super-cooling criteria
Rejected solute lowers the liquidus temperature
Comparison between bulk liquid gradient and equilibrium liquidus temperature
Introduction
Experiments – Solidification without forced convection
Experiments – Solidification with forced convection
o Enthalpy method
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
= 𝜕𝜕𝜕𝜕𝜕𝜕
𝐾𝐾 𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
o Boundary conditions
Cooling curves measured by the thermocouples imersed into the liquid silicon. o Finite volumes method, in explicit formulation.
Mathematical model of the directional solidification of the ingot
o Micro e macrostructures of the solidified ingot without forced convection
Results and discussion
o Micro e macrostructures of the solidified ingot without forced convection o Approximate 8 mm layer, close to the base, showing columnar grains with regular and
smooth boundaries oriented parallel to the direction of the heat extraction. o The microstructure analysis did not showed intermetallic precipitates up to 8 mm high,
indicating that the solid-liquid interface has a planar morphology.
o From 8 mm and up, the ingot shows columnar grains with irregulars and serrated boundaries, without a preferred orientation.
o From 8 mm and up, the microstructure analysis showed intermetallic precipitates, indicating that the solid-liquid interface has a non-planar morphology.
Results and discussion
o Micro e macrostructures of the solidified ingot with forced convection
Results and discussion
o Micro e macrostructures of the solidified ingot with forced convection
o Approximate 80mm layer, close to the base, showing columnar grains with regular and smooth boundaries oriented parallel to the direction of the heat extraction.
o The microstructure analysis did not showed intermetallic precipitates from the base up to 80 mm high, indicating reduced impurities concentration and that the solid-liquid interface has a planar morphology.
o From 80 mm and up, the ingot shows columnar grains with irregulars and serrated
boundaries, without a preferred orientation. o From 80 mm and up, the microstructure analysis showed intermetallic precipitates,
indicating that the solid-liquid interface has a non-planar morphology.
Results and discussion
o Heat and mass transport analysis at the directional solidification o Interface position
Results and discussion
0 2000 4000 6000 80000,00
0,05
0,10S
olid
-liqu
id in
terfa
ce p
ositi
on (m
)
time (s)
Experiment without forced convection Experiment with forced convection
o Heat and mass transport analysis at the directional solidification o Interface velocity
Results and discussion
0,00 0,02 0,04 0,06 0,08 0,100,0
5,0x10-6
1,0x10-5
1,5x10-5
2,0x10-5
2,5x10-5
Vel
ocity
(m.s
-1)
Solid-liquid interface position (m)
Experiment without forced convection Experiment with forced convection
o Heat and mass transport analysis at the directional solidification o Bulk liquid temperature gradient
Results and discussion
0,00 0,02 0,04 0,06 0,08 0,100
500
1000
Tem
pera
ture
gra
dien
t (K
.m-1
)
Solid-liquid interface position (m)
Experiment without forced convection Experiment with forced convection
o Heat and mass transport analysis at the directional solidification o Constitutional super cooling criteria
𝑆𝑆𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = −𝑚𝑚𝑚𝑚𝐶𝐶𝐿𝐿∞ 1 − 𝑘𝑘
𝐷𝐷 𝑘𝑘 + 1 − 𝑘𝑘 𝑒𝑒−∆− 𝐺𝐺𝐿𝐿
o Convection-diffusion parameter Δ:
∆=𝑚𝑚𝑉𝑉𝐷𝐷
o 𝑆𝑆𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 < 0 , there is no constitutional super cooling, so stable planar interface can exist.
o 𝑆𝑆𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 > 0, there is constitutional super cooling, so cellular or dendritic interface is more
probable.
Results and discussion
o Heat and mass transport analysis at the directional solidification
o Convection-diffusion parameter Δ:
∆=𝑚𝑚𝑉𝑉𝐷𝐷
o No convection:
𝑉𝑉 → ∞ and ∆→ ∞
o So, the constitutional super cooling criteria becomes:
𝑆𝑆𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = −𝑚𝑚𝑚𝑚𝐶𝐶𝐿𝐿∞ 1 − 𝑘𝑘
𝐷𝐷 𝑘𝑘 + 1 − 𝑘𝑘 𝑒𝑒−∆− 𝐺𝐺𝐿𝐿 → 𝑆𝑆𝑑𝑑𝑑𝑑𝑑𝑑 = −
𝑚𝑚𝑚𝑚𝐶𝐶0 1 − 𝑘𝑘𝐷𝐷𝑘𝑘
− 𝐺𝐺𝐿𝐿
Results and discussion
o Heat and mass transport analysis at the directional solidification
o When 𝑆𝑆𝑑𝑑𝑑𝑑𝑑𝑑 > 0 and there are evidences that the interface is planar, there shall be any convection that stabilizes the interface.
o Making 𝑆𝑆𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 0, it is possible to calculate the maximum layer thickness of the stagnant layer (𝑉𝑉𝑚𝑚𝑚𝑚𝜕𝜕) to have a stable planar interface.
𝑉𝑉𝑚𝑚𝑚𝑚𝜕𝜕 = −𝐷𝐷𝑚𝑚
ln −𝑚𝑚𝑚𝑚𝐶𝐶𝐿𝐿∞𝐺𝐺𝐿𝐿𝐷𝐷
−𝑘𝑘
1 − 𝑘𝑘
Results and discussion
o Heat and mass transport analysis at the directional solidification
o As convection at the system increases 𝑉𝑉 → 0 and ∆→ 0.
o 𝑉𝑉 → 0 indicates the minimum constitutional super-cooling level that the system can achieve at the presence of convection.
𝑆𝑆𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = − 𝑚𝑚𝑚𝑚𝐶𝐶𝐿𝐿∞ 1−𝑘𝑘𝐷𝐷 𝑘𝑘+ 1−𝑘𝑘 𝑒𝑒−∆
− 𝐺𝐺𝐿𝐿 → 𝑆𝑆𝑚𝑚𝑑𝑑𝑐𝑐 = −𝑚𝑚𝑚𝑚𝐶𝐶𝐿𝐿∞ 1−𝑘𝑘𝐷𝐷
− 𝐺𝐺𝐿𝐿
o When 𝑆𝑆𝑚𝑚𝑑𝑑𝑐𝑐 > 0, there is no possible convection that can stabilizes the solid-liquid interface.
Results and discussion
o Heat and mass transport analysis at the directional solidification
o Solidification without forced convection
o 𝑆𝑆𝑑𝑑𝑑𝑑𝑑𝑑 > 0 o Planar interface up to 8mm with 𝑉𝑉 = 7,86𝑚𝑚𝑚𝑚
Results and discussion
Sdif
Sconv
δmax
0 20 40 60 80 1008-1,0
-0,5
0,0
0,5
1,0
1,5
50
100
150
200
250
S (K
.mm
-1)
Solid-liquid interface position (mm)
0
2
4
6
8
10
12
14
16
18
20
δ max
(mm
)
o Heat and mass transport analysis at the directional solidification
o Solidification with forced convection
o 𝑆𝑆𝑑𝑑𝑑𝑑𝑑𝑑 > 0 o Planar interface up to 80 mm with 𝑉𝑉 = 2,57𝑚𝑚𝑚𝑚
Results and discussion
0 20 40 60 10080-0,5
0,0
0,5
1,0
1,5
50
100
150
200
250
S (K
.mm
-1)
Solid-liquid interface position (mm)
Sdif Smin
Sconv δmax
0
2
4
6
8
10
12
14
16
18
20
δ max
(mm
)
o Heat and mass transport analysis at the directional solidification
o Experiments comparison
o 𝑆𝑆𝑑𝑑𝑑𝑑𝑑𝑑(𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑒𝑒𝑐𝑐𝑤𝑤𝑤𝑤𝑐𝑐𝑐𝑐) > 𝑆𝑆𝑑𝑑𝑑𝑑𝑑𝑑(𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑐𝑐𝑜𝑜𝑤𝑤 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑒𝑒𝑐𝑐𝑤𝑤𝑤𝑤𝑐𝑐𝑐𝑐)
Results and discussion
0 20 40 60 80 1000
50
100
150
200
250
Sdi
f (K
.mm
-1)
Solid-liquid interface position (mm)
Experiment without forced convection Experiment with forced convection
o The ingot from the directional solidification without forced convection had a layer without the presence of intermetallic precipitations of an approximate 8 mm thickness.
o The ingot from the directional solidification with forced convection had a layer without the presence of intermetallic precipitations of an approximate 80 mm thickness.
o The forced convection enhanced the macrossegregation of the metallic impurities, and apparently the stability of the planar solid-liquid interface.
o The implemented mathematical model showed that the higher solute transport by the forced convection can explain the higher stability of the planar interface, at the conditions of the present experiments.
Conclusions
o CAPES o FIPT o CNPq
Acknowlodgements
![Escória de Aciaria: Caminhos para uma Gestão Sustentável ... · Escória de Aciaria [manuscrito]: caminhos para uma Gestão Sustentável / Suzy Magaly Alves Cabral Freitas. - 2018](https://img.document.onl/doc/110x75/5f6f568ae2b29f3dad0f1d4a/escria-de-aciaria-caminhos-para-uma-gesto-sustentvel-escria-de-aciaria.jpg)