Lattice Thermal Conductivity (LTC)¶
- utprøving av minste kvadraters metode med data fra Periodic Table
- oblig_3_periodic_table.ipynb
14.11.2025 Sverre Stikbakke
In [1]:
# fra read_csv.jl (med tillegg)
using CSV, DataFrames, PeriodicTable, Unitful, Statistics, Plots
df = CSV.read("LTC_with_atomic_numbers.csv", DataFrame)
# Convert string like "[72, 28, 50]" → Vector{Int}
df.atomic_numbers = [eval(Meta.parse(s)) for s in df.atomic_numbers];
first(df, 5)
Out[1]:
5×3 DataFrame
| Row | System | LTC | atomic_numbers |
|---|---|---|---|
| String31 | Float64 | Array… | |
| 1 | AlAuHf | 2.962 | [13, 79, 72] |
| 2 | AlGeLi | 12.208 | [13, 32, 3] |
| 3 | AlSiLi | 2.367 | [13, 14, 3] |
| 4 | AsNiSc | 15.121 | [33, 28, 21] |
| 5 | BaBiK | 2.959 | [56, 83, 19] |
In [2]:
# Info om grunnstoffer
names(PeriodicTable)
Out[2]:
3-element Vector{Symbol}:
:Element
:PeriodicTable
:elements
In [3]:
# Karbon (atomnummer 6)
elements[6]
Out[3]:
Carbon (C), number 6:
| category | polyatomic nonmetal |
|---|---|
| atomic mass | 12.011 u |
| density | 1.821 g/cm³ |
| molar heat | 8.517 J/mol⋅K |
| phase | Solid |
| shells | [2, 4] |
| electron configuration | 1s² 2s² 2p² |
| summary | Carbon (from Latin:carbo "coal") is a chemical element with symbol C and atomic number 6. On the periodic table, it is the first (row 2) of six elements in column (group) 14, which have in common the composition of their outer electron shell. It is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds. |
| discovered by | Ancient Egypt |
| source | https://en.wikipedia.org/wiki/Carbon |
In [4]:
propertynames(elements[6])
Out[4]:
(:name, :appearance, :atomic_mass, :boil, :category, :color, :cpk_hex, :density, :discovered_by, :el_config, :melt, :molar_heat, :named_by, :number, :period, :phase, :source, :spectral_img, :summary, :symbol, :xpos, :ypos, :shells)
In [5]:
# Hente ut en egenskap
#elements[6].atomic_mass
elements[1].boil
Out[5]:
20.271 K
In [6]:
# Create a new 'atomic_mass' column by mapping a function
# over the entire 'atomic_numbers' column
df.atomic_mass = map(df.atomic_numbers) do atomic_nums
# This inner part runs for each row
values = [ustrip(elements[el].atomic_mass) for el in atomic_nums]
mean(values)
end;
df.density = map(df.atomic_numbers) do atomic_nums
# This inner part runs for each row
values = [ustrip(elements[el].density) for el in atomic_nums]
mean(values)
end;
df.boil = map(df.atomic_numbers) do atomic_nums
# This inner part runs for each row
values = [ustrip(elements[el].boil) for el in atomic_nums]
mean(values)
end;
df.boil_max = map(df.atomic_numbers) do atomic_nums
# This inner part runs for each row
values = [ustrip(elements[el].boil) for el in atomic_nums]
maximum(values)
end;
df.melt = map(df.atomic_numbers) do atomic_nums
# This inner part runs for each row
values = [ustrip(elements[el].melt) for el in atomic_nums]
mean(values)
end;
df.melt_max = map(df.atomic_numbers) do atomic_nums
# This inner part runs for each row
values = [ustrip(elements[el].melt) for el in atomic_nums]
maximum(values)
end;
df.melt_min = map(df.atomic_numbers) do atomic_nums
# This inner part runs for each row
values = [ustrip(elements[el].melt) for el in atomic_nums]
minimum(values)
end;
df.atomic_num_max = map(df.atomic_numbers) do atomic_nums
# This inner part runs for each row
values = [el for el in atomic_nums]
maximum(values)
end;
df.atomic_num_min = map(df.atomic_numbers) do atomic_nums
# This inner part runs for each row
values = [el for el in atomic_nums]
minimum(values)
end;
df.atomic_num_avg = map(df.atomic_numbers) do atomic_nums
# This inner part runs for each row
values = [el for el in atomic_nums]
mean(values)
end;
In [7]:
# Normalisere til verdi mellom 0 og 1
"""
col = df.atomic_mass
min_val = minimum(col)
max_val = maximum(col)
df.atomic_mass_norm = (col .- min_val) ./ (max_val - min_val);
col = df.LTC
min_val = minimum(col)
max_val = maximum(col)
df.LTC_norm = (col .- min_val) ./ (max_val - min_val);
col = df.density
min_val = minimum(col)
max_val = maximum(col)
df.density_norm = (col .- min_val) ./ (max_val - min_val);
col = df.boil
min_val = minimum(col)
max_val = maximum(col)
df.boil_norm = (col .- min_val) ./ (max_val - min_val);
""";
In [8]:
first(df, 5)
Out[8]:
5×13 DataFrame
| Row | System | LTC | atomic_numbers | atomic_mass | density | boil | boil_max | melt | melt_max | melt_min | atomic_num_max | atomic_num_min | atomic_num_avg |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| String31 | Float64 | Array… | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Int64 | Int64 | Float64 | |
| 1 | AlAuHf | 2.962 | [13, 79, 72] | 134.145 | 11.77 | 3620.67 | 4876.0 | 1592.27 | 2506.0 | 933.47 | 79 | 13 | 54.6667 |
| 2 | AlGeLi | 12.208 | [13, 32, 3] | 35.5172 | 2.85233 | 2484.0 | 3106.0 | 866.173 | 1211.4 | 453.65 | 32 | 3 | 16.0 |
| 3 | AlSiLi | 2.367 | [13, 14, 3] | 20.6688 | 1.85433 | 2628.0 | 3538.0 | 1024.71 | 1687.0 | 453.65 | 14 | 3 | 10.0 |
| 4 | AsNiSc | 15.121 | [33, 28, 21] | 59.5236 | 5.87333 | NaN | NaN | NaN | NaN | NaN | 33 | 21 | 27.3333 |
| 5 | BaBiK | 2.959 | [56, 83, 19] | 128.469 | 4.71733 | 1662.33 | 2118.0 | 627.133 | 1000.0 | 336.7 | 83 | 19 | 52.6667 |
In [9]:
# Fjerner rader med NaN-verdier
for col in names(df)
df[!, col] = replace(df[!, col], NaN => missing)
end
df = dropmissing(df);
In [10]:
A = Matrix(df[!, [:atomic_mass, :atomic_num_avg, :boil, :density, :melt]]);
b = Matrix(df[!, [:LTC]]);
display(A)
display(b)
x = A \ b
203×5 Matrix{Float64}:
134.145 54.6667 3620.67 11.77 1592.27
35.5172 16.0 2484.0 2.85233 866.173
20.6688 10.0 2628.0 1.85433 1024.71
128.469 52.6667 1662.33 4.71733 627.133
104.21 44.0 2649.67 7.22433 1362.23
118.86 50.0 2681.0 7.72 1357.23
120.119 50.0 2727.33 8.26267 1395.58
73.7743 33.3333 3564.33 7.796 1593.64
148.585 60.6667 4167.33 14.6833 1878.1
104.105 44.0 4147.67 10.8157 2239.13
148.8 60.6667 3304.33 10.6633 1606.23
119.726 50.0 3328.0 9.63567 1725.93
193.228 77.3333 3705.33 15.2167 1923.23
⋮
142.142 58.0 1039.0 7.4764 421.4
119.915 49.0 992.555 5.9266 374.3
73.559 30.8 1047.42 4.77562 513.098
65.351 27.6 636.218 3.79902 286.024
58.0886 26.5 3155.25 6.9145 1526.98
91.2572 39.3333 3337.0 8.38233 1897.93
60.644 27.3333 3728.67 6.913 2035.67
72.1755 32.0 1069.0 5.975 593.34
91.4985 40.0 4150.5 9.18575 2138.35
105.296 45.3333 3508.67 8.54233 1756.26
80.3623 35.5 4258.5 8.43725 2257.25
103.019 44.5 4092.75 9.69625 1961.77
203×1 Matrix{Float64}:
2.962
12.208
2.367
2.959
10.849
9.204
6.891
24.564
24.391
25.8
20.412
19.509
10.844
⋮
0.386
0.758
1.451
1.757
37.282
14.537
36.258
13.379
17.717
16.788
14.217
19.181
Out[10]:
5×1 Matrix{Float64}:
1.40406717773646
-3.2421308994880373
0.0019499296035468338
-5.315141099698021
0.03274618650817724
In [11]:
# --- Predict and plot --- Ikke helt heldig med denne (?)
pred = A * x
#plot(df.LTC, pred, lw=2, label="modell", xlims=(-5,100), ylims=(-50,50))
plot(df.LTC, pred, lw=1, label="model", xlims=(-5,50), ylims=(-25,50))
scatter!(df.LTC, df.LTC, lw=2, label="data")
Out[11]:
In [12]:
# Nytt forsøk - sorterer data etter LTC-kolonnen
df_ltc = sort(df, :LTC);
first(df_ltc, 5)
Out[12]:
5×13 DataFrame
| Row | System | LTC | atomic_numbers | atomic_mass | density | boil | boil_max | melt | melt_max | melt_min | atomic_num_max | atomic_num_min | atomic_num_avg |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| String31 | Float64 | Array… | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Int64 | Int64 | Float64 | |
| 1 | CsRb3_mp-1183945 | 0.182 | [55, 37, 37, 37] | 97.3272 | 1.6315 | 956.75 | 961.0 | 309.762 | 312.45 | 301.7 | 55 | 37 | 41.5 |
| 2 | KRb3_mp-1185080 | 0.25 | [19, 37, 37, 37] | 73.8754 | 1.3645 | 978.75 | 1032.0 | 318.512 | 336.7 | 312.45 | 37 | 19 | 32.5 |
| 3 | TlBr_mp-22875 | 0.386 | [35, 81] | 142.142 | 7.4764 | 1039.0 | 1746.0 | 421.4 | 577.0 | 265.8 | 81 | 35 | 58.0 |
| 4 | K3Na_mp-1184844 | 0.41 | [19, 19, 19, 11] | 35.0712 | 0.8885 | 1063.02 | 1156.09 | 345.261 | 370.944 | 336.7 | 19 | 11 | 17.0 |
| 5 | AgBr_mp-866291 | 0.437 | [47, 35] | 93.8861 | 6.7964 | 1383.5 | 2435.0 | 750.365 | 1234.93 | 265.8 | 47 | 35 | 41.0 |
In [13]:
A_ltc = Matrix(df_ltc[!, [:atomic_mass, :atomic_num_avg, :boil, :density, :melt]]);
#A_ltc = Matrix(df_ltc[!, [:boil]]);
b_ltc = Matrix(df_ltc[!, [:LTC]]);
x_ltc = A_ltc \ b_ltc;
pred_ltc = A_ltc * x_ltc;
x_ltc
Out[13]:
5×1 Matrix{Float64}:
1.4040671777364582
-3.2421308994880316
0.001949929603546818
-5.315141099698018
0.03274618650817723
In [14]:
plot(df_ltc.LTC, pred_ltc, lw=1, label="model", xlims=(-5,50), ylims=(-25,50))
scatter!(df_ltc.LTC, df_ltc.LTC, lw=2, label="data")
Out[14]:
